optistruct 13.0 user guide

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OptiStruct 13.0 User's Guidei Altair Engineering

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OptiStruct 13.0 User's Guide

........................................................................................................................................... 1User's Guide

............................................................................................................................................... 2Overview

................................................................................................................................... 5Features

................................................................................................................................... 12Capabilities

................................................................................................................................... 13Formats

................................................................................................................................... 14Enhancing the Design Process

................................................................................................................................... 17Pre-processing and Post-processing in HyperWorks

............................................................................................................................................... 21Running OptiStruct

................................................................................................................................... 25Run Options for OptiStruct

................................................................................................................................... 39OptiStruct GPU

................................................................................................................................... 41OptiStruct SPMD

................................................................................................................................... 60Platforms and Hardware Recommendations

................................................................................................................................... 62OptiStruct Configuration File

................................................................................................................................... 67Expanded Error Message File

................................................................................................................................... 69Memory Limitations

................................................................................................................................... 71Restarting OptiStruct

................................................................................................................................... 72OptiStruct Compression Run

............................................................................................................................................... 74Structural Analysis

................................................................................................................................... 75Linear Static Analysis

................................................................................................................................... 76Linear Buckling Analysis

................................................................................................................................... 78Nonlinear Analysis

................................................................................................................................... 103Normal Modes Analysis

................................................................................................................................... 107Frequency Response Analysis

................................................................................................................................... 113Complex Eigenvalue Analysis

................................................................................................................................... 115Random Response Analysis

................................................................................................................................... 119Response Spectrum Analysis

................................................................................................................................... 123Transient Response Analysis

............................................................................................................................................... 129Thermal Analysis

................................................................................................................................... 130Linear Steady-State Heat Transfer Analysis

................................................................................................................................... 133Linear Transient Heat Transfer Analysis

................................................................................................................................... 135Nonlinear Steady-State Heat Transfer Analysis

................................................................................................................................... 137Contact-based Thermal Analysis

............................................................................................................................................... 140Acoustic Analysis

................................................................................................................................... 141Coupled Frequency Response Analysis of Fluid-Structure Models

................................................................................................................................... 258Radiated Sound Analysis

............................................................................................................................................... 266Fatigue Analysis

............................................................................................................................................... 282Multi-body Dynamics Simulation

OptiStruct 13.0 User's Guide iiAltair Engineering


................................................................................................................................... 284Transient Analysis for MBD

................................................................................................................................... 286Static Analysis for MBD

................................................................................................................................... 287Quasi-static Analysis for MBD

................................................................................................................................... 288Linear Analysis for MBD

................................................................................................................................... 289Bodies

................................................................................................................................... 290Markers

................................................................................................................................... 291Constraints

................................................................................................................................... 293Contact

................................................................................................................................... 295Compliant Elements

................................................................................................................................... 296Applied Forces and Motions

................................................................................................................................... 297Initial Velocity

................................................................................................................................... 298Function Expressions

................................................................................................................................... 299Results of a Multi-body Dynamics Analysis

............................................................................................................................................... 300Rotor Dynamics

............................................................................................................................................... 309NVH Applications and Techniques

................................................................................................................................... 310Transfer Path Analysis on an Automobile

................................................................................................................................... 316Residual Runs using Super Elements

................................................................................................................................... 319Basic OptiStruct NVH Output Files

................................................................................................................................... 322Global Search Option

................................................................................................................................... 325Create Door and Deck Lid Seals

................................................................................................................................... 328Create a HyperGraph Template for Reading in Multiple Files

................................................................................................................................... 329Using AMSES (Automatic Multi-Level Sub-Structuring Eigensolver Solution)

............................................................................................................................................... 331Modeling Techniques

................................................................................................................................... 332Parts and Instances

................................................................................................................................... 341Subcase Specific Modeling

................................................................................................................................... 345Direct Matrix Input (Superelements)

................................................................................................................................... 364Flexible Body Generation

................................................................................................................................... 369Poroelastic Materials (Biot theory)

................................................................................................................................... 371Elements and Materials

................................................................................................................................... 385Loads and Boundary Conditions

................................................................................................................................... 404Modeling Errors

............................................................................................................................................... 407Results

............................................................................................................................................... 417Coupling OptiStruct with Third Party Software

............................................................................................................................................... 425Design Optimization

................................................................................................................................... 426Optimization Problem

................................................................................................................................... 429Responses

................................................................................................................................... 446Topology Optimization

................................................................................................................................... 460Free-size Optimization

................................................................................................................................... 467Topography Optimization

................................................................................................................................... 471Size Optimization

................................................................................................................................... 473Shape Optimization

OptiStruct 13.0 User's Guideiii Altair Engineering


................................................................................................................................... 475Free-shape Optimization

................................................................................................................................... 493Manufacturing Constraints

................................................................................................................................... 558Reliability-based Design Optimization (Beta)

................................................................................................................................... 564Optimization of Arbitrary Beam Sections

................................................................................................................................... 565Optimization of Composite Structures

................................................................................................................................... 573Equivalent Static Load Method (ESLM)

................................................................................................................................... 587Gradient-based Optimization Method

................................................................................................................................... 596Global Search Option

............................................................................................................................................... 598Design Interpretation - OSSmooth

................................................................................................................................... 601OSSmooth Parameter File

................................................................................................................................... 606Running OSSmooth

................................................................................................................................... 607Interpretation of Topology Optimization Results

................................................................................................................................... 608Laplacian Smoothing

................................................................................................................................... 610Interpretation of Topography Optimization Results

................................................................................................................................... 613FEA Topology for Reanalysis

................................................................................................................................... 615FEA Topography for Reanalysis

............................................................................................................................................... 617OptiStruct References

Altair Engineering OptiStruct 13.0 User's Guide 1


User's Guide

Overview

Running OptiStruct

Structural Analysis

Thermal Analysis

Acoustic Analysis

Fatigue Analysis

Multi-body Dynamics Simulation

Rotor Dynamics

NVH Applications and Techniques

Modeling Techniques

Results

Coupling OptiStruct with Third Party Software

Design Optimization

Design Interpretation - OSSmooth

OptiStruct References

OptiStruct 13.0 User's Guide2 Altair Engineering


Overview

Altair® OptiStruct® is an industry proven, modern structural analysis solver for linear andnon-linear structural problems under static and dynamic loadings. It is the market-leadingsolution for structural design and optimization. Based on finite element and multi-bodydynamics technology, and through advanced analysis and optimization algorithms, OptiStructhelps designers and engineers rapidly develop innovative, lightweight and structurallyefficient designs. OptiStruct is used by thousands of companies worldwide to analyze andOptimize structures for their strength, durability and NVH (noise, vibration and harshness)characteristics. Refer to the Features page for a list of solutions available in OptiStruct.

Finite element solutions via OptiStruct include:

Linear static analysis

Nonlinear implicit quasi-static analysis

Linear buckling analysis

Normal modes analysis

Complex eigenvalue analysis

Frequency response analysis

Random response analysis

Linear transient response analysis

Geometric non-linear explicit and implicit analysis

Linear fluid-structure coupled (acoustic) analysis

Linear steady-state heat transfer analysis

Coupled thermal-structural analysis

Nonlinear steady-state heat transfer analysis

Linear transient heat transfer analysis

Contact-based thermal analysis

Inertia relief analysis with static, non-linear contact, modal frequency response, andmodal transient response analyses

Component Mode Synthesis (CMS) for the generation of flexible bodies for multi-bodydynamics analysis

Reduced matrix generation

One-step (inverse) sheet metal stamping analysis

Fatigue analysis

A typical set of finite elements including shell, solid, bar, scalar, and rigid elements as well asloads and materials are available for modeling complex events.

Multi-body dynamics solutions integrated via OptiStruct for rigid and flexible bodies include:

Kinematics analysis

Dynamics analysis



Static and quasi-static analysis

Linearization

All typical types of constraints like joints, gears, couplers, user-defined constraints, and high-pair joints can be defined. High pair joints include point-to-curve, point-to-surface, curve-to-curve, curve-to-surface, and surface-to-surface constraints. They can connect rigid bodies,flexible bodies, or rigid and flexible bodies. For this multi-body dynamics solution, the powerof Altair MotionSolve has been integrated with OptiStruct.

Structural Design and Optimization

Structural design tools include topology, topography, and free-size optimization. Sizing,shape and free-shape optimization are available for structural optimization.

In the formulation of design and optimization problems, the following responses can beapplied as the objective or as constraints: compliance, frequency, volume, mass, moment ofinertia, center of gravity, displacement, velocity, acceleration, buckling factor, stress, strain,composite failure, force, synthetic response, and external (user-defined) functions. Static,inertia relief, nonlinear quasi-static (contact), normal modes, buckling, and frequencyresponse solutions can be included in a multi-disciplinary optimization setup.

Topology, topography, size, and shape optimization can be combined in a general problemformulation.

Topology Optimization

Topology optimization generates an optimized material distribution for a set of loads andconstraints within a given design space. The design space can be defined using shell or solidelements, or both. The classical topology optimization set up solving the minimumcompliance problem, as well as the dual formulation with multiple constraints are available. Constraints on von Mises stress and buckling factor are available with limitations. Manufacturing constraints can be imposed using a minimum member size constraint, drawdirection constraints, extrusion constraints, symmetry planes, pattern grouping, and patternrepetition. A conceptual design can be imported in a CAD system using an iso-surfacegenerated with OSSmooth, which is part of the OptiStruct package.

Free-size optimization is available for shell design spaces. The shell thickness or compositeply-thickness of each element is the design variable.

Topography Optimization

Topography optimization generates an optimized distribution of shape based reinforcementssuch as stamped beads in shell structures. The problem set up is simply done by definingthe design region, the maximum bead depth and the draw angle. OptiStruct automaticallyprovides the design variable creation and optimization control. Manufacturing constraintscan be imposed using symmetry planes, pattern grouping, and pattern repetition.

Size and Shape Optimization

General size and shape optimization problems can be solved. Variables can be assigned toperturbation vectors, which control the shape of the model. Variables can also be assigned to



properties, which control the thickness, area, moments of inertia, stiffness, and non-structural mass of elements in the model. All of the variables supported by OptiStruct can beassigned using HyperMesh. Shape perturbation vectors can be created using HyperMorph.

The reduction of local stress can be accomplished easily using free-shape optimization. Shape perturbations are automatically determined by OptiStruct (based on the stress levelsin the design) when using this technique.

The layout of laminated shells can be improved by modifying the ply thickness and ply angleof these materials.

Multi-body Dynamics Analysis

Different solution sequences for the analysis of mechanical systems are available; theseinclude Kinematics, Dynamics, Static, and Quasi-static solutions.

Flexible bodies can be derived from any finite element model defined in OptiStruct.



Features

Finite Element Analysis using OptiStruct

Structural Analysis

- Linear Static Analysis

- Linear Buckling Analysis

- Nonlinear Quasi-Static Analysis

- Large Displacement Nonlinear Static Analysis

- Geometric Nonlinear Analysis (RADIOSS Integration)

- Normal Modes Analysis

- Frequency Response Analysis

- Complex Eigenvalue Analysis

- Random Response Analysis

- Response Spectrum Analysis

- Transient Response Analysis

Thermal Analysis

- Linear Steady-State Heat Transfer Analysis

- Linear Transient Heat Transfer Analysis

- Nonlinear Steady-State Heat Transfer Analysis

- Contact-based Thermal Analysis

Acoustic Analysis

- Coupled Frequency Response Analysis of Fluid-Structure Models

- Radiated Sound Analysis

Fatigue Analysis

- Stress-Life method

- Strain-Life method

Rotor Dynamics

Fast equation solver

- Sparse matrix solver

- Iterative PCG solver

- Lanczos eigensolver

- SMP parallelization

- SPMD parallelization

- DMIG input

- AMLS Interface

- FastFRS Interface



Advanced element formulations

- Triangular, quadrilateral, first and second order shells

- Laminated shells

- Hexahedron, pyramid, tetrahedron first and second order solids

- Bar, beam, bushing, and rod elements

- Spring, mass, and damping scalar elements

- Mesh independent gap and weld elements

- Rigid elements

- Concentrated and non-structural mass

- Direct matrix input

Geometric element quality check

Local coordinate systems

Multi-point constraints

Contact, tie interfaces

Prestressed analysis

Linear-elastic materials

- Isotropic

- Anisotropic

- Orthotropic

Nonlinear materials

- Elastoplastic

- Hyperelastic

- Viscoelastic

Material consistency checks

Ground check for unintentionally constrained rigid body modes.

Modeling Techniques

Parts and Instances

Subcase Specific Modeling

Direct Matrix Input (Superelements)

- Direct Matrix Input

- Creating Superelements

- Component Dynamic Analysis

Flexible Body Generation

Poroelastic Materials



Multi-body Dynamics using OptiStruct

Solution sequences

- Kinematics

- Dynamics

- Static

- Quasi-static

- Linearization

Bodies

- Rigid

- Flexible

- Flexible body generation in using the CMS modeling technique, integrated withmulti-body analysis if the model is set up in OptiStruct.

Constraints (between any body, flexible, or rigid)

- Joints: Ball (spherical), free, fixed, revolute, translational, cylindrical, universal,planar, at-point, in-plane, parallel-axes, orient, perpendicular-axes, constantvelocity, and in-line.

- Gear

- Couplers

- Higher-pair joints: point-to-curve, point-to-surface, curve-to-curve, curve-to-surface, and surface-to-surface constraints.

Loads

- Forces

- Gravity

- Motions (Joint and Marker)

- Initial velocities (Body and Joint)

Function Expressions

Optimization

General optimization problem formulation for all optimization types

- Response based

- Equation utility

- Interface to external user-defined routines

- Minmax (maxmin) problems

- System identification

- Continuous and discrete design variables

Solution sequences for optimization

- Linear static

- Normal modes



- Linear buckling

- Quasi-static nonlinear (gap/contact)

- Frequency response (modal method with residual vectors)

- Acoustic response

- Random response

- Linear steady-state heat transfer

- Coupled thermo-mechanical

- Multi-body Dynamics

- Fatigue

Responses for optimization

- All optimization types:

- Compliance- Frequency- Compliance index- Volume- Mass- Volume fraction- Mass fraction- Center of gravity- Moments of inertia- Displacement- Velocity- Acceleration- Temperature- Pressure - Stress (global von Mises stress in topology/free-size optimization)- Buckling factor (with limitations in topology/free-size optimization)- Fatigue life/damage- User-defined responses

- Size, shape, free-shape, and topography optimization: (In problems with topology/free-size design domains, these responses can be used inthe non-design domain)

- Strain- Force- Composite stress, strain, and failure (linear static analysis only)

Automatic selection of best optimization algorithm

- Optimality criteria method

- Convex approximation method

- Method of feasible directions

- Sequential quadratic programming

- Advanced approximations

Automatic selection of best method for design sensitivity analysis

- Direct method

- Adjoint variable method

Topology, free-size, topography, size, shape, and free-shape optimization problems can



be solved simultaneously

Multi-disciplinary optimization using combinations of the supported solution sequences

Mode tracking


Generalized optimization problem formulation

Multiple load cases with different solution sequences in combination

Global von Mises stress constraint for static loads

Density method

1-D, 2-D, and 3-D elements in the design space

Non-design space can contain any element type and response

Extensive manufacturing control:

- Minimum member size control to avoid mesh dependent results

- Maximum member size control to avoid large material concentrations

- Draw direction constraints

- Extrusion constraints

- Pattern grouping

- Pattern repetition

- Multiple symmetry planes

Checkerboard control

Discreteness control

Smoothing and geometry generation for 3-D results

Free-Size Optimization

Generalized optimization problem formulation

Multiple load cases with different solution sequences in combination

Global von Mises stress constraint for static loads

Shell element thickness and composite ply-thickness design variables

Non-design space can contain any element type and response

Extensive manufacturing control:

- Minimum member size control to avoid mesh dependent results

- Maximum member size control to avoid large material concentrations

- Draw direction constraints

- Extrusion constraints

- Pattern grouping






Shape optimization for shells with automated design variable definition

Easy set up with one DTPG card

Extensive bead pattern control to allow for manufacturing constraints

- Pattern grouping



- Discreteness control

Size Optimization

Shell, rod, and beam properties can be designed

Spring and concentrated mass properties can be designed

Composite ply thickness and ply angle can be designed

Material properties can be designed

Continuous and discrete design variables

Shape Optimization

Perturbation vector approach

Shape functions are defined through DVGRID cards

Continuous and discrete design variables

Free-shape Optimization

Perturbation vector approach

Automatic generation of perturbation vectors

Reduction of stress concentrations

Structural Optimization in Multi-body Dynamics Systems

Equivalent Static Load (ESL) method

Size, shape, free-shape, topology, topography, free-size, and material optimization offlexible bodies in multi-body dynamics systems



Generalized optimization problem definition

Large number of design variables and constraints

Pre-processing

Fully supported in HyperMesh and MotionView

Nastran type input format

Post-processing

HyperView

- Direct output of H3D format for model and results

- Direct output for iteration history

- Export of iso-density surface in STL format

HyperGraph

- Iteration history graphs

- Sensitivity bar charts

- Complex frequency response displacement, velocity, and acceleration plots for up to500 nodes

- Random response PSD and auto/cross correlation of displacement, velocity, andacceleration

- Transient response displacement, velocity, and acceleration time history plots for upto 500 nodes

- Bar chart for effective mass

HTML report

- Model summary

- Model and result displayed using HyperView Player

HyperMesh

- Direct binary result file output

Microsoft Excel

- Design sensitivities for size and shape variable approximations

Support of Nastran Punch and OP2 output formats



Capabilities

OptiStruct can be used to solve and optimize a wide variety of design problems in which thestructural and system behavior can be simulated using finite element and multi-bodydynamics analysis.

The design and optimization capabilities of OptiStruct allow for the development ofpreliminary design concepts and for the improvement of existing designs based on finiteelement analyses. Some types of optimization problems are listed below:

Two-dimensional truss structure optimization

Ribbed reinforcement patterns for 3-D shell structures

Ribbed reinforcements for solid structures

Spotweld reduction

Lightening holes for existing 2-D planar and 3-D bending shell problems

Discrete optimized structures for problems modeled using 3 dimensional solid elementproblems

Bead (Swages) reinforcements in 3-D shell structures

Shape modifications for volume parts

Gage optimization of 3-D shell structures

Beam cross-section optimization of structures modeled with beam elements

Layout of laminated shell by modifying ply thickness and ply angle

Reduction of stress concentrations

Optimization of mechanisms and mechanical systems to minimize weight and reducestress



Formats

OptiStruct supports the following input/output formats:

Formats

Input Nastran Bulk Data Format

Output HyperMesh Result File (Results)

H3D Binary File (Results)

Patran ASCII (Results)

Nastran Output2 (Results)

Nastran Punch File (Results)

OptiStruct 2.0 (Results)

HyperView Format (Iteration history, sensitivities,effective mass)

Microsoft Excel (Sensitivities)

From Bulk Data Format input:

HyperMesh Result File

Nastran Output2 File

Nastran Punch File

OptiStruct 2.0 File

Patran ASCII File



Enhancing the Design Process

OptiStruct enhances the design process by:

Accelerating the design process

Shortening the number of design cycles

Increasing the design performance

Providing fast and accurate finite element analysis

Generating optimal design concepts using topology and topography optimization

Providing traditional size and shape optimization to maximize the design performance

The design process can be viewed as an optimization process to find structures, mechanicalsystems, and structural parts that fulfill certain expectations towards their economy,functionality, and appearance. Generally, the design process is an iterative procedureconsisting of the following components:

Conceptual design

Design

Testing

Optimization

Today’s testing ground is usually the computer. Finite element analysis (FEA) and Multi-bodydynamics analysis (MBD) are the most used tools for computational design testing. Theresults of computational analyses are used to determine design improvements.

Changes to the design are introduced in all phases of the process. At a certain stage of thisprocess, changes to the concept become prohibitive. The concept phase plays a fundamentalrole concerning overall efficiency of the design and the cost of the overall developmentprocess.

In the concept phase of a design process, the freedom of the designer is limited only by thespecifications of the design (Figure 1). Today, the decision on how a new design should lookis based largely upon a benchmark design or on previous designs. The decision making isbased on the experience of those involved in the design process. Conceptual design toolssuch as topology and topography optimization can be introduced to enhance the process. The concept can be based on results of a computational optimization rather than onestimations. Using topology and topography optimization, the initial design step is alreadybased on input generated using computational analysis. Topology and topographyoptimization redefine the role of computational analysis and simulation in the design process. Finite element analysis has matured from a testing tool to a design tool.



Figure 1: Decision making in the design process.

Figure 2 compares the design process using topology optimization with the conventionalmethod of leaving the concept entirely to experience and intuition. The overall cost of designdevelopment can be reduced substantially by avoiding concept changes introduced in thetesting phase of the design. This is the major benefit of modifying the design process byintroducing topology and topography optimization.

In the real world, the design process is not as straightforward as described above. Thedesign is not just driven by one performance measure -- it has to be viewed as amultidisciplinary task. Today, the different disciplines work more or less independently. Analysis and optimization is performed for single phenomena such as linear static behavior ornoise, vibration and harshness. Still, the idea persists that if one performance measureimproves, the whole performance improves. A simple example shows that this is not quitetrue. Take the design of a car -- a high stiffness is necessary for good driving and handling,and high deformability is important for the crashworthiness of the design. This shows thatimproving one measure may result in degrading another. Therefore, compromises must gointo the formulation of the optimization problem. The definition of the design problem and ofthe design target is most important. The solution can be left to computational means. Multidisciplinary considerations, especially in the conceptual design, are, in many ways, stillactive research topics and are being covered by future developments of topologyoptimization. However, the inclusion of manufacturing constraints into topology andtopography optimization is already implemented in OptiStruct.

Figure 2: The design process without and with the use of topology optimization.



OptiStruct also provides size and shape optimization to completely support the designprocess with finite element based structural optimization. Using the advanced interfacingwith HyperMesh, the generation of input data for structural optimization becomes an easytask. This allows structural optimization to be integrated into the design process seamlessly.



Pre-processing and Post-processing in HyperWorks

Pre-processing

Pre-processing tools must be used to prepare models for OptiStruct, RADIOSS, andMotionSolve. HyperWorks provides specialized pre-processors interfacing with the solvers.

HyperMesh can be used to mesh and set up finite element simulations for OptiStruct andRADIOSS. Two user profiles are provided:

OptiStruct

RADIOSS (with sub-profiles for the different input formats)

HyperCrash is useful to set up finite element models for automotive crash simulation inRADIOSS. It provides a number of useful tools for dummy positioning and modelinterrogation that are not available in HyperMesh. Translation of models from OptiStruct toRADIOSS and vice versa can be performed efficiently in HyperCrash.

HyperForm is used to set up and execute sheet metal stamping simulations. Two userprofiles are provided to run RADIOSS:

One_Step

Incremental_Radioss

MotionView is used to set up multi-body dynamics models for MotionSolve. The respectiveSolverMode has to be chosen.

Figure 1. HyperMesh



Figure 2. HyperCrash

Figure 3. HyperForm



Figure 4. MotionView

Post-processing

Graphical tools must be used to visualize and evaluate the results of OptiStruct, RADIOSS,and MotionSolve. HyperWorks provides HyperView, a specialized post-processor, for this.

HyperView allows animation, 2D and 3D plotting, video and text processing to work with thesolver results and to generate reports. It can be used for all post-processing purposes infinite element and multi-body dynamics analysis.

Direct readers are provided for the animation and time history file written by OptiStruct,RADIOSS, and MotionSolve.



Figure 1. HyperView



Running OptiStruct

Note: Your system administrator may need to modify the scriptto make it compatible with your system.

This section describes the execution of OptiStruct.

There are several ways to run OptiStruct:

From the script.

From the HyperWorks Solver Run Manager.

From inside the preprocessors HyperMesh.

From inside HyperView and HyperGraph.

In all the above cases, HyperWorks will initialize $PATH and other environment variables

required to run the selected solver, however you are responsible for initializing environmentvariables for third party products. In particular, MPI and AMLS/FFRS external solvers (ifneeded) may require PATH and LD_LIBRARY_PATH.

Running OptiStruct from the Script

To run on UNIX from the command line, type the following:

<install_dir>/altair/scripts/optistruct "filename" –option argument

To run OptiStruct from a Windows DOS prompt, type the following:

<install_dir>\hwsolvers\bin\win64\optistruct.bat "filename" –option argument

The options and arguments are described under Run Options for OptiStruct.

OptiStruct looks for "filename" in the following manner ("filename" may contain a file path

that is either absolute or relative to the run directory):

First, it checks to see if "filename" exists exactly as input.

If "filename" does not exist exactly as input, and if "filename" does not contain an

extension (that is, if the actual file name without the path does not contain a period),then it checks for "filename".parm and then for "filename".fem.

If none of these checks results in a match, OptiStruct reports an error and terminates.

Running OptiStruct from HyperWorks Solver Run Manager

On Windows, a utility to start each solver is provided through Start > Programs > AltairHyperWorks 13.0 > OptiStruct. This utility allows you to start multiple solver runs, selectoptions from the menu, and maintains a history of solutions. On UNIX platforms, this utilitycan be started from command line as:

<install_dir>/altair/scripts/<solver name> -gui



Running OptiStruct from HyperMesh

If you set up a finite element model in HyperMesh, you can run the simulation directly out ofHyperMesh by going to the OptiStruct panel in the respective user profiles. The panels canbe accessed through the Analysis page, from the Utility menu, or through the Applicationspull down. The panels ask for the file name. After clicking the solver button, the model isexported using the given export options. Then the solver runs the script that is providedlocally on the machine. After solver execution, the results can be viewed in HyperView. Youcan bring up HyperView with the results loaded by clicking HyperView.

Note: When running OptiStruct from HyperMesh on UNIX andLinux, a shell is spawned with the DISPLAY setting <hostname>:0.0. If this is different from the DISPLAY

setting for HyperMesh, 50 HyperWorks units (in additionto the 21 HyperWorks units being used for HyperMesh)will be checked out. To avoid the checking out ofadditional units, be sure that the DISPLAY is set to <hostname>:0.0 before starting HyperMesh.

Running OptiStruct from HyperView or HyperGraph

If you are in HyperView or HyperGraph, OptiStruct can be run from the Applications pull-down. After selecting OptiStruct, the HyperWorks Solver Run Manager main form willappear, which will allow you to select a file, enter run options, and run the simulation.

The OptiStruct Configuration File

The configuration file optistruct.cfg may be used to establish default settings for

OptiStruct either system wide, for a particular user, or for a local directory. A full descriptionof the settings allowed and the usage of the configuration file is provided on the OptiStructConfiguration File page.

Environment Variables

The following environment variable is optional and may be set on either UNIX or PCplatforms; however, the preferred way is to define them using the OptiStruct ConfigurationFile.

OS_TMP_DIR =path

Path – Path name to directory for scratch filestorage (Default = directory where the solver isstarted – can be overwritten by the definition inthe script or input deck).

The following environment variable is optional and may only be set on UNIX platforms;however, the preferred way is to define this using the OptiStruct Configuration File.



DOS_DRIVE_$ =path

This environment variable allows drive letters tobe assigned to UNIX paths. This facilitatescopying files which contain INCLUDE, TMPDIR,INFILE or OUTFILE definitions containing driveletters from PC to UNIX on hybrid networks.

$ - Drive letter to be defined (case sensitive).

Path - UNIX path with which you want to replacethe drive letter.

Note that after such expansion, the paths arealways interpreted as if there were a ‘\’immediately after the drive letter in the originalPC path.

Memory Allocation

Memory is dynamically allocated for a run. The allocation starts with the initial memory.

The default setting for the memory limit is 1GB for 64-bit solver version (PC and Linux). Thissetting can be changed by using the SYSSETTING option OS_RAM, or by defining the –len

option in the run script. The script overwrites the environment variable.

OptiStruct will always attempt to assign enough memory for a minimum core solution.

The initial memory is 10% of the memory limit by default. This setting can be changed byusing the SYSSETTING option OS_RAM_INIT.

A check run can be very helpful in estimating the memory and disk space usage. In a checkrun, the memory necessary is automatically allocated.

The solver automatically chooses an in-core, out-of-core, or minimum core solution based onthe memory allocated. A solution type can be forced by defining the –core option in the run

script; the memory necessary for the specified solution type is then assigned.

Refer to the Memory Limitations section for detailed information on the following topics: 32-bit versus 64-bit computations, virtual versus physical memory, and automatic memoryallocation versus fixed memory runs.

Summary Information

OptiStruct always creates an .out file which contains summary information for the job. Thisinformation can be echoed to the screen through the inclusion of the SCREEN I/O option inthe input data or through the use of the -out command line option (see Run Options for

OptiStruct).

This file also contains memory and disk space estimates. The disk space estimates foreigenvalue analyses (normal modes, linear buckling, modal methods of frequency, transientresponse, and fluid-structure coupling (acoustics)) are sometimes very conservative and canbe three times as much as is truly used. This is because it is not fully predictable how muchdata needs to be saved to scratch files.

The true usage of memory and disk space is reported at the bottom of the file after the solverhas finished.



Should the job be re-run in the same location, the .out file is not overwritten, but is instead

moved to _#.out, where # is the lowest available three digit number that creates a unique

file name.

For example, if filename.fem were run in a directory already containing filename.out, the

existing filename.out would be moved to filename_001.out, and the summary information

for the new job would be written to filename.out. Should the job be repeated again, the

existing filename.out would be moved to filename_002.out, and the summary information

for the latest job would be written to filename.out.

filename.out is the only file that is saved in this manner. All other results files will be

overwritten.

Recommendations

1. Try running OptiStruct with the default setting first (without specification of the –len or –

core options).

2. Do a check run before submitting large jobs (>500,000 dof) to NQS to make suresufficient NQS memory is being provided. The –lM option can be used to change the NQS

memory. Be sure to include at least 12Mb for the executable in addition to the memorynecessary to solve the problem. A check run can also assist in debugging input datawithout having to wait in a queue.



Run Options for OptiStruct

Option Argument Description Available on

-acf N/A Option to specify that the input file is an ACFfile for a multi-body dynamics solutionsequence.

All Platforms

-amls YES/NO Invokes the external AMLS eigenvalue solver. The AMLS_EXE environment variable needs to

point to the AMLS executable for this settingto work.

Overrides the PARAM, AMLS setting in theinput file.

(Example: optistruct infile.fem –amls

yes)

Linux

-amlsncpu 1, 2, or 4 Defines the number of CPUs to be used by theexternal AMLS eigenvalue solver. Thisparameter will set the environment variable OMP_NUM_THREADS.

The default value is the current value of OMP_NUM_THREADS. Note that this value can

be set by the command line arguments –

nproc or –ncpu.

OptiStruct and AMLS can be run with differentallocations of processors. For example,OptiStruct can be run with 1 processor andAMLS with 4 processors in the same run.

Only valid with –amls run option or when

PARAM, AMLS is set to YES.

Overrides the PARAM, AMLSNCPU setting inthe input file.

Default: Number of processors used byOptiStruct.

(Example: optistruct infile.fem –amls

yes –amlsncpu 4)

Linux

-amlsmem Memory inGB<Real>

Defines the amount of memory in Gigabytesto be used by the external AMLS eigenvaluesolver. This run option is only supported forAMLS versions 5 and later.

Note:

Linux




1. This run option will override the memoryvalue set by PARAM, AMLSMEM in the inputfile and the environment variableAMLS_MEM.

2. This run option is valid only if –amls or

PARAM, AMLS is set to YES.

-analysis N/A Submit an analysis run. This option will alsocheck the optimization data; the job will beterminated if any errors exist.

-optskip will skip checking the optimization

data and the analysis will be performed.

Cannot be used with -check or -restart

(Example: optistruct infile.fem –

analysis)

All Platforms

-buildinfo N/A Displays build information for selected solverexecutables.

OptiStruct

-check N/A Submit a check job through the commandline.

The memory needed is automaticallyallocated.

Cannot be used with –analysis, -optskip or -restart

(Example: optistruct infile.fem –check)

All Platforms

-checkel yes, no,full

Note:

An

argument

for –

checkel is

optional. If

an

argument is

not

specified,

the default

argument

If NO, element quality checks are notperformed, but mathematical validity checksare performed.

If YES, or if no argument is given, thegeometric quality of each element is checked. Any violation of the error limits is counted asa fatal error and the run will stop. Anyviolation of warning limits is non-fatal. Erroror warning messages are printed for elementsviolating the limits along with the offendingproperty values. The amount of output islimited to the first 3 occurrences for eachindividual case, plus a summary table of allerrors.

If FULL, the same checks are performed as forYES, but the error or warning messages are

All Platforms




(yes) is

assigned.printed for all of the elements violating theerror or warning limits.

Default is YES.

(Example: optistruct infile.fem

–checkel full)

(Example: optistruct infile.fem

–checkel)

Note: An argument for –checkel is optional.

If an argument is not specified, thedefault argument (yes) is assigned.

-compress N/A Submits a compression run.

Reduces out matching material and propertydefinitions.

Property definitions referencing deletedmaterial definitions are updated with theretained matching material definition(reduction of property definition occurs afterthis process).

Element definitions referencing deletedproperty definitions are updated with theretained matching property definition. Theresulting bulk data file will be written to a filenamed <filename>.echo.

It is assumed that there is no optimization,nonlinear or thermal-material data in the bulkdata. If such data are present in the inputfile, the resulting file (<filename>.echo) may

not be valid.

The –compress run option cannot be used in

combination with any other option asOptiStruct terminates the run after the .echo

file is generated.


compress)

See OptiStruct Compression Run for moreinformation.

All Platforms

-core in, out,min

in – in-core solution is forced

out – out-of-core solution is forced

All Platforms




min – minimum core solution is forced

The solver assigns the appropriate memoryrequired. If there is not enough memoryavailable, OptiStruct will error out. Overwrites the –len option.

(Example: optistruct infile.fem –core

in)

-cpu

or -proc

or -nproc

or -ncpu

or-nt

Number ofcores

Number of cores to be used for SMP solution. (See comment 2).

(Example: optistruct infile.fem -ncpu

2)

All Platforms

-ddm N/A Runs MPI based OptiStruct SPMD in DomainDecomposition Mode.

Not all platformsare supported.Refer to the OptiStruct SPMDUser's Guide forthe list ofsupportedplatforms.

-delay Number ofseconds

Delays the start of an OptiStruct run for thespecified number of seconds. Thisfunctionality does not use licenses, computermemory or CPU before the start of the run(the delay expires).

Note:

The –delay option can only be used for

a single job. Delays cannot bescheduled for multiple jobs in a queue.

If the run is started using the HWSolverRun Manager (GUI), the Scheduledelay option should be used.

All Platforms

-dir N/A Change directory to the location of input filebefore starting the solver.

All Platforms

-ffrs YES/NO Invokes the external FastFRS (Fast FrequencyResponse Solver) solver. The FASTFRS_EXE

Linux




environment variable should point to theFastFRS executable for this setting to work.

Overrides the PARAM, FFRS setting in theinput file.

(Example: optistruct infile.fem –ffrs

yes)

-ffrsncpu 1, 2, or 4 Defines the number of CPUs to be used by theexternal FastFRS eigenvalue solver. Thisparameter will set the environment variable OMP_NUM_THREADS.

The default value is the current value of OMP_NUM_THREADS. Note that this value can

be set by the command line arguments –

nproc or –ncpu.

OptiStruct and FastFRS can be run withdifferent allocations of processors. Forexample, OptiStruct can be run with 1processor and FastFRS with 4 processors inthe same run.

Valid only when the –ffrs run option or

PARAM, FFRS is set to YES.

Overrides the PARAM, FFRSNCPU setting inthe input file.

Default: Number of processors used byOptiStruct.

(Example: optistruct infile.fem –ffrs

yes –ffrsncpu 4)

Linux

-ffrsmem Memory inGB<Real>

Defines the amount of memory in Gigabytesto be used by the external FastFRSeigenvalue solver. This run option is onlysupported for FastFRS versions 2 and later.

Note:

1. This run option will override the memoryvalue set by PARAM, FFRSMEM in the inputfile and the environment variableFFRS_MEM.

2. This run option is valid only when the –

ffrs run option or PARAM, FFRS is set to

YES.

Linux




-fixlen RAM inMBytes

Disables dynamic memory allocation.

OptiStruct will allocate the given amount ofmemory and use it throughout the run. Ifthis memory is not available, or if theallocated amount is not sufficient for thesolution process, OptiStruct will terminatewith an error.

To avoid over specifying the memory whenusing this option, it is suggested first to runOptiStruct with the -check option and use the

results of that run to properly define thememory size for the -fixlen option.

This option allows, on certain platforms, toavoid memory fragmentation and allocatemore memory than is possible with dynamicmemory allocation.

Overwritten by -len and -core options.

(Example: optistruct infile.fem -

fixlen 500)

All Platforms

-gpu N/A Activates GPU Computing All Platforms

-gpuid N/A N: Integer, Optional, Selects the GPU Card.Default = 1.

All Platforms

-h N/A Displays script usage. All Platforms

-len RAM inMBytes

Preferred upper bound on dynamic memoryallocation.

When different algorithms can be chosen, thesolver will try to use the fastest algorithmwhich can run within the specified amount ofmemory. If no such algorithm is available,then the algorithm with minimum memoryrequirement will be used. For example, thesparse linear solver, which can run in-core,out-of-core or min-core will be selected. The –

core option will override the –len option. The

default for –len is 1000MB, this means that

all except for very small models, OptiStructwill use only the minimum memory needed torun the job. If –len value is larger than the

amount of available physical RAM, it maycause excessive swapping during

All Platforms




computations, and significantly slow down thesolution process.

Default = 1000 MB.

(Example: optistruct infile.fem –len

32)

Best practices for –len specification:For proper memory allocation while using –

len in an OptiStruct run, avoid using the

exact reported memory estimate value (foreg. Using Check). The –len value should be

provided based on the actual memory of thesystem. This would be the recommendedmemory limit to run the job, it may notnecessarily represent the memory utilized bythe job or the actual memory limit. This way,the job is more likely to run with the bestpossible performance. If the same system isshared by multiple jobs, then the memoryallocation should follow the same procedureas above; except, that the individualmaximum memory should be used in place ofthe total system memory. (If a job runs out-of-core instead of in-core (it exceeded thememory allocation) it will still run veryefficiently. However, make sure that the jobdoes not exceed the actual memory of thesystem itself as this will slow the run down bya large factor. The recommended method todeal with this is to specify –maxlen as the

actual memory of the system to limit themaximum memory that can be used on thesystem.

-lic FEA, OPT FEA - FE analysis only(OptiStructFEA).

All Platforms

OPT - Optimization (OptiStruct orOptiStructMulti).

The solver checks out a license of thespecified type before reading the input data. Once the input data is read, the solververifies that the requested license is of thecorrect type. If this is not the case,OptiStruct will terminate with an error.




No default

(Example: OptiStruct infile.fem -lic

FEA)

-licwait Hours towait for alicense tobecomeavailable

Note:

An

argument

for –

licwait is

optional. If

the

argument is

not

specified,

the default

argument

(12) is

assigned.

If present and there are not 50 HyperWorksUnits available, OptiStruct will wait for up tothe number of hours specified (default=12)for licenses to become available and thenstart to run. The maximum wait period thatcan be specified to wait is 168 hours (aweek). OptiStruct will check for availableHyperWorks Units every two minutes.

All Platforms

-manual N/A Launches the online OptiStruct User’smanual.

All Platforms

-maxlen RAM inMbytes

Hard limit on the upper bound of dynamicmemory allocation.

OptiStruct will not exceed this limit.

No default

(Example: optistruct infile.fem –maxlen

1000)

All Platforms

-mmo N/A The –mmo option can be used to run multiple

optimization models in a single run.

Not all platformsare supported.Refer to the OptiStruct SPMDUser's Guide forthe list ofsupported




platforms.

-monitor N/A Monitor convergence from an optimization ornonlinear run. Equivalent to SCREEN, LOG inthe input deck.

All Platforms

-mpi i (Intel

MPI),

pl (IBM

Platform-MPI(formerlyHP-MPI)),

ms (MS-

MPI),

pl8 (for

versions 8and newerof IBMPlatform-MPI)

Note:

An

argument

for –mpi is

optional. If

an

argument is

not

specified,

the default

argument is

assigned.

Initiate an MPI-based SPMD run on supportedplatforms.

(Example: optistruct infile.fem –mpi –

np 4)

Not all platforms

are supported.

Refer to the

OptiStruct SPMD

User's Guide for

the list of

supported

platforms.

-mpipath path Specify the directory containing HP-MPI’smpirun executable.

Note: This option is useful if MPIenvironments from multiple MPI vendorsare installed on the system. Valid for anMPI run only.


np 4 –mpipath /apps/hpmpi/bin)

Not all platforms

are supported.

Refer to the

OptiStruct SPMD

User's Guide for

the list of

supported

platforms.




-nlrestart Subcase ID Restart a geometric nonlinear solutionsequence from specified subcase ID.

If Subcase ID is not specified, it will restartfrom the first geometric nonlinear subcaseending with error in previous run.

Note: The geometric nonlinear solutionsequence is a series of geometricnonlinear subcases (ANALYSIS =NLGEOM, IMPDYN or EXPDYN) linked by CNTNLSUB.

All Platforms

-np Number ofprocessors

Number of processors to be used in SPMDanalysis.


np 4)

All Platforms

-optskip N/A Submit an analysis run without performingcheck on optimization data (skip reading alloptimization related cards).

Cannot be used with –check or –restart.


optskip)

All Platforms

-out N/A Echos the output file to the screen. Thistakes precedence over the I/O optionSCREEN.

(Example: optistruct infile.fem -out)

All Platforms

-outfile Prefix foroutputfilenames

Option to direct the output files to a directorydifferent from the one in which the input fileexists. If such a directory does not exist, thelast part of the path is assumed to be theprefix of the output files. This takesprecedence over the I/O option OUTFILE.


outfile results); here OptiStruct will

output results.out, etc.

All Platforms

-rad RunRADIOSSoptimization inOptiStruct

Option to run RADIOSS optimization inOptiStruct. A RADIOSS optimization file <name>.rad should be input to OptiStruct and

the –rad run option should be specified to

request an optimization run for a RADIOSS

All Platforms




input deck.

Note: The RADIOSS Starter and input filessupporting the optimization input shouldbe available in the same directory asthe <name>.rad file.

Refer to RADIOSS Optimization in the User’sGuide for more information.

-ramdisk Size ofvirtualdisk (inMB)

Option to specify area in RAM allocated tostore information which otherwise would bestored in scratch files on the hard drive.


ramdisk 800)

For a more detailed description, see theRAMDISK setting on I/O option SYSSETTING.

All Platforms

-reanal Densitythreshold

This option can only be used in combinationwith -restart.

Inclusion of this option on a restart run willcause the last iteration to be reanalyzedwithout penalization.

If the "density threshold" given is less thanthe value of MINDENS (default = 0.01) usedin the optimization, all elements will beassigned the densities they had during thefinal iteration of the optimization. As there isno penalization, stiffness will now beproportional to density.

If the "density threshold" given is greaterthan the value of MINDENS, those elementswhose density is less than the given value willhave density equal to MINDENS, all otherswill have a density of 1.0.


restart -reanal 0.3)

All Platforms

-restart filename.sh

Specify a restart run. If no argument isprovided, OptiStruct will look for the restartfile, which will have the same root as theinput file with the extension .sh. If you enter

an argument On PC, you will need to providethe full path to the restart file including thefile name.

All Platforms




Cannot be used with –check, -analysis or –

optskip.


restart); here OptiStruct looks for the

restart file infile.sh.


restart C:\oldrun\old_infile.sh); here

OptiStruct looks for the restart fileold_infile.sh.

-rnp Number ofprocessors

Number of processors to be used inOptiStruct SPMD for IMPDYN, EXPDYN, andNLGEOM analysis types.


rnp 4)

All Platforms

-rnt Number ofcores

Number of cores to be used for OptiStructSMP for IMPDYN, EXPDYN, and NLGEOManalysis types.

(Example: optistruct infile.fem -rnt 2)

All Platforms

-rsf Safetyfactor

Specify a safety factor over the limit ofallocated memory.

Not applicable when -maxlen is used.

(Example: optistruct infile.fem –rsf

1.2)

(Example: optistruct infile.fem –len 32

–rsf 1.2)

(Example: optistruct infile.fem –core

out –rsf 1.2)

All Platforms

-scr

or-tmpdir

Path,filesize=n, slow=1

Option to choose directories in which thescratch files are to be written. filesize=n

and slow=1 arguments are optional. Multiple

arguments may be comma separated.

path ; give the path to the directory for

scratch file storage.

filesize=n ; defines the maximum file size

(in GB) that may be written to that location.

slow=1 ; indicates a network drive.

All Platforms




(Example: optistruct infile.fem –scr

filesize=2,slow=1,/network_dir/tmp)

Multiple scratch directories may be definedthrough repeated instances of –tmpdir or –

scr.

(Example: optistruct infile.fem –tmpdirC:\tmp –tmpdir filesize=2,slow=1,Z:

\network_drive\tmp)

This overwrites the environment variable OS_TMP_DIR, and the TMPDIR definition in the

I/O section of the input deck.

For a more detailed description, see the I/OOption TMPDIR.

-scrfmode basic,buffered,unbuffer,smbuffer,stripe,mixfcio

Option to select different mode of storingscratch files for linear solver (especially forout-of-core and minimum-core solutionmodes). Multiple arguments may be commaseparated.

(Example: optistruct infile.fem –scrfmode buffered, stripe – tmpdir C:

\tmp)

For a description of the arguments, see theSCRFMODE setting on I/O option SYSSETTING.

All Platforms

-testmpi N/A Check if MPI is configured properly and if theSPMD version of the OptiStruct executables isavailable for this system.


np 4 –mpipath /apps/hpmpi/bin -testmpi)

All Platforms

-uselen RAM inMBytes

Suggested dynamic memory usage limit.OptiStruct will use more than the minimummemory required up to this limit, but onlywhen it improves the speed of the solution.This value is used only for some solutionsequences, which can profit from additionalmemory available (for example, to use biggerbuffers to store intermediate results).

This value is automatically limited by thevalue specified by –len, so –uselen can be

All Platforms




set safely to a very large value.

-version N/A Checks version and build time informationfrom OptiStruct.

All Platforms

-xml N/A Option to specify that the input file is an XMLfile for a multi-body dynamics solutionsequence.

All Platforms

Comments

1. Any arguments containing spaces or special characters must be quoted in {} , forexample: -mpipath {C:\Program Files\MPI}. File paths on Windows may use

backward "\" or forward slash "/" but must be within quotes when using a backslash "\".

2. Currently, the solver executable (OptiStruct) does not have a specific limit on the numberof processors/cores assigned to the SMP part of the run ( -nt/-nthread ). However,

practical tests indicate that there is little advantage in increasing this value beyond 4, andif the value for this option is set too high, it may actually increase the run time. Thereforethe solver script is programmed to error out if the value of -nt exceeds 16. Users

interested in testing this limitation may edit the hwsolver.tcl script (text file) located

at:

{ALTAIR_HOME}/hwsolvers/scripts/

To do so, increase '16' in the following lines:

add_arg nthread "-nproc=" range { 1 16 }

(Or)

add_arg nthread "-nt=" range { 1 16 }

This line appears several times in the script, each appearance is clearly commented toindicate the specific solver executable it applies to.

3. The above arguments are processed by solver script(s) and not by the actual executable.If you are developing internal scripts which use the executable directly, then you may getspecific information about command line arguments that are accepted by the executableby looking at the content of the .stat file, where these arguments are listed for each run,

or you can contact [email protected] for more information.

4. The order of the above options is arbitrary. However, options for which arguments areoptional should not be followed immediately by the INPUT_FILE_NAME argument.



OptiStruct GPU

Introduction

A Graphics Processing Unit (GPU) is a system which can be used to improve the performanceof computationally intensive engineering applications. GPU Computing is a process whichuses the GPU to execute the time consuming sections of the application and the rest of thecode runs on the CPU.

Implementation

Starting from OptiStruct version 12.0, the GPU can be used to accelerate the sparse directequation solver through the NVIDIA CUDA programming model. GPU computing isimplemented by off-loading most of the computation intensive work to the GPU andconcurrently overlapping the communication and data transfer between the CPU cores andthe GPU.

Speedup

A speedup in the equation solver of up to 4 times, and up to 3 times overall when comparedto a Quad-core Intel Nehalem Xeon run, can be achieved. This heterogeneous computingmodel is particularly suitable for jobs dominated by the equation solver. For example:nonlinear static analysis on power train structures, topology optimization on blocky structuresand so on.

Compatibility

1. GPU computing is available for static analysis/optimization.

2. GPU computing is available in 64-bit Linux platform only.

3. GPU computing is NOT supported in the SPMD module.

4. NVIDIA Fermi and Kepler architecture based Tesla and Quadro graphic cards aresupported. Tesla C2050/C2070/M2090/K10/K20, Quadro 6000/K5000/K6000 cards arerecommended for computing by NVIDIA.

Activating OptiStruct GPU

Command option “-gpu” is used to activate OptiStruct GPU. Currently, only one graphics card

is supported, and “–gpuid” can be used to pick the desired graphic card for computation

when multiple cards are present. Compatible drivers for the graphics card needs to beinstalled by the user prior to launching OptiStruct GPU using the option “-gpu”.



Command LineOption

Value Action

-gpu Activates GPU computing

-gpuid N Integer: Optional, selects the GPU cardDefault = 1

Note: I/O usually accounts for an appreciable percentage of the totalsolution time in OptiStruct for an out-of-core or min-core run. Thiscannot be addressed or improved through GPU computing.Therefore, -core in (at least –core out) is recommended when

the memory in system is large enough.

OptiStruct, currently only supports one graphics card of a GPU in aspecific solution. Each GPU card may typically consist of amultitude of small cores (not comparable to a CPU core). Each GPUgraphics card is considered equivalent to 1 CPU core for licensingpurposes. Refer to the Altair HyperWorks 13.0 Product LicensingUnit Draw page for OptiStruct GPU licensing information.

Recommended Tesla GPU Computing Processor List for OptiStruct

The following table lists the recommended Tesla graphic boards for use with the AltairHyperWorks Solver suite of applications for high-powered GPU computing.

Manufacturer Adaptor TypeDriver Version(minimum or

higher)

NVIDIA(Tesla C-CLASS

series)

C2070C2075

Linux (64-bit):295.59

NVIDIA(Tesla M-CLASS

series)M2090

Linux (64-bit):295.59

NVIDIA(Tesla Kepler)

K20 Linux (64-bit)

Note: The most recent vendor/manufacturer drivers should be used andall driver support for these cards should be addressed to theappropriate manufacturer of the graphic board.



OptiStruct SPMD

Single Program, Multiple Data (SPMD) is a parallelization technique in computing that isemployed to achieve faster results by splitting the program into multiple subsets and runningthem simultaneously on multiple processors/machines. SPMD typically implies running thesame process or program on different machines (Nodes) with different input data for eachindividual task.

Supported Platforms

Supported platforms and MPI versions for subcase based parallelization are listed in Table 1:

Application Version Supported Platforms MPI

OptiStruct SPMD 13.0

Linux (64-bit)

Requires IBM PlatformMPI (formerly HP-MPI)

(Version 7.1);(or)

Intel MPI(Version 3.2.011 (or)

Version 4.1)

Windows (64-bit)

Requires IBM Platform MPI(formerly HP-MPI)

(Version 7.1);(or)

Intel MPI(Version 3.2.011 (or)

Version 4.1)(or)

Microsoft MPI(Version 3.04.4169)

Table 1: Supported Platforms for OptiStruct SPMD

However, SPMD can sometimes be implemented on a single machine with multiple processorsdepending upon the program and hardware limitations/requirements. SPMD in OptiStruct isimplemented by the following three MPI-based functionalities:

Task-based parallelization (TBP)

Domain Decomposition Method (DDM)

Multi-model optimization (MMO)

Task-based parallelization

Task-based parallelization (TBP) in OptiStruct can be used when a run is distributed intoparallel tasks, as shown in Figure 1. The schematic shown in Figure 1 is applicable to anSPMD run on multiple machines. The entire model is divided into parallelizable subcases,Table 2 lists the various supported solution sequences and parallelizable steps.



Figure 1: Overview of Task-based Parallelization in OptiStruct

In Task-based parallelization, the model (analysis/optimization) is split into several tasks,as shown in Figure 1. The tasks are assigned to various nodes that run in parallel. Ideally,if the model is split into N parallel tasks, then (N+1) nodes/machines would be required formaximum efficiency. (This is dependent on various other factors like: type of tasks,processing power of the nodes, memory allocation at each node and so on. During a TBPrun, using more than (N+1) nodes for N parallelizable tasks would not increase efficiency).The extra node is known as the Manager Node. The manager node decides the nature ofdata assigned to each node and the identity of the Master Node. The manager node alsodistributes multiple input decks and tasks to various nodes. It does not require a machinewith high processing power, as no analysis or optimization is run on the manager node.The Master Node, however, requires a higher amount of memory, since it contains themain input deck and it also collects all results and performs all processes that cannot beparallelized. Optimization is run on the Master Node. The platform dependent MessagePassing Interface (MPI) helps in the communication between various nodes and alsobetween the Master Node and the Slave Nodes.



Note:

1. A Task is a minimum distribution unit used in parallelization.Each buckling analysis subcase is one task. Each Left-HandSide (LHS) of the static analysis subcases is one task. Typically,the static analysis subcases sharing the same SPC (Single PointConstraint) belong to one task. Not all tasks can be run inparallel at the same time (For example: A buckling subcase cannot start before the execution of its STATSUB subcase).

2. The manager can also be included within the master node byspecifying np = N+1 for N nodes and repeating the first node inthe appfile/hostfile in a cluster setup (-np option, appfile/

hostfile are explained in the following sections).

Supported Solution Sequences

OptiStruct can handle a variety of solution sequences as listed in the overview. However,all solution sequences do not lend themselves to parallelization. In general, many steps ina program execution are not parallelized. Steps like Pre-processing and Matrix Assemblyare repeated on all nodes, while response recovery, screening, approximation, optimizationand output of results are all executed on the Master Node.

SolutionSequences that

SupportParallelization

Parallelizable Steps Non-Parallelizable Steps

Static Analysis Two or more staticBoundary Conditions areparallelized (MatrixFactorization is the stepthat is parallelized sinceit is computationallyintensive.)

Sensitivities areparallelized (Even for asingle BoundaryCondition as analysis isrepeated on all slavenodes).

Iterative Solution is notparallelized. (Only DirectSolution is parallelized).

Buckling Analysis Two or more BucklingSubcases areparallelized.

Sensitivities areparallelized.



SolutionSequences that

SupportParallelization

Parallelizable Steps Non-Parallelizable Steps

Direct FrequencyResponse Analysis

Loading Frequencies areparallelized.

No Optimization.

Modal FrequencyResponse Analysis

Loading Frequencies areparallelized.

Modal FRF pre-processing is notparallelized.

Sensitivities are notparallelized.

Table 2: Task-based parallelization - Parallelizable Steps for various solution sequences

As of HyperWorks 11.0, the presence of non-parallelizable subcases WILL NOT make theentire program non-parallelizable. The program execution will continue in parallel and thenon-parallelizable subcase will be executed as a serial run.

Number and Type of Nodes available for Parallelization

The types and functions of the nodes that are used in Task-based Parallelization areindicated in Table 3. The first node is automatically selected as the manager, the secondnode is the master node and the rest are slave nodes.

Node Type Functions

Master Node

(1 Node)

Runs all non-parallelizable tasks

Optimization is run here

Slave Node

(N-2 Nodes)

Runs all parallelizable tasks

Input deck copies are provided

Manager Node

(1 Node)

No tasks are run on this node, it manages theway nodes are assigned tasks.

Manager makes multiple copies of the inputdeck and sends them to the slave nodes.

Table 3: Types and functions of the Nodes

This assignment is based on the sequence of nodes that you specify in the appfile. The

appfile is a text file which contains process counts and the list of programs. Nodes can be

repeated in the appfile, multiple cores of the repeated nodes will be assigned parallel

jobs in the same sequence discussed here.



Frequently Asked Questions

How many nodes should I use?

Parallelization is based on task distribution. If the maximum number of tasks which can berun at the same time is N, then using (N+1) nodes is ideal (the extra one node for themanager distributing tasks). Using more than (N+1) nodes will not improve theperformance.

The .out file suggests the number of nodes you can use, based on your model.

When there are only M physical nodes available (M < N), then the correct way to start thejob is to use M+1 nodes in the hostfile/appfile. The manager node requires only a smallamount of resources and can be safely shared with the master: The way to assign such adistribution is repeating the first physical host in the hostfile/appfile. For example: Hostfilefor Intel MPI can be:

Node1Node1Node2Node3…….

Note: For Frequency Response Analysis any number of nodes may be used.(up to the number of loading frequencies in the model.)

How to run OptiStruct SPMD on a dual/quad CPU’s/Cores machine?

Follow the instructions to run OptiStruct SPMD on a single machine. The ideal number ofnodes is min(N+1, M), where N is the maximum number of tasks that can be run at thesame time, and M is the number of CPU’s/Cores.

Note: For dual/quad code machines it may be more efficient to run OptiStructin serial + SMP mode. (that is, use –nt argument in the solver script).

How to run OptiStruct SPMD over LAN?

It is possible to run OptiStruct SPMD over LAN. Follow the HP-MPI manual to setupdifferent working directories of each node the OptiStruct SPMD is launched.

Is it better to run on cluster of separate machines or on shared memorymachine(s) with multiple CPU’s?

There is no easy answer to this question. If the computer has enough memory to run alltasks in-core, then we can expect faster solution times as MPI communication is not sloweddown by the network speed. But if the tasks have to run out-of-core, then computationsare slowed down by disk read/write delay. Multiple tasks on the same machine maycompete for disk access, and (in extreme situations) even result in wall clock time slowerthan that for serial (non-MPI) runs.



Will OptiStruct SPMD use less memory on each node than in the serial run?

No, Memory estimates for serial runs and parallel runs on each node are the same. Theyare based on the solution of a single (most demanding) subcase.

Will OptiStruct SPMD use less disk space on each node than in the serial run?

Yes. Disk space usage on each node will be smaller, because only temporary files related totask(s) solved on this node will be stored. But the total amount of disk space will be largerthan that in the serial run and this can be noticed, especially in parallel runs on a shared-memory machine.

I have a cluster with N nodes each with M cores. What is the most efficient way Ican use the resources that I possess?

1. When each host has sufficient RAM to execute only a single serial OptiStruct run, thenuse multiple cores to activate SMP on each node. (using more than four cores is usuallynot effective). For example: on a 4 host cluster, each with 8 cores, you can run:

optistruct <inputfile> -mpi <mode> -np 5 –nt 4 –hostfile…

2. When each host has sufficient RAM to efficiently execute more than one serial run, thenyou can assign multiple MPI nodes to each host. For example:

optistruct <inputfile> -mpi <mode> -np 9 –nt 4 –hostfile…

Domain Decomposition Method

In addition to Task-based parallelization (TBP), OptiStruct SPMD includes another approachfor parallelization called Domain Decomposition Method (DDM) for static analysis andoptimization. DDM allows you to run a single subcase of static analysis and/or optimizationwith multiple processors in either Shared Memory Processing (SMP) or Distributed MemoryProcessing (DMP) cluster computers. The solution time will be significantly reduced in DDMmode and the scalability is much higher compared to the legacy shared memoryprocessing parallelization approach, especially on machines with a high number ofprocessors (for example, greater than 8).



Figure 2: Example illustrating Graph Partitioning for the DDM implementation in OptiStruct

The DDM process utilizes graph partition algorithms to automatically partition thegeometric structure into multiple domains (equal to the number of MPI nodes). During FEAanalysis/optimization, an individual domain only processes its domain related calculations.Such procedures include element matrix assembly, linear solution, stress calculations,sensitivity calculations, and so on. The necessary communication across domains isaccomplished by OptiStruct and is required to guarantee the accuracy of the final solution.When the solution is complete, result data is collected and output to a single copy of the .out file. From the user’s perspective, there will be no difference between DDM and serial

runs in this aspect.


Linear and nonlinear static analysis/optimization solution sequences are generallysupported. The following solutions, however, are currently not supported.

1. Static analysis (iterative solver)

2. Level set method (Static optimization)

3. Preloading (static analysis)

Note:

1. The –ddm run option can be used to activate DDM. Refer to the Setting up OptiStruct

SPMD and Launching OptiStruct SPMD for information on setting up and launchingDomain Decomposition in OptiStruct.

2. The installation steps and supported platforms for DDM are the same as that of the Task-based parallelization (TBP) mode.

3. In DDM mode, there is no distinction between node types (for example, manager node,master node, slave node, and so on). All nodes are considered as working nodes. If –np

n is specified, OptiStruct partitions n geometric domains and assigns each domain to

one MPU node.



4. Hybrid computation is supported. –nt can be used to specify the number of threads in

an SMP run. Sometimes, hybrid performance may be better than pure MPI or pure SMPmode, especially for blocky structures. It is also recommended that the total number ofcores (n x m) should not exceed the physical cores of the machine.

Multi-Model Optimization

In addition to Task-based parallelization (TBP) and Domain Decomposition Method (DDM),OptiStruct SPMD includes another approach for MPI-based parallelization called Multi-ModelOptimization (MMO) for optimization of multiple structures with common design variablesin a single optimization run.

ASSIGN, MMO can be used to include multiple solver decks in a single run. Common designvariables are identified by common user identification numbers in multiple models. Designvariables with identical user identification numbers are linked across the models.Responses in multiple models can be referenced via the DRESPM continuation lines on DRESP2/DRESP3 entries. Common responses in different models can be qualified by usingthe name of the model on the DRESPM continuation line. The model names can bespecified via ASSIGN, MMO for each model.

Figure 3: Example usecase for Multi-Model Optimization

Multi-model optimization is a MPI based parallelization method, requiring OptiStruct MPIexecutables for it to run. Existing solver decks do not need any additional input, can beeasily included, and are fully compatible with the MMO mode. MMO allows greaterflexibility to optimize components across structures. The –mmo run option can be used to

activate Multi-Model Optimization in OptiStruct.


1. All optimization types are currently supported.

2. Multi-body Dynamics (OS-MBD) and Geometric Nonlinear Analysis (RADIOSSIntegration) are currently not supported.

3. MMO currently cannot be used in conjunction with the Domain Decomposition Method(DDM).

4. The DTPG and DSHAPE entries are supported; however linking of design variables isnot. For example, it makes no difference to the solution if multiple DSHAPE entries indifferent slave files contain the same ID’s or not.



Note:

1. The number of processes should be equal to one more than the number of models.

2. Refer to the Setting up OptiStruct SPMD and Launching OptiStruct SPMD sections forinformation on setting up and launching Multi-Model Optimization in OptiStruct.

3. The installation steps and supported platforms for MMO are the same as that of the Task-based parallelization (TBP) and Domain Decomposition (DDM) modes.

4. If multiple objective functions are defined across different models in the master/slaves,then OptiStruct always uses minmax [Objective(i)] (where, i is the number ofobjective functions) to define the overall objective for the solution.

5. The following entries are allowed in the Master deck:

Control cards: SCREEN, DIAG/OSDIAG, DEBUG/OSDEBUG, TITLE, ASSIGN, RESPRINT, DESOBJ, DESGLB, REPGLB, MINMAX, MAXMIN, ANALYSIS, LOADLIB

Bulk data cards:DSCREEN, DOPTPRM (see section below), DRESP3, DRESP3, DOBJREF, DCONSTR,DCONADD, DREPORT, DREPADD, DEQATN, DTABLE, PARAM

DOPTPRM parameters (these work from within the master deck – all other DOPTPRM’sshould be specified in the slave):CHECKER, DDVOPT, DELSHP, DELSIZ, DELTOP, DESMAX, DISCRETE, OBJTOL,OPTMETH, SHAPEOPT

Setting up OptiStruct SPMD

Linux Machines

Below are detailed instructions on installing and launching OptiStruct SPM on Linuxmachines.

Installing OptiStruct SPMD

System Requirements

Operating system: Linux64

The MPI library: IBM Platform-MPI (Formerly HP-MPI) or Intel MPI must be installedand accessible from every machine in the cluster.

Installing Software and activating the License

1. OptiStruct SPMD is included with the OptiStruct solver package and the SPMDexecutables are included in the installation.

2. Test if OptiStruct SPMD is able to run in serial mode.



Configuring the machines

1. The account used to run OptiStruct SPMD must exist on every node in the cluster.

2. OptiStruct SPMD executables must be accessible to all cluster nodes.

3. The local scratch directories must be the same (same path).

4. It is highly recommended to have all the computation (working) directories at the samelocation on all cluster nodes.

SSH installation

1. IBM Platform MPI (formerly HP-MPI) default installation uses ssh to launch OptiStruct

SPMD on different nodes.

2. ssh should be configured to permit the connection on all hosts of the cluster without theneed to type passwords.

3. Refer to ssh man pages to generate and install rsa keys (ssh-keygen tool).

To check the functionality of ssh, the following test can be performed on the different

nodes:

[optistruct@host1] ssh host1 ls

[optistruct@host1] ssh host2 ls

...

[optistruct@host1] ssh host[n] ls

RSH (An alternative to SSH)

1. It is also possible to use rsh instead of ssh to launch OptiStruct SPMD.

2. Computation nodes need to be accessible to all the other nodes without need for apassword.

3. Refer to the rsh manpages for installation instructions. Check with IBM Platform MPI

(formerly HP-MPI) manual for instructions on how to use RSH instead of SSH.

4. To check the functionality of rsh, the following test can be performed on the different

nodes:

[optistruct@host1] rsh host1 ls

[optistruct@host1] rsh host2 ls

...

[optistruct@host1] rsh host[n] ls

IBM Platform MPI (formerly HP-MPI) installation

1. IBM Platform MPI (formerly HP-MPI) should be accessible to all computation nodes onwhich OptiStruct SPMD will be launched.

2. Download the IBM Platform MPI images for the platform you desire to use from thevendor (Contact IBM for help with procuring IBM Platform MPI).

3. Install the IBM Platform MPI package on each node.



4. No license is required for Platform-MPI to run OptiStruct SPMD.

5. Add $MPI_ROOT/platform_mpi/lib/[platform] into LD_LIBRARY_PATH, if needed.

Intel-MPI installation

1. Intel-MPI must be accessible from all computation nodes on which OptiStruct SPMD willbe launched.

2. Users can download (purchase/trial) the Intel-MPI images for their respective platformsfrom the following Intel MPI download site:http://software.intel.com/en-us/intel-mpi-library

3. Install the Intel-MPI package on each node.

[root@host[i]] ./install.sh

A license is required to install Intel-MPI libraries. (However, OptiStruct SPMD does notrequire a separate license).

4. Add $MPI_ROOT/intel/impi/3.2.2.006/lib into LD_LIBRARY_PATH, if needed.

Launching OptiStruct SPMD

There are several ways to launch parallel programs with OptiStruct SPMD. Remember topropagate environment variables when launching OptiStruct SPMD, if needed. Refer to therespective MPI vendor’s manual for more details.

Note:

1. A minimum of three processes are required to launchOptiStruct SPMD.

2. OptiStruct SPMD must match the MPI implementation youuse.

Using Solver Scripts

On a single host (for IBM Platform MPI (Formerly HP-MPI) using solver script

Task-based Parallelization (TBP)

[optistruct@host1~]$ $ALTAIR_HOME/scripts/optistruct –mpi [MPI_TYPE] –np[n] [INPUTDECK] [OS_ARGS]


[optistruct@host1~]$ $ALTAIR_HOME/scripts/optistruct –ddm [MPI_TYPE] –np[n] [INPUTDECK] [OS_ARGS]

Multi Model Optimization (MMO)

[optistruct@host1~]$ $ALTAIR_HOME/scripts/optistruct –mmo [MPI_TYPE] –np[n] [INPUTDECK] [OS_ARGS]

Where,

[MPI_TYPE]: is the MPI implementation used:

pl for IBM Platform-MPI (Formerly HP-MPI)

i for Intel MPI



-- ( [MPI_TYPE] is optional, default MPI implementation on Linux machines is pl

Refer to the Run Options page for further information).

[n]: is the number of processors

[INPUTDECK]: is the input deck file name

[OS_ARGS]: lists the arguments to OptiStruct

-- ( [OS_ARGS] is optional. Refer to the Run Options page for further information).

Note:

1. Adding the command line option “-testmpi”, runs a small

program which verifies whether your MPI installation,setup, library paths and so on are accurate.

2. OptiStruct SPMD can also be launched using the RunManager GUI. (Refer to HyperWorks Solver Run Manager)

3. It is also possible to launch OptiStruct SPMD without theGUI/ Solver Scripts. (Refer to the Appendix)

4. Adding the optional command line option “–mpipath PATH”

helps you find the MPI installation if it is not included in thecurrent search path or when multiple MPI’s are installed.

Windows Machines

Below are detailed instructions on installing and launching OptiStruct SPM on Windowsmachines.

Installing OptiStruct SPMD

System Requirements

Operating system: Windows XP/Vista/7: 64-bit only

The MPI library: IBM Platform-MPI (Formerly HP-MPI), Intel MPI or MS-MPI must beinstalled and accessible to each machine in the cluster.

Software Installation and License Activation

1. OptiStruct SPMD is included with the OptiStruct solver package and the SPMDexecutables are included in the installation.

2. Test if the OptiStruct SPMD be able to run in serial mode.

Machine Configuration

1. The account used to run OptiStruct SPMD must exist on every node in a cluster.

2. OptiStruct SPMD executables must be accessible to all cluster nodes. The local scratchdirectories must be the same (same path). It is highly recommended that the

computation (working) directories also remain the same on all nodes in a cluster.



IBM Platform-MPI, MS-MPI installation

On windows it is quite straightforward to install the MPI implementation. Refer to theirrespective Installation Guides for further assistance.

Below are the instructions for MPI download:

1. Download the IBM Platform MPI images for the platform you desire to use from thevendor (Contact IBM for help with procuring IBM Platform MPI).

2. Users can download (purchase/trial) the Intel-MPI images for their respective platformsfrom the following Intel MPI download site:

http://software.intel.com/en-us/intel-mpi-library

3. Users can download (purchase/trial) the Microsoft-MPI images for their respectiveplatforms from the following Microsoft MPI (MS-MPI) download site:

http://www.microsoft.com/en-us/download/details.aspx?id=14737

Launching OptiStruct SPMD

There are several ways to launch parallel programs with each MPI. Below are some typicalways to launch OptiStruct SPMD. Remember to propagate environment variables whenlaunching OptiStruct SPMD, if needed. Refer to corresponding MPI’s manual for moredetails.

Note:

1. A minimum of three processes are required to launchOptiStruct SPMD.

2. OptiStruct SPMD must match the MPI implementation youuse.

Using Solver Scripts

On a single host using solver script (for HP-MPI, Platform-MPI, Intel-MPI and MS-MPI)


[optistruct@host1~]$ $ALTAIR_HOME/hwsolvers/scripts/optistruct.bat –mpi[MPI_TYPE] –np [n] [INPUTDECK] [OS_ARGS]


[optistruct@host1~]$ $ALTAIR_HOME/hwsolvers/scripts/optistruct.bat –ddm[MPI_TYPE] –np [n] [INPUTDECK] [OS_ARGS]

Multi Model Optimization (MMO)

[optistruct@host1~]$ $ALTAIR_HOME/hwsolvers/scripts/optistruct.bat –mmo[MPI_TYPE] –np [n] [INPUTDECK] [OS_ARGS]

Where,

[MPI_TYPE]: is the MPI implementation used:

pl for versions 7 and older of IBM Platform-MPI (Formerly HP-MPI).



pl8 for versions 8 and newer of IBM Platform-MPI

i for Intel MPI

ms for MS-MPI

-- ( [MPI_TYPE] is optional, default MPI implementation on Windows machines is pl

Refer to the Run Options page for further information)



[OS_ARGS]: lists the arguments to OptiStruct

-- ( [OS_ARGS] is optional. Refer to the Run Options page for further information)

Notes:

1. Adding the command line option “-testmpi”, runs a small

program which verifies whether your MPI installation,setup, library paths and so on are accurate.

2. OptiStruct SPMD can also be launched using the RunManager GUI. (Refer to HyperWorks Solver Run Manager)

3. It is also possible to launch OptiStruct SPMD without theGUI/ Solver Scripts. (Refer to the Appendix)

4. Adding the optional command line option “–mpipath PATH”

helps you find the MPI installation if it is not included in thecurrent search path or when multiple MPI’s are installed.

Appendix

Launching OptiStruct SPMD on Linux Machines using Direct calls toExecutable

On a Single Host (for IBM Platform-MPI and Intel MPI)


[optistruct@host1~]$ mpirun -np [n] $ALTAIR_HOME/hwsolvers/optistruct/bin/linux64/optistruct_spmd [INPUTDECK] [OS_ARGS] -mpimode


[optistruct@host1~]$ mpirun -np [n] $ALTAIR_HOME/hwsolvers/optistruct/bin/linux64/optistruct_spmd [INPUTDECK] [OS_ARGS] -ddmmode

Multi-Model Optimization (MMO)

[optistruct@host1~]$ mpirun -np [n] $ALTAIR_HOME/hwsolvers/optistruct/bin/linux64/optistruct_spmd [INPUTDECK] [OS_ARGS] -mmomode

Where,



optistruct_spmd is the OptiStruct SPMD binary



[OS_ARGS]: lists the arguments to OptiStruct other than –mpimode/-ddmmode/-mmomode

-- ( [OS_ARGS] is optional. Refer to the Run Options page for further information).

Note: Running OptiStruct SPMD, using direct calls to theexecutable, requires an additional command-line option –

mpimode/-ddmmode/-mmomode (as shown above). If one of

these run options is not used, there will be no parallelizationand the entire program will be run on each node.

On a Linux cluster (for IBM Platform-MPI)


[optistruct@host1~]$ mpirun –f [appfile]

-h [host i] -np [n] $ALTAIR_HOME/hwsolvers/optistruct/bin/linux64/optistruct_spmd [INPUTDECK] -mpimode



-h [host i] -np [n] $ALTAIR_HOME/hwsolvers/optistruct/bin/linux64/optistruct_spmd [INPUTDECK] -ddmmode



-h [host i] -np [n] $ALTAIR_HOME/hwsolvers/optistruct/bin/linux64/optistruct_spmd [INPUTDECK] -mmomode

Where,

[appfile]: is a text file which contains process counts and a list of programs.

Note: Running OptiStruct SPMD, using direct calls to theexecutable, requires an additional command-line option –


these options is not used, there will be no parallelization andthe entire program will be run on each node.

Example: 4 CPU job on 2 dual-CPU hosts (the two machines are named: c1 and c2)

[optistruct@host1~]$ cat appfile

-h c1 –np 2 $ALTAIR_HOME/hwsolvers/optistruct/bin/linux64/optistruct_spmd [INPUTDECK] -mpimode

-h c2 –np 2 $ALTAIR_HOME/hwsolvers/optistruct/bin/linux64/optistruct_spmd [INPUTDECK] –mpimode



On a Linux cluster (for Intel-MPI)


[optistruct@host1~]$ mpirun –f [hostfile] -np [n] $ALTAIR_HOME/hwsolvers/optistruct/bin/linux64/optistruct_spmd [INPUTDECK] [OS_ARGS] -mpimode


[optistruct@host1~]$ mpirun –f [hostfile] -np [n] $ALTAIR_HOME/hwsolvers/optistruct/bin/linux64/optistruct_spmd [INPUTDECK] [OS_ARGS] -ddmmode


[optistruct@host1~]$ mpirun –f [hostfile] -np [n] $ALTAIR_HOME/hwsolvers/optistruct/bin/linux64/optistruct_spmd [INPUTDECK] [OS_ARGS] -mmomode

Where,

[hostfile]: is a text file which contains the host names.

Line format is as follows:

[host i]

Note:

1. One host requires only one line.

2. Running OptiStruct SPMD, using direct calls to the executable,requires an additional command-line option –mpimode/-

ddmmode/-mmomode (as shown above). If one of these options is

not used, there will be no parallelization and the entireprogram will be run on each node.


[optistruct@host1~]$ cat hostfile

c1

c2

Launching OptiStruct SPMD on Windows Machines using Direct callsto Executable

On a Single Host (for IBM Platform-MPI)


[optistruct@host1~]$ mpirun -np [n]

$ALTAIR_HOME/hwsolvers/optistruct/bin/win64/optistruct_spmd [INPUTDECK][OS_ARGS] -mpimode



$ALTAIR_HOME/hwsolvers/optistruct/bin/win64/optistruct_spmd [INPUTDECK][OS_ARGS] -ddmmode





$ALTAIR_HOME/hwsolvers/optistruct/bin/win64/optistruct_spmd [INPUTDECK][OS_ARGS] -mmomode

Where,

optistruct_spmd is the OptiStruct SPMD binary



[OS_ARGS]: lists the arguments to OptiStruct other than –mpimode/-ddmmode/-mmomode


Note: Running OptiStruct SPMD, using direct calls to theexecutable, requires an additional command-line option -mpimode/-ddmmode/-mmomode (as shown above). If one

of these options is not used, there will be noparallelization and the entire program will be run oneach node.

On a Single Host (for Intel-MPI and MS-MPI)


[optistruct@host1~]$ mpiexec -np [n]

$ALTAIR_HOME/hwsolvers/optistruct/bin/win64/optistruct_spmd [INPUTDECK][OS_ARGS] -mpimode



$ALTAIR_HOME/hwsolvers/optistruct/bin/win64/optistruct_spmd [INPUTDECK][OS_ARGS] -ddmmode



$ALTAIR_HOME/hwsolvers/optistruct/bin/win64/optistruct_spmd [INPUTDECK][OS_ARGS] -mmomode

Where,

optistruct_spmd is the OS SPMD binary



[OS_ARGS]: lists the arguments to OptiStruct SPMD other than –mpimode




Note: Running OptiStruct SPMD, using direct calls to theexecutable, requires an additional command-line option –mpimode/-ddmmode/-mmomode (as shown above). If

one of these options is not used, there will be noparallelization and the entire program will be run oneach node.

On Multiple Windows Hosts (for IBM Platform-MPI)



-h [host i] -np [n] $ALTAIR_HOME\optistruct [INPUTDECK] -mpimode



-h [host i] -np [n] $ALTAIR_HOME\optistruct [INPUTDECK] -ddmmode



-h [host i] -np [n] $ALTAIR_HOME\optistruct [INPUTDECK] -mmomode

Where,

[appfile]: is a text file which contains process counts and a list of programs.

Note: Running OptiStruct SPMD, using direct calls to theexecutable, requires an additional command-line option –mpimode/-ddmmode/-mmomode (as shown above). If one

of these options is not used, there will be noparallelization and the entire program will be run oneach node.


[optistruct@host1~]$ cat appfile

-h c1 –np 2 $ALTAIR_HOME/hwsolvers/optistruct/bin/win64/optistruct_spmd [INPUTDECK] -mpimode

-h c2 –np 2 $ALTAIR_HOME/hwsolvers/optistruct/bin/win64/optistruct_spmd [INPUTDECK] –mpimode

On Multiple Windows Hosts (for Intel-MPI and MS-MPI)


[optistruct@host1~]$ mpiexec –configfile [config_file]

-host [host i] –n [np] $ALTAIR_HOME/hwsolvers/optistruct/bin/win64/optistruct_spmd [INPUTDECK] -mpimode



Domain Decomposition Mode (DDM)


-host [host i] –n [np] $ALTAIR_HOME/hwsolvers/optistruct/bin/win64/optistruct_spmd [INPUTDECK] –ddmmode



-host [host i] –n [np] $ALTAIR_HOME/hwsolvers/optistruct/bin/win64/optistruct_spmd [INPUTDECK] -mmomode

Where,

[config_file]: is a text file which contains the command for each host.

Note:

1. One host needs only one line.

2. Running OptiStruct SPMD, using direct calls to theexecutable, requires an additional command-line option –


these options is not used, there will be no parallelizationand the entire program will be run on each node.


[optistruct@host1~]$ cat hostfile

-host c1 –n 2 $ALTAIR_HOME/hwsolvers/optistruct/bin/win64/optistruct_spmd [INPUTDECK] -mpimode

-host c2 –n 2 $ALTAIR_HOME/hwsolvers/optistruct/bin/win64/optistruct_spmd [INPUTDECK] –mpimode



Platforms and Hardware Recommendations

Platforms

OptiStruct runs on the following platforms:

Operating System

Architecture Version SMP SPMD

Linux 64-bitRHEL 5.9RHEL 6.2

SLES 11 SP2Yes Yes

Windows 64-bitWindows/Vista/7/8.1 Yes* Yes

Server 2008 (R2/HPC) Yes Yes

Mac OS X 64-bit 10.8 Yes No

SMP Symmetric Multiprocessing (Multiple processors, single memory).

SPMDSingle Process Multiple Data (Massive parallel processing, Multiple

processors each having its own memory).

RHEL Red Hat Enterprise Linux

SLES SUSE Linux Enterprise Server

*Performance gain for SMP runs on Windows platforms is poor,

therefore using more than one processor on these platforms is notrecommended.

Hardware Recommendations

Altair does not recommend any particular brand of hardware. All hardware purchases aregoing to balance the cost versus performance. The following are some items which can affectthe performance with OptiStruct.

CPU – The faster the clock speed of the processor, along with the speed at which data isexchanged between CPU cores of processor the better the performance.

Memory – The amount of memory required by an analysis depends on the solution type,types of elements in the model, and model size. Large OptiStruct solutions can require largeamounts of memory. Also, memory that is not used by OptiStruct is still available for I/Ocaching. So the amount of free memory can dramatically effect the wall clock time of therun. The more free memory, the less I/O wait time and the faster the job will run. Even if ananalysis is too large to run in-core, having extra memory available will increase the speed ofthe analysis because unused RAM will be used by the operating system to buffer disk



requests.

Disk drives – OptiStruct solutions often require the writing of large temporary scratch files tothe hard drive. Therefore, it is important to have fast hard drives. The best solution is touse two or more fast hard drives in RAID 0 (striped) as a dedicated place for scratch filesduring the solution. A typical configuration is to have one drive for the operating system andsoftware, and then 2-15 drives striped together as the scratch space for the runs.

Interconnect – The parallel SPMD versions of OptiStruct can run on multiple processors and/or on multiple nodes in the cluster. To run parallel jobs on a cluster, each should haveenough RAM to run a full job in non-parallel mode. And, each node in a cluster should haveits own disk space that is sufficient to store all the scratch files on that node. Clusterarchitecture with separate disks for each node will achieve better performance than singleshared RAID array of disks. A fast interconnect is important, but anything over GigabitEthernet will not speed the solution visibly. When nodes use a shared scratch disk area, theinterconnect speed is a critical factor for all out-of-core jobs.

For a large NVH analysis, it is recommended to have at least 8 GB per CPU with at least 4disks in RAID 0 for temporary scratch files.



OptiStruct Configuration File

OptiStruct configuration files may be used to establish default settings for the OptiStruct. Configuration files must be named optistruct.cfg. Any errors or warnings caused by the

content of these files will be echoed to the screen only.

Any default setting will be ignored if it is defined by an environment variable (see RunningOptiStruct), bulk data input deck entry (see The Input File), or command line argument (seeRun Options for OptiStruct).

File Location

The configuration file allows default settings to be established on five different levels:

1. System level

If a configuration file is located in the ${ALTAIR_HOME}/hwsolvers directory, the

default settings defined in this file apply to all solver runs.

A configuration file is included in the installation at this location. This configurationfile contains all of the configuration file options in a comment format. Uncommentingan option will activate it. This file may be used as a template for all configurationfiles.

If the ${ALTAIR_HOME} environment variable is not set, then the configuration file at

this location will not be used. This variable is automatically set when therecommended HyperWorks installation and execution procedures are followed.

2. Corporate level

If a configuration file is located in the ${HW_CORPORATE_CUSTOMIZATION_DIR}

directory, the default settings defined in this file are added to the system defaults.

If a default setting, which was defined at the system level, is redefined at this level,the redefined setting is used.

If the ${HW_CORPORATE_CUSTOMIZATION_DIR} environment variable is not set, then

the configuration file at this location will not be used.

3. Group level

If a configuration file is located in the ${HW_GROUP_CUSTOMIZATION_DIR} directory,

the default settings defined in this file are added to the system and corporatedefaults.

If a default setting, which was defined at the system or corporate level, is redefinedat this level, the redefined setting is used.

If the ${HW_GROUP_CUSTOMIZATION_DIR} environment variable is not set, then the

configuration file at this location will not be used.

4. User level

If a configuration file is located in the ${HOME} directory, the default settings defined

in this file are added to the system, corporate and group defaults.

If a default setting, which was defined at the system, corporate or group level, isredefined at this level, the redefined setting is used.



If the ${HOME} environment variable is not set, then the configuration file at this

location will not be used. This variable is normally set for UNIX and Linux operatingsystems to point to a user's home directory, but it may vary for different versions ofthe Windows operating system.

5. Local level

If a configuration file is located in the current directory, the default settings definedin this file are added to the system, corporate, group and user defaults.

If a default setting, which was defined at the system, corporate, group or user level,is redefined at this level, the redefined setting is used.

Entries and Format

Below is a list of entries recognized in the configuration file. As stated above, theconfiguration file contained in the installation may be used as a template for otherconfiguration files.

The format of the entries (with the exception of ELEMQUAL) is similar to the format of the I/

O Options in the input deck, namely:

ENTRY = Argument

Comments may be inserted using the $ character; which indicates that everything which

follows on that line is a comment.

ELEMQUAL is a recognized entry in the configuration file. It is used as described in the bulk

data entry description ELEMQUAL with the condition that it must be written in free format(see Guidelines for Bulk Data Entries).

Entry Argument Description

DOS_DRIVE_$ Path Same as DOS_DRIVE_$ environment

variable (see Running OptiStruct).

SYNTAX <ALLOWINT,STRICT>

Same as SYNTAX setting on the I/O

option SYSSETTING.

SPSYNTAX <STRICT, CHECK, MIXED>

Same as SPSYNTAX setting on the I/O

option SYSSETTING.

CORE <OFF, AUTO, IN,OUT,MMIN>

Same as the –core run option in the

Run Options for OptiStruct section.

SAVEFILE <ALL, OUT, NONE> Same as SAVEFILE setting on the I/O

option SYSSETTING.

RAMDISK Integer Same as RAMDISK setting on the I/O

option SYSSETTING.




SKIP10FIELD <CHECK, WARN> Same as SKIP10FIELD setting on the

I/O option SYSSETTING.

CARDLENGTH Integer Same as CARDLENGTH setting on the I/

O option SYSSETTING.

TABSTOPS Integer Used to change the default tab lengthfrom 8 to another value.

MAXLEN Integer Used to define the maximumallowable amount of memory to beused in MB. There is no default.

MINLEN Integer Used to define the initial memoryallocation in MB. The default is 10%of OS_RAM.

BUFFSIZE IntegerDefault = 16832

The maximum size in 8 byte words ofthe records of data written to the .op2 file. Use -1 to turn off buffering.

MSGLMT Various See MSGLMT setting on the I/O options

section MSGLMT.

ASSIGN, UPDATE,filename

Various See ASSIGN in the I/O options section.

LOADTEMP <SHAREID> Same as LOADTEMP setting on the I/O

option SYSSETTING.

OS_RAM RAM in Mbytes Same as SYSSETTING option OS_RAM.

PLOTELID <UNIQUE,ALLOWFIX>

Same as SYSSETTING option

PLOTELID.

RAM_SAFETY_FACTOR

Multiplier Same as -rsf option for running from

the script (see Run Options forOptiStruct).

FORMAT <HM, H3D, ASCII, OPTI, OS, NASTRAN, PUNCH, O2, OUT2, OUTPUT2, PATRAN, APATRAN>

Same as I/O option FORMAT.




SCREEN <OUT, LOG, NONE> Same as I/O option SCREEN.

TMPDIR Path Same as I/O option TMPDIR.

SCRFMODE <BASIC,

BUFFERED,

UNBUFFER,

STRIPE, MIXFCIO>

Same as SCRFMODE setting on the I/O

option SYSSETTING.

CHECKEL <YES, NO, FULL> Same as CHECKEL option for bulk data

entry PARAM.

OutputDefault <AUTO, NONE> The OutputDefault entry allows

default outputs to be disabled. Thisentry controls output for subcases forwhich there is no output requested.

AUTO: Output is automatically

generated for certain solutionsequences.

NONE: No output that is not

specifically requested is output.

CHECKMAT <YES, NO, FULL> Same as CHECKMAT option for bulk

data entry PARAM.

COUPMASS <-1, 0, 1, YES, NO> Same as COUPMASS option for bulk

data entry PARAM.

EFFMASS Integer Same as EFFMASS option for bulk data

entry PARAM.

PRGPST <YES, NO> Same as PRGPST option for bulk data

entry PARAM.

KGRGD <YES, NO> Same as KGRGD option for bulk data

entry PARAM.

WTMASS Real > 0.0 Same as WTMASS option for bulk data

entry PARAM.

MBDH3D <NODAL, MODAL, BOTH, NONE>

Same as MBDH3D option for bulk data

entry PARAM.




FLEXH3D <AUTO, YES, NO> Same as FLEXH3D option for bulk data

entry PARAM.

USERAM RAM in Mbytes Same as SYSSETTING option USERAM.



Expanded Error Message File

OptiStruct Expanded Error Message files may be used to expand the error and warningmessages for the OptiStruct. In this way, you can customize the error and warningmessages so that they are more meaningful and informative for you and others in yourorganization. The Expanded Error Message file must be named optistruct_err.msg.

The file contains an expanded message for each message you wish to expand. If the samemessage is expanded in multiple files, then all expansions will be printed. The expandederror message is printed only for the first instance of the error.

The format of the file is to have four asterisks left justified on a line followed by the errornumber to be expanded. The next lines contain the expanded error message. An examplefor error 9009 and 9008 are below. Note that the order of the error message numbers doesnot matter.

**** 9009This error usually happens when there isnot enough room on the disk, but it canhappen also when one of the output filesdoes not have write permissions for thecurrent user, or when the directoryassigned for output or temporary filesdoes not exist, does not have writepermission or is located on a read-onlyfilesystem (e.g. on a CD). Please checkfollowing cards: OUTFILE, TMPDIR,EIGVSAVE, ASSIGN, or the command linearguments. Note that TMPDIR may belocated in any of config files, and (onUnix) the filenames may be affected byDos_drive conversion (e.g. DOS_DRIVE_nenvironment variable).

**** 9008This error usually happens when theinput file name is mistyped, either on acommand line or on any of followingcards: INFILE, INCLUDE, EIGVNAE,RESTART, LOADLIB, ASSIGN. It can alsohappen if the user does not have readpermission to an input file, or to anydirectory on a path leading to the inputfile.

File Location

The expanded error message file allows default settings to be established on four differentlevels:

1. System level

If an expanded error message file is located in the ${ALTAIR_HOME}/hwsolvers



directory, the expanded error messages defined in this file are added to all solverruns.

An expanded error message file is included in the installation at this location. Thisfile contains samples of expanded messages. This file may be used as a template forall expanded error message files.

If the ${ALTAIR_HOME} environment variable is not set, then the expanded error

message file at this location will not be used.

2. Corporate level

If an expanded error message file is located in the ${HW_CORPORATE_CUSTOMIZATION_DIR} directory, the expanded messages defined in

this file are added to the system expanded messages.

If the ${HW_CORPORATE_CUSTOMIZATION_DIR} environment variable is not set, then

the expanded error message file at this location will not be used.

3. Group level

If an expanded error message file is located in the ${HW_GROUP_CUSTOMIZATION_DIR}

directory, the expanded error message defined in this file are added to the systemand corporate messages.

If the ${HW_GROUP_CUSTOMIZATION_DIR} environment variable is not set, then the

expanded error message file at this location will not be used.

4. User level

If an expanded error message file is located in the ${HOME} directory, the expanded

error messages defined in this file are added to the system, corporate and groupexpanded error messages.

If the ${HOME} environment variable is not set, then the expanded error message file

at this location will not be used. This variable is normally set for UNIX and Linuxoperating systems to point to a user's home directory, but it may vary for differentversions of the Windows operating system.



Memory Limitations

32-bit Versus 64-bit Computations

On 64-bit machines, when using a 64-bit compiled version of OptiStruct and a 64-bitoperating system, OptiStruct can use all memory available in the system (real RAM andvirtual memory). There are still some size limitations as a result of the size of standardinteger variables, but they should only occur in very rare cases. Currently, OptiStruct is builtwith two versions of linear solvers: one using 32-bit integers, and the other one using 64-bitintegers. By default, the 32-bit solver is used (as it requires less memory/disk and runsvisibly faster), but the 64-bit solver is automatically selected when the size of a problemrequires it.

Virtual Versus Physical Memory

OptiStruct can use more memory than is actually installed on a given system (i.e. more thanthe installed RAM). This is what the virtual memory (swap space) is for. OptiStruct is moreefficient, however, if it uses only actual RAM (remember to allow some RAM to be used by theoperating system and other codes running at the same time). When more memory isrequested than actual available RAM, OptiStruct will run much slower due to swapping. Youwill hear disks working constantly with little CPU being used, and there will be a significantdifference between the elapsed time and the CPU time.

Memory specification for OptiStruct (using –len command line option) is actually only giving

OptiStruct a hint about the amount of physical RAM available for the run (i.e. it shouldspecify the amount of physical memory not used by the operating system and other runningprograms, and as explained above, always less than the total amount of RAM in thecomputer). Based on this information, OptiStruct will try to use the fastest algorithm whichcan run within the specified amount of memory. If no such algorithm is available, then thealgorithm with minimum memory requirement will be used. Specifying a larger value for –

len than the amount of physical RAM may cause excessive swapping during computations,

and will significantly slow down the solution process.

On most machines OptiStruct asks operating systems for information about availablememory. This information is printed in the header of the .out file, and can be used to issue

a warning, when it is possible that the run may fail because of lack of this resource. Thisinformation is dynamic (changes with other programs running at the machine) and thereforeis never used inside OptiStruct – user supplied information (example: with –len argument or

from the config file) is used instead.

Automatic Memory Allocation Versus Fixed Memory Runs

In standard modes of operation, OptiStruct automatically estimates the amount of memoryrequired, and this memory is requested in successive steps from the operating system. Sometimes the memory could be used more efficiently if requested at once and not inincrements. This can be done using the "-fixlen" command line option (see Run Options).

When using the "-fixlen" option, OptiStruct may start to run, but fail after some time with a

memory allocation error. This can happen when almost all available memory is requested by



the "-fixlen" argument, because in addition to the memory required by the OptiStruct

solver, OptiStruct launches a bandwidth minimizer, which uses an additional small amount ofmemory. Requesting slightly less memory with the "-fixlen" option is a possible solution.

Again, you see that it is incorrect to assign too much memory to OptiStruct.

Additional Control of Used Memory

OptiStruct has new command line argument "-maxlen" which can be used in automatic

mode. This switch can be useful in some batch scheduling installations, as it will not allowOptiStruct to use more than a given amount of memory. Note that for models which requiremore memory than allowed by this argument, OptiStruct will abort during the solution,potentially after spending some time in computations.

OptiStruct has a new command line argument “-uselen” which can be used in automatic

mode. –uselen is used to specify an increased dynamic memory usage limit. If –uselen is

not defined, then the algorithms which may use variable amount of memory try to use asminimal an amount as possible. When this option is used, OptiStruct will use more than theminimum memory required, up to this limit, but only when it improves the speed of thesolution. This value is used only for some solution sequences, which can profit fromadditional memory available (for example, to use bigger buffers to store intermediateresults).

This value is automatically limited by the value specified by –len, so –uselen can be set

safely to a very large value.

(Example: optistruct infile.fem –uselen 32)

Best practices for –uselen specification:

The speed gain is usually modest, and is limited to certain solution sequences, therefore, thisrun option should not be used unless solution speed is critical and excess memory isavailable. For single-user hosts, it is useful to set this value to the same as –len (or higher).

This maximizes the use of available memory to achieve possible better performance.

Different values of this run option may be used on systems shared by multiple jobs (forexample HyperMesh or other solvers). In such scenarios, using a lower value of this runoption (or not using it at all), will result in a lower use of memory and may improve overallspeed an response time.

OptiStruct Configuration File

All options for memory control can be specified in the OptiStruct Configuration File, however,this is not advisable if the configuration file is shared on the common file server. Theconfiguration files should be tuned for specific hardware independently, and should be placedin the configuration file local to each machine.



Restarting OptiStruct

It is possible to restart an OptiStruct optimization by using the command line option -

restart (see Run Options), by adding the I/O option RESTART to the input file, or from the

OptiStruct panel in HyperMesh.

To restart an optimization, you will need information about the final iteration of the previousoptimization run. This information is stored in the .sh file.

The DESMAX entry on the DOPTPRM card, in the .fem file, specifies the maximum number of

additional iterations. To perform an analysis on the optimized structure, restart with DESMAX

set to 0. If DESMAX is not defined, then the default value of DESMAX is assumed (30 iterations

is the default value for DESMAX unless topology manufacturing constraints are used, in which

case the default is 80 iterations).

There are a number of conditions that must be observed when restarting an optimization:

The number of design variables or design elements cannot be changed.

It is invalid to restart with minimum member size control removed if it was present inthe original run.

It is invalid to restart with checkerboard control turned on if it was not activated in theoriginal run. It is, however, acceptable to deactivate checkerboard control in the restartif it was activated in the original run.

It is invalid to restart with manufacturing constraints that differ from those of theoriginal run.

The purpose of the restart functionality is for restarting with unconverged optimization runsor optimization runs that were terminated before completion (due to a power outage, etc.).

Output files from a restart run are appended with the extension _rst#, where # is a 3 digit

number indicating the starting iteration for the restart run. For example, filename_rst030.out is the .out file created when restarting filename.fem from iteration

30.

Iterations for the restart are numbered starting with the iteration number in the .sh file (the

last iteration from the previous run).

You may manually append new .dens, .disp, and .strs files to old ones and post-process

the combined files.



OptiStruct Compression Run

The OptiStruct solver can be used as a simple input deck preprocessor, intended to reduceout matching material and property definitions. It is useful for models (produced on somesimpleminded mesh generator tools) which sometimes have unique property IDs and uniquematerial IDs assigned to each element, even in cases where actual data is identical. Suchmodels (although technically correct) will be expensive to solve, or slow to process inHyperMesh or HyperView. In this special run mode, OptiStruct will simply read the model,compare all material and property data, and remove redundant data.

Example of Run

optistruct infile.fem -compress

will produce a new bulk data file named:

infile.echo

which will contain a new model with all duplicate materials and properties deleted. Allreferences to removed data will be replaced with the remaining ones, so for all practicalpurposes the model should yield identical results.

The additional argument to -compress represents the tolerance value in percent. All floating

point values in material and property data are compared using that tolerance. Usingtolerance may increase significantly run time.

Restrictions

1. Comparison is performed exactly (meaning all data are compared without allowing for anytolerance or round-off). If optional tolerance value is specified, then the run is performedin two passes: exact matches are removed first, then all remaining materials andproperties are compared with each other using following formula:

(2 * abs(value1-value2)) / (abs(value1)+abs(value2)) < tolerance *0.01.

2. Optimization data, nonlinear data, and thermal materials are not processed. If such dataare present they may reference removed entities, but a compress run will not adjustreferences. The resulting file (<filename>.echo) may not be valid.

3. Cards which extend or modify Materials or Properties (such as MATT1, MATX02, MATS1,or PSHELLX) are not used in comparison, and can also be left orphaned as a result of acompress run.

4. SETs referencing Materials or Properties are not processed. This will not result in a baddeck because SETs are allowed to reference non-existent IDs, however SETs in the outputfile may be different from the input file.

5. After the .echo file is produced, OptiStruct terminates the run, therefore -compress

cannot be combined with any other option.



The following cards are processed:

1. Properties:

PBEAM, PBAR, PBEAML, PBARL, PSOLID (also fluid), PCOMP, PSHELL, PROD, PWELD, andPSHEAR

as well as properties not referring to materials:

PELAS, PBUSH, PVISC, PDAMP, PGAP, PCONT, PAABSF, and PACABS.

2. Materials:

MAT1, MAT2, MAT4, MAT5, MAT8, MAT9, and MAT10.

3. All elements referencing properties or materials, including PRBODY and PFBODY.

Any other cards present in the deck are allowed only if they do not reference materials orproperties; however OptiStruct does not verify this assumption. If such a card is present inthe deck (for example, DTPG referring to a list of properties), it may be printed with negativeIDs for removed entities.

The resulting file (<filename>.echo) is produced using the same routines which produce

ECHO; all restrictions present for ECHO will affect a -compress run; in particular:

Some optimization cards are currently known to produce incorrect ECHO, meaning anECHO of these cards cannot be read back into OptiStruct.

Results are formatted in fixed format, irrespective of the format used in the input file. This limits the accuracy of most coefficients because of 8 character fields. Currentformatting preserves as many decimal places as possible within 8 characters, but forvalues which require an exponential form, it is sometimes possible to retain accuracy toonly 3-4 decimal places. Exceptions: GRID and DMIG cards are printed in free formatwith accuracy to at least 10 decimal places.

Only bulk data is printed to .echo file (no i/o or control sections).

Some cards are not printed: in particular, PARAM and DOPTRM do not appear in ECHOfiles.



Structural Analysis

The Structural Analysis section provides an overview of the following analyses:

Linear Static Analysis

Linear Buckling Analysis

Nonlinear Analysis

Normal Modes Analysis

Frequency Response Analysis

Complex Eigenvalue Analysis

Random Response Analysis

Response Spectrum Analysis

Transient Response Analysis




The basic finite element equation to be solved for structures experiencing static loads can beexpressed as:

Ku P

Where, K is the stiffness matrix of the structure (an assemblage of individual element

stiffness matrices). The vector u is the displacement vector, and P is the vector of loads

applied to the structure. The above equation is the equilibrium of external and internalforces.

The stiffness matrix is singular, unless displacement boundary conditions are applied to fixthe rigid body degrees of freedom of the model.

The equilibrium equation is solved either by a direct or an iterative solver. By default, thedirect solver is invoked, whereby the unknown displacements are simultaneously solvedusing a Gauss elimination method that exploits the sparseness and symmetry of the stiffnessmatrix, K, for computational efficiency. Alternatively, an iterative solver using the

preconditioning conjugate gradient method may be used. While the direct solver is veryrobust, accurate and efficient, the iterative solver is sometimes superior, in terms of speed,for thick-walled solid structures. The iterative solver is selected through the SOLVTYPsubcase information entry, which in turn references a SOLVTYP bulk data entry.

Once the unknown displacements at the nodal points of the elements are calculated, thestresses can be calculated by using the constitutive relations for the material. For linear

static analysis where the deformations are in the elastic range, ta=hat is the stresses, , are

assumed to be linear functions of the strains, , Hooke’s law can be used to calculate thestresses. Hooke’s law can be stated as:

C

with the elasticity matrix C of the material. The strains are a function of the

displacements.

The static loads and boundary conditions are defined in the bulk data section of the inputdeck. They need to be referenced in the subcase information section using an SPC and LOADstatement in a SUBCASE. Each SUBCASE defines a load vector. Thermal loading is definedby referencing bulk data entries with the TEMPERATURE statement in a SUBCASE.

Unconstrained models can be solved using inertia relief. SUPORT1 subcase statements canthen reference the boundary conditions that restrain the rigid body motions. Up to sixdegrees of freedom can be restrained. These restraints can also be defined without subcasereference using the SUPORT bulk data entry or automated using PARAM, INREL, -2.




The problem of linear buckling in finite element analysis is solved by first applying areference level of loading, PRef , to the structure. A standard linear static analysis is then

carried out to obtain stresses which are needed to form the geometric stiffness matrix KG.

The buckling loads are then calculated by solving an eigenvalue problem:

0GK K x

Where, K is the stiffness matrix of the structure and is the multiplier to the reference load.

The solution of the eigenvalue problem generally yields n eigenvalues , where n is thenumber of degrees of freedom (in practice, only a subset of eigenvalues is usuallycalculated). The vector x is the eigenvector corresponding to the eigenvalue.

The eigenvalue problem is solved using a matrix method called the Lanczos method. Not alleigenvalues are required. Only a small number of the lowest eigenvalues are normallycalculated for buckling analysis.

The lowest eigenvalue Cr is associated with buckling. The critical or buckling load is:

ReCr Cr fP P

In order to run a linear buckling analysis, an EIGRL bulk data entry needs to be givenbecause it defines the number of modes to be extracted. The EIGRL card needs to bereferenced by a METHOD statement in a SUBCASE in the subcase information section. Inaddition, it is necessary to use a STATSUB card to reference the appropriate referential staticloading, fre , SUBCASE. STATSUB cannot refer to a subcase that uses inertia relief.

The buckling analysis will ignore zero-dimensional elements, MPC, RBE3, and CBUSHelements. These elements can be used in buckling analysis, but they do not contribute to thegeometric stiffness matrix, KG. By default, the contribution from the rigid elements to the

geometric stiffness matrix is not included. You have to add PARAM,KGRGD,YES to the bulkdata section to include the contribution of rigid elements to the geometric stiffness matrix.

In addition, through the EXCLUDE subcase information entry, you may decide to omit thecontribution of other elements to the geometric stiffness matrix, effectively allowing you tocontrol which parts of the structure are analyzed for buckling. The excluded properties areonly removed from the geometric stiffness matrix, resulting in a buckling analysis with elasticboundary conditions. This means that the excluded properties may still be showingmovement in the buckling mode.

Buckling analysis cannot be performed if the referential static loading subcase uses inertiarelief. In such cases, the stiffness matrix is positive semi-definite and the bucklingeigenvalue solution ends in singularity.

Linear Buckling and Offset Elements

Some one-dimensional and shell elements can use offset to “shift” the element stiffnessrelative to the location determined by element’s nodes. For example, shell elements can beoffset from the plane defined by element nodes by means of ZOFFS. In this case all other



information, such as material matrices or fiber locations for the calculation of stresses, aregiven relative to the offset reference plane. Similarly, shell results, such as shell elementforces, are output on the offset reference plane.

Offset is applied to all element matrices (stiffness, mass, and geometric stiffness), and torespective element loads (such as gravity). Hence, in principle offset can be used in all typesof analysis and optimization, including linear buckling. However, caution is advised wheninterpreting the results. Without offset, a typical simple structure will bifurcate and loosestability “instantly” at the critical load. With offset, though, the loss of stability is gradualand asymptotically reaches a limit load, as shown below in figure (b):

In practice then, the structure with offset can reach excessive deformation before the limitload is reached. (Note that more complex structures, such as frames or structuresexperiencing bending moments, buckle via limit load, even in absence of ZOFFS on theelement card). Furthermore, in a fully nonlinear approach, additional instability points maybe present on the limit load path.



Nonlinear Analysis

Nonlinear Quasi-Static Analysis

Large Displacement Nonlinear Static Analysis

Geometric Nonlinear Analysis



Nonlinear Quasi-Static Analysis

This solution sequence performs quasi-static nonlinear analysis. Presently, the sources ofnonlinearity include CONTACT interfaces, GAP elements, and MATS1 elastic-plastic material.

Small deformation theory is used in the solution of nonlinear problems, similar to the way itis used with Linear Static Analysis. Inertia relief is also possible. Small deformation theorymeans that strains should be within linear elasticity range (some 5 percent strain), androtations within small rotation range (some 5 degrees rotation). This also means that thereis no update of gap/contact element locations or orientation due to the deformations – theyremain the same throughout the nonlinear computations. The orientation may change,however, due to geometry changes in optimization runs.

Nonlinear Solution Method

The basic Newton method is used for the solution of nonlinear problems. The principle of thismethod is illustrated for a one-dimensional problem in the figure below and can beformulated as follows:

Consider a nonlinear problem:

( )L u P

Where, u is the displacement vector, P is the global load vector, and L(u) is the nonlinear

response of the system (nodal reactions). Note that for a linear problem, L(u) would simply

be Ku (as described in the Linear Static Analysis section). Application of Newton's method to

this equation leads to an iterative solution procedure:

1

n n n

n nn

K u R

u u u



Where,

( ) /n n

n n

K L u u at u

R P L u

In the above formulas, Kn represents a "slope" matrix, defined as a tangent to the L(u) curve

at a point un , and Rn is the nonlinear residual. Repeating this procedure iteratively, under

certain convergence conditions, leads to systematic reduction of residual Rn and hence,

convergence.

Note that the above scheme is somewhat modified to an equivalent format wherein, instead

of calculating u , the new solution un+1 is directly obtained:

1n n n nnK u R K u

This form is readily produced by adding Kn un to both sides of Newton's equation, and has

certain advantages in practical implementations.

Incremental Loading

For a large class of problems satisfying certain stability and smoothness conditions, theNewton's iterative method is proven to converge, provided that the initial guess is sufficientlyclose to the true force-displacement path L(u). Hence, to improve convergence for strongly

nonlinear problems, the total loading P is often applied in smaller increments, as shown inthe figure below. At each of the intermediate loads, P1, P2, etc., the standard Newton

iterations are performed.

This procedure, known as incremental loading, helps to keep the consecutive iterations closerto the true load path, thereby improving the chances of obtaining a final, converged solution(though usually at the expense of an increased total number of iterations).



Nonlinear Convergence Criteria

In order to assess whether the nonlinear process has converged, a number of convergencecriteria are available. These criteria and respective tolerances can be selected on the NLPARM bulk data card. The basic principle in assessing nonlinear convergence is tocompare an error measure of the solution with a pre-determined tolerance level. When theerror falls below the prescribed tolerance, the problem is considered converged. In a case ofmultiple, simultaneous convergence criteria, all criteria need to be satisfied for the solutionto be converged.

The relative error in displacements (printed in the convergence summary as EUI) iscalculated as:

1UA uq

Eq A u

Here, A is a normalizing vector consisting of square roots of diagonal elements of stiffness

matrix 1 iiK A K

and the vector norm II. II is calculated as:

i ii

A u A u

Furthermore, q is a contraction factor that corrects the increment of solution nu to better

represent the actual error in the nonlinear solution. It is expressed as:

1

n

n

uq

u

In order to stabilize the behavior of q in practical computations, it is updated iteratively

according to the formula:

11

2 13 3

nn n

n

uq q

u

starting from initial value q1 = 0.99. Note that the contraction factor is meaningful when the

solution is close to having converged – it then reasonably well estimates the actual errorremaining in the nonlinear solution.

The relative error in terms of loads (printed in convergence summary as EPI) measures therelative strength of the residual R, and is calculated as:

P

R uE

P u

The load vector P in this formula includes nodal reactions due to prescribed displacements.



The relative error in terms of work (printed in convergence summary as EWI) measuresthe relative change in solution energy, and is calculated as:

W

R uE

P u

Note that the above norms only measure the error of the nonlinear iterative process. Theirvalues do not represent the accuracy of the finite element solution, only the fact that thenonlinear process has converged properly.

Nonlinear Problem Setup

The setup for the nonlinear solution is very straightforward. The static loads and boundaryconditions are defined in the bulk data section of the input deck. They need to be referencedin the subcase information section using an SPC and LOAD statement in a SUBCASE. EachSUBCASE defines a load vector. Loads or enforced displacements are not mandatory fornonlinear quasi-static solutions, if GAP or CONTACT elements are present in the model.

Unconstrained models can be solved using inertia relief. SUPORT1 subcase statements canthen reference the boundary conditions that restrain the rigid body motions. Up to sixdegrees of freedom can be restrained. These restraints can also be defined without subcasereference using the SUPORT bulk data entry or automated using PARAM, INREL, -2.

To indicate that a nonlinear solution is required for any subcase, a subcase informationcommand NLPARM needs to be present for the subcase. This command, in turn, points to thebulk data NLPARM card that contains the convergence tolerances and other nonlinearparameters.

Example:

SUBCASE 10 SPC = 1 LOAD = 2 NLPARM = 99..BEGIN BULKNLPARM 99 12 UPW+1.1e-5

.

Note that nonlinear gap and contact analysis are also supported in optimization.

Nonlinear Convergence Considerations

The Newton's method is a reliable tool for the solution of nonlinear problems and can providea fast quadratic convergence rate. However, convergence is not guaranteed under allcircumstances. Contact problems, especially those with friction, often cause convergencedifficulties.

In order to improve the chances of a successfully converged solution, methods have beenbuilt in to help problems converge that would otherwise oscillate back-and-forth and never



converge. One method involves a "sticky gap," wherein a residual stickiness is introduced toprevent the "undecided" nodes from bouncing in and out of contact. Another method is gap/contact status freezing where, after a number of oscillating iterations, gap/contact elementsare not allowed to change their open/closed status. Note that these methods are activatedonly for near-converging yet stagnated problems, and do not interfere with converging (orradically diverging) cases.

User's Considerations for Nonlinear Convergence

There are a number of precautions you can take to increase the chances of a successfulconvergence.

Realistic Problem Setup

Make sure that the nonlinear problem represents a realistic physical situation for which afeasible solution exists. In particular, special care needs to be taken in selecting the properorientation of gap elements. This is especially important when using a prescribed gapcoordinate system. See the description of the CGAP and CGAPG elements for more details.

Sufficient Support

Since gap/contact elements only provide one-way support, it is possible to formulate theproblem in such a way that the individual components will have rigid body freedom undercertain loading conditions. This will manifest as zero pivot in the solution process. To avoidsuch situations, it is advisable to provide sufficient support to all components so that, evenwithout gap/contact elements, there are no rigid body modes. If "solid" supports are notfeasible for all parts (the part needs to move), a very weak set of springs can be used toprevent the part from "flying away" when gap/contact elements are not engaged. Thestiffness of such auxiliary springs can be selected so as to allow for large motion of the part,compatible with the overall size of the model. If the gap elements and contact interfaces areproperly set up, such weak springs will exert virtually no effect when the solution hasconverged.

Reasonable Gap Stiffness

The gap stiffness values KA and KT essentially represent penalty springs that are hard enoughto prevent perceptible penetration of contacting nodes. While, theoretically, higher stiffnessvalues enforce the contact conditions more precisely, excessively high values may causedifficulties in convergence or poor conditioning of the stiffness matrix (this is especially truefor KT). If any such symptoms are observed, it may be beneficial to reduce the value of gapstiffness. As a baseline recommendation, a reasonable range of gap stiffness is of the orderof:

3 610 10 * *to E h

Where, E is the typical value of elastic modulus and h is the typical element size in the area

surrounding the gap elements. Such range will generally keep the gap penetration below onethousandth / one millionth of the element size, respectively. A good value for KT is of theorder of 0.1*KA.

To facilitate reasonable values of KA and KT, OptiStruct supports the automatic calculation ofthese parameters, specifically:



Option KA=AUTO determines the value of KA for each gap element using the stiffnessof surrounding elements. Additional options SOFT and HARD create respectively softeror harder penalties. SOFT can be used in cases of convergence difficulties and HARDcan be used if undesirable penetration is detected in the solution.

Option KT=AUTO automatically calculates the value of KT. If MU1>0, the result here isthe same as with blank KT -- its value is calculated as MU1*KA. However, if MU1=0 orblank, KT=AUTO produces a non-zero value of KT, calculated as KT=0.1*KA. Therefore, KT=AUTO can be used to prescribe enforced stick conditions.

Friction

The presence of friction, due to its strongly nonlinear, non-conservative nature, may causedifficulties in nonlinear convergence, especially when sliding is present. Therefore, solvingthe problem without friction can often provide convergence in otherwise failing problems. Or,in cases when presence of frictional resistance is necessary and minimal sliding is expected,enforcing a stick condition may be a viable solution, and will often lead to a betterconvergence than Coulomb friction (see the PGAP and PCONT bulk data card for details). Note that in cases of larger sliding motions, the stick condition may lead to divergencethrough a "tumbling" mode.

Gap Offset

In order to provide theoretical correctness, friction produces bending moments in gap/contactelements of non-zero length (this results from the transfer of frictional force from the contactsurface to the end nodes). This offset operation can, however, cause convergence problemsand counter-intuitive results. In problems with friction, it may be advisable to turn off theoffset operation via a parameter:

GAPPRM,GAPOFFS,NO

This will produce more intuitive results in the presence of friction. However, it may violatethe rigid body balance of the body, and should therefore be used with caution, especially forproblems without full SPC support. See the PGAP and PCONT bulk data card for details.

Incremental Loading

If the nonlinear procedure diverges in spite of taking the measures described above, theincremental loading procedure (applying the total load in a number of increments) can beused to achieve convergence. See the description of the NLPARM bulk data card for details. Note, however, that if the problem is incorrectly formulated (the solution exhibits excessivedeformations, free rigid body motions, an ill-conditioned stiffness matrix, extremely highnonlinear error, etc.), then incremental loading cannot be counted on to provide a convergedsolution.

Nonlinear Expert System

In some difficult to converge cases an expert system can be used to achieve convergence:

PARAM,EXPERTNL,YES

The expert system will try to adjust the load increment and other nonlinear parameters toachieve convergence. Note, however, that if the problem is incorrectly formulated (thesolution exhibits excessive deformations, free rigid body motions, an ill-conditioned stiffnessmatrix, extremely high nonlinear error, etc.), then expert system cannot be counted on toprovide a converged solution.

Moreover, in some cases it can lead to long computational times without success. This may



be due to using very small load increments or re-running the solution with modified nonlinearparameters.



Large Displacement Nonlinear Static Analysis

Large displacement nonlinear static analysis is used for the solution of problems wherein theload-response relationship is nonlinear and structural large displacements are involved. Thesource of this nonlinearity can be attributed to multiple system properties, for example,materials, geometry, nonlinear loading and constraint. Currently, in OptiStruct the followinglarge displacement nonlinear capabilities are available, including large strain elasto-plasticity,hyperelasticity of polynomial form, contact with small tangential motion, and rigid bodyconstraints.

Geometric Nonlinearity

In analyses involving geometric nonlinearity, changes in geometry as the structure deformsare considered in formulating the constitutive and equilibrium equations. Many engineeringapplications require the use of large deformation analysis based on geometric nonlinearity.Applications such as metal forming, tire analysis, and medical device analysis. Smalldeformation analysis based on geometric nonlinearity is required for some applications, likeanalysis involving cables, arches and shells. Such applications involve small deformation,except finite displacement or rotation.

Material Nonlinearity

Material nonlinearity involves the nonlinear behavior of a material based on currentdeformation, deformation history, rate of deformation, temperature, pressure, and so on.

Constraint and Contact Nonlinearity

Constraint nonlinearity in a system can occur if kinematic constraints are present in themodel. The kinematic degrees of freedom of a model can be constrained by imposingrestrictions on its movement. In OptiStruct, constraints are enforced with Lagrangemultipliers.

In the case of contact, the constraint condition is based on inequalities and such a constraintgenerally does not allow penetration between any two bodies in contact.

Nonlinear Solution Method

Nonlinear problems are generally history dependent. In order to achieve a certain level ofaccuracy, the solution must be obtained in a series of small increments. For this purpose weneed to solve the equilibrium equation at each increment and a corresponding increment sizeis selected.

Newton’s method is used to solve the nonlinear equilibrium equation in OptiStruct. If thesolution is smooth, quadratic of rate of convergence may be achieved when compared withother methods. This method is also very robust in highly nonlinear situations.

Choosing a suitable time increment is very important. In OptiStruct, an automatic timeincrement control is available. It should be suitable for a wide range of nonlinear problemsand, in general, is a very reliable approach.

The automatic time increment control functionality measures the difficulty of convergence atthe current increment. If the calculated number of iterations is equal to optimal number ofiterations for convergence, OptiStruct will proceed with the same increment size. If a lessernumber of iterations is required to achiever convergence, the increment size will be increasedfor next increment. Similarly if it is determined that too many iterations are required, thecurrent increment will be attempted again with a smaller increment size.



Nonlinear Large Displacement Analysis Problem Setup

The setup for the large displacement nonlinear static solution is straightforward.

1. PARAM, LGDISP,1 is used to activate large displacement analysis.

2. To indicate that a nonlinear solution is required for any subcase, the NLPARM subcaseinformation entry should be included in the corresponding subcase.

3. This subcase entry, in turn, references a NLPARM bulk data entry that contains theconvergence tolerances and other nonlinear parameters.

4. If constraints or contacts are defined in the model, the matrix profile may be updatedover time, so it is recommended that hash assembly is used for nonlinear analysis. This isactivated using PARAM, HASHASSM,1.

5. The material MATS1 (TYPE=PLASTIC) is required in conjunction with PARAM, LGDISP,1 toactivate large strain elasto-plasticity analysis.

6. The material MATHE can be used in conjunction with PARAM, LGDISP, 1 to activate largedisplacement analysis with hyperelastic materials.

ExamplePARAM,LGDISP,1PARAM,HASHASSM,YESSUBCASE 10 SPC = 1 LOAD = 2 NLPARM = 99..BEGIN BULKNLPARM 99 12 UPW+1.1e-5

Note:

1. Large displacement nonlinear analysis is supported only for solid elements, RROD, RBAR,and RBE2 entries. (see Note 8 for further details).

2. 1D/3D Bolt Pretensioning and RBE3 rigid elements are not currently supported in largedisplacement nonlinear analysis.

3. Direct Matrix Input (using the DMIG entry) is currently not supported in largedisplacement nonlinear analysis.

4. Linear Buckling Analysis and Preloaded Analysis are not supported with largedisplacement nonlinear analysis. However, you can use PARAM,PRESUBNL,YES to forceOptiStruct to run in such models. Linear Buckling Analysis or Preloaded Analysis is notrecommended in models with nonlinear materials or in large displacement nonlinearanalysis. It is the user’s responsibility to interpret the results with caution.

5. Currently, MATS1 (TYPE=PLASTIC) should be specified to conduct a large displacementnonlinear analysis. However, if linear material properties are required, then a very largevalue can be specified for the LIMIT1 field on the MATS1 entry.

6. The expert system (PARAM, EXPERTNL) is currently not supported with large displacementnonlinear analysis.



7. Nonlinear Heat Transfer Analysis is currently not supported with Large DisplacementNonlinear Analysis.

8. Large Displacement Nonlinear Analysis is not supported in conjunction with the followingelements:

(a) The following elements can exist in the model, but they will be resolved using smalldisplacement theory:

SHELL, GASKET, BUSHING, RROD, RBAR, RBE2, CROD, CELAS, CONM

(b) The following elements are not allowed and OptiStruct will error out if they arepresent:

CBAR, CBEAM, CGAP, CGAPG, CWELD, CSEAM, CFAST, RBE1, RBE3



Geometric Nonlinear Analysis (RADIOSS Integration)

Geometric nonlinear analysis in OptiStruct is provided thru an integration of the RADIOSSStarter and RADIOSS Engine via a translator. Implicit (static and dynamic), as well asexplicit integration schemes, are available. Transparent to you, OptiStruct input data isdirectly translated into RADIOSS input data. The RADIOSS Starter and RADIOSS Engine arethen executed and the results are brought back into the OptiStruct output module to exportthe different output formats.

Solution Method

This section discusses the basic concepts of the solution methods to highlight thecharacteristics of the solution methods and to identify the use of certain parameters tocontrol convergence. The geometric nonlinear solution utilizes a general Newmarkintegration scheme. The following equation of motion shall be solved.

Mu Cu Ku P&& &

The matrix M is the mass matrix, C is the damping matrix and K is the stiffness matrix.

These matrices are derived using finite elements. The vector P describes the external loads

and u is the displacement vector. The dots describe the derivatives with respect to time.

The equation of motion can be solved using a general Newmark integration scheme. Newmark is a one-step time integration method. All solutions can be derived from it and areformulated in terms of a time history (Figure 1).

Figure 1: Time History



In general Newmark, the state vector is computed as follows:

11 1 tut ttu u t u &&& & &&

2 21 1

12t t tt tu u tu t u t u& && &&

Then the equation of motion yields:

2 21

11 2t t t t ttM tC t K u P C u tu K u tu t u&& & && & &&

This can be rewritten into:

2

1t tM C K u P

tt%

using:

1 t ttu u u

In short:

A u P%

The matrix A is the dynamic stiffness. In nonlinear time-dependent problems, this system

becomes nonlinear and its solution requires an additional iteration loop at each time stepusing a Newton-type method.

An implicit (quasi-)static analysis scheme follows directly when omitting mass anddamping terms. Therefore:

( ) t tK u u P

The linear static case reduces to the systems equation:

Ku P

Normal modes analysis is a linear analysis that solves the eigenvalues problem.

0K M x

For implicit dynamic analysis, an extension of Newmark method, known as a-HHT, is the

default time integrator. This method is named after Hilber, Hughes, and Taylor – it allows foreffective algorithmic damping of high-frequency spurious vibrations. This method introducesadditional parameter α and assumes:



211 2 1, 032 4

with

2

1 11 t tM C K u P

tt%

The smaller the value of a, the more algorithmic damping is included in the numerical

solution. With a = 0.0 there is no numerical damping and the method is the trapezoidal

method.

The second method available is the general Newmark with user-defined and . Thedefaults are typically:

1 1,2 4

which is equivalent to HHT method with a = 0.0. This is an unconditionally stable implicit

integration scheme with:

1 11

2t tt tu u t u u& & && &&

21 1

14t t tt tu u tu t u u& && &&

And from the equation of motion:

2

4 2t tM C K u P

tt%

By default a Modified Newton method is employed to solve the implicit problems stated above(Figure 2).

( )t i iK u u R

1 i iiu u u



Figure 2: Implicit scheme

Convergence for implicit (quasi-)static and dynamic analysis is controlled via NLPARM,TSTEPNL bulk data entries, respectively. Modified Newton requires that the stiffness matrixis kept constant thru a number of iterations (KSTEP) before it is rebuilt. This savescomputation time in terms of matrix factorizations, but may increase the number ofiterations. Full Newton can be achieved by using KSTEP = 1.

Convergence is defined by a change in results less than a specified tolerance. Relativeresidual force (EPSP), relative displacement (EPSU), or relative residual energy (EPSW) canbe chosen as convergence criteria (CONV).

In implicit analysis the time step is controlled via NLPARMX, TSTEPNX bulk data entries,respectively. Time step control includes a minimum (DTMIN) which terminates the solution,a maximum (DTMAX) time step, as well as a maximum number of time steps which cannotbe exceeded. Using convergence acceleration methods (SACC), more control can beasserted. If the number of iterations within a time step reaches a specified limit (LDTN),then the iteration is repeated with a smaller time step. The time step is also reduced shouldthe iteration diverge. If the number of iterations is below a certain limit (ITW), then the timestep is increased.

A BFGS Quasi-Newton method is also available to solve the implicit equations. It workssimilarly to Modified Newton. However, in addition to the tangential stiffness, it uses anapproximate Hessian to improve convergence.

A conditionally stable explicit integration scheme can be derived from the Newmarkscheme by setting:

12 , 0

1 11

2t tt tu u t u u& & && &&



21

12t t ttu u tu t u& &&

From these relationships the central differences explicit integration scheme can be derived.

121/2 1/2t t tu u t u& & &&

1 2 1 1/2ttu u t u&

1 11 1/2t tMu P Cu Ku&& &

Figure 3 illustrates the relationships.

Figure 3: Explicit integration

Assuming that

1 1/2t tCu Cu& &

The equation of motion for the central differences scheme simplifies to:

1 1 1t t tMu P Cu Ku&& &

1 11t

t ttMu P B dV&&

This central differences scheme is used if explicit analysis is selected. The time step mustalways be smaller than the critical time step to ensure stability of the solution. The criticaltime step depends on the highest frequency in the system and is computed from thecorresponding angular frequency max as:

max

2crt

For a discrete system, the time step must be small enough to excite all frequencies in thefinite element mesh. This requires such a short time step that a shock wave does not missany node when traveling the mesh. Therefore,



cltc

with lc being the critical length of an element and c is the speed of sound in the given

material.

Different ways of time step control are available. The default method is the nodal time stepwhich is computed from the nodal mass m and the equivalent nodal stiffness k such that:

2mincrn

n

mt

k

The element time step based on the critical length of each element is also available. Thechoice can be made on the XSTEP bulk data entry.

Problem Setup

Geometric nonlinear analysis is defined thru a SUBCASE.

For implicit (quasi-)static analysis an NLPARM statement as well as ANALYSIS = NLGEOMmust be present in the subcase. To define the termination time a TTERM subcase entry canbe used. TTERM is mandatory if a nonlinear load NLOAD is used. NLPARM references an NLPARM bulk data entry. Additional parameters to control the geometric nonlinear solutioncan be defined on the optional NLPARMX bulk data entry. These include convergenceacceleration methods. In the case of post-buckling analysis Riks method can be selected.

Linear static analysis is provided as a debugging option. It is defined thru NLPARMX, ILIN. Such analysis can help investigate the model for modeling errors. In linear static analysisthe load vector is determined at the termination time. Normal modes analysis requires aMETHOD subcase statement in addition.

For implicit dynamic analysis a TSTEPNL statement as well as ANALYSIS = IMPDYN must bepresent in the subcase. To define the termination time a TTERM subcase entry is mandatory. TSTEPNL references a TSTEPNL bulk data entry. Additional parameters to control thegeometric nonlinear solution can be defined on the optional TSTEPNX bulk data entry.

For explicit dynamic analysis an XSTEP statement as well as ANALYSIS = EXPDYN must bepresent in the subcase. To define the termination time a TTERM subcase entry is mandatory. XSTEP references an XSTEP bulk data entry. Time step control can be defined on the XSTEPbulk data entry.

The implicit schemes require the solution of linear systems equations. By default, the directsolver is invoked, whereby the unknowns are simultaneously solved using a Gausselimination method that exploits the sparseness and symmetry of the stiffness matrix, K, for

computational efficiency. Alternatively, an iterative solver using the preconditioningconjugate gradient method may be used. While the direct solver is very robust, accurate andefficient, the iterative solver is sometimes superior in terms of speed, for example for bulkysolid structures. The iterative solver is selected through the SOLVTYP subcase informationentry, which in turn references a SOLVTYP bulk data entry.

The definition of a unit system thru the DTI, UNITS or UNITS bulk data statement is required.

The geometric nonlinear analysis loads and boundary conditions are defined in the bulk data



section of the input deck. They need to be referenced under the SUBCASE using an SPC,NLOAD, LOAD, IC and RWALL statements in a SUBCASE. Each SUBCASE defines one loadingcondition that is executed separately.

Subcase continuation is available thru the use of CNTNLSUB. Any number of explicit andimplicit analyses can be linked. However, geometric nonlinear (ANALYSIS = NLGEOM,EXPDYN, or IMPDYN) analysis subcases cannot yet be linked with small displacement quasi-static nonlinear (ANALYSIS = NLSTAT) analysis subcases and vice versa.

Example for implicit (quasi-)static analysis

SUBCASE 1 ANALYSIS = NLGEOM SPC = 1 NLOAD = 2 NLPARM = 3 TTERM = 1.0 DISP = ALL STRESS = ALLBEGIN BULKNLPARM,3NLOAD1,2,2,,L,88TABLED1,88,+,0.0,0.0,1.0,1.0,ENDTDTI,UNITS,1,kg,N,m,s

Alternative example for implicit (quasi-)static analysis

SUBCASE 1 ANALYSIS = NLGEOM SPC = 1 LOAD = 4 NLPARM = 3 DISP = ALL STRESS = ALLBEGIN BULKNLPARM,3 FORCE,4,233,,1.0,0.0,0.0,1.0DTI,UNITS,1,kg,N,m,s

Example for implicit dynamic analysis

SUBCASE 2 ANALYSIS = IMPDYN SPC = 1 IC = 5 TSTEPNL = 3 TTERM = 0.2 DISP = ALL STRESS = ALLBEGIN BULKTSTEPNL,3TIC,5,123,1,,13.88DTI,UNITS,1,kg,N,m,s



Example for explicit analysis

SUBCASE 3 ANALYSIS = EXPDYN SPC = 1 NLOAD = 2 XSTEP = 3 TTERM = 1.0 DISP = ALL STRESS = ALLBEGIN BULKXSTEP,3NLOAD1,2,2,,L,88TABLED1,88,+,0.0,0.0,1.0,1.0,ENDTDTI,UNITS,1,kg,N,m,s

Example for subcase continuation

DISP = ALL STRESS = ALLSUBCASE 1 ANALYSIS = NLGEOM SPC = 1 NLOAD = 2 NLPARM = 3 TTERM = 1.0SUBCASE 2 ANALYSIS = EXPDYN IC = 5 XSTEP = 4 TTERM = 1.1 CNTNLSUB = 1BEGIN BULKNLPARM,3XSTEP,4NLOAD1,2,2,,L,88GRAV,2,,9.81,0.0,0.0,1.0TABLED1,88,+,0.0,0.0,1.0,1.0ENDT TIC,5,123,1,,13.88DTI,UNITS,1,kg,N,m,s

Alternative example for subcase continuation for implicit (quasi-)static analysis

DISP = ALL STRESS = ALL ANALYSIS = NLGEOM CNTNLSUB, YESSUBCASE 1 SPC = 1 LOAD = 2 NLPARM = 3SUBCASE 2



SPC = 1 LOAD = 4 NLPARM = 3BEGIN BULKNLPARM,3GRAV,2,,9.81,0.0,0.0,1.0FORCE,4,233,,1.0,0.0,0.0,1.0UNITS = SI

User's Considerations

Geometric Nonlinear Analysis Properties and Materials

Special element types and nonlinear materials are available for geometric nonlinear analysis. As a general rule property and material definitions that are only applicable in geometricnonlinear analysis are defined on extensions to the original property and to a MAT1 material,respectively. The extensions are grouped with the base entry by sharing the same PID orMID. In the case of a subcase that is not a geometric nonlinear analysis, these extensionsare ignored. Property defaults can be set for shells (XSHLPRM) and solids (XSOLPRM) thatmay replace the use of property extensions.

Property example:

PSHELL, 3, 7, 1.0, 7, , 7PSHELLX, 3, 24, , , 5

Material example:

MAT1, 102, 60.4, , 0.33, 2.70e-6MATX02, 102, 0.09026, 0.22313, 0.3746, 100.0, 0.175

Coordinate Systems

In geometric nonlinear analysis there are moving and fixed coordinate systems. Rectangularcoordinate systems that are defined thru grid points (CORD1R, CORD3R) are moving with thedeformations of the model. Systems defined in terms of point coordinates (CORD2R,CORD4R) are fixed.

The behavior of loads depends on the coordinate system referenced. If the loads FORCE,MOMENT are desired to be follower forces, a CID that references a moving coordinate system(CORD1R, CORD3R) must be defined. Otherwise these loads are not following thedeformation. PLOAD always follows the deformations.

Difference Between Geometric Linear and Geometric Nonlinear Analysis

In geometric linear analysis all deformations and rotations are small (infinitesimal). As ageneral rule, displacements of say 5% of the model dimension and rotations up to 5 degreescan be treated as small. Rotations are trickier. A rotating body seems to get bigger linearlyunder deformation even if defined as rigid. Nonlinearities can only come from contact ormaterials. This type of analysis is supported in Nonlinear Quasi-Static Analysis withANALYSIS = NLSTAT. Loads stay in the undeformed coordinates and simply move along the



axis they are defined in.

In geometric nonlinear analysis, displacements and rotations are large (finite). Themagnitude of a force actually matters. Changes in magnitude of a load can changeconvergence behavior considerably. Also the direction of a force needs to be controlled. Forces may follow the deformation or keep their direction. This can be controlled thru thechoice of coordinate systems (see above).

The images below display two examples of these differences. Figure 4 shows a cantileverbeam solved with small displacements, large displacements with a follower force, and large

displacements without a follower force. Figure 5 shows a simple rigid rotated by an angle solved with small and finite rotations.

Figure 4: Cantilever beam with small (GLIN) and large (GNL) displacements

Figure 5: Small (GLIN) vs. finite (GNL) rotations

Difference Between Implicit and Explicit Analysis

Implicit static analysis has the following characteristics:

Involves matrix factorization

Stiffness matrix must be positive definite



- Model must be sufficiently constraint

- No unattached parts

Iteration is needed to reach equilibrium

Equilibrium is achieved within iteration tolerances

Larger time steps

Long-term, (quasi-)static events

Implicit dynamic analysis has the following characteristics:

Involves matrix factorization

Dynamic stiffness matrix must be positive definite

Iteration is needed to reach equilibrium

Equilibrium is achieved within iteration tolerances

Larger time steps

Long-term events

Explicit (dynamic) analysis has the following characteristics:

In general a diagonal mass matrix is used

No matrix factorization necessary

Equilibrium is always guaranteed

Maximum stable time step needs to be respected

Small time steps

Short-term events

Implicit Contact

In an implicit contact analysis, you need to take care of the following two concerns:

First, there should be no initial penetrations in the mesh. Sometimes, initial penetration isnecessary to begin the simulation then only a small (< 0.01*GAP) value is recommended tonot change reality too much. With high initial penetrations, the solution will progress butmay lead to incorrect results. You will be warned about initial penetration during the checkrun.

Secondly, in quasi-static analysis the model needs to be sufficiently constrained. Forexample, having two blocks on top of each other (Figure 6) the top part is not constrained. It is recommended to have the meshes completely depenetrated and to define a very smallGAP. This would create small springs constraining the upper body in vertical direction. Ofcourse, the other rigid body motions of the part have to be constrained too.

More information can be found in CONTACT, CONTPRM, and PCONTX bulk data definitions.



Figure 6: Initial GAP

Implicit Snap-thru, Post-buckling Analysis

Some nonlinear problems with large deformations encounter bifurcations. The solutionbecomes instable and the structure buckles or snaps from one state to another (Figure 7). The load vs. displacement does not simply increase but may reduce until another stable pointis reached from which the load then can continue to increase (Figure 8). In the implicitsolution procedure it is clear that a simple load increment may not be sufficient to determinethe point where the force starts reducing.

A special method needs to be employed to find the proper search direction s for the solutionto stay on its path. This solution is called Riks method and can be defined via NLPARMX,SACC. The search direction is defined by satisfying certain constraints of which two methodscan be selected via NLPARMX, CTYP.

There are currently some limitations in the way the results are written. Internal forcescannot be plotted yet.

Figure 7: Snap-thru



Figure 8: Snap-thru - Load vs. displacement

Not Sufficiently Constrained Model in Implicit (Quasi-)static Analysis

For models that are not sufficiently constrained, inertia stiffness can be used to overcome asingular stiffness matrix (NLPARMX, KINER = ON). The inertia stiffness, Kinertia = 1 /

(DTSCQ * dt)2M, is added to the stiffness matrix K in a (quasi-)static analysis. Care needsto be taken in the selection of DTSCQ. An added mass that is too large may lead to incorrectresults. This function is similar to inertia relief in other analysis types.

Implicit Convergence Issues

Sometimes the iteration process stops with TIME STEP LIMIT ERROR. This means the timestep reached DTMIN. In this case, the following measures can be taken to remedy thesituation:

Implicit (Quasi-)static

Check if there is any rigid motion by launching a linear run or eigenvalue analysis.

Double check the values and units of input parameters (material properties, loads, etc). It is usually helpful to view the results of intermediate animation outputs.

Increase the number of load increments (NLPARM, NINC), decrease minimum time step(NLPARMX, DTMIN), and/or decrease maximum time step (NLPARMX, DTMAX).

If post-buckling happens, activate RIKS method (NLPARMX, TSCTRL = RIKS).

Check the displacement, force and energy residual values during the iteration in the .out file, find out which convergence criteria is causing the divergence, and then

modify convergence control criteria (NLPARM, CONV) and relax the tolerances(NLPARM, EPSU, EPSW, and EPSP). It must be understood that reducing theconvergence tolerance may lead to inaccurate results.



Use small displacement formulation (PARAM, SMDISP, 1) if the displacements androtations are small.

Implicit Dynamic

Double check the values and units of input parameters (material properties, loads, etc). It is usually helpful to view the results of intermediate animation outputs.

Decrease the initial time step (TSTEPNL, NX), decrease minimum time step (TSTEPNX,DTMIN), and/or decrease maximum time step (TSTEPNX, DTMAX).

Check the displacement, force and energy residual values during the iteration in the .out file, find out which convergence criteria is causing the divergence, and then

modify convergence control criteria (NLPARM, CONV) and relax the tolerances(NLPARM, EPSU, EPSW, and EPSP). It must be understood that reducing theconvergence tolerance may lead to inaccurate results.

Use small displacement formulation (PARAM, SMDISP, 1) if the displacements androtations are small.

Limitations

The solution will be terminated if unsupported Bulk Data entries are encountered.

The following Bulk Data properties and elements are currently not translated:

- PBUSHT (partially, KN is translated)

- PDAMP, CDAMPi

- PGAP, CGAP, CGAPG (partially, friction is not allowed)

- PMASS, CMASSi

- PSHEAR, CSHEAR

- PVISC, CVISC

Additional relevant Bulk Data entries (except loads) that are currently not translated:

- CORD1C, CORD1S, CORD2S

- DMIG

- MAT2, MAT4, MAT5, MAT8, MAT9, MAT10

- MATTi, TABLEST

- MPC, MPCADD

- RBE1, RROD

Relevant loads that are currently not translated:

- PLOAD1, PLOAD2

- PLOAD4 (partially, N1, N2, N3 cannot be used)

- RFORCE (partially, RACC is not supported)

- TLOAD1, TLOAD2




Normal Modes Analysis, also called eigenvalue analysis or eigenvalue extraction, is atechnique used to calculate the vibration shapes and associated frequencies that a structurewill exhibit. It is important to know these frequencies because if cyclic loads are applied atthese frequencies, the structure can go into a resonance condition that will lead tocatastrophic failure. It is also important to know the shapes in order to make sure that loadsare not applied at points that will cause the resonance condition.

Normal modes analysis is also required for modal frequency response and modal transientanalysis. In these analyses the problem is transformed from the direct mesh coordinates,where the number of degrees of freedom can be in the millions, to the modal coordinateswhere the number of degrees of freedom is just the number of modes used. Typically, theupper bound frequency in this case is 1.5 times the highest loading frequency or responsefrequency of interest.

In OptiStruct, normal modes analysis can be performed using one of two algorithms: Lanczosor the automated multi-level sub-structuring eigenvalue solution (AMSES). The eigenvalueextraction data for Lanczos is specified on the EIGRL data and for the automated multi-levelsub-structuring eigenvalue solution method, the EIGRA data is used.

In addition, OptiStruct has an interface to the AMLS software developed at the University ofTexas. AMLS uses the automated multi-level sub-structuring method for eigenvalueextraction. The use of AMLS is triggered by using the PARAM, AMLS set to YES input data inconjunction with the EIGRL card (only).

The Lanczos Method

The Lanczos method has the advantage that the eigenvalues and associated mode shapes arecalculated exactly. This method is efficient for calculations in which the number of modes issmall and the full shape of each mode is required. The disadvantage of the Lanczos methodis that it is slow for large problems with millions of degrees of freedom for which hundreds ofmodes are required. The run times for these types of problems can easily stretch into days. In these cases, the AMSES or AMLS method must be used.

The Automated Multi-level Sub-structuring Eigenvalue Solution Method (AMSES)

The AMSES method has the advantage that only a portion of the eigenvector need becalculated. Since only a portion of the eigenvector is calculated, the disk space and disk I/Ois greatly reduced. This leads to much shorter run times. For typical NVH frequencyresponse analysis there is only about 100 degrees of freedom of interest. In these cases,solutions of thousands of modes for meshes of millions of degrees of freedom can be solvedin just a few hours. The disadvantage of the AMSES method is that the calculations are notexact. However, the modal frequencies are still accurate to a few digits. Also, for NVHanalysis it is important that the mode shapes form modal space that covers all possibledeformation patterns, but not so important that each individual mode shape is accurate.

AMSES Usage Guidelines

The following guidelines list the factors affecting AMSES usage:

1. The AMSES solution is, generally, much faster than Lanczos, but the results areapproximate. Accuracy of the lower modes is very high; therefore, AMSES is a goodcandidate for solutions with a large number of modes (greater than a few hundred) wherean approximated eigen-space is sufficient (as in Modal Frequency Response and ModalTransient Response Analysis). Although approximate, the large number of modes used for



modal analysis will encompass the modal space and the resulting motion will match veryclosely with the Lanczos results. Lanczos is recommended in solutions where accuratemode shapes of a small number of modes are required.

2. AMSES is also recommended in cases where: 1) A low number of eigenvalues arerequested but the model consists of more than a million degrees of freedom, and/or; 2)The upper bound (V2) is specified or the number of modes (ND) is greater than 50 on theEIGRL entry. In such cases, it is likely that Lanczos runs are slower than AMSES runs.

3. For optimization runs, if accuracy of the eigenvector is important, normal modes analysiswith AMSES can be run first and then Lanczos can be run with precise lower and upperbounds to check the AMSES run for accuracy. The AMSES upper bound can then beadjusted to achieve acceptable accuracy of the desired eigenvectors. Now, AMSES can beused for all optimization runs in this analysis.

4. The AMSES solution is much faster for flexible body generation and modal solutions withmany residual vectors.

5. AMSES should be used cautiously in situations with very large RBE3’s (if the RBE3 isconnected to 1/4th of the structure). It may be better to eliminate such RBE3’s.

6. AMSES solution speeds depend on the number of eigenvector degrees of freedom (DOF)to be calculated. DISP=ALL will cause the entire eigenvector to be calculated and thespeedup will not be large. However, if results for only a few DOF are required (typical forNVH analysis), AMSES can be up to 100 times faster than Lanczos. To improve AMSESrun times, it is recommended to request results only for the required DOF.

7. For an AMSES run with V1, V2 and ND specified on the EIGRA entry, AMSES calculates allthe modes up to the specified V2 (upper bound) regardless of the value of ND. Then “ND”number of requested modes is output. Therefore, reducing ND by keeping the upperbound (V2) the same will not significantly improve the AMSES run times, the upper boundmust also be correspondingly reduced to prevent the extraction of extra modes.

8. AMSES is also useful in checking for model irregularities. AMSES can be used to print thelist of grids associated with a massless mechanism or a singularity.

The Governing Equations


The equilibrium equation for a structure performing free vibration appears as the eigenvalueproblem:

0K M x

Where, K is the stiffness matrix of the structure and M is the mass matrix. Damping is

neglected.

The solution of the eigenvalue problem yields n eigenvalues , where n is the number of

degrees of freedom. The vector { i } is the eigenvector corresponding to the eigenvalue.



The eigenvalue problem is solved using Lanczos, AMSES, or AMLS.

The natural frequency fi follows directly from the eigenvalue .

2i

if

Input Specification

In order to run a normal modes analysis, an EIGRL or EIGRA bulk data entry needs to begiven to define the number of modes to be extracted. EIGRL or EIGRA data needs to bereferenced by a METHOD statement in a SUBCASE in the subcase information section.

It is not necessary to define boundary conditions using an SPC statement. If no boundaryconditions are applied, a zero eigenvalue is computed for each rigid body degree of freedomof the model.

It is possible to request the computation of residual vectors in conjunction with a normalmodes analysis. Residual vectors are static displacements ortho-normalized with theeigenvectors to be used in an external frequency response analysis. In order to get thisoutput, users have to define degrees of freedom using USET, USET1. The degrees of freedomare then used to define loads in the unit load method to compute the residual vectors. RESVEC = YES needs to be defined in the normal modes subcase, if the Lanczos eigensolveris used. Residual vectors associated with USET and USET1 data are always created, if theAMSES or AMLS eigensolvers are used. Boundary conditions defined using SPC or inertiarelief must be applied to create residual vectors.

Subcase Definition

A normal modes subcase may be explicitly identified by setting ANALYSIS=MODES, but it isalso implicitly chosen for any subcase containing the METHOD data selector (when theANALYSIS entry is not present).

The following data selectors are recognized for an normal modes subcase definition.

1. METHOD – references an eigenvalue extraction bulk data definition (EIGRL or EIGRA).This reference is required.

2. SPC – references single point constraint bulk data entries (SPCADD, SPC or SPC1).

3. MPC – references multi-point constraint bulk data entries (MPCADD or MPC).

Bulk Data

Bulk data entries which have particular significance for normal modes analysis include:

1. EIGRL – specifies the modes to be calculated and solution parameters for the Lanczoseigenvalue extraction method.

2. EIGRA – specifies the modes to be calculated and solution parameters for the AMSESeigenvalue extraction method.

3. PARAM,AMLS,YES – specifies that the AMLS software will be used for eigenvalueextraction based on the modal parameters on the EIGRL or EIGRA data.



4. SPC, SPC1, and SPCADD - specify the base where excitation is applied and otherconstraints.

5. MPC and MPCADD - specify multi-point constraints.

Sample Input

SUBCASE 100SPC = 5METHOD = 24

$BEGIN BULK$EIGRL, 24, 0.0, 1000.ENDDATA$

Output

Results of interest from eigenvalue extraction include maximum displacement, modalstresses, energies and multi-point constraint forces. These are requested via the I/O Options DISPLACEMENT, EKE, ESE, STRESS, GPSTRESS and MPCFORCE respectively.




Frequency response analysis is used to calculate the response of a structure to steady stateoscillatory excitation. Typical applications are noise, vibration and harshness (NVH) analysisof vehicles, rotating machinery, transmissions, and powertrain systems.

Frequency response analysis is used to compute the response of the structure, which isactually transient, in a static frequency domain. The loading is sinusoidal. A simple case is aload of given amplitude at a specified frequency. The response occurs at the samefrequency, and damping would lead to a phase shift (Figure 1).

The loads can be forces, displacements, velocity, and acceleration. They are dependent onthe excitation frequency .

The results from a frequency response analysis are displacements, velocities, accelerations,forces, stresses, and strains. The responses are usually complex numbers that are eithergiven as magnitude and phase angle or as real and imaginary part.

OptiStruct supports Direct and Modal frequency response analysis.

Figure 1: Excitation and response of a frequency response analysis.

Direct Frequency Response Analysis

Direct frequency response analysis can be used to compute the structural responses directlyat discrete excitation frequencies by solving a set of complex matrix equations.

i tMu Bu Ku Pe&& &

The quantity is the angular loading frequency. The applied harmonic excitation can beassumed to generate a harmonic response.

i tu de



The vector u is the displacement vector. Substituting the assumed harmonic displacementresponse into the equation of motion and rewriting the damping matrix (B), you get:

21

i t i tEK M iGK iK i B de Pe

The matrix K is the stiffness matrix and the matrix M is the mass matrix.

There are three ways to define damping in the system.

1. Using a uniform structural damping coefficient G.

2. Structural element damping using the damping coefficients GE on the materials as well

as GE on bushing and spring element property definitions. These form the matrix KE.

3. Viscous damping generated by damper elements. These form the matrix B1.

The equation of motion is solved directly using complex algebra.

Running Direct Frequency Response Analysis using OptiStruct

The frequency response loads and boundary conditions are defined in the bulk data section ofthe input deck. They need to be referenced in the subcase information section using an SPCand DLOAD statement in a SUBCASE.

OptiStruct does not support inertia relief for direct frequency response analysis. The solverwill error out if it is attempted.

A frequency set must be referenced using a FREQUENCY statement.

In addition to the various damping elements and material damping, uniform structuraldamping G can be applied using PARAM, G.

Modal Frequency Response Analysis

The modal method first performs a normal modes analysis to obtain the eigenvalues 2

i i

and the corresponding eigenvectors iX X

of the system. The response can be expressedas a scalar product of the eigenvectors X and the modal responses d.

i tu Xde

The equation of motion without damping is then transformed into modal coordinates usingthe eigenvectors.

T T i t T i tX MX X KX de X Pe

The modal mass matrix TX MX and the modal stiffness matrix

TX KX are diagonal. If theeigenvectors are normalized with respect to the mass matrix, the modal mass matrix is the



unity matrix and the modal stiffness matrix is a diagonal matrix holding the eigenvalues ofthe system. This way, the system equation is reduced to a set of uncoupled equations for thecomponents of d that can be solved easily.

The inclusion of damping, as discussed in the direct method, yields:

21

T T T T T i t T i tEX KX X MX iGX KX iX K X i X B X de X Pe

Here, the matrices T

EX K Xand 1

TX B Xare generally non-diagonal. Then the coupled

problem is similar to the system solved in the direct method, but of much lesser degree offreedom. It is solved using the direct method.

The evaluation of the equation of motion is much faster if the equations can be keptdecoupled. This can be achieved if the damping is applied to each mode separately. This isdone through a damping table TABDMP1 that lists damping values gi versus natural

frequency fi . If this approach is used, no structural element or viscous damping should be

defined.

The decoupled equation is:

2 i t i ti i i i im i b k d e p e

Where, / (2 )i i i ib m

is the modal damping ratio, and 2i is the modal eigenvalue.

Three types of modal damping values ( )i ig f

can be defined: G – Structural damping, CRIT– Critical damping, and Q – Quality factor. They are related through the following three

equations at resonance:

:2

i ii

cr

b gG

b

: 2cr i iCRIT b m

1 1:

2i

i i

Q Qg

Modal damping is entered in to the complex stiffness matrix as structural damping if PARAM,KDAMP, -1 is used. Then the uncoupled equation becomes:

2 (1 ( ))* i t i ti i i im ig k d e p e

A METHOD statement is required for the modal method to control the normal modes analysis. The METHOD statement can refer to either EIGRL or EIGRA data.



Residual Vector Generation (Increases accuracy)

The accuracy of the modal method can be vastly improved by adding the displacementvectors of a static analysis based on the dynamic loading to the matrix of eigenvectors X. These vectors are frequently referred to as residual vectors, the method as the modalacceleration.

There are two ways this is implemented.

The unit load method generates residual vectors based on static loads which are unitvectors at the dynamic load degrees of freedom. That is, the static loads for theresidual vector generation are unit vectors at the degrees of freedom where thedynamic load is applied. The number of residual vectors is equal to the number ofloaded degrees of freedom. This is the default method since it is generally moreaccurate.

The applied load method generates a maximum of two residual vectors which are thedynamic load vector at a loading frequency of zero. If the real and the imaginary partsof the dynamic load are the same, or if one of them is zero, only one of them is used.

In the case of excited displacements, the residual vectors are obtained by solving static loadcases with unit displacements at the same degrees of freedom as the dynamic exciteddisplacement degrees of freedom.

The following image illustrates the effect that the use of the residual vectors has on the resultaccuracy of the modal frequency response analysis (FRA) compared to the accurate directmethod.

Running Modal Frequency Response Analysis using OptiStruct

The frequency response loads and boundary conditions are defined in the bulk data section ofthe input deck. They need to be referenced in the subcase information section using an SPCand DLOAD statement in a SUBCASE.

Residual vectors are relevant for modal FRF/acoustics/transient analysis. They enhance theaccuracy of these analyses and, hence, are computed by default. You can control RESVECcalculations using the case control statement:

RESVEC(APPLOD/UNITLOD,DAMPLOD/NODAMP)=Value



Where, Value can be Yes or No. The keyword(s) within parentheses are ignored if the Valuespecified is No – in this case all RESVEC calculations are turned off. The keyword APPLODgenerates RESVECs based on the dynamic loading of the modal FRF/acoustics/transientanalysis. The keyword UNITLOAD generates RESVECs based on unit loads at the dynamicloading’s degrees of freedom. The keyword DAMPLOD generates viscous damping RESVECsbased on unit loads at the viscous damping degrees of freedom. The keyword NODAMP turnsoff the generation of the viscous damping RESVECs that are otherwise generated by default. Even though DAMPLOD and NODAMP are options in the case control, they are global switchesthat will be applied to all the modal FRF/acoustics/transient subcases in the model.

When the underlying eigenvalue analysis is done using the Lanczos method, the defaultRESVECs are generated based on the applied loading and viscous damping degrees offreedom. If the underlying eigenvalue analysis is done using AMSES or AMLS, the defaultRESVECs are generated based on unit loading at the load degrees of freedom and viscousdamping degrees of freedom. Residual vectors are always generated if enforceddisplacements, velocities or accelerations are defined. In addition, if there is USET U6 data,residual vectors will be calculated if the AMSES or AMLS eigensolver is used. USET U6residual vectors will not be calculated if the Lanczos eigensolver is used.

When residual vectors are included, inertia relief will be applied by default to unconstrainedmodels. If inertia relief is not desired for RESVECs, it has to be turned off using PARAM,INREL, 0.

When residual vectors are included, the eigenmodes from the underlying eigenvalue analysisof the FRF/transient subcase are used in inertia relief. All modes with eigenvalues below alimit value (FZERO) are used as rigid body modes in the inertia relief analysis. If there areno eigenmodes below FZERO, up to 6 global rigid body modes are internally generated basedon the geometry of the model and used in the inertia relief. You can set FZERO using PARAM, FZERO, Value. The default value for FZERO is 0.1

A frequency set must be referenced using a FREQUENCY statement. A METHOD statement isrequired for the modal method to control the normal modes analysis. In order to savecomputational effort, previously saved eigenvectors can be retrieved using the EIGVRETRIEVEsubcase statement.


Modal damping is being applied using the SDAMPING reference of a damping table TABDMP1. The parameter PARAM, KDAMP is to define the method of applying the damping table.

Frequency-dependent materials (MATFi bulk data entries) can be used in Direct and ModalFrequency Response Analysis, via TABLEDi entries for corresponding fields on the MATientries. MATF1, MATF2, MATF3, MATF8, MATF9 and MATF10 bulk data entries can be used todefine the currently available frequency-dependent materials.

Frequency-dependent properties (PBUSHT bulk data entry) can also be used in FrequencyResponse Analysis, via TABLEDi entries for the corresponding fields on the PBUSHT entry.



Output

The results of a frequency response analysis are displacements, velocities, accelerations,forces, stresses, and strains. The usual output entries like STRESS, STRAIN, DISPLACEMENT,etc. can be used to request corresponding output values.

PARAM, ENFMOTN, REL can be used to generate displacement, velocity and accelerationoutput relative to the specified enforced motion. In such cases, subsequently calculatedoutputs like stresses and forces are also generated relative to the specified enforced motion.PARAM, ENFMOTN, TOTAL/ABS can be used to generate the total output values including thespecified enforced motion (TOTAL/ABS is the default).




Real eigenvalue analysis is used to compute the normal modes of a structure. Complexeigenvalue analysis computes the complex modes of the structure. The complex modescontain the imaginary part, which represents the cyclic frequency, and the real part whichrepresents the damping of the mode. If the real part is negative, then the mode is said to bestable. If the real part is positive, then the mode is unstable. Complex eigenvalue analysisis usually used to determine the stability of a structure when unsymmetric matrices arepresented due to special physical behavior. It is also used to determine the modes of adamped structure.

The complex eigenvalue analysis is formulated in the following manner:

2 0E f fp M pB K igK i G K

Where,

K is the stiffness matrix of the structure

M is the mass matrix

GE is the element structural damping matrix

B is viscous damping matrix

g is global structural damping coefficient

Kf is the extra stiffness matrix by direct matrix input

f is the coefficient of extra stiffness matrix

The solution of the complex eigenvalue problem yields complex eigenvalue, ip, and

complex mode shape, . Complex modes with positive real parts are considered unstablemodes. Unstable modes are often in pairs.

The circular frequency f is then calculated through the relationship:

2f

The damping coefficient is also computed from the equation:

2g

This corresponds to the real part of a complex eigenvalue; modes with negative dampingcoefficients have positive real parts and are unstable modes.

The extraction of complex modes directly from the above formulation is usually quitecomputationally expensive, especially if the problem size is not small. Instead, a modalmethod is used to solve the complex eigenvalue problem. First, the real modes arecalculated via a normal modes analysis. Then, a complex eigenvalue problem is formed on



the projected subspace spanned by the real modes and thus much smaller than the realspace. Finally, the complex modes extraction of the reduced problem follows the well knownHessenberg reduction method.

In order to run a complex eigenvalue analysis, both the EIGRL bulk data and the EIGC bulkdata entry need to be given. They define the number of the real modes and the number ofcomplex modes to be extracted, respectively. The EIGRL card has to be referenced by aMETHOD statement in a SUBCASE definition. The EIGC card is referenced by a CMETHODstatement in the same SUBCASE definition.

The complex eigen value analysis usually involves an unsymmetric matrix which representsthe source of the physical instability. The external matrix should be provided as a DMIG bulkdata entry, and then referenced by a K2PP statement in the SUBCASE definition. You candefine a specific coefficient for the external matrix by PARAM, FRIC. Otherwise, the defaultvalue of the coefficient is 1.0.




Random response analysis is used when a structure is subjected to a nondeterministic,continuous excitation. Cases likely to involve nondeterministic loads are those linked toconditions such as turbulence on an airplane structure, road surface imperfections on a carstructure, noise loads on a given structure, etc.

The complex frequency response can be achieved by direct and modal frequency response. If Hxa( f ) and Hxb( f ) are the complex frequency responses (displacement, velocity or

acceleration) of x th degree of freedom, due to load cases a and b respectively, the power

spectral density of the response of x th degree of freedom Rx( f ) is as follows:

( ) H ( ) ( ) ( )x xa ab xbR f f S f H f

Sab( f ) is the power spectral density of the two sources, where the individual source a is the

excited load case and b is the applied load case. If Sa( f ) is the spectral density of the

individual source (a th load case), the power spectral density of the response of x th degree of

freedom due to a th load case will be:

2( ) ( ) ( )x xa aR f H f S f

The cross spectral density Sab( f ) with two different sources b

could possibly be a

complex number. The power spectral density of the response of x th degree of freedom due

to a th and b th load cases will be:

( ) ( ) ( ) ( )x xa ab xbR f H f S f H f

The total power spectral density of the response will be the summation of the power spectraldensity of all individual load cases as well as all cross load cases.

The autocorrelation of a variable x(t) can be defined by the following equation:

/2

/2

( ) ( ) ( )limT

xT T

A x t x t dt

The variance of the x(t) will be equal to Ax(0). The variance can be expressed as a

function of power spectral density Sx( f ) as follows:

2(0) (x) ( )x xA S f df

The root mean square value of the response x(t) can also be written in the following equation:

( )xS f dfRMSx



The autocorrelation function and the power spectral density are Fourier transforms of eachother. Therefore, the auto correlation can be described as follows:

( ) ( ) exp( 2 )x xA S f i f df

There could be fatigue failure due to random vibration. The number of fatigue cycles ofrandom vibration is evaluated by multiplying the vibration duration and another parametercalled maximum number of positive zero crossing. The maximum number of positive zerocrossing is defined in the following equation:

2 ( )

( )

xc

x

f S f dfP

S f df

Whenever there is a request for XYPLOT, XYPEAK or XYPUNCH, the root mean square valueand the maximum number of positive crossing will be exported to the *.peak file.

Setup for Random Response Analysis

Random response analysis is activated, for all subcases, through the inclusion of the RANDOM data selector in the Subcase Information section of the input. This selectoridentifies RANDPS and RANDT1 bulk data entries to be used for random response analysis. The input spectral density is described by the RANDPS bulk data entry. The RANDPS datarefers to a TABRND1 bulk data entry, which contains the power spectral density of theloading versus frequency. The RANDT1 bulk data entry describes the time span for the auto-correlation. The RCROSS bulk data is used to request the output of the cross-power spectraldensity function for random response analysis and is referred to by the RCROSS I/O sectionselector. Loading for each frequency response subcase may be distinct, but all frequencyresponse subcases must reference the same frequency data.

Results Output from Random Response Analysis

The random response Power Spectral Density Function (PSDF) can be written to the .h3d file

for DISP, VELO, and ACCE using the PSDF output option on these I/O option data selectors. At the end of the output for all the frequencies is the RMS over frequencies output selector inHyperView as shown below.

The random response Power Spectral Density Function (PSDF) can be written to the .h3d file

for CBUSH element forces using the FORCE I/O option by specifying the PSDF output option. At the end of the output for each frequency is the RMS over frequencies output selector forthe .h3d file in HyperView as shown below.

The random response Power Spectral Density Function (PSDF) can be written to the .h3d and

.op2 files for solid and shell elements for stress and strain with the STRESS and STRAIN I/O

options using the PSDF output option. At the end of the output for each frequency is theRMS over frequencies output selector for the .h3d file and the Simulation selector for the

.op2 file in HyperView as shown below.

Additionally, PSDF and RMS von Mises stress and strain results based on the SegalmanMethod are also written to the .h3d file for Random Response Analysis (only available in the

H3D format).



RMS output selection in .h3d file in HyperView

RMS output selection in .op2 file in HyperView

Plotting Output from Random Response Analysis

Three plotting output requests may be used for random response analysis results. Theseoutput requests are placed in the I/O Options section of the input data. The three plottingcontrollers are:

XYPEAK Generates a .peak file containing a summary of therequested output.

XYPLOT Generates a HyperGraph session file (_rand.mvw file) andrelated data file (.rand file) for the requested output. Alsogenerates the .peak file.

XYPUNCH Generates a .pch file for the requested output. Alsogenerates the .peak file.

These output requests are different from most other OptiStruct output requests in that theymay be combined on the same line.



The requests are formatted as follows:

Operation, Curve-type, Plot-type or / Grid (Component) list.

"Operation" can be any combination of XYPLOT, XYPUNCH, and XYPEAK.

"Curve-type" can be FORCE, STRESS, STRAIN, DISP, VELO, or ACCE to request force,stress, strain, displacement, velocity or acceleration, respectively.

"Plot-type" can be either PSDF or AUTO to request power spectral density function orautocorrelation, respectively.

"Grid (Component) list" must come after a slash "/". Each entry in the list is commaseparated. Each entry consists of a GRID or SPOINT ID followed by a component ofmotion (T1, T2, T3, R1, R2, or R3) in parentheses. For SPOINTs the component must beT1.

In addition, plot titles and axis labels may be controlled using TCURVE (plot title), XTITLE (x-axis label), and YTITLE (y-axis label). Default titles and labels are generated when thesecontrols are not used.

Example 1

Requesting random response results in a HyperGraph session file for the velocity PSDF forGRIDs 3 and 6 for component T2:

XYPLOT, VELO, PSDF / 3(T2), 6(T2)

Example 2

Requesting random response summary results to be written to the .peak file for the

autocorrelation of displacement for GRID 223 for component R3:

XYPEAK, DISP, AUTO / 223(T3)

Example 3

Requesting random response results output, in all formats, for the acceleration PSDF forGRIDS 8 and 9 for components T1 and T2:

XYPEAK, XYPLOT, XYPUNCH, ACCE, PSDF / 8(T1), 9(T1), 8(T2), 9(T2)

Here the XYPEAK request is valid, but redundant as it is always created when XYPLOT orXYPUNCH is present.



Response Spectrum Analysis

Response Spectrum Analysis (RSA) is a technique used to estimate the maximum response ofa structure for a transient event. Maximum displacement, stresses, and/or forces may bedetermined in this manner. The technique combines response spectra for a prescribeddynamic loading with results of a normal modes analysis. The time-history of the responsesare not available.

Response spectra describes the maximum response versus natural frequency of a 1-DOFsystem for a prescribed dynamic loading. They are employed to calculate the maximummodal response for each structural mode. These modal maxima may then be combined usingvarious methods, such as the Absolute Sum (ABS) method or the Complete QuadraticCombination (CQC) method, to obtain an estimate of the peak structural response.

RSA is a simple and computationally inexpensive method to provide an approximation ofpeak response, compared to conventional transient analysis. The major computational effortis to obtain a sufficient number of normal modes in order to represent the entire frequencyrange of input excitation and resulting response. Response spectra are usually provided bydesign specifications; given these, peak responses under various dynamic excitations can bequickly calculated. Therefore, it is widely used as a design tool in areas such as seismicanalysis of buildings.

The Governing Equations


The equilibrium equation for a structure performing free vibration appears as the eigenvalueproblem:

[ ] 0K M

Where, K is the stiffness matrix of the structure and M is the mass matrix. Damping is

neglected.

The solution of the eigenvalue problem yields n eigenvalues i , where n is the number of

degrees of freedom. The vector { }i is the eigenvector corresponding to the eigenvalue.

The eigenvalue problem is solved using the Lanczos or the AMLS method. Not all eigenvaluesare required and only a small number of the lowest eigenvalues are normally calculated. Theresults of eigenvalue analysis are the fundamentals of response spectrum analysis.

Response spectrum analysis can be performed together with normal modes analysis in asingle run, or eigenvalue analysis with Lanczos solver can be performed first to saveeigenvalues and eigenvectors by using EIGVSAVE, which can be retrieved later by usingEIGVRETRIEVE for response spectrum analysis.



Modal Combination

It is assumed each individual mode behaves like a single degree-of-freedom system. Thetransient response at a degree of freedom is:

k ik ii

u

Where, is the eigenvector, is modal participation factor, and X is the response

spectrum

For loading due to base acceleration, the modal participation factor can be expressed as:

[ ] [ ]{ }Ti i M T

Where, is the eigenvector, M is the mass matrix, and T is rigid body motion due to

excitation

In ABS modal combination, the peak response is estimated by:

k ik ii

u

In CQC modal combination, the peak response is estimated by:

k m mn nm n

u v

Where, mv is the modal response associated with mode m, and mn is the cross-modal

coefficient.

Directional combination

In order to estimate peak response due to dynamic excitations in different directions, thepeak response in each direction must be combined to obtain total peak response. Methodssuch as ALG (algebraic) and SRSS (square root of sum of squares) can be used.

Input Specification

Subcase Definition

An RSA subcase may be explicitly identified by setting ANALYSIS=RSPEC, but it is alsoimplicitly chosen for any subcase containing the RSPEC data selector (when the ANALYSISentry is not present).

The following data selectors are recognized for an RSA subcase definition.

METHOD – references an eigenvalue extraction bulk data definition (EIGRL). OnlyMETHOD(STRUCTURE) is supported. This reference is required.

RSPEC – references an RSPEC bulk data entry where the combination rules, excitationDOF, and the input spectra are identified. This reference is required.



SDAMPING – references damping table bulk data entries (TABDMP1) to specify modaldamping. This reference is required.

SPC – references single point constraint bulk data entries (SPCADD, SPC and SPC1). For RSA analysis, these entries define the base degrees of freedom where excitation isapplied.

MPC – references multi-point constraint bulk data entries (MPCADD or MPC).

Bulk Data

Bulk data entries which have particular significance for RSA include:

RSPEC – specifies combination rules, excitation DOF, and references the input spectra.

DTI,SPECSEL – defines response spectra.

EIGRL – defines parameters for eigenvalue extraction.

PARAM, LFREQ and PARAM, HFREQ – define the range of modes used in modalcombinations.

TABDMP1 – specifies modal damping

SPC, SPC1, and SPCADD - specifies base where excitation is applied and otherconstraints.

Sample input

SUBCASE 100

RSPEC = 2

SPC = 5

SDAMPING = 12

METHOD = 24

$

BEGIN BULK

$

PARAM, LFREQ, 0.1

PARAM, HFREQ, 1000.

EIGRL, 24, 0.0, 1000.

RSPEC, 2, ABS, CQC, 0.1

, 99, 2.0, 1.0, 0.0, 0.0

DTI, SPECSEL, 99, , A, 2, 0., 3, 0.02,

, 4, 0.04, ENDREC

TABDMP1, 12, …

TABLED1, 2

+,…

TABLED1, 3

+,…

TABLED1, 4

+,…



ENDDATA

$

Output

Results of interest from RSA include maximum displacement, stress and force. These arerequested via the I/O Options DISPLACEMENT, STRESS and FORCE respectively.



Transient Response Analysis

Transient response analysis is used to calculate the response of a structure to time-dependent loads. Typical applications are structures subject to earthquakes, wind,explosions, or a vehicle going through a pothole.

The loads are time-dependent forces and displacements. Initial conditions define the initialdisplacement and initial velocities in grid points.

The results of a transient response analysis are displacements, velocities, accelerations,forces, stresses, and strains. The responses are usually time-dependent.

The transient response analysis computes the structural responses solving the followingequation of motion with initial conditions in matrix form.

( )Mu Bu Ku P t&& &

0( 0)u t u

0( 0)u t v&

The matrix K is the global stiffness matrix, the matrix M the mass matrix, and the matrix B is

the damping matrix formed by the damping elements. The initial conditions are part of theproblem formulation and are applicable for the direct transient response only. The equationof motion is integrated over time using the Newmark beta method. A time step and an endtime need to be defined.

Direct and modal transient response analysis methods are implemented as follows.

Direct Transient Response

The equation of motion is solved directly using the Newmark Beta method.

The use of complex coefficients for damping is not allowed in transient response analysis. Therefore, structural damping is included using equivalent viscous damping.

The damping matrix B is composed of several contributions as follows:

1

3 4

1E

GB B K K

Where, B1 is the matrix of the viscous damper elements, plus the external damping matrices

input through the DMIG bulk data entry; G is the overall structural damping (PARAM, G); 3

is the frequency of interest for the conversion of the overall structural damping into

equivalent viscous damping (PARAM, W3); 4 is the frequency of interest for the conversionof the element structural damping into equivalent viscous damping (PARAM, W4); and KE is

the contribution from structural element damping coefficients GE.



Running Direct Transient Response Analysis using OptiStruct

The transient response loads and boundary conditions are defined in the bulk data section ofthe input deck. They need to be referenced in the subcase information section using an SPCstatement and a DLOAD statement in a SUBCASE.

Inertia relief is not supported for direct transient response analysis. OptiStruct will error out ifthis is attempted.

Only one transient subcase can be defined. Initial conditions need to be referenced throughthe IC subcase statement. The analysis time step and termination time need to be definedthrough a TSTEP(TIME) subcase reference.


Modal Transient Response

In the modal method, a normal modes analysis to obtain the eigenvalues 2

i i and the

corresponding eigenvectors iX X of the system is performed first. The state vector u

can be expressed as a scalar product of the eigenvectors X and the modal responses d.

u Xd

The equation of motion without damping is then transformed into modal coordinates usingthe eigenvectors:

T T TX MXd X KXd X P&&

The modal mass matrix TX MX and the modal stiffness matrix

TX KX are diagonal. Thisway the system equation is reduced to a set of uncoupled equations for the components of dthat can be solved easily.

The inclusion of damping yields:

T T T TX MXd X BXd X KXd X P&& &

Here, the matrices TX BX are generally non-diagonal. Then coupled problem is similar to

the system solved in the direct method, but of a much lesser degree of freedom. Thesolution of the reduced equation of motion is performed using the Newmark Beta method.

The decoupling of the equations can be maintained if the damping is applied to each mode

separately. This is done through a damping table TABDMP1 that lists damping values ig

versus natural frequency if .

The decoupled equation is:

( ) ( ) ( ) ( )i i i i i i im d t b d t k d t p t&& &



or

2 1( ) 2 ( ) ( ) ( )i i i i i i i

i

d t d t d t p tm

&& &

Where, / (2 )i i i ib m

is the modal damping ratio, and 2i is the modal eigenvalue.

Three types of modal damping values ( )i ig f

can be defined: G – Structural damping, CRIT– Critical damping, and Q – Quality factor. They are related through the following three

equations at resonance:

:2

i ii

cr

b gG

b

: 2cr i iCRIT b m

1 1:

2i

i i

Q Qg

Residual Vector Generation (Increases accuracy)

The accuracy of the modal method can be vastly improved by adding the displacementvectors of a static analysis based on the dynamic loading to the matrix of eigenvectors X.

These vectors are frequently referred to as residual vectors, the method as modalacceleration.

There are two ways this is implemented.

The unit load method generates residual vectors based on static loads, which are unitvectors at the dynamic load degrees of freedom. That is, the static loads for theresidual vector generation are unit vectors at the degrees of freedom, where thedynamic load is applied. The number of residual vectors is equal to the number ofloaded degrees of freedom.

The applied load method generates a maximum of two residual vectors which are thedynamic load vector at loading frequency of zero. If the real and the imaginary parts ofthe dynamic load are the same, or if one of them is zero, only one of them is used. This is the default method since it is generally more efficient.

In the case of excited displacements, the residual vectors are obtained by solving static loadcases with unit displacements at the same degrees of freedom as the dynamic exciteddisplacement degrees of freedom.

Running Modal Transient Response Analysis using OptiStruct

Transient response loads and boundary conditions are defined in the bulk data section of theinput deck. They need to be referenced in the subcase information section using an SPCstatement and a DLOAD statement in a SUBCASE.

Residual vectors can be activated using the subcase statement RESVEC with the optionsAPPLOD or UNITLOD. They are computed by default. Residual vectors are always generatedif enforced displacements, velocities or accelerations are defined. Residual vectors are alsocalculated for viscous damping DOF. These are created by default and can be turned off with



the RESVEC option NODAMP. In addition, if there is USET U6 data, residual vectors will becalculated if the AMSES or AMLS eigensolver is used. USET U6 residual vectors will not becalculated if the Lanczos eigensolver is used.

When residual vectors are included, inertia relief can be applied to unconstrained models. ASUPORT1 subcase entry references the boundary conditions that restrain the rigid bodymotions. These restraints can also be defined without subcase reference using the SUPORTbulk data entry or automated using PARAM, INREL, -2.

Only one transient subcase can be defined. Initial conditions cannot be defined if the modalmethod is used. A METHOD statement is required for the modal method to control thenormal modes analysis. The METHOD statement can refer to either EIGRL or EIGRA data.

The analysis time step and termination time need to be defined through a TSTEP(TIME)subcase reference. In order to save computational effort, previously saved eigenvectors canbe retrieved using the EIGVRETRIEVE subcase statement.

In addition to the various damping elements and material damping, uniform structuraldamping G is applied using PARAM, G.

Modal damping can be applied using the SDAMPING reference of a damping table TABDMP1.

Output

The results of a transient response analysis are displacements, velocities, accelerations,forces, stresses, and strains. The responses are usually time-dependent. The usual outputentries like STRESS, STRAIN, DISPLACEMENT, etc. can be used to request correspondingoutput values.

PARAM, ENFMOTN, REL can be used to generate displacement, velocity and accelerationoutput relative to the specified enforced motion. In such cases, subsequently calculatedoutputs like stresses and forces are also generated relative to the specified enforced motion.PARAM, ENFMOTN, TOTAL/ABS can be used to generate the total output values including thespecified enforced motion (TOTAL/ABS is the default).

Transient Response Analysis by Fourier Transformation

Using the Fourier transformation method, frequency response analysis can be used for thetransient analysis. The Fourier transformation method may be used to solve for thetransient response of structural models under periodic loads. A typical application for thismethod is a vehicle on a bumpy road.

Time-dependent applied loads are transformed into the frequency domain and allfrequency dependent matrix calculations are completed. The frequency response resultsare then transformed back into the time domain.

The results are displacements, velocities, accelerations, forces, stresses, and strains. Theresponses are usually time-dependent.

The following equation of motion with initial conditions in matrix form is solved.

( )Mu Bu Ku P t&& &

The matrix K is the stiffness matrix, the matrix M is the mass matrix, and the matrix B is

the damping matrix formed by the damping elements. Initial conditions cannot be defined.



The load vector is transformed from the time domain into the frequency domain using:

The response in given by:

u h P%%

Where, h( ) is the frequency response due to unit load.

After the frequency response analysis, the time-dependent response can be recoveredusing:

For the results to be accurate it is important to note that:

1. The system has to be reasonably well damped. Too little damping may lead toincorrect results.

2. The forcing function should be zero for some time interval to allow decay.

3. The frequency interval should follow:

.

The direct and modal methods are implemented.

Direct Method

Direct frequency response analysis is applied (Frequency Response Analysis).

Transient response loads and boundary conditions are defined in the bulk data section ofthe input deck. They need to be referenced in the subcase information section using an SPC and DLOAD statement in a SUBCASE.

Inertia relief is not implemented for direct frequency response. The solver will error out ifit is attempted.

A frequency set must be referenced using a FREQUENCY statement. Initial conditionscannot be applied. The analysis time step and termination time need to be definedthrough a TSTEP(FOURIER) subcase reference.


Modal Method

Modal frequency response analysis is applied (Frequency Response Analysis).



Transient response loads and boundary conditions are defined in the bulk data section ofthe input deck. They need to be referenced in the subcase information section using anSPC statement and a DLOAD statement in a SUBCASE.

Residual vectors can be activated using the subcase statement RESVEC with the optionsAPPLOD or UNITLOD. They are computed by default. Residual vectors are alwaysgenerated if enforced displacements, velocities or accelerations are defined.

When residual vectors are included, inertia relief can be applied to unconstrained models. A SUPORT1 subcase entry references the boundary conditions that restrain the rigid bodymotions. These restraints can also be defined without subcase reference using the SUPORT bulk data entry or automated using PARAM, INREL, -2.

A frequency set must be referenced using a FREQUENCY statement. Initial conditionscannot be defined. A METHOD statement is required for the modal method to control thenormal modes analysis. The analysis time step and termination time need to be definedthrough a TSTEP(FOURIER) subcase reference. In order to save computational effort,previously saved eigenvectors can be retrieved using the EIGVRETRIEVE subcasestatement.


Modal damping can be applied using the SDAMPING reference of a damping tableTABDMP1. The parameter PARAM, KDAMP is to define the method of applying thedamping table.



Thermal Analysis

The Thermal Analysis section provides an overview of the following analyses:

Linear Steady-State Heat Transfer Analysis

Linear Transient Heat Transfer Analysis

Nonlinear Steady-State Heat Transfer Analysis

Contact-based Thermal Analysis



Linear Steady-State Heat Transfer Analysis

Heat transfer analysis solves for unknown temperatures and fluxes under thermal loading. Temperature represents the amount of thermal energy available, and fluxes represent theflow of thermal energy. Conduction deals with thermal energy exchange by molecularmotion. Free convection deals with thermal energy exchange between solids andsurrounding fluids. Thermal loading is defined as energy flows into and out of the system.

In linear steady state analysis, material properties such as conductivity and convectioncoefficient are linear. Temperature and fluxes at the final thermal equilibrium state are ofinterest. The basic finite element equation is:

Kc H T p(1)

Where, [Kc] is the conductivity matrix, [H] is the boundary convection matrix due to free

convection, {T} is an unknown nodal temperature, {p} is the thermal loading vector. The

system of linear equation is solved to find nodal temperature {T}.

Thermal load vector can be expressed as:

B H Qp P P P(2)

Where, {PB} is the power due to heat flux at boundary specified by QBDY1 card, {PH} is the

boundary convection vector due to convection specified by CONV card, and {PQ} is the power

vector due to internal heat generation specified by QVOL card.

The matrix on the left hand side of equation (1) is singular unless temperature boundaryconditions are specified. The equilibrium equation is solved simultaneously for the unknowntemperatures using a Gauss elimination method that exploits the sparseness and symmetryfor computational efficiency. Once the unknown temperatures at the nodal points of theelements are calculated, temperature gradient { } can be calculated according to element

shape functions. Element fluxes can be calculated by using:

f k T(3)

Where, [k] is the conductivity of the material.

An analogy of heat transfer analysis and structural analysis is shown in Table 1.

Heat Transfer Structural

Unknown

Temperature Displacement

Temperature gradient Strain

Flux Stress

[Kc] Conductivity matrix Stiffness matrix

[H] Boundary convection matrix Elastic foundation stiffness matrix

{p} Heat flux vector Load vector



Heat Transfer Structural

{PQp} Element volumetric Gravity load

Table 1. Analogy of heat transfer and structural analysis

The thermal loads and boundary conditions are defined in the bulk data section of the inputdeck. They need to be referenced in the SUBCASE information section using an SPC or MPCand LOAD statement in a SUBCASE.

Input Data for Thermal Structural Analysis

Both GRID and SPOINT can be used to specify a thermal point. Fixed temperatures arespecified with SPC/SPC1/SPCD data with the component ID blank or zero. MPC data can beused to specify the relationship between temperatures of different points using component IDblank or zero. If you want to use component ID 1, then SPSYNTAX=mixed must be specifiedin the input deck. Rigid elements are ignored in heat transfer analysis.

For all elements that have property data that reference material data (CROD, CONROD,CBAR, CBEAM, CQUAD4, CTRIA3, CQUAD8, CTRIA6, CHEXA, CHEXA20, CPENTA, CPENTA15,CPYRA, CPYRA13, CTETRA, and CTET10) can be used as conduction elements. The propertydata references MAT4 data for the isotropic conduction coefficient and MAT5 data foranisotropic conduction coefficients. Note that the thermal material property data has thesame ID as the structural property data for any element. For CELAS1-4, the value of K istreated as the conduction coefficient.

Elements that generate heat are listed in QVOL data. The heat generated by an element isequal to the element volume * QVOL * HGEN, where HGEN is a scale factor (default=1.0)listed on the material (MAT4 or MAT5) data.

Heat flux load QBDY1 and convective heat transfer CONV are applied to the structure throughsurfaces identified by the CHBDYE card. The CHBDYE elements associate heat exchangesurfaces with conduction elements. A 1D element can have heat flux applied at each end andalong its length. A 2D element can have heat flux on its surface and along any edge. A 3Delement can have head flux applied on any face.

Fixed values of heat flux are specified using the QBDY1 card. This data lists the CHBDYEelement ID and the heat flux value (Q0). The power exchanged through a CHBDYE elementis equal to Q0 multiplied by the effective area of the CHBDYE element. For a 1D element, thearea at the end is the cross-sectional area of the element. For flux into the side of a 1Delement, the effective area is the length times the circumference of the element which iscalculated from the cross-sectional area, assuming that the cross-section is circular. For 2Delements, the effective area for the surface of the element is its area and the effective area ofa side is equal to the length of the side multiplied by the thickness of the element. For 3Delements, the effective area is just the area of the face.

Free convection heat flux is specified for CHBDYE elements using the CONV data which liststhe CHBDYE element ID, the ambient temperature (TAMB), and the ID of the PCONV datawhich lists the MAT4 material ID. The MAT4 data contains the convection coefficient H. Theheat flux per unit area from convection is H*(T-TAMB), where T is the grid temperature.



Coupled Thermal Structural Analysis and Optimization

Each heat transfer SUBCASE defines a temperature set, which can be referred by a structuralSUBCASE by TEMP(LOAD) to perform thermal-structural analysis. The temperature setidentification is the same as heat transfer SUBCASE identification by default. It can bechanged by using TSTRU card. If the temperature set identification is the same as a bulkdata temperature set identification, the temperatures from heat transfer analysis overridebulk data temperatures.

Coupled thermal structural analysis is done in the following fashion. Heat transfer analysis isperformed first to determine the temperature field of the structure. The temperature field isused as part of the loading for structural analysis. A single finite element mesh is usuallyused for both thermal and structural analysis. The finite element governing equation forstatic structural analysis is:

TK D f f(4)

Where, [K] is the global stiffness matrix, {D} is the unknown displacement vector, {fT} is the

temperature loading, and {f} is the structural loading such as forces, pressures, etc. Displacement vector {D} is solved by the linear equation solver.

In coupled thermal structural optimization, {fT} sensitivities due to design changes are

calculated. Besides the usual responses such as displacement, stress, mass, etc.,temperature can also be a response in optimization.

The coupling in thermal structural analysis is sequential, i.e. the thermal analysis affects thesubsequent structural analysis. On the other hand, in coupled thermal structuraloptimization, the coupling works both ways, that is the thermal influence on structural andthe structural influence on thermal. In other words, the optimizer modifies the structuraldesign to satisfy constraints, which in turn affects the thermal analysis.

Temperature responses are supported in Sizing, Shape, Topography, and TopologyOptimization, but the CHBDYE element cannot be used in the Design Domain of TopologyOptimization.



Linear Transient Heat Transfer Analysis

Linear transient heat transfer analysis can be used to calculate the temperature distributionin a system with respect to time. The applied thermal loads can either be time-dependent ortime-invariant; transient thermal analysis is used to capture the thermal behavior of asystem over a specific period in time.

The basic finite element equation for transient heat transfer analysis is given by:

C T K H T p&(1)

Where,

[C] is the heat capacity matrix

[K] is the conductivity matrix

[H] is the boundary convection matrix due to free convection

is the temperature derivative with respect to time

{T} is the unknown nodal temperature

{p} is the thermal loading vector.

The differential equation (1) is solved to find nodal temperature {T} at the specified time

steps. When equation (1) is compared to the steady-state heat transfer equation, you see

that there is an additional term that captures the transient nature of the analysis.

Guide to Request a Linear Transient Heat Transfer Analysis

The following steps can be considered as a guide to define the linear transient heat transfersubcase.

1. Use the solution sequence identifier (ANALYSIS) in the subcase information section to

select the linear transient heat transfer analysis using: ANALYSIS=HEAT.

2. Define the time step intervals at which the solutions will be calculated for transientanalysis using the TSTEP bulk data entry. This is referenced in the subcase information

section by the TSTEP subcase information entry which is used to select the integration

type (TSTEP=SID) for transient analysis.

3. The initial conditions for transient heat transfer analysis are selected by the use of the IC

subcase information entry. This entry can be used in the subcase information section tospecify the set identification number of the temperature field defined by TEMP or TEMPD

bulk data entries.

4. Use the single point constraint (SPC) data entry to specify the fixed boundary conditions

for this analysis.

5. Use the DLOAD subcase information entry to reference the set ID’s of DLOAD, TLOAD1 and

TLOAD2 bulk data entries Use the TLOAD1 and TLOAD2 bulk data entries to specify:

(a) Time dependent thermal loading The EXCITEID field of the TLOAD1 and TLOAD2 bulk data entries should point to the ID’s

of QVOL, QBDY1 bulk data entries or a combination of them using LOADADD.



(b) Temperature boundary condition The EXCITEID field of the TLOAD1 and TLOAD2 bulk data entries should point to the ID of

the SPCD bulk data entry. Also, the TYPE field in the TLOAD1 and TLOAD2 entries should be

set to 1.

6. The MAT4 and MAT5 bulk data entries can be used to define thermal material properties

such as thermal conductivity [K], heat capacity [C], density [RHO], convection heat

transfer coefficient [H] and heat generation capability [HGEN] used in the QVOL data

entry.

7. The THERMAL I/O option can be used to request nodal temperature output {T} for

transient heat transfer analysis subcases. The FLUX I/O options entry can be used to

request temperature gradient and flux output for transient heat transfer analysissubcases.

Applying Heat Flux Loads

In Step 5(a) of the guide above, the ability to use QBDY1 data to apply heat flux loading is

illustrated. This is accomplished as explained in the following steps:

1. The value of the heat flux load is input in the Q0 field of a QBDY1 data entry.

2. The EID# field in the QBDY1 data entry requires the identification number of CHBDYE

surface elements. These surface elements should be created on the surfaces of the modelto which heat flux loads are to be applied.

3. This is done in HyperMesh by creating an interface of type CONDUCTION, selecting all the

relevant surfaces and then adding CHBDYE surface elements to those surfaces.

4. These newly created surface elements via the interface group can then be referenced inthe EID# field of the QBDY1 data entry.

Refer to the OS-1090 tutorial for detailed information on setting up heat flux loads and freeconvection for transient heat transfer analysis.

Coupled Thermal-structural Analysis

The temperature results from the final time step of a linear transient heat transfer analysiscan be applied to a structural subcase. Both TEMPERATURE(LOAD) and

TEMPERATURE(MATERIAL) are allowed to reference the subcase ID or temperature result sets

from the linear transient heat transfer analysis for use in either material property calculationsor thermal loading.

Note: Non-zero SPC will be considered as zero SPC fortransient thermal analysis, except when non-zero SPC areused to specify ambient points for convection. When anambient point is controlled by TLOAD1/TLOAD2 via SPCD,the corresponding SPC should be zero.



Nonlinear Steady-State Heat Transfer Analysis

Nonlinear steady-state heat transfer analysis can be used to calculate the temperaturedistribution in a system, in which material properties are a function of temperature.

The basic finite element equation for nonlinear heat transfer can be written as:

L(T) = P (1)

Where, {T} is unknown temperature, P is the global power vector, and L(T) is the global

response (nodal power).

The system of equations (1) is solved using the Newton’s method. Solution control isprovided by defining parameters on the NLPARM bulk data entry. TEMPERATURE (INITIAL)can be used to provide a likely initial temperature distribution. The temperature results fromthe nonlinear heat transfer analysis can be used in subsequent structural analysis.

Nonlinear Steady-State Heat Transfer Analysis Setup

The following steps can be considered as a guide to setup a nonlinear steady-state heattransfer analysis:

1. Use the solution sequence identifier (ANALYSIS) in the subcase information section toselect the nonlinear steady-state heat transfer analysis using: ANALYSIS=NLHEAT.

2. The likely initial temperature distribution can be defined using the TEMPERATURE subcaseinformation entry (type=INITIAL). A good initial temperature estimate improves theconvergence of the solver.

3. The MATT4 bulk data entry can be used to define temperature dependent thermalmaterial properties.

4. To indicate that a nonlinear solution is required for any subcase, a NLPARM subcaseinformation entry is required. This subcase entry points to a NLPARM bulk data entry thatspecifies convergence tolerances and other nonlinear parameters.

5. Loads and boundary conditions are defined in the bulk data section of the input deck.These should be referenced in the subcase information section using SPC and LOADentries in a subcase. Each subcase defines a load vector.

Example

An example solver deck section showing the usage of ANALYSIS and NLPARM is shownbelow:

SUBCASE 5ANALYSIS=NLHEATSPC=10LOAD=20NLPARM=30…BEGIN BULK…NLPARM, 30…



ENDDATA

Note: Optimization based on nonlinear heat transfer analysis iscurrently not supported.



Contact-based Thermal Analysis

Introduction

In OptiStruct structural models involving contact are solved by using nonlinear quasi-staticanalysis. The analysis involves finding the contact status, such as contact clearance andpressure. Contact clearance spans the distance between the master and slave, while contactpressure is developed between two surfaces in contact.

Motivation

The traditional thermal structural analysis is one-way coupling, in the sense that thermalanalysis influences structural analysis by providing temperature, but structural problem doesnot affect the thermal problem.

Figure 1: Traditional thermal-structural analysis – Thermal results affect the structural problem.

When contact problems are involved, thermal structural analysis becomes fully coupled sincecontact status changes thermal conductivity.

Figure 2: Contact based (Coupled) Thermal-Structural Analysis – contact status affects the thermal problem

In Figure 1, you can see that a change in contact status does not affect the thermal problem.This may lead to inaccurate solutions if thermal conductivity depends on the contact status.In Figure 2, the contact clearance and/or pressure changes during the course of the quasi-static nonlinear analysis, the corresponding change in the thermal conductivity will affect thesolution of the thermal problem.

Implementation

Thermal analysis is performed first using initial contact status. Nonlinear structural analysis isemployed to find contact status. Thermal conductivity at the contact interface is calculatedbased on contact clearance or pressure or based on user-defined values. Coupling is essentialbecause the contact status is used to determine thermal conductivity. An iterative solutionprocess is developed to solve fully coupled nonlinear thermal structural problem, as shown inFigure 3. Temperature results from thermal analysis are used as convergence criteria.



Thermal conductivity across contact interface can be based on user-defined values,clearance, or pressure. The PGAPHT and PCONTHT entries can be used to define the thermalconductivity values.

Note:

1. For thermal contact problems with CGAP/CGAPG, PGAPHT isrequired. The PGAPHT entry should have the same PID asPGAP. For problems with CONTACT and PCONT, thePCONTHT entry should be used and it requires the same PIDas PCONT.

2. For problems without PCONT, PCONTHT is not required.

3. Thermal conductivity based on the AUTO option (KC/KAHTfields on PCONTHT/PGAPHT entries) can be used in thermalanalysis to allow OptiStruct to automatically determine theconductivity values based on the conductivity of surroundingelements.

Figure 3: Fully coupled contact-based thermal-structural analysis.

Theoretically, while higher conductivity values enforce a perfect conductor, excessively highvalues may cause poor conditioning of the conductivity matrix. If such effects are observed, itmay be beneficial to reduce the value of conductivity, or use conductivity based contactclearance and pressure.

Clearance based thermal conductivity (TCID on PCONTHT/PGAPHT, via TABLED#)

The clearance based conductivity values can be specified by you via TABLED# entries. Thetypical conductivity values vary as follows:



Figure 4: Thermal conductivity based on contact clearance.

Pressure based thermal conductivity (TPID on PCONTHT, via TABLED#)

The pressure based conductivity values can be specified by you via TABLED# entries. Thetypical conductivity values vary as follows:

Figure 5: Thermal conductivity based on contact pressure.

Clearance and pressure based thermal conductivity (TCID and TPID on PCONTHT viaTABLED#)

The clearance and pressure based conductivity values can be specified by you via TABLED#entries. The typical conductivity values vary as follows:

Figure 6: Thermal conductivity based on contact clearance and pressure.

Typical thermal conductivity values increase as the clearance between the master and slavedecreases. In the case of contact pressure, the thermal conductivity increases with acorresponding increase in pressure.



Acoustic Analysis

The Acoustic Analysis section provides an overview of the following analyses:

Coupled Frequency Response Analysis of Fluid-Structure Models

Radiated Sound Analysis



Coupled Frequency Response Analysis of Fluid-StructureModels

Coupled frequency response analysis of fluid-structure models, commonly termed acousticanalysis, is generally performed to model sound propagation within a structural cavity, suchas the interior of a vehicle or a musical instrument.

OptiStruct allows both direct and modal frequency response analysis for fluid-structuremodels. The responses of both the structural and fluid domains are computed; for thestructural domain, these responses are the displacements and rotations of the structuralgrids, and for the fluid domain, these responses are the pressures at the fluid grid points.

The accelerations of structural grids at the fluid-structure interface excite the fluid domainand conversely, the pressures on the fluid grids at the fluid-structure interface excite thestructural domain. Hence the problem is coupled and the motions of structural and fluiddegrees-of-freedom are solved simultaneously.

Loading is sinusoidal with excitation frequency , and can be in the form of forces, acousticsources enforced displacements, enforced velocities, and/or enforced accelerations. Frequency response loads and boundary conditions are defined in the bulk data section of theinput deck. These are then referenced in a subcase definition through an SPC or DLOAD dataselector.

Damping may be defined for both the structural and fluid domains. For the structural domaindamping may be defined through structural damping elements, material damping, structuraldamping (PARAM,G), or modal damping (SDAMPING referenced by a SDAMPING(STRUCT)subcase data selector). For the fluid domain damping may be defined through materialdamping, fluid damping (PARAM,GFL), or modal damping (SDAMPING referenced by aSDAMPING(FLUID) subcase data selector). In addition, the normalized admittance coefficientfor porous materials can be specified by ALPHA on the MAT10 data.

Frequency dependent fluid acoustic absorber elements can be specified on the fluid faces ofthe fluid-structure boundary using the CAABSF elements. The absorber elements can bepoint, line, triangular, or quadrilateral in shape. The CAABSF data references the PAABSFdata which is used to specify the frequency dependent resistance (real part of theimpendence) and reactance (imaginary part of the impendence) as well as the area factorsfor point and line elements.

Frequency dependent structural acoustic absorber elements can be specified on the fluid-structure boundary using the CHACAB elements. These absorbers are solid elementsbetween the fluid and structural meshes. The CHACAB data references the PACABS datawhich is used to specify the frequency dependent resistance (real part of the impendence)and reactance (imaginary part of the impendence). Another option is to calculate thesevalues mass, stiffness, and damping values per unit area specified in this data.

PARAM, LFREQFL and PARAM, HFREQFL can be used to exclude modes from a coupled modalfrequency response analysis (Acoustic analysis).

The acoustic analysis is based on inviscid flow with linear pressure-density relation as:

10P u&&



and the continuity equation is:

. 0P u

Where,

P and u are the pressure of the fluid domain and displacement of the structural domain

respectively,

and are the compressibility of the fluid domain and density of the structural domainrespectively.

Combining the above equations, the governing equation of the fluid domain is:

210

PP

&&

Effect of the structure on the fluid domain at the interface

After finite element discretization, the assembly of equations for the fluid domain is:

p p p pM P B P K P Au S&& & &&

Where, Mp, Bp, Kp and Sp are the mass matrix, damping matrix, stiffness matrix and source

vector respectively, of the fluid domain.

The matrix A represents the interface matrix and is the acceleration of the structural grids

at the fluid-structure interface. (The pressure gradient at the interface will be influenced bythe acceleration of the structural grids).

Effect of fluid on the structural domain at the interface

The structural equation assembly can be written as:

TS S S SM u B u K u A P S&& &&

Where, MS, BS, KS and SS are the mass matrix, damping matrix, stiffness matrix and source

vector respectively, of the structural domain.

The matrix A represents the transpose of the interface matrix and is the pressure at the

interface fluid grids at the fluid-structure interface (The displacement, velocity andacceleration of the structural grids at the interface will be influenced by the pressure at theinterface fluid grids).



Coupled Fluid-Structure interface equation

Therefore the combined fluid structure interface equation is:

The above equations are solved simultaneously for unknowns in the structural and the fluiddomains, either by direct frequency response or modal frequency response. For modalfrequency response, OptiStruct will calculate the eigenspace for both structure and fluiddomain automatically.

Loads on the Fluid Mesh

The fluid grid points can be loaded by specifying the load magnitude and GRID using theSLOAD data. The SLOAD data is referenced by the ACSRCE data which defines the dynamiccharacteristics of the load (DELAY, DPHASE, and a tabular listing of the load scale factor vs.frequency). In addition, the density and bulk modulus of the loaded fluid are specified on theASRCE data. The material characteristics of the fluid must be specified in the ASRCE in casethe same fluid GRID is shared by two different fluid meshes.

Fluid-Structure Interface Visualization and Refinement

OptiStruct has support for both grid-to-grid matching and non-matching interfaces. Theinterface is specified through the ACMODL card. If an ACMODL card is not specified in theinput deck, the fluid-structure interface is automatically defined by OptiStruct based ondefault values for the ACMODL parameters.

Based on a search box specified on the ACMODL card, OptiStruct outputs an *.interface file,containing information about the fluid-structure interface. With the model loaded inHyperMesh, you can import the *.interface file to visualize the fluid-structure interface

(ensure that the “FE overwrite” option is activated on import). The “^Fluid Faces atInterface” component is created, which allows you to view the interface found between thestructural and fluid domains. If a component “^Acoustically Rigid Fluid Faces” is created,that means at those fluid surfaces, there are no structural grids found. A structural grid set “^Structural grids at Interface” is also created to display the structural grids found at theinterface.

There are several steps you can take to improve the interface:

1. Perform an OptiStruct check run. This will create the *.interface file, allowing you to

visualize the interface.

2. If the interface is not as desired, you may create a new SET containing those fluid gridsthat describe the fluid boundary.

3. You can then specify the newly created set on the ACMODL card under FSET.

4. Perform another OptiStruct check run, and review the new interface.



Using an External Fluid Structure Coupling Definition File

OptiStruct can use the binary ftn.70 coupling file generated by AKUSMOD instead of

internally calculating the coupling. To use this option, add PARAM,AKUSMOD,YES to theinput deck.

Modal and Panel Participation

Modal participation is a measure of how much each mode participates at a given frequency ina modal frequency response calculation. Output of modal participation may be requested forstructural degrees of freedom as well as for fluid degrees of freedom. Calculation and outputof modal participation can be requested, for any number of degrees of freedom, using the PFMODE I/O Option.

Panel participation is a measure of the influence of sets of specified structural grids, definedby PANEL bulk data entries. The response of a fluid grid is influenced through each panel oreach grid at the acoustic interface. Calculation and output of the contribution from each panelat specific loading frequencies can be requested through the PFPANEL I/O Option, for modalfrequency response. Also, the calculation and output of the contribution from each grid atthe interface can be requested through the PFGRID I/O Option.

A file *.pfmode.pch is generated based on the definition of the I/O Options PFMODE and

PFPANEL. The output for PFGRID would be in a H3D file. The results for PFMODE andPFPANEL are best plotted in HyperGraph, whereas the contour results for PFGRID are bestvisualized in HyperView.

Non-Reflecting Boundary

To create a non-reflecting boundary, set the values of the TABLEDi entry referenced by theTZREID field (Resistance-real part of Impedance) in the PAABSF data entry to be equal to

*fluid fluidCfor all frequencies. This will allow the acoustic wave to propagate normally

through the boundary, without reflection. This condition is called the Sommerfeld boundarycondition.

Where, is the density of the fluid, and is the speed of sound in the fluid.

Input File - chacab.fem

$$------------------------------------------------------------------------------$$$ $$$ NASTRAN Input Deck Generated by HyperMesh Version : 8.0SR1 $$$ Generated using HyperMesh-Nastran Template Version : 8.0sr1$$ $$$ Template: general $$$ $$$------------------------------------------------------------------------------$$$------------------------------------------------------------------------------$$$ Executive Control Cards $$$------------------------------------------------------------------------------$SOL 111



CEND$$------------------------------------------------------------------------------$$$ Case Control Cards $$$------------------------------------------------------------------------------$SET 1 = 1734DISPLACEMENT = 1$$HMNAME LOADSTEP 1"Load2"SUBCASE 1 LABEL= Load2 SPC = 4 FREQUENCY = 5 DLOAD = 2$$------------------------------------------------------------------------------$$$ Bulk Data Cards $$$------------------------------------------------------------------------------$BEGIN BULK

$CHEXA 1056 2 1650 1661 1662 1651 1671 1682+ $+ 1683 1672CHACAB 1056 100 1650 1645 1657 1658 1676 1675+ + 1671 1672PACABS,100,YES,1,2,3,1.5,10.0,2.0PARAM,G,0.001PARAM,COUPMASS,-1 PARAM,POST,-1 $ACMODL DIFF 0.1 $$EIGRL,20,,,300EIGRL,21,,,300$$ GRID Data$$GRID 1 2.0 2.0 0.0 -1 GRID 2 2.0 1.5 0.0 -1 GRID 3 2.0 1.0 0.0 -1 GRID 4 2.0 0.5 0.0 -1 GRID 5 2.0 0.0 0.0 -1 GRID 6 2.0 -0.5 0.0 -1 GRID 7 2.0 -1.0 0.0 -1 GRID 8 2.0 -1.5 0.0 -1 GRID 9 2.0 -2.0 0.0 -1 GRID 10 1.5 2.0 0.0 -1 GRID 11 1.5 1.5 0.0 -1 GRID 12 1.5 1.0 0.0 -1 GRID 13 1.5 0.5 0.0 -1 GRID 14 1.5 0.0 0.0 -1 GRID 15 1.5 -0.5 0.0 -1 GRID 16 1.5 -1.0 0.0 -1 GRID 17 1.5 -1.5 0.0 -1 GRID 18 1.5 -2.0 0.0 -1 GRID 19 1.0 2.0 0.0 -1 GRID 20 1.0 1.5 0.0 -1 GRID 21 1.0 1.0 0.0 -1 GRID 22 1.0 0.5 0.0 -1 GRID 23 1.0 0.0 0.0 -1 GRID 24 1.0 -0.5 0.0 -1 GRID 25 1.0 -1.0 0.0 -1 GRID 26 1.0 -1.5 0.0 -1 GRID 27 1.0 -2.0 0.0 -1 GRID 28 0.5 2.0 0.0 -1 GRID 29 0.5 1.5 0.0 -1 GRID 30 0.5 1.0 0.0 -1 GRID 31 0.5 0.5 0.0 -1 GRID 32 0.5 0.0 0.0 -1 GRID 33 0.5 -0.5 0.0 -1 GRID 34 0.5 -1.0 0.0 -1 GRID 35 0.5 -1.5 0.0 -1 GRID 36 0.5 -2.0 0.0 -1 GRID 37 0.0 2.0 0.0 -1



GRID 38 0.0 1.5 0.0 -1 GRID 39 0.0 1.0 0.0 -1 GRID 40 0.0 0.5 0.0 -1 GRID 41 0.0 0.0 0.0 -1 GRID 42 0.0 -0.5 0.0 -1 GRID 43 0.0 -1.0 0.0 -1 GRID 44 0.0 -1.5 0.0 -1 GRID 45 0.0 -2.0 0.0 -1 GRID 46 -0.5 2.0 0.0 -1 GRID 47 -0.5 1.5 0.0 -1 GRID 48 -0.5 1.0 0.0 -1 GRID 49 -0.5 0.5 0.0 -1 GRID 50 -0.5 0.0 0.0 -1 GRID 51 -0.5 -0.5 0.0 -1 GRID 52 -0.5 -1.0 0.0 -1 GRID 53 -0.5 -1.5 0.0 -1 GRID 54 -0.5 -2.0 0.0 -1 GRID 55 -1.0 2.0 0.0 -1 GRID 56 -1.0 1.5 0.0 -1 GRID 57 -1.0 1.0 0.0 -1 GRID 58 -1.0 0.5 0.0 -1 GRID 59 -1.0 0.0 0.0 -1 GRID 60 -1.0 -0.5 0.0 -1 GRID 61 -1.0 -1.0 0.0 -1 GRID 62 -1.0 -1.5 0.0 -1 GRID 63 -1.0 -2.0 0.0 -1 GRID 64 -1.5 2.0 0.0 -1 GRID 65 -1.5 1.5 0.0 -1 GRID 66 -1.5 1.0 0.0 -1 GRID 67 -1.5 0.5 0.0 -1 GRID 68 -1.5 0.0 0.0 -1 GRID 69 -1.5 -0.5 0.0 -1 GRID 70 -1.5 -1.0 0.0 -1 GRID 71 -1.5 -1.5 0.0 -1 GRID 72 -1.5 -2.0 0.0 -1 GRID 73 -2.0 2.0 0.0 -1 GRID 74 -2.0 1.5 0.0 -1 GRID 75 -2.0 1.0 0.0 -1 GRID 76 -2.0 0.5 0.0 -1 GRID 77 -2.0 0.0 0.0 -1 GRID 78 -2.0 -0.5 0.0 -1 GRID 79 -2.0 -1.0 0.0 -1 GRID 80 -2.0 -1.5 0.0 -1 GRID 81 -2.0 -2.0 0.0 -1 GRID 82 2.5 2.0 0.0 -1 GRID 83 2.5 1.5 0.0 -1 GRID 84 2.5 1.0 0.0 -1 GRID 85 2.5 0.5 0.0 -1 GRID 86 2.5 0.0 0.0 -1 GRID 87 2.5 -0.5 0.0 -1 GRID 88 2.5 -1.0 0.0 -1 GRID 89 2.5 -1.5 0.0 -1 GRID 90 2.5 -2.0 0.0 -1 GRID 91 -2.5 2.0 0.0 -1 GRID 92 -2.5 1.5 0.0 -1 GRID 93 -2.5 1.0 0.0 -1 GRID 94 -2.5 0.5 0.0 -1 GRID 95 -2.5 0.0 0.0 -1 GRID 96 -2.5 -0.5 0.0 -1 GRID 97 -2.5 -1.0 0.0 -1 GRID 98 -2.5 -1.5 0.0 -1 GRID 99 -2.5 -2.0 0.0 -1 GRID 100 2.5 2.5 0.0 -1 GRID 101 2.5 -2.5 0.0 -1 GRID 102 2.0 2.5 0.0 -1 GRID 103 2.0 -2.5 0.0 -1 GRID 104 1.5 2.5 0.0 -1 GRID 105 1.5 -2.5 0.0 -1 GRID 106 1.0 2.5 0.0 -1 GRID 107 1.0 -2.5 0.0 -1



GRID 108 0.5 2.5 0.0 -1 GRID 109 0.5 -2.5 0.0 -1 GRID 110 0.0 2.5 0.0 -1 GRID 111 0.0 -2.5 0.0 -1 GRID 112 -0.5 2.5 0.0 -1 GRID 113 -0.5 -2.5 0.0 -1 GRID 114 -1.0 2.5 0.0 -1 GRID 115 -1.0 -2.5 0.0 -1 GRID 116 -1.5 2.5 0.0 -1 GRID 117 -1.5 -2.5 0.0 -1 GRID 118 -2.0 2.5 0.0 -1 GRID 119 -2.0 -2.5 0.0 -1 GRID 120 -2.5 2.5 0.0 -1 GRID 121 -2.5 -2.5 0.0 -1 GRID 727 2.5 2.5 1.0 -1 GRID 728 2.5 2.0 1.0 -1 GRID 729 2.0 2.0 1.0 -1 GRID 730 2.0 2.5 1.0 -1 GRID 731 2.5 1.5 1.0 -1 GRID 732 2.0 1.5 1.0 -1 GRID 733 2.5 1.0 1.0 -1 GRID 734 2.0 1.0 1.0 -1 GRID 735 2.5 0.5 1.0 -1 GRID 736 2.0 0.5 1.0 -1 GRID 737 2.5 -4.2E-191.0 -1 GRID 738 2.0 -6.5E-201.0 -1 GRID 739 2.5 -0.5 1.0 -1 GRID 740 2.0 -0.5 1.0 -1 GRID 741 2.5 -1.0 1.0 -1 GRID 742 2.0 -1.0 1.0 -1 GRID 743 2.5 -1.5 1.0 -1 GRID 744 2.0 -1.5 1.0 -1 GRID 745 2.5 -2.0 1.0 -1 GRID 746 2.0 -2.0 1.0 -1 GRID 747 2.5 -2.5 1.0 -1 GRID 748 2.0 -2.5 1.0 -1 GRID 749 1.5 2.0 1.0 -1 GRID 750 1.5 2.5 1.0 -1 GRID 751 1.5 1.5 1.0 -1 GRID 752 1.5 1.0 1.0 -1 GRID 753 1.5 0.5 1.0 -1 GRID 754 1.5 -9.8E-211.0 -1 GRID 755 1.5 -0.5 1.0 -1 GRID 756 1.5 -1.0 1.0 -1 GRID 757 1.5 -1.5 1.0 -1 GRID 758 1.5 -2.0 1.0 -1 GRID 759 1.5 -2.5 1.0 -1 GRID 760 1.0 2.0 1.0 -1 GRID 761 1.0 2.5 1.0 -1 GRID 762 1.0 1.5 1.0 -1 GRID 763 1.0 1.0 1.0 -1 GRID 764 1.0 0.5 1.0 -1 GRID 765 1.0 -1.5E-211.0 -1 GRID 766 1.0 -0.5 1.0 -1 GRID 767 1.0 -1.0 1.0 -1 GRID 768 1.0 -1.5 1.0 -1 GRID 769 1.0 -2.0 1.0 -1 GRID 770 1.0 -2.5 1.0 -1 GRID 771 0.5 2.0 1.0 -1 GRID 772 0.5 2.5 1.0 -1 GRID 773 0.5 1.5 1.0 -1 GRID 774 0.5 1.0 1.0 -1 GRID 775 0.5 0.5 1.0 -1 GRID 776 0.5 -2.3E-221.0 -1 GRID 777 0.5 -0.5 1.0 -1 GRID 778 0.5 -1.0 1.0 -1 GRID 779 0.5 -1.5 1.0 -1 GRID 780 0.5 -2.0 1.0 -1 GRID 781 0.5 -2.5 1.0 -1 GRID 782 0.0 2.0 1.0 -1



GRID 783 0.0 2.5 1.0 -1 GRID 784 0.0 1.5 1.0 -1 GRID 785 0.0 1.0 1.0 -1 GRID 786 0.0 0.5 1.0 -1 GRID 787 0.0 -3.5E-231.0 -1 GRID 788 0.0 -0.5 1.0 -1 GRID 789 0.0 -1.0 1.0 -1 GRID 790 0.0 -1.5 1.0 -1 GRID 791 0.0 -2.0 1.0 -1 GRID 792 0.0 -2.5 1.0 -1 GRID 793 -0.5 2.0 1.0 -1 GRID 794 -0.5 2.5 1.0 -1 GRID 795 -0.5 1.5 1.0 -1 GRID 796 -0.5 1.0 1.0 -1 GRID 797 -0.5 0.5 1.0 -1 GRID 798 -0.5 -5.3E-241.0 -1 GRID 799 -0.5 -0.5 1.0 -1 GRID 800 -0.5 -1.0 1.0 -1 GRID 801 -0.5 -1.5 1.0 -1 GRID 802 -0.5 -2.0 1.0 -1 GRID 803 -0.5 -2.5 1.0 -1 GRID 804 -1.0 2.0 1.0 -1 GRID 805 -1.0 2.5 1.0 -1 GRID 806 -1.0 1.5 1.0 -1 GRID 807 -1.0 1.0 1.0 -1 GRID 808 -1.0 0.5 1.0 -1 GRID 809 -1.0 -8.1E-251.0 -1 GRID 810 -1.0 -0.5 1.0 -1 GRID 811 -1.0 -1.0 1.0 -1 GRID 812 -1.0 -1.5 1.0 -1 GRID 813 -1.0 -2.0 1.0 -1 GRID 814 -1.0 -2.5 1.0 -1 GRID 815 -1.5 2.0 1.0 -1 GRID 816 -1.5 2.5 1.0 -1 GRID 817 -1.5 1.5 1.0 -1 GRID 818 -1.5 1.0 1.0 -1 GRID 819 -1.5 0.5 1.0 -1 GRID 820 -1.5 -9.3E-181.0 -1 GRID 821 -1.5 -0.5 1.0 -1 GRID 822 -1.5 -1.0 1.0 -1 GRID 823 -1.5 -1.5 1.0 -1 GRID 824 -1.5 -2.0 1.0 -1 GRID 825 -1.5 -2.5 1.0 -1 GRID 826 -2.0 2.0 1.0 -1 GRID 827 -2.0 2.5 1.0 -1 GRID 828 -2.0 1.5 1.0 -1 GRID 829 -2.0 1.0 1.0 -1 GRID 830 -2.0 0.5 1.0 -1 GRID 831 -2.0 -2.0E-181.0 -1 GRID 832 -2.0 -0.5 1.0 -1 GRID 833 -2.0 -1.0 1.0 -1 GRID 834 -2.0 -1.5 1.0 -1 GRID 835 -2.0 -2.0 1.0 -1 GRID 836 -2.0 -2.5 1.0 -1 GRID 837 -2.5 2.0 1.0 -1 GRID 838 -2.5 2.5 1.0 -1 GRID 839 -2.5 1.5 1.0 -1 GRID 840 -2.5 1.0 1.0 -1 GRID 841 -2.5 0.5 1.0 -1 GRID 842 -2.5 -1.0E-181.0 -1 GRID 843 -2.5 -0.5 1.0 -1 GRID 844 -2.5 -1.0 1.0 -1 GRID 845 -2.5 -1.5 1.0 -1 GRID 846 -2.5 -2.0 1.0 -1 GRID 847 -2.5 -2.5 1.0 -1 GRID 848 2.5 2.5 2.0 -1 GRID 849 2.5 2.0 2.0 -1 GRID 850 2.0 2.0 2.0 -1 GRID 851 2.0 2.5 2.0 -1 GRID 852 2.5 1.5 2.0 -1



GRID 853 2.0 1.5 2.0 -1 GRID 854 2.5 1.0 2.0 -1 GRID 855 2.0 1.0 2.0 -1 GRID 856 2.5 0.5 2.0 -1 GRID 857 2.0 0.5 2.0 -1 GRID 858 2.5 -6.0E-192.0 -1 GRID 859 2.0 -1.2E-192.0 -1 GRID 860 2.5 -0.5 2.0 -1 GRID 861 2.0 -0.5 2.0 -1 GRID 862 2.5 -1.0 2.0 -1 GRID 863 2.0 -1.0 2.0 -1 GRID 864 2.5 -1.5 2.0 -1 GRID 865 2.0 -1.5 2.0 -1 GRID 866 2.5 -2.0 2.0 -1 GRID 867 2.0 -2.0 2.0 -1 GRID 868 2.5 -2.5 2.0 -1 GRID 869 2.0 -2.5 2.0 -1 GRID 870 1.5 2.0 2.0 -1 GRID 871 1.5 2.5 2.0 -1 GRID 872 1.5 1.5 2.0 -1 GRID 873 1.5 1.0 2.0 -1 GRID 874 1.5 0.5 2.0 -1 GRID 875 1.5 -2.1E-202.0 -1 GRID 876 1.5 -0.5 2.0 -1 GRID 877 1.5 -1.0 2.0 -1 GRID 878 1.5 -1.5 2.0 -1 GRID 879 1.5 -2.0 2.0 -1 GRID 880 1.5 -2.5 2.0 -1 GRID 881 1.0 2.0 2.0 -1 GRID 882 1.0 2.5 2.0 -1 GRID 883 1.0 1.5 2.0 -1 GRID 884 1.0 1.0 2.0 -1 GRID 885 1.0 0.5 2.0 -1 GRID 886 1.0 -3.8E-212.0 -1 GRID 887 1.0 -0.5 2.0 -1 GRID 888 1.0 -1.0 2.0 -1 GRID 889 1.0 -1.5 2.0 -1 GRID 890 1.0 -2.0 2.0 -1 GRID 891 1.0 -2.5 2.0 -1 GRID 892 0.5 2.0 2.0 -1 GRID 893 0.5 2.5 2.0 -1 GRID 894 0.5 1.5 2.0 -1 GRID 895 0.5 1.0 2.0 -1 GRID 896 0.5 0.5 2.0 -1 GRID 897 0.5 -6.7E-222.0 -1 GRID 898 0.5 -0.5 2.0 -1 GRID 899 0.5 -1.0 2.0 -1 GRID 900 0.5 -1.5 2.0 -1 GRID 901 0.5 -2.0 2.0 -1 GRID 902 0.5 -2.5 2.0 -1 GRID 903 0.0 2.0 2.0 -1 GRID 904 0.0 2.5 2.0 -1 GRID 905 0.0 1.5 2.0 -1 GRID 906 0.0 1.0 2.0 -1 GRID 907 0.0 0.5 2.0 -1 GRID 908 0.0 -1.2E-222.0 -1 GRID 909 0.0 -0.5 2.0 -1 GRID 910 0.0 -1.0 2.0 -1 GRID 911 0.0 -1.5 2.0 -1 GRID 912 0.0 -2.0 2.0 -1 GRID 913 0.0 -2.5 2.0 -1 GRID 914 -0.5 2.0 2.0 -1 GRID 915 -0.5 2.5 2.0 -1 GRID 916 -0.5 1.5 2.0 -1 GRID 917 -0.5 1.0 2.0 -1 GRID 918 -0.5 0.5 2.0 -1 GRID 919 -0.5 -2.0E-232.0 -1 GRID 920 -0.5 -0.5 2.0 -1 GRID 921 -0.5 -1.0 2.0 -1 GRID 922 -0.5 -1.5 2.0 -1



GRID 923 -0.5 -2.0 2.0 -1 GRID 924 -0.5 -2.5 2.0 -1 GRID 925 -1.0 2.0 2.0 -1 GRID 926 -1.0 2.5 2.0 -1 GRID 927 -1.0 1.5 2.0 -1 GRID 928 -1.0 1.0 2.0 -1 GRID 929 -1.0 0.5 2.0 -1 GRID 930 -1.0 -1.4E-182.0 -1 GRID 931 -1.0 -0.5 2.0 -1 GRID 932 -1.0 -1.0 2.0 -1 GRID 933 -1.0 -1.5 2.0 -1 GRID 934 -1.0 -2.0 2.0 -1 GRID 935 -1.0 -2.5 2.0 -1 GRID 936 -1.5 2.0 2.0 -1 GRID 937 -1.5 2.5 2.0 -1 GRID 938 -1.5 1.5 2.0 -1 GRID 939 -1.5 1.0 2.0 -1 GRID 940 -1.5 0.5 2.0 -1 GRID 941 -1.5 -1.3E-172.0 -1 GRID 942 -1.5 -0.5 2.0 -1 GRID 943 -1.5 -1.0 2.0 -1 GRID 944 -1.5 -1.5 2.0 -1 GRID 945 -1.5 -2.0 2.0 -1 GRID 946 -1.5 -2.5 2.0 -1 GRID 947 -2.0 2.0 2.0 -1 GRID 948 -2.0 2.5 2.0 -1 GRID 949 -2.0 1.5 2.0 -1 GRID 950 -2.0 1.0 2.0 -1 GRID 951 -2.0 0.5 2.0 -1 GRID 952 -2.0 -4.1E-182.0 -1 GRID 953 -2.0 -0.5 2.0 -1 GRID 954 -2.0 -1.0 2.0 -1 GRID 955 -2.0 -1.5 2.0 -1 GRID 956 -2.0 -2.0 2.0 -1 GRID 957 -2.0 -2.5 2.0 -1 GRID 958 -2.5 2.0 2.0 -1 GRID 959 -2.5 2.5 2.0 -1 GRID 960 -2.5 1.5 2.0 -1 GRID 961 -2.5 1.0 2.0 -1 GRID 962 -2.5 0.5 2.0 -1 GRID 963 -2.5 -2.5E-182.0 -1 GRID 964 -2.5 -0.5 2.0 -1 GRID 965 -2.5 -1.0 2.0 -1 GRID 966 -2.5 -1.5 2.0 -1 GRID 967 -2.5 -2.0 2.0 -1 GRID 968 -2.5 -2.5 2.0 -1 GRID 969 2.5 2.5 3.0 -1 GRID 970 2.5 2.0 3.0 -1 GRID 971 2.0 2.0 3.0 -1 GRID 972 2.0 2.5 3.0 -1 GRID 973 2.5 1.5 3.0 -1 GRID 974 2.0 1.5 3.0 -1 GRID 975 2.5 1.0 3.0 -1 GRID 976 2.0 1.0 3.0 -1 GRID 977 2.5 0.5 3.0 -1 GRID 978 2.0 0.5 3.0 -1 GRID 979 2.5 -6.7E-193.0 -1 GRID 980 2.0 -1.5E-193.0 -1 GRID 981 2.5 -0.5 3.0 -1 GRID 982 2.0 -0.5 3.0 -1 GRID 983 2.5 -1.0 3.0 -1 GRID 984 2.0 -1.0 3.0 -1 GRID 985 2.5 -1.5 3.0 -1 GRID 986 2.0 -1.5 3.0 -1 GRID 987 2.5 -2.0 3.0 -1 GRID 988 2.0 -2.0 3.0 -1 GRID 989 2.5 -2.5 3.0 -1 GRID 990 2.0 -2.5 3.0 -1 GRID 991 1.5 2.0 3.0 -1 GRID 992 1.5 2.5 3.0 -1



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GRID 1705 -2.0 -2.5 1.0 GRID 1706 -2.0 2.5 1.0 GRID 1707 -1.5 -2.5 1.0 GRID 1708 -1.5 2.5 1.0 GRID 1709 -1.0 -2.5 1.0 GRID 1710 -1.0 2.5 1.0 GRID 1711 -0.5 -2.5 1.0 GRID 1712 -0.5 2.5 1.0 GRID 1713 -2.5E-18-2.5 1.0 GRID 1714 -2.5E-182.5 1.0 GRID 1715 0.5 -2.5 1.0 GRID 1716 0.5 2.5 1.0 GRID 1717 1.0 -2.5 1.0 GRID 1718 1.0 2.5 1.0 GRID 1719 1.5 -2.5 1.0 GRID 1720 1.5 2.5 1.0 GRID 1721 2.0 -2.5 1.0 GRID 1722 2.497764-2.497761.0 GRID 1723 2.5 -2.0 1.0 GRID 1724 2.5 -1.5 1.0 GRID 1725 2.5 -1.0 1.0 GRID 1726 2.5 -0.5 1.0 GRID 1727 2.5 -2.9E-181.0 GRID 1728 2.5 0.5 1.0 GRID 1729 2.5 1.0 1.0 GRID 1730 2.5 1.5 1.0 GRID 1731 2.0 2.5 1.0 GRID 1732 2.5 2.0 1.0 GRID 1733 2.4977642.4977641.0 GRID 1734 -0.25 3.33E-165.0 $$$$ SPOINT Data$$$$$$------------------------------------------------------------------------------$$$ Group Definitions $$$------------------------------------------------------------------------------$$$$$ RBE2 Elements - Multiple dependent nodes$$RBE2 1553 1734 123456 1478 1479 1480 1481 1482+ + 1489 1493 1500 1504 1511 1515 1522 1526+ + 1533 1534 1535 1536 1537 $$HMMOVE 6$ 1553$$ CQUAD4 Elements$CQUAD4 1101 4 1332 1341 1342 1333 CQUAD4 1102 4 1333 1342 1343 1334 CQUAD4 1103 4 1334 1343 1344 1335 CQUAD4 1104 4 1335 1344 1345 1336 CQUAD4 1105 4 1336 1345 1346 1337 CQUAD4 1106 4 1337 1346 1347 1338 CQUAD4 1107 4 1338 1347 1348 1339 CQUAD4 1108 4 1339 1348 1349 1340 CQUAD4 1109 4 1341 1350 1351 1342 CQUAD4 1110 4 1342 1351 1352 1343 CQUAD4 1111 4 1343 1352 1353 1344 CQUAD4 1112 4 1344 1353 1354 1345 CQUAD4 1113 4 1345 1354 1355 1346 CQUAD4 1114 4 1346 1355 1356 1347 CQUAD4 1115 4 1347 1356 1357 1348 CQUAD4 1116 4 1348 1357 1358 1349 CQUAD4 1117 4 1350 1359 1360 1351 CQUAD4 1118 4 1351 1360 1361 1352 CQUAD4 1119 4 1352 1361 1362 1353 CQUAD4 1120 4 1353 1362 1363 1354 CQUAD4 1121 4 1354 1363 1364 1355



CQUAD4 1122 4 1355 1364 1365 1356 CQUAD4 1123 4 1356 1365 1366 1357 CQUAD4 1124 4 1357 1366 1367 1358 CQUAD4 1125 4 1359 1368 1369 1360 CQUAD4 1126 4 1360 1369 1370 1361 CQUAD4 1127 4 1361 1370 1371 1362 CQUAD4 1128 4 1362 1371 1372 1363 CQUAD4 1129 4 1363 1372 1373 1364 CQUAD4 1130 4 1364 1373 1374 1365 CQUAD4 1131 4 1365 1374 1375 1366 CQUAD4 1132 4 1366 1375 1376 1367 CQUAD4 1133 4 1368 1377 1378 1369 CQUAD4 1134 4 1369 1378 1379 1370 CQUAD4 1135 4 1370 1379 1380 1371 CQUAD4 1136 4 1371 1380 1381 1372 CQUAD4 1137 4 1372 1381 1382 1373 CQUAD4 1138 4 1373 1382 1383 1374 CQUAD4 1139 4 1374 1383 1384 1375 CQUAD4 1140 4 1375 1384 1385 1376 CQUAD4 1141 4 1377 1386 1387 1378 CQUAD4 1142 4 1378 1387 1388 1379 CQUAD4 1143 4 1379 1388 1389 1380 CQUAD4 1144 4 1380 1389 1390 1381 CQUAD4 1145 4 1381 1390 1391 1382 CQUAD4 1146 4 1382 1391 1392 1383 CQUAD4 1147 4 1383 1392 1393 1384 CQUAD4 1148 4 1384 1393 1394 1385 CQUAD4 1149 4 1386 1395 1396 1387 CQUAD4 1150 4 1387 1396 1397 1388 CQUAD4 1151 4 1388 1397 1398 1389 CQUAD4 1152 4 1389 1398 1399 1390 CQUAD4 1153 4 1390 1399 1400 1391 CQUAD4 1154 4 1391 1400 1401 1392 CQUAD4 1155 4 1392 1401 1402 1393 CQUAD4 1156 4 1393 1402 1403 1394 CQUAD4 1157 4 1395 1404 1405 1396 CQUAD4 1158 4 1396 1405 1406 1397 CQUAD4 1159 4 1397 1406 1407 1398 CQUAD4 1160 4 1398 1407 1408 1399 CQUAD4 1161 4 1399 1408 1409 1400 CQUAD4 1162 4 1400 1409 1410 1401 CQUAD4 1163 4 1401 1410 1411 1402 CQUAD4 1164 4 1402 1411 1412 1403 CQUAD4 1165 4 1413 1332 1333 1414 CQUAD4 1166 4 1414 1333 1334 1415 CQUAD4 1167 4 1415 1334 1335 1416 CQUAD4 1168 4 1416 1335 1336 1417 CQUAD4 1169 4 1417 1336 1337 1418 CQUAD4 1170 4 1418 1337 1338 1419 CQUAD4 1171 4 1419 1338 1339 1420 CQUAD4 1172 4 1420 1339 1340 1421 CQUAD4 1173 4 1404 1422 1423 1405 CQUAD4 1174 4 1405 1423 1424 1406 CQUAD4 1175 4 1406 1424 1425 1407 CQUAD4 1176 4 1407 1425 1426 1408 CQUAD4 1177 4 1408 1426 1427 1409 CQUAD4 1178 4 1409 1427 1428 1410 CQUAD4 1179 4 1410 1428 1429 1411 CQUAD4 1180 4 1411 1429 1430 1412 CQUAD4 1181 4 1431 1433 1332 1413 CQUAD4 1182 4 1433 1435 1341 1332 CQUAD4 1183 4 1421 1340 1434 1432 CQUAD4 1184 4 1340 1349 1436 1434 CQUAD4 1185 4 1435 1437 1350 1341 CQUAD4 1186 4 1349 1358 1438 1436 CQUAD4 1187 4 1437 1439 1359 1350 CQUAD4 1188 4 1358 1367 1440 1438 CQUAD4 1189 4 1439 1441 1368 1359 CQUAD4 1190 4 1367 1376 1442 1440 CQUAD4 1191 4 1441 1443 1377 1368



CQUAD4 1492 4 1468 1457 1458 1469 CQUAD4 1493 4 1578 1457 1456 1577 CQUAD4 1494 4 1467 1456 1457 1468 CQUAD4 1495 4 1577 1456 1455 1576 CQUAD4 1496 4 1466 1455 1456 1467 CQUAD4 1497 4 1576 1455 1454 1575 CQUAD4 1498 4 1465 1454 1455 1466 CQUAD4 1499 4 1575 1454 1453 1574 CQUAD4 1500 4 1464 1453 1454 1465 $$ CHEXA Elements: First Order$CHEXA 601 1 100 102 1 82 727 730+ + 729 728CHEXA 602 1 82 1 2 83 728 729+ + 732 731CHEXA 603 1 83 2 3 84 731 732+ + 734 733CHEXA 604 1 84 3 4 85 733 734+ + 736 735CHEXA 605 1 85 4 5 86 735 736+ + 738 737CHEXA 606 1 86 5 6 87 737 738+ + 740 739CHEXA 607 1 87 6 7 88 739 740+ + 742 741CHEXA 608 1 88 7 8 89 741 742+ + 744 743CHEXA 609 1 89 8 9 90 743 744+ + 746 745CHEXA 610 1 90 9 103 101 745 746+ + 748 747CHEXA 611 1 102 104 10 1 730 750+ + 749 729CHEXA 612 1 1 10 11 2 729 749+ + 751 732CHEXA 613 1 2 11 12 3 732 751+ + 752 734CHEXA 614 1 3 12 13 4 734 752+ + 753 736CHEXA 615 1 4 13 14 5 736 753+ + 754 738CHEXA 616 1 5 14 15 6 738 754+ + 755 740CHEXA 617 1 6 15 16 7 740 755+ + 756 742CHEXA 618 1 7 16 17 8 742 756+ + 757 744CHEXA 619 1 8 17 18 9 744 757+ + 758 746CHEXA 620 1 9 18 105 103 746 758+ + 759 748CHEXA 621 1 104 106 19 10 750 761+ + 760 749CHEXA 622 1 10 19 20 11 749 760+ + 762 751CHEXA 623 1 11 20 21 12 751 762+ + 763 752CHEXA 624 1 12 21 22 13 752 763+ + 764 753CHEXA 625 1 13 22 23 14 753 764+ + 765 754CHEXA 626 1 14 23 24 15 754 765+ + 766 755CHEXA 627 1 15 24 25 16 755 766+ + 767 756CHEXA 628 1 16 25 26 17 756 767+ + 768 757CHEXA 629 1 17 26 27 18 757 768+ + 769 758



CHEXA 630 1 18 27 107 105 758 769+ + 770 759CHEXA 631 1 106 108 28 19 761 772+ + 771 760CHEXA 632 1 19 28 29 20 760 771+ + 773 762CHEXA 633 1 20 29 30 21 762 773+ + 774 763CHEXA 634 1 21 30 31 22 763 774+ + 775 764CHEXA 635 1 22 31 32 23 764 775+ + 776 765CHEXA 636 1 23 32 33 24 765 776+ + 777 766CHEXA 637 1 24 33 34 25 766 777+ + 778 767CHEXA 638 1 25 34 35 26 767 778+ + 779 768CHEXA 639 1 26 35 36 27 768 779+ + 780 769CHEXA 640 1 27 36 109 107 769 780+ + 781 770CHEXA 641 1 108 110 37 28 772 783+ + 782 771CHEXA 642 1 28 37 38 29 771 782+ + 784 773CHEXA 643 1 29 38 39 30 773 784+ + 785 774CHEXA 644 1 30 39 40 31 774 785+ + 786 775CHEXA 645 1 31 40 41 32 775 786+ + 787 776CHEXA 646 1 32 41 42 33 776 787+ + 788 777CHEXA 647 1 33 42 43 34 777 788+ + 789 778CHEXA 648 1 34 43 44 35 778 789+ + 790 779CHEXA 649 1 35 44 45 36 779 790+ + 791 780CHEXA 650 1 36 45 111 109 780 791+ + 792 781CHEXA 651 1 110 112 46 37 783 794+ + 793 782CHEXA 652 1 37 46 47 38 782 793+ + 795 784CHEXA 653 1 38 47 48 39 784 795+ + 796 785CHEXA 654 1 39 48 49 40 785 796+ + 797 786CHEXA 655 1 40 49 50 41 786 797+ + 798 787CHEXA 656 1 41 50 51 42 787 798+ + 799 788CHEXA 657 1 42 51 52 43 788 799+ + 800 789CHEXA 658 1 43 52 53 44 789 800+ + 801 790CHEXA 659 1 44 53 54 45 790 801+ + 802 791CHEXA 660 1 45 54 113 111 791 802+ + 803 792CHEXA 661 1 112 114 55 46 794 805+ + 804 793CHEXA 662 1 46 55 56 47 793 804+ + 806 795CHEXA 663 1 47 56 57 48 795 806+ + 807 796CHEXA 664 1 48 57 58 49 796 807+ + 808 797



CHEXA 1050 1 1143 1154 1155 1144 1264 1275+ + 1276 1265CHEXA 1051 1 1146 1157 1156 1145 1267 1278+ + 1277 1266CHEXA 1052 1 1145 1156 1158 1147 1266 1277+ + 1279 1268CHEXA 1053 1 1147 1158 1159 1148 1268 1279+ + 1280 1269CHEXA 1054 1 1148 1159 1160 1149 1269 1280+ + 1281 1270CHEXA 1055 1 1149 1160 1161 1150 1270 1281+ + 1282 1271

CHEXA 1057 1 1151 1162 1163 1152 1272 1283+ + 1284 1273CHEXA 1058 1 1152 1163 1164 1153 1273 1284+ + 1285 1274CHEXA 1059 1 1153 1164 1165 1154 1274 1285+ + 1286 1275CHEXA 1060 1 1154 1165 1166 1155 1275 1286+ + 1287 1276CHEXA 1061 1 1157 1168 1167 1156 1278 1289+ + 1288 1277CHEXA 1062 1 1156 1167 1169 1158 1277 1288+ + 1290 1279CHEXA 1063 1 1158 1169 1170 1159 1279 1290+ + 1291 1280CHEXA 1064 1 1159 1170 1171 1160 1280 1291+ + 1292 1281CHEXA 1065 1 1160 1171 1172 1161 1281 1292+ + 1293 1282CHEXA 1066 1 1161 1172 1173 1162 1282 1293+ + 1294 1283CHEXA 1067 1 1162 1173 1174 1163 1283 1294+ + 1295 1284CHEXA 1068 1 1163 1174 1175 1164 1284 1295+ + 1296 1285CHEXA 1069 1 1164 1175 1176 1165 1285 1296+ + 1297 1286CHEXA 1070 1 1165 1176 1177 1166 1286 1297+ + 1298 1287CHEXA 1071 1 1168 1179 1178 1167 1289 1300+ + 1299 1288CHEXA 1072 1 1167 1178 1180 1169 1288 1299+ + 1301 1290CHEXA 1073 1 1169 1180 1181 1170 1290 1301+ + 1302 1291CHEXA 1074 1 1170 1181 1182 1171 1291 1302+ + 1303 1292CHEXA 1075 1 1171 1182 1183 1172 1292 1303+ + 1304 1293CHEXA 1076 1 1172 1183 1184 1173 1293 1304+ + 1305 1294CHEXA 1077 1 1173 1184 1185 1174 1294 1305+ + 1306 1295CHEXA 1078 1 1174 1185 1186 1175 1295 1306+ + 1307 1296CHEXA 1079 1 1175 1186 1187 1176 1296 1307+ + 1308 1297CHEXA 1080 1 1176 1187 1188 1177 1297 1308+ + 1309 1298CHEXA 1081 1 1179 1190 1189 1178 1300 1311+ + 1310 1299CHEXA 1082 1 1178 1189 1191 1180 1299 1310+ + 1312 1301CHEXA 1083 1 1180 1191 1192 1181 1301 1312+ + 1313 1302CHEXA 1084 1 1181 1192 1193 1182 1302 1313+ + 1314 1303



CHEXA 1085 1 1182 1193 1194 1183 1303 1314+ + 1315 1304CHEXA 1086 1 1183 1194 1195 1184 1304 1315+ + 1316 1305CHEXA 1087 1 1184 1195 1196 1185 1305 1316+ + 1317 1306CHEXA 1088 1 1185 1196 1197 1186 1306 1317+ + 1318 1307CHEXA 1089 1 1186 1197 1198 1187 1307 1318+ + 1319 1308CHEXA 1090 1 1187 1198 1199 1188 1308 1319+ + 1320 1309CHEXA 1091 1 1190 1201 1200 1189 1311 1322+ + 1321 1310CHEXA 1092 1 1189 1200 1202 1191 1310 1321+ + 1323 1312CHEXA 1093 1 1191 1202 1203 1192 1312 1323+ + 1324 1313CHEXA 1094 1 1192 1203 1204 1193 1313 1324+ + 1325 1314CHEXA 1095 1 1193 1204 1205 1194 1314 1325+ + 1326 1315CHEXA 1096 1 1194 1205 1206 1195 1315 1326+ + 1327 1316CHEXA 1097 1 1195 1206 1207 1196 1316 1327+ + 1328 1317CHEXA 1098 1 1196 1207 1208 1197 1317 1328+ + 1329 1318CHEXA 1099 1 1197 1208 1209 1198 1318 1329+ + 1330 1319CHEXA 1100 1 1198 1209 1210 1199 1319 1330+ + 1331 1320$$$$------------------------------------------------------------------------------$$$ HyperMesh name information for generic property collectors $$$------------------------------------------------------------------------------$$$$$------------------------------------------------------------------------------$$$ Property Definition for 1-D Elements $$$------------------------------------------------------------------------------$$$$$------------------------------------------------------------------------------$$$ HyperMesh name and color information for generic components $$$------------------------------------------------------------------------------$$HMNAME COMP 6"auto1"$HWCOLOR COMP 6 3$$$$$------------------------------------------------------------------------------$$$ Property Definition for Surface and Volume Elements $$$------------------------------------------------------------------------------$$$$$ PSHELL Data$$HMNAME COMP 4"shells"$HWCOLOR COMP 4 7PSHELL 4 20.2 2 2 $$$$ PSOLID Data$$HMNAME COMP 1"solids"$HWCOLOR COMP 1 26PSOLID 1 1 PFLUIDPSOLID 2 2$$$$------------------------------------------------------------------------------$$$ Material Definition Cards $$$------------------------------------------------------------------------------$$$--------------------------------------------------------------$$ HYPERMESH TAGS



$$--------------------------------------------------------------$$BEGIN TAGS$$END TAGS$$$$ MAT1 Data$$HMNAME MAT 2"MAT1"$HWCOLOR MAT 2 18MAT1 2200000.0 0.3 0.9e-5 $$$$$$ MAT10 Data$HMNAME MAT 1"MAT10_1"$HWCOLOR MAT 1 3MAT10 11.0 0.01 $$$$$$------------------------------------------------------------------------------$$$ HyperMesh name information for generic materials $$$------------------------------------------------------------------------------$$$$$------------------------------------------------------------------------------$$$ Material Definition Cards $$$------------------------------------------------------------------------------$$$$$------------------------------------------------------------------------------$$$ Loads and Boundary Conditions $$$------------------------------------------------------------------------------$$$$$HyperMesh name and color information for generic loadcollectors$$$HMNAME LOADCOL 4"SPC"$HWCOLOR LOADCOL 4 3$$HMNAME LOADCOL 6"spcd"$HWCOLOR LOADCOL 6 4$$$$$$$$$$$ FREQ1 cards$$$HMNAME LOADCOL 5"freq"$HWCOLOR LOADCOL 5 4FREQ1 50.1 10.0 5$$$$$$$$$$$$ RLOAD2 cards$$$HMNAME LOADCOL 2"rload2"$HWCOLOR LOADCOL 2 5RLOAD2 2 6 1 0 ACCE$$$HMNAME LOADCOL 3"darea"$HWCOLOR LOADCOL 3 5RLOAD2 3 3 1 0 LOAD$$$$$$$$ TABLED1 cards$$$HMNAME LOADCOL 1"tab"$HWCOLOR LOADCOL 1 41TABLED1 1 LINEAR LINEAR+ 0.0 0.0 1000.0 1.0ENDT $$



TABLED1 2 LINEAR LINEAR+ 0.0 0.0 1000.0 1.0ENDT$$TABLED1 3 LINEAR LINEAR+ 0.0 5.0 1000.0 5.0ENDT$$ DLOAD cards$$$HMNAME LOADCOL 11"DLOAD11"$HWCOLOR LOADCOL 11 3DLOAD 111.0 1.0 2 1.0 3$$$$$$$$$$$$$$$$ SPC Data$$SPC 4 1431 1234560.0 SPC 4 1432 1234560.0 SPC 4 1451 1234560.0 SPC 4 1452 1234560.0 SPC 4 1734 3 0.0 $$$$ SPCD Data$$SPCD 6 1734 3 3.0 $$ DAREA Data$$$$$ DAREA Data$$DAREA 3 1734 3-10.0 ENDDATA

ALTDOCTAG "HqTD_ARNMI\S\pMpN13G;5oANN]l[enE7fmSbTJro20LOpNriZFOQfUk]_`5hfS5ATf6pT7RXMjA3e@k_r^K?GP;?OeEbD0"ADI0.1.0 2011-05-13T19:57:45 0of1 OSQAENDDOCTAG

Input File - mdcaabsf.parm

$$$$ Optistruct Input Deck Generated by HyperMesh Version : 10.0build60$$ Generated using HyperMesh-Optistruct Template Version : 10.0-SA1-120$$$$ Template: optistruct$$$$$DISPLACEMENT(PHASE) = 1OUTPUT,HGFREQ,ALLOUTPUT,OPTI,ALLOUTPUT,H3D,ALLOUTPUT,PUNCH,ALL$$------------------------------------------------------------------------------$$$ Case Control Cards $$$------------------------------------------------------------------------------$



$$HMNAME LOADSTEP 1"Piston_Load" 6$SUBCASE 1 LABEL Piston_Load SPC = 12 METHOD(STRUCTURE) = 4 METHOD(FLUID) = 5 FREQUENCY = 3 DLOAD = 9XYPUNCH DISP 1/ 11(T1) XYPUNCH DISP 1/ 43(T1) XYPUNCH DISP 1/ 55(T1) XYPUNCH DISP 1/ 67(T1) XYPUNCH DISP 1/ 79(T1) XYPUNCH DISP 1/ 91(T1) XYPUNCH DISP 1/ 103(T1) XYPUNCH DISP 1/ 115(T1) XYPUNCH DISP 1/ 127(T1) XYPUNCH DISP 1/ 139(T1) XYPUNCH DISP 1/ 151(T1) XYPUNCH DISP 1/ 163(T1) XYPUNCH DISP 1/ 175(T1) XYPUNCH DISP 1/ 187(T1) XYPUNCH DISP 1/ 199(T1) XYPUNCH DISP 1/ 531(T1) XYPUNCH DISP 1/ 543(T1) XYPUNCH DISP 1/ 555(T1) XYPUNCH DISP 1/ 567(T1) XYPUNCH DISP 1/ 579(T1) XYPUNCH DISP 1/ 591(T1) XYPUNCH DISP 1/ 603(T1) XYPUNCH DISP 1/ 615(T1) XYPUNCH DISP 1/ 627(T1) XYPUNCH DISP 1/ 639(T1) XYPUNCH DISP 1/ 651(T1) XYPUNCH DISP 1/ 663(T1) XYPUNCH DISP 1/ 675(T1) XYPUNCH DISP 1/ 687(T1) $$HMSET 1 1 "pressure"SET 1 = 43,55,67,79,91,103,115, 127,139,151,163,175,187,199, 531,543,555,567,579,591,603, 615,627,639,651,663,675,687, 6798

$$$--------------------------------------------------------------$$ HYPERMESH TAGS $$--------------------------------------------------------------$$BEGIN TAGS$$END TAGS$BEGIN BULKACMODL $$$$ Stacking Information for Ply-Based Composite Definition$$

PARAM,AUTOSPC,YES PARAM,POST,-1 $$$$ DESVARG Data$$$$$$ GRID Data$$GRID 9 0.492 0.0 -1.72-15 -1



GRID 10 0.246 0.0 -8.59-16 -1 GRID 11 0.0 0.0 0.0 -1 GRID 12 -0.246 0.0 8.589-16 -1 GRID 13 -0.492 0.0 1.718-15 -1 GRID 14 -0.492 0.246 1.718-15 -1 GRID 15 -0.492 0.492 1.718-15 -1 GRID 16 -0.246 0.492 8.589-16 -1 GRID 17 0.0 0.492 0.0 -1 GRID 18 0.246 0.492 -8.59-16 -1 GRID 19 0.492 0.492 -1.72-15 -1 GRID 20 0.492 0.246 -1.72-15 -1 GRID 21 0.0 0.246 0.0 -1 GRID 22 -0.246 0.246 8.589-16 -1 GRID 23 0.246 0.246 -8.59-16 -1 GRID 24 0.492 -0.246 -1.72-15 -1 GRID 25 0.492 -0.492 -1.72-15 -1 GRID 26 0.246 -0.492 -8.59-16 -1 GRID 27 0.0 -0.492 0.0 -1 GRID 28 -0.246 -0.492 8.589-16 -1 GRID 29 -0.492 -0.492 1.718-15 -1 GRID 30 -0.492 -0.246 1.718-15 -1 GRID 31 0.0 -0.246 0.0 -1 GRID 32 0.246 -0.246 -8.59-16 -1 GRID 33 -0.246 -0.246 8.589-16 -1 GRID 34 0.246 5.049-29-.300073 -1 GRID 35 -5.99-130.0 -.300073 -1 GRID 36 -5.62-130.246 -.300073 -1 GRID 37 0.246 0.246 -.300073 -1 GRID 38 0.246 2.524-29-.600146 -1 GRID 39 -1.2-12 0.0 -.600146 -1 GRID 40 -1.12-120.246 -.600146 -1 GRID 41 0.246 0.246 -.600146 -1 GRID 42 0.246 2.919-29-0.90022 -1 GRID 43 -1.79-120.0 -.900219 -1 GRID 44 -1.68-120.246 -.900219 -1 GRID 45 0.246 0.246 -0.90022 -1 GRID 46 0.246 3.787-29-1.20029 -1 GRID 47 -2.39-120.0 -1.20029 -1 GRID 48 -2.24-120.246 -1.20029 -1 GRID 49 0.246 0.246 -1.20029 -1 GRID 50 0.246 4.733-29-1.50037 -1 GRID 51 -3.0-12 0.0 -1.50037 -1 GRID 52 -2.81-120.246 -1.50037 -1 GRID 53 0.246 0.246 -1.50037 -1 GRID 54 0.246 5.364-29-1.80044 -1 GRID 55 -3.6-12 0.0 -1.80044 -1 GRID 56 -3.37-120.246 -1.80044 -1 GRID 57 0.246 0.246 -1.80044 -1 GRID 58 0.246 6.311-29-2.10051 -1 GRID 59 -4.2-12 0.0 -2.10051 -1 GRID 60 -3.93-120.246 -2.10051 -1 GRID 61 0.246 0.246 -2.10051 -1 GRID 62 0.246 7.258-29-2.40059 -1 GRID 63 -4.79-120.0 -2.40059 -1 GRID 64 -4.49-120.246 -2.40059 -1 GRID 65 0.246 0.246 -2.40059 -1 GRID 66 0.246 8.204-29-2.70066 -1 GRID 67 -5.39-120.0 -2.70066 -1 GRID 68 -5.06-120.246 -2.70066 -1 GRID 69 0.246 0.246 -2.70066 -1 GRID 70 0.246 8.835-29-3.00073 -1 GRID 71 -5.99-120.0 -3.00073 -1 GRID 72 -5.62-120.246 -3.00073 -1 GRID 73 0.246 0.246 -3.00073 -1 GRID 74 0.246 9.782-29-3.30081 -1 GRID 75 -6.59-120.0 -3.30081 -1 GRID 76 -6.18-120.246 -3.30081 -1 GRID 77 0.246 0.246 -3.30081 -1 GRID 78 0.246 1.073-28-3.60088 -1 GRID 79 -7.19-120.0 -3.60088 -1



GRID 80 -6.74-120.246 -3.60088 -1 GRID 81 0.246 0.246 -3.60088 -1 GRID 82 0.246 1.136-28-3.90095 -1 GRID 83 -7.78-120.0 -3.90095 -1 GRID 84 -7.3-12 0.246 -3.90095 -1 GRID 85 0.246 0.246 -3.90095 -1 GRID 86 0.246 1.231-28-4.20102 -1 GRID 87 -8.38-120.0 -4.20102 -1 GRID 88 -7.86-120.246 -4.20102 -1 GRID 89 0.246 0.246 -4.20102 -1 GRID 90 0.246 1.294-28-4.5011 -1 GRID 91 -8.99-120.0 -4.5011 -1 GRID 92 -8.43-120.246 -4.5011 -1 GRID 93 0.246 0.246 -4.5011 -1 GRID 94 0.246 1.388-28-4.80117 -1 GRID 95 -9.59-120.0 -4.80117 -1 GRID 96 -8.99-120.246 -4.80117 -1 GRID 97 0.246 0.246 -4.80117 -1 GRID 98 0.246 1.452-28-5.10124 -1 GRID 99 -1.02-110.0 -5.10124 -1 GRID 100 -9.55-120.246 -5.10124 -1 GRID 101 0.246 0.246 -5.10124 -1 GRID 102 0.246 1.515-28-5.40132 -1 GRID 103 -1.08-110.0 -5.40132 -1 GRID 104 -1.01-110.246 -5.40132 -1 GRID 105 0.246 0.246 -5.40132 -1 GRID 106 0.246 1.609-28-5.70139 -1 GRID 107 -1.14-110.0 -5.70139 -1 GRID 108 -1.07-110.246 -5.70139 -1 GRID 109 0.246 0.246 -5.70139 -1 GRID 110 0.246 1.672-28-6.00146 -1 GRID 111 -1.2-11 0.0 -6.00146 -1 GRID 112 -1.12-110.246 -6.00146 -1 GRID 113 0.246 0.246 -6.00146 -1 GRID 114 0.246 1.735-28-6.30154 -1 GRID 115 -1.26-110.0 -6.30154 -1 GRID 116 -1.18-110.246 -6.30154 -1 GRID 117 0.246 0.246 -6.30154 -1 GRID 118 0.246 1.83-28 -6.60161 -1 GRID 119 -1.32-110.0 -6.60161 -1 GRID 120 -1.23-110.246 -6.60161 -1 GRID 121 0.246 0.246 -6.60161 -1 GRID 122 0.246 1.893-28-6.90168 -1 GRID 123 -1.38-110.0 -6.90168 -1 GRID 124 -1.29-110.246 -6.90168 -1 GRID 125 0.246 0.246 -6.90168 -1 GRID 126 0.246 1.956-28-7.20176 -1 GRID 127 -1.44-110.0 -7.20176 -1 GRID 128 -1.35-110.246 -7.20176 -1 GRID 129 0.246 0.246 -7.20176 -1 GRID 130 0.246 2.019-28-7.50183 -1 GRID 131 -1.5-11 0.0 -7.50183 -1 GRID 132 -1.4-11 0.246 -7.50183 -1 GRID 133 0.246 0.246 -7.50183 -1 GRID 134 0.246 2.083-28-7.8019 -1 GRID 135 -1.55-110.0 -7.8019 -1 GRID 136 -1.46-110.246 -7.8019 -1 GRID 137 0.246 0.246 -7.8019 -1 GRID 138 0.246 2.146-28-8.10198 -1 GRID 139 -1.61-110.0 -8.10198 -1 GRID 140 -1.51-110.246 -8.10198 -1 GRID 141 0.246 0.246 -8.10198 -1 GRID 142 0.246 2.209-28-8.40205 -1 GRID 143 -1.67-110.0 -8.40205 -1 GRID 144 -1.57-110.246 -8.40205 -1 GRID 145 0.246 0.246 -8.40205 -1 GRID 146 0.246 2.272-28-8.70212 -1 GRID 147 -1.73-110.0 -8.70212 -1 GRID 148 -1.63-110.246 -8.70212 -1 GRID 149 0.246 0.246 -8.70212 -1



GRID 150 0.246 2.335-28-9.0022 -1 GRID 151 -1.79-110.0 -9.0022 -1 GRID 152 -1.68-110.246 -9.0022 -1 GRID 153 0.246 0.246 -9.0022 -1 GRID 154 0.246 2.398-28-9.30227 -1 GRID 155 -1.85-110.0 -9.30227 -1 GRID 156 -1.74-110.246 -9.30227 -1 GRID 157 0.246 0.246 -9.30227 -1 GRID 158 0.246 2.461-28-9.60234 -1 GRID 159 -1.91-110.0 -9.60234 -1 GRID 160 -1.79-110.246 -9.60234 -1 GRID 161 0.246 0.246 -9.60234 -1 GRID 162 0.246 2.524-28-9.90241 -1 GRID 163 -1.97-110.0 -9.90241 -1 GRID 164 -1.85-110.246 -9.90241 -1 GRID 165 0.246 0.246 -9.90241 -1 GRID 166 0.246 2.556-28-10.2025 -1 GRID 167 -2.03-110.0 -10.2025 -1 GRID 168 -1.91-110.246 -10.2025 -1 GRID 169 0.246 0.246 -10.2025 -1 GRID 170 0.246 2.619-28-10.5026 -1 GRID 171 -2.09-110.0 -10.5026 -1 GRID 172 -1.96-110.246 -10.5026 -1 GRID 173 0.246 0.246 -10.5026 -1 GRID 174 0.246 2.682-28-10.8026 -1 GRID 175 -2.15-110.0 -10.8026 -1 GRID 176 -2.02-110.246 -10.8026 -1 GRID 177 0.246 0.246 -10.8026 -1 GRID 178 0.246 2.745-28-11.1027 -1 GRID 179 -2.21-110.0 -11.1027 -1 GRID 180 -2.07-110.246 -11.1027 -1 GRID 181 0.246 0.246 -11.1027 -1 GRID 182 0.246 2.777-28-11.4028 -1 GRID 183 -2.27-110.0 -11.4028 -1 GRID 184 -2.13-110.246 -11.4028 -1 GRID 185 0.246 0.246 -11.4028 -1 GRID 186 0.246 2.84-28 -11.7029 -1 GRID 187 -2.33-110.0 -11.7029 -1 GRID 188 -2.19-110.246 -11.7029 -1 GRID 189 0.246 0.246 -11.7029 -1 GRID 190 0.246 2.871-28-12.0029 -1 GRID 191 -2.39-110.0 -12.0029 -1 GRID 192 -2.24-110.246 -12.0029 -1 GRID 193 0.246 0.246 -12.0029 -1 GRID 194 0.246 2.935-28-12.303 -1 GRID 195 -2.45-110.0 -12.303 -1 GRID 196 -2.3-11 0.246 -12.303 -1 GRID 197 0.246 0.246 -12.303 -1 GRID 198 0.246 2.966-28-12.6031 -1 GRID 199 -2.51-110.0 -12.6031 -1 GRID 200 -2.35-110.246 -12.6031 -1 GRID 201 0.246 0.246 -12.6031 -1 GRID 522 0.246 2.935-28-12.903 -1 GRID 523 -7.36-110.0 -12.903 -1 GRID 524 -6.9-11 0.246 -12.903 -1 GRID 525 0.246 0.246 -12.903 -1 GRID 526 0.246 2.903-28-13.2031 -1 GRID 527 -7.42-110.0 -13.2031 -1 GRID 528 -6.95-110.246 -13.2031 -1 GRID 529 0.246 0.246 -13.2031 -1 GRID 530 0.246 2.84-28 -13.5032 -1 GRID 531 -7.48-110.0 -13.5032 -1 GRID 532 -7.01-110.246 -13.5032 -1 GRID 533 0.246 0.246 -13.5032 -1 GRID 534 0.246 2.777-28-13.8032 -1 GRID 535 -7.54-110.0 -13.8032 -1 GRID 536 -7.06-110.246 -13.8032 -1 GRID 537 0.246 0.246 -13.8032 -1 GRID 538 0.246 2.745-28-14.1033 -1 GRID 539 -7.6-11 0.0 -14.1033 -1



GRID 540 -7.12-110.246 -14.1033 -1 GRID 541 0.246 0.246 -14.1033 -1 GRID 542 0.246 2.682-28-14.4034 -1 GRID 543 -7.67-110.0 -14.4034 -1 GRID 544 -7.19-110.246 -14.4034 -1 GRID 545 0.246 0.246 -14.4034 -1 GRID 546 0.246 2.619-28-14.7034 -1 GRID 547 -7.73-110.0 -14.7034 -1 GRID 548 -7.24-110.246 -14.7034 -1 GRID 549 0.246 0.246 -14.7034 -1 GRID 550 0.246 2.587-28-15.0035 -1 GRID 551 -7.78-110.0 -15.0035 -1 GRID 552 -7.3-11 0.246 -15.0035 -1 GRID 553 0.246 0.246 -15.0035 -1 GRID 554 0.246 2.524-28-15.3036 -1 GRID 555 -7.84-110.0 -15.3036 -1 GRID 556 -7.35-110.246 -15.3036 -1 GRID 557 0.246 0.246 -15.3036 -1 GRID 558 0.246 2.461-28-15.6037 -1 GRID 559 -7.9-11 0.0 -15.6037 -1 GRID 560 -7.41-110.246 -15.6037 -1 GRID 561 0.246 0.246 -15.6037 -1 GRID 562 0.246 2.398-28-15.9037 -1 GRID 563 -7.96-110.0 -15.9037 -1 GRID 564 -7.47-110.246 -15.9037 -1 GRID 565 0.246 0.246 -15.9037 -1 GRID 566 0.246 2.335-28-16.2038 -1 GRID 567 -8.02-110.0 -16.2038 -1 GRID 568 -7.52-110.246 -16.2038 -1 GRID 569 0.246 0.246 -16.2038 -1 GRID 570 0.246 2.272-28-16.5039 -1 GRID 571 -8.08-110.0 -16.5039 -1 GRID 572 -7.58-110.246 -16.5039 -1 GRID 573 0.246 0.246 -16.5039 -1 GRID 574 0.246 2.209-28-16.804 -1 GRID 575 -8.14-110.0 -16.804 -1 GRID 576 -7.63-110.246 -16.804 -1 GRID 577 0.246 0.246 -16.804 -1 GRID 578 0.246 2.146-28-17.104 -1 GRID 579 -8.2-11 0.0 -17.104 -1 GRID 580 -7.69-110.246 -17.104 -1 GRID 581 0.246 0.246 -17.104 -1 GRID 582 0.246 2.083-28-17.4041 -1 GRID 583 -8.26-110.0 -17.4041 -1 GRID 584 -7.75-110.246 -17.4041 -1 GRID 585 0.246 0.246 -17.4041 -1 GRID 586 0.246 2.019-28-17.7042 -1 GRID 587 -8.32-110.0 -17.7042 -1 GRID 588 -7.8-11 0.246 -17.7042 -1 GRID 589 0.246 0.246 -17.7042 -1 GRID 590 0.246 1.956-28-18.0042 -1 GRID 591 -8.38-110.0 -18.0042 -1 GRID 592 -7.86-110.246 -18.0042 -1 GRID 593 0.246 0.246 -18.0042 -1 GRID 594 0.246 1.893-28-18.3043 -1 GRID 595 -8.44-110.0 -18.3043 -1 GRID 596 -7.91-110.246 -18.3043 -1 GRID 597 0.246 0.246 -18.3043 -1 GRID 598 0.246 1.83-28 -18.6044 -1 GRID 599 -8.5-11 0.0 -18.6044 -1 GRID 600 -7.97-110.246 -18.6044 -1 GRID 601 0.246 0.246 -18.6044 -1 GRID 602 0.246 1.735-28-18.9045 -1 GRID 603 -8.56-110.0 -18.9045 -1 GRID 604 -8.03-110.246 -18.9045 -1 GRID 605 0.246 0.246 -18.9045 -1 GRID 606 0.246 1.672-28-19.2045 -1 GRID 607 -8.62-110.0 -19.2045 -1 GRID 608 -8.08-110.246 -19.2045 -1 GRID 609 0.246 0.246 -19.2045 -1



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GRID 3510 0.246 -0.246 -5.10124 -1 GRID 3511 0.492 -0.246 -5.10124 -1 GRID 3512 0.246 -0.246 -5.40132 -1 GRID 3513 0.492 -0.246 -5.40132 -1 GRID 3514 0.246 -0.246 -5.70139 -1 GRID 3515 0.492 -0.246 -5.70139 -1 GRID 3516 0.246 -0.246 -6.00146 -1 GRID 3517 0.492 -0.246 -6.00146 -1 GRID 3518 0.246 -0.246 -6.30154 -1 GRID 3519 0.492 -0.246 -6.30154 -1 GRID 3520 0.246 -0.246 -6.60161 -1 GRID 3521 0.492 -0.246 -6.60161 -1 GRID 3522 0.246 -0.246 -6.90168 -1 GRID 3523 0.492 -0.246 -6.90168 -1 GRID 3524 0.246 -0.246 -7.20176 -1 GRID 3525 0.492 -0.246 -7.20176 -1 GRID 3526 0.246 -0.246 -7.50183 -1 GRID 3527 0.492 -0.246 -7.50183 -1 GRID 3528 0.246 -0.246 -7.8019 -1 GRID 3529 0.492 -0.246 -7.8019 -1 GRID 3530 0.246 -0.246 -8.10198 -1 GRID 3531 0.492 -0.246 -8.10198 -1 GRID 3532 0.246 -0.246 -8.40205 -1 GRID 3533 0.492 -0.246 -8.40205 -1 GRID 3534 0.246 -0.246 -8.70212 -1 GRID 3535 0.492 -0.246 -8.70212 -1 GRID 3536 0.246 -0.246 -9.0022 -1 GRID 3537 0.492 -0.246 -9.0022 -1 GRID 3538 0.246 -0.246 -9.30227 -1 GRID 3539 0.492 -0.246 -9.30227 -1 GRID 3540 0.246 -0.246 -9.60234 -1 GRID 3541 0.492 -0.246 -9.60234 -1 GRID 3542 0.246 -0.246 -9.90241 -1 GRID 3543 0.492 -0.246 -9.90242 -1 GRID 3544 0.246 -0.246 -10.2025 -1 GRID 3545 0.492 -0.246 -10.2025 -1 GRID 3546 0.246 -0.246 -10.5026 -1 GRID 3547 0.492 -0.246 -10.5026 -1 GRID 3548 0.246 -0.246 -10.8026 -1 GRID 3549 0.492 -0.246 -10.8026 -1 GRID 3550 0.246 -0.246 -11.1027 -1 GRID 3551 0.492 -0.246 -11.1027 -1 GRID 3552 0.246 -0.246 -11.4028 -1 GRID 3553 0.492 -0.246 -11.4028 -1 GRID 3554 0.246 -0.246 -11.7029 -1 GRID 3555 0.492 -0.246 -11.7029 -1 GRID 3556 0.246 -0.246 -12.0029 -1 GRID 3557 0.492 -0.246 -12.0029 -1 GRID 3558 0.246 -0.246 -12.303 -1 GRID 3559 0.492 -0.246 -12.303 -1 GRID 3560 0.246 -0.246 -12.6031 -1 GRID 3561 0.492 -0.246 -12.6031 -1 GRID 3722 0.246 -0.246 -12.903 -1 GRID 3723 0.492 -0.246 -12.903 -1 GRID 3724 0.246 -0.246 -13.2031 -1 GRID 3725 0.492 -0.246 -13.2031 -1 GRID 3726 0.246 -0.246 -13.5032 -1 GRID 3727 0.492 -0.246 -13.5032 -1 GRID 3728 0.246 -0.246 -13.8032 -1 GRID 3729 0.492 -0.246 -13.8032 -1 GRID 3730 0.246 -0.246 -14.1033 -1 GRID 3731 0.492 -0.246 -14.1033 -1 GRID 3732 0.246 -0.246 -14.4034 -1 GRID 3733 0.492 -0.246 -14.4034 -1 GRID 3734 0.246 -0.246 -14.7034 -1 GRID 3735 0.492 -0.246 -14.7034 -1 GRID 3736 0.246 -0.246 -15.0035 -1 GRID 3737 0.492 -0.246 -15.0035 -1 GRID 3738 0.246 -0.246 -15.3036 -1 GRID 3739 0.492 -0.246 -15.3036 -1



GRID 3740 0.246 -0.246 -15.6037 -1 GRID 3741 0.492 -0.246 -15.6037 -1 GRID 3742 0.246 -0.246 -15.9037 -1 GRID 3743 0.492 -0.246 -15.9037 -1 GRID 3744 0.246 -0.246 -16.2038 -1 GRID 3745 0.492 -0.246 -16.2038 -1 GRID 3746 0.246 -0.246 -16.5039 -1 GRID 3747 0.492 -0.246 -16.5039 -1 GRID 3748 0.246 -0.246 -16.804 -1 GRID 3749 0.492 -0.246 -16.804 -1 GRID 3750 0.246 -0.246 -17.104 -1 GRID 3751 0.492 -0.246 -17.104 -1 GRID 3752 0.246 -0.246 -17.4041 -1 GRID 3753 0.492 -0.246 -17.4041 -1 GRID 3754 0.246 -0.246 -17.7042 -1 GRID 3755 0.492 -0.246 -17.7042 -1 GRID 3756 0.246 -0.246 -18.0042 -1 GRID 3757 0.492 -0.246 -18.0042 -1 GRID 3758 0.246 -0.246 -18.3043 -1 GRID 3759 0.492 -0.246 -18.3043 -1 GRID 3760 0.246 -0.246 -18.6044 -1 GRID 3761 0.492 -0.246 -18.6044 -1 GRID 3762 0.246 -0.246 -18.9045 -1 GRID 3763 0.492 -0.246 -18.9045 -1 GRID 3764 0.246 -0.246 -19.2045 -1 GRID 3765 0.492 -0.246 -19.2045 -1 GRID 3766 0.246 -0.246 -19.5046 -1 GRID 3767 0.492 -0.246 -19.5046 -1 GRID 3768 0.246 -0.246 -19.8047 -1 GRID 3769 0.492 -0.246 -19.8047 -1 GRID 3770 0.246 -0.246 -20.1048 -1 GRID 3771 0.492 -0.246 -20.1048 -1 GRID 3772 0.246 -0.246 -20.4048 -1 GRID 3773 0.492 -0.246 -20.4048 -1 GRID 3774 0.246 -0.246 -20.7049 -1 GRID 3775 0.492 -0.246 -20.7049 -1 GRID 3776 0.246 -0.246 -21.005 -1 GRID 3777 0.492 -0.246 -21.005 -1 GRID 3778 0.246 -0.246 -21.3051 -1 GRID 3779 0.492 -0.246 -21.3051 -1 GRID 3780 0.246 -0.246 -21.6051 -1 GRID 3781 0.492 -0.246 -21.6051 -1 GRID 3782 0.246 -0.246 -21.9052 -1 GRID 3783 0.492 -0.246 -21.9052 -1 GRID 3784 0.246 -0.246 -22.2053 -1 GRID 3785 0.492 -0.246 -22.2053 -1 GRID 3786 0.246 -0.246 -22.5053 -1 GRID 3787 0.492 -0.246 -22.5053 -1 GRID 3788 0.246 -0.246 -22.8054 -1 GRID 3789 0.492 -0.246 -22.8054 -1 GRID 3790 0.246 -0.246 -23.1055 -1 GRID 3791 0.492 -0.246 -23.1055 -1 GRID 3792 0.246 -0.246 -23.4056 -1 GRID 3793 0.492 -0.246 -23.4056 -1 GRID 3794 0.246 -0.246 -23.7056 -1 GRID 3795 0.492 -0.246 -23.7056 -1 GRID 3796 0.246 -0.246 -24.0057 -1 GRID 3797 0.492 -0.246 -24.0057 -1 GRID 3798 0.246 -0.246 -24.3058 -1 GRID 3799 0.492 -0.246 -24.3058 -1 GRID 3800 0.246 -0.246 -24.6059 -1 GRID 3801 0.492 -0.246 -24.6059 -1 GRID 3802 0.246 -0.246 -24.9059 -1 GRID 3803 0.492 -0.246 -24.9059 -1 GRID 3804 0.246 -0.246 -25.206 -1 GRID 3805 0.492 -0.246 -25.206 -1 GRID 3806 0.246 -0.492 -.300073 -1 GRID 3807 0.492 -0.492 -.300074 -1 GRID 3808 0.246 -0.492 -.600146 -1 GRID 3809 0.492 -0.492 -.600146 -1



GRID 4110 0.246 -0.492 -21.9052 -1 GRID 4111 0.492 -0.492 -21.9052 -1 GRID 4112 0.246 -0.492 -22.2053 -1 GRID 4113 0.492 -0.492 -22.2053 -1 GRID 4114 0.246 -0.492 -22.5053 -1 GRID 4115 0.492 -0.492 -22.5053 -1 GRID 4116 0.246 -0.492 -22.8054 -1 GRID 4117 0.492 -0.492 -22.8054 -1 GRID 4118 0.246 -0.492 -23.1055 -1 GRID 4119 0.492 -0.492 -23.1055 -1 GRID 4120 0.246 -0.492 -23.4056 -1 GRID 4121 0.492 -0.492 -23.4056 -1 GRID 4122 0.246 -0.492 -23.7056 -1 GRID 4123 0.492 -0.492 -23.7056 -1 GRID 4124 0.246 -0.492 -24.0057 -1 GRID 4125 0.492 -0.492 -24.0057 -1 GRID 4126 0.246 -0.492 -24.3058 -1 GRID 4127 0.492 -0.492 -24.3058 -1 GRID 4128 0.246 -0.492 -24.6059 -1 GRID 4129 0.492 -0.492 -24.6059 -1 GRID 4130 0.246 -0.492 -24.9059 -1 GRID 4131 0.492 -0.492 -24.9059 -1 GRID 4132 0.246 -0.492 -25.206 -1 GRID 4133 0.492 -0.492 -25.206 -1 GRID 6776 -0.246 -0.246 8.589-16 GRID 6777 0.246 -0.246 -8.59-16 GRID 6778 0.0 -0.246 0.0 GRID 6779 -0.492 -0.246 1.718-15 GRID 6780 -0.492 -0.492 1.718-15 GRID 6781 -0.246 -0.492 8.589-16 GRID 6782 0.0 -0.492 0.0 GRID 6783 0.246 -0.492 -8.59-16 GRID 6784 0.492 -0.492 -1.72-15 GRID 6785 0.492 -0.246 -1.72-15 GRID 6786 0.246 0.246 -8.59-16 GRID 6787 -0.246 0.246 8.589-16 GRID 6788 0.0 0.246 0.0 GRID 6789 0.492 0.246 -1.72-15 GRID 6790 0.492 0.492 -1.72-15 GRID 6791 0.246 0.492 -8.59-16 GRID 6792 0.0 0.492 0.0 GRID 6793 -0.246 0.492 8.589-16 GRID 6794 -0.492 0.492 1.718-15 GRID 6795 -0.492 0.246 1.718-15 GRID 6796 -0.492 0.0 1.718-15 GRID 6797 -0.246 0.0 8.589-16 GRID 6798 0.0 0.0 0.0 GRID 6799 0.246 0.0 -8.59-16 GRID 6800 0.492 0.0 -1.72-15 $$$$ SPOINT Data$$$$ CQUAD4 Elements$CQUAD4 5627 1 6778 6798 6799 6777 CQUAD4 5629 1 6782 6778 6777 6783 CQUAD4 6116 1 6777 6799 6800 6785 CQUAD4 6122 1 6783 6777 6785 6784 CQUAD4 6125 1 6799 6798 6788 6786 CQUAD4 6520 1 6779 6796 6797 6776 CQUAD4 6521 1 6776 6797 6798 6778 CQUAD4 6523 1 6780 6779 6776 6781 CQUAD4 6528 1 6781 6776 6778 6782 CQUAD4 6954 1 6797 6796 6795 6787 CQUAD4 7220 1 6788 6787 6793 6792 CQUAD4 7647 1 6787 6795 6794 6793 CQUAD4 7652 1 6798 6797 6787 6788 CQUAD4 7945 1 6786 6788 6792 6791 CQUAD4 7948 1 6789 6786 6791 6790



CQUAD4 7955 1 6800 6799 6786 6789 $$HMMOVE 5$ 5627 5629 6116 6122 6125 6520THRU 6521 6523$ 6528 6954 7220 7647 7652 7945 7948 7955$ $$ CHEXA Elements: First Order$ CHEXA 17 2 10 11 21 23 34 35+ 36 37CHEXA 18 2 34 35 36 37 38 39+ 40 41CHEXA 19 2 38 39 40 41 42 43+ 44 45CHEXA 20 2 42 43 44 45 46 47+ 48 49CHEXA 21 2 46 47 48 49 50 51+ 52 53CHEXA 22 2 50 51 52 53 54 55+ 56 57CHEXA 23 2 54 55 56 57 58 59+ 60 61CHEXA 24 2 58 59 60 61 62 63+ 64 65CHEXA 25 2 62 63 64 65 66 67+ 68 69CHEXA 26 2 66 67 68 69 70 71+ 72 73CHEXA 27 2 70 71 72 73 74 75+ 76 77CHEXA 28 2 74 75 76 77 78 79+ 80 81CHEXA 29 2 78 79 80 81 82 83+ 84 85CHEXA 30 2 82 83 84 85 86 87+ 88 89CHEXA 31 2 86 87 88 89 90 91+ 92 93CHEXA 32 2 90 91 92 93 94 95+ 96 97CHEXA 33 2 94 95 96 97 98 99+ 100 101CHEXA 34 2 98 99 100 101 102 103+ 104 105CHEXA 35 2 102 103 104 105 106 107+ 108 109CHEXA 36 2 106 107 108 109 110 111+ 112 113CHEXA 37 2 110 111 112 113 114 115+ 116 117CHEXA 38 2 114 115 116 117 118 119+ 120 121CHEXA 39 2 118 119 120 121 122 123+ 124 125CHEXA 40 2 122 123 124 125 126 127+ 128 129CHEXA 41 2 126 127 128 129 130 131+ 132 133CHEXA 42 2 130 131 132 133 134 135+ 136 137CHEXA 43 2 134 135 136 137 138 139+ 140 141CHEXA 44 2 138 139 140 141 142 143+ 144 145CHEXA 45 2 142 143 144 145 146 147+ 148 149CHEXA 46 2 146 147 148 149 150 151+ 152 153CHEXA 47 2 150 151 152 153 154 155



+ 156 157CHEXA 48 2 154 155 156 157 158 159+ 160 161CHEXA 49 2 158 159 160 161 162 163+ 164 165CHEXA 50 2 162 163 164 165 166 167+ 168 169CHEXA 51 2 166 167 168 169 170 171+ 172 173CHEXA 52 2 170 171 172 173 174 175+ 176 177CHEXA 53 2 174 175 176 177 178 179+ 180 181CHEXA 54 2 178 179 180 181 182 183+ 184 185CHEXA 55 2 182 183 184 185 186 187+ 188 189CHEXA 56 2 186 187 188 189 190 191+ 192 193CHEXA 57 2 190 191 192 193 194 195+ 196 197CHEXA 58 2 194 195 196 197 198 199+ 200 201CHEXA 139 2 198 199 200 201 522 523+ 524 525CHEXA 140 2 522 523 524 525 526 527+ 528 529CHEXA 141 2 526 527 528 529 530 531+ 532 533CHEXA 142 2 530 531 532 533 534 535+ 536 537CHEXA 143 2 534 535 536 537 538 539+ 540 541CHEXA 144 2 538 539 540 541 542 543+ 544 545CHEXA 145 2 542 543 544 545 546 547+ 548 549CHEXA 146 2 546 547 548 549 550 551+ 552 553CHEXA 147 2 550 551 552 553 554 555+ 556 557CHEXA 148 2 554 555 556 557 558 559+ 560 561CHEXA 149 2 558 559 560 561 562 563+ 564 565CHEXA 150 2 562 563 564 565 566 567+ 568 569CHEXA 151 2 566 567 568 569 570 571+ 572 573CHEXA 152 2 570 571 572 573 574 575+ 576 577CHEXA 153 2 574 575 576 577 578 579+ 580 581CHEXA 154 2 578 579 580 581 582 583+ 584 585CHEXA 155 2 582 583 584 585 586 587+ 588 589CHEXA 156 2 586 587 588 589 590 591+ 592 593CHEXA 157 2 590 591 592 593 594 595+ 596 597CHEXA 158 2 594 595 596 597 598 599+ 600 601CHEXA 159 2 598 599 600 601 602 603+ 604 605CHEXA 160 2 602 603 604 605 606 607+ 608 609CHEXA 161 2 606 607 608 609 610 611+ 612 613CHEXA 162 2 610 611 612 613 614 615



+ 3768 4096CHEXA 2623 2 3277 2785 3768 4096 3279 2787+ 3770 4098CHEXA 2624 2 3279 2787 3770 4098 3281 2789+ 3772 4100CHEXA 2625 2 3281 2789 3772 4100 3283 2791+ 3774 4102CHEXA 2626 2 3283 2791 3774 4102 3285 2793+ 3776 4104CHEXA 2627 2 3285 2793 3776 4104 3287 2795+ 3778 4106CHEXA 2628 2 3287 2795 3778 4106 3289 2797+ 3780 4108CHEXA 2629 2 3289 2797 3780 4108 3291 2799+ 3782 4110CHEXA 2630 2 3291 2799 3782 4110 3293 2801+ 3784 4112CHEXA 2631 2 3293 2801 3784 4112 3295 2803+ 3786 4114CHEXA 2632 2 3295 2803 3786 4114 3297 2805+ 3788 4116CHEXA 2633 2 3297 2805 3788 4116 3299 2807+ 3790 4118CHEXA 2634 2 3299 2807 3790 4118 3301 2809+ 3792 4120CHEXA 2635 2 3301 2809 3792 4120 3303 2811+ 3794 4122CHEXA 2636 2 3303 2811 3794 4122 3305 2813+ 3796 4124CHEXA 2637 2 3305 2813 3796 4124 3307 2815+ 3798 4126CHEXA 2638 2 3307 2815 3798 4126 3309 2817+ 3800 4128CHEXA 2639 2 3309 2817 3800 4128 3311 2819+ 3802 4130CHEXA 2640 2 3311 2819 3802 4130 3313 2821+ 3804 4132$$HMMOVE 2$ 17THRU 58 139THRU 222 303THRU 386$ 467THRU 550 631THRU 714 795THRU 878$ 959THRU 1042 1123THRU 1206 1287THRU 1370$ 1451THRU 1534 1615THRU 1698 1779THRU 1862$ 1943THRU 2026 2107THRU 2190 2271THRU 2354$ 2435THRU 2518 2599THRU 2640$ $$$$------------------------------------------------------------------------------$$$ HyperMesh name and color information for generic components $$$------------------------------------------------------------------------------$$HMNAME COMP 2"Air" 2 "Air" 5 $HWCOLOR COMP 2 5$$HMNAME COMP 5"Piston" $HWCOLOR COMP 5 8$$HMNAME COMP 6"absorber" $HWCOLOR COMP 6 3$$$HMDPRP $ 17THRU 58 139THRU 222 303THRU 386$ 467THRU 550 631THRU 714 795THRU 878$ 959THRU 1042 1123THRU 1206 1287THRU 1370$ 1451THRU 1534 1615THRU 1698 1779THRU 1862$ 1943THRU 2026 2107THRU 2190 2271THRU 2354$ 2435THRU 2518 2599THRU 2640 5627 5629 6116$ 6122 6125 6520THRU 6521 6523 6528 6954 7220$ 7647 7652 7945 7948 7955$



$$$$$ PSHELL Data$$$ $ $ $ $ $ $ $HMNAME PROP 1"tube" 4$HWCOLOR PROP 1 52PSHELL 1 20.1 2 2 0.0 $$$$ PSOLID Data$$$HMNAME PROP 2"Air" 5$HWCOLOR PROP 2 4PSOLID 2 1 PFLUID$$$$ MAT1 Data$$$HMNAME MAT 2"alum" "MAT1"$HWCOLOR MAT 2 3MAT1 21.0+7 0.3 0.000254 $$$$ MAT10 Data$HMNAME MAT 1"Air" "MAT10"$HWCOLOR MAT 1 3MAT10 1 1.21-7 13000.0 $$$$------------------------------------------------------------------------------$$$ HyperMesh Commands for loadcollectors name and color information $$$------------------------------------------------------------------------------$$HMNAME LOADCOL 2"spc"$HWCOLOR LOADCOL 2 6$$$HMNAME LOADCOL 8"Force"$HWCOLOR LOADCOL 8 7$$$HMNAME LOADCOL 12"SPC"$HWCOLOR LOADCOL 12 5$$$$$$ FREQi cards$$$HMNAME LOADCOL 3"Freq"$HWCOLOR LOADCOL 3 6$FREQ1 3 0.0 5.0 600FREQ 3480.$$$$$ RLOAD1 cards$$$HMNAME LOADCOL 6"Rload"$HWCOLOR LOADCOL 6 6RLOAD1 6 8 7 0 VELO$$$$$$ TABLED1 cards$$$HMNAME LOADCOL 7"Table"$HWCOLOR LOADCOL 7 6TABLED1 7 LINEAR LINEAR+ 0.0 1.0 3000.0 1.0ENDT $$$HMNAME LOADCOL 10"reactance"



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CAABSF 7985 5 2821 687 2162 2820 CAABSF 7988 5 2820 2162 2163 2985 CAABSF 7990 5 3313 2821 2820 3312 CAABSF 7994 5 3312 2820 2985 3477 CAABSF 7996 5 3805 1016 686 3804 CAABSF 7998 5 3804 686 687 2821 CAABSF 8003 5 4132 3804 2821 3313 PAABSF 5 11 10 ENDDATA$$$$------------------------------------------------------------------------------$$$$ Data Definition for AutoDV $$$$------------------------------------------------------------------------------$$$$$$-----------------------------------------------------------------------------$$$$ Design Variables Card for Control Perturbations $$$$-----------------------------------------------------------------------------$$$$------------------------------------------------------------------------------$$ Domain Element Definitions $$------------------------------------------------------------------------------$$$$$------------------------------------------------------------------------------$$$$ Nodeset Definitions $$$$------------------------------------------------------------------------------$$$$ Design domain node sets$$$$------------------------------------------------------------------------------$$$$ Control Perturbation $$$$------------------------------------------------------------------------------$$$$$$$$ CONTROL PERTURBATION Data$$

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Radiated Sound Analysis

Radiated Sound Output

Radiated Sound Output can be requested for grid points on the structural surface and in theexterior acoustic field. Grid points are used to represent microphones to record the radiatedsound, sound power, and sound intensity.

Guide for Requesting Radiated Sound Output

The following procedure can be considered as a guide for requesting radiated soundoutput:

1. Microphones that record sound levels in the acoustic field can be defined as grid pointsets using the RADSND (MSET field) bulk data entry.

2. PANELG (TYPE=SOUND/Blank) can be used to define the sound generating panel(s)which are to be considered for radiated sound output calculations.

3. The PANEL continuation line in the RADSND bulk data entry can be used to list thepanel ID’s of the panels defined using PANELG (TYPE=SOUND/Blank). This allows thedefinition of the sound generating panels that contribute to the calculation of radiatedsound output at the microphones (Grid points) listed in the MSET field of the RADSNDbulk data entry.

4. The value of the speed of sound “c” required to define the wave number and the

complex particle velocity vector is input using PARAM, SPLC. The density of the acousticmedium “e” used in the calculation of the complex acoustic sound pressure and thecomplex particle velocity vector is defined using PARAM, SPLRHO. An additional scalefactor “q” can be specified using PARAM, SPLFAC in the Sound Pressure Levelcalculation.

5. Various outputs can be requested for this analysis. SPOWER output request can beused to request sound power, SINTENS can be used to request sound intensity and SPLcan be used to request sound pressure.



Figure 1: Radiated sound output from a panel.

The set up guide for radiated sound output calculation is described in the previous section.The procedure is based on the following set of equations for the calculation of each outputtype.

Analytical Background for Radiated Sound Output

The sound radiated from the sound generating panel is reduced to sound generation fromdiscrete point sources. The grid points of the finite element mesh on the surface of the panelare considered as sound sources. Sound power and sound intensity can be requested forboth the source grids and the microphone grids.

At the Microphone Location

Wave Number

The wave number, k is defined as follows:

2 fk

c

Where,

c is the speed of sound defined by PARAM, SPLC.

f is the frequency of the sound wave in the medium.



Velocity Flux of the Source Grid

The velocity flux of the source grid is the rate at which panel material in an infinitesimalarea surrounding the grid point moves through the medium.

Figure 2: Defining the Velocity Flux

For each frequency, it is calculated as follows:

uuurflux f V f AV

Where,

is the velocity vector of the source grid.

is the area vector associated with the source grid defined as follows:

uuur rn s

A XA

Where,

A is the area associated with the source grid.

is the unit normal to the panel surface at the source grid (see Figure 2).

Complex Acoustic Sound Pressure (Requested using SPL)

The complex acoustic sound pressure is the deviation from the ambient atmospheric

pressure caused by a sound wave. This is denoted by and is defined as the sound

pressure deviation, due to a single sound panel grid j at the microphone location for each

frequency as follows:

Total Complex Acoustic Sound Pressure requested by SPL is:



Where,

is the frequency of the sound wave in the medium.

is the density of the acoustic medium defined by PARAM, SPLRHO.

rj is the distance from the acoustic source grid j on the panel to the microphone

location grid (see Figure 1).

is the velocity flux of the source grid.

k is the wave number as defined in Wave Number.

i is the square root of -1

np is the number of source grids (see Figure 1).

q is the value of the scale factor specified using the parameter PARAM, SPLFAC.

The Sound Pressure Level in decibels (SPLdB - Also requested using SPL) can be calculated

using the following equation:

1020.0* log ( )dB

SPLSPL

SPLREFDB

Where,

SPLdB is the Sound Pressure Level in decibels.

SPL is the magnitude of the acoustic sound pressure.

SPLREFDB is the reference sound pressure value specified using the parameter PARAM,

SPLREFDB

Complex Particle Velocity Vector

The complex particle velocity vector is the velocity of a particle in a medium measured as awave passes through it. The particle velocity is not the velocity of the wave itself; rather itis the velocity of a particle as it oscillates about a mean position, due to the passage of the

wave. It is denoted by at the location of the microphone, due to the source grid j(see Figure 1) and is defined for each frequency as follows:

ˆ( ) X) ( )( 1

uuurj j

j

j

pvp f i

fc kr



Where,

is the complex acoustic pressure, due to source grid, j at the microphone location.

is the unit vector from the source grid j to the microphone grid (see Figure 1).

X XX̂

X

r r

rj j

j

jjr


c is the speed of sound defined by PARAM, SPLC.


rj is the distance from the acoustic source grid j on the panel to the microphone grid

(see Figure 1).


Total Sound Power (Requested using SPOWER)

The total sound power is the rate of change of sound energy with time in the domain of

reference. The total sound power , due to all the source grids can be calculated at amicrophone location for each frequency as follows:

1

( ) ( ). ( )np

j jj

sp f real p f p f

Where,

is the acoustic pressure at a microphone location, due to the source grid "j".

is the complex conjugate of .


Total Complex Intensity Vector (Requested using SINTENS)

The total complex intensity vector is the sound power per unit area. The sound intensitycan be defined as a product of sound pressure and the particle velocity vector. For multiplesource grids, the total sound intensity at a microphone location for each frequency is givenas follows:

1

1( ) ( ).( ) ( )

2

uuuuruur np

j jj

iv pf real p f fv



Where,

is the acoustic pressure at the microphone location due to the sound generated at

the source grid "j".

is the complex conjugate of , which is the complex particle velocity

vector at the microphone location, due to the sound generated at the source grid "j".

At the Source Grid Location

Wave Number

The wave number is independent of the location of the grid points. Now define a set ofdisplacement vectors that relate source grids to one another. To do this, each source grid

is considered to be associated with an area (A) on the panel.

Figure 3: Displacement vectors at the source grids.

The vector addition operation for displacement vectors from Figure 3 is as follows:

uuur uur uuurrsX X X

Where,

is the vector from a source grid (1) to the source grid (2) of interest.

is defined as:

12

uuur rr n s

AX X

Where,

A is the area associated with a source grid.

is the unit normal to the area, A associated with a source grid.

Complex Acoustic Sound Pressure [at the source grid]

The complex acoustic sound pressure is the deviation from the ambient atmospheric



pressure caused by a sound wave. This is denoted using and is defined at thesource grid for each frequency as follows:

i ( )( ) ie

( )s jk r

s j flux js j

fp f V f

r

Total Complex Acoustic Sound Pressure at a source grid requested by SPL is:

( 1)i ( )

1

( ) ie( )

s j

npk r

s flux js

totalj j

fp f V f

r

Where,

is the frequency of the sound wave in the medium.


is equal to , for each grid, j (j=1 to np), the magnitude (length) of as defined

in At the Source Grid Location (see Figure 1).

is the velocity flux of the source grid, j (see Velocity Flux of the Source Grid)




q is the value of the scale factor specified using the parameter PARAM, SPLFAC.

Total Sound Power (Requested using SPOWER) [at the source grid]

The total sound power is the rate of change of sound energy with time in the domain of

reference. The total sound power , due to all the source grids can be calculated at asource grid of interest for each frequency as follows:

*( 1)

1

( ) (( ) ( . )) s j s j

np

sj

p f p fsp f real

Where,

is the acoustic pressure at a source grid, due to the source grid "j".

is the complex conjugate of .




Total Complex Intensity Vector (Requested using SINTENS) [at thesource grid]

The total complex intensity vector is the sound power per unit area. The sound intensitycan be defined as a product of sound pressure and the normal velocity vector. For multiple

source grids, the sound intensity for each frequency is given as follows:

( 1)

1

1( ) . ) ( )( ) ( ) (

2

uuuuur uuuurnp

sj

sj

s jiv p ff real pv f

Where,

is the acoustic pressure at the source grid location of interest, due to the

sound generated at the source grid "j".

is the complex conjugate of the normal velocity vector of thesource grid of interest.

Where the normal velocity vector of the source grid of interest is given as:

.r r

n n s n sj

V f V f X X

Refer to at the source grid location and velocity flux of the source grid sections for adescription of the terms.



Fatigue Analysis

Fatigue analysis, using S-N (stress-life), E-N (strain-life), and Dang Van Criterion (Factor ofSafety) approaches for predicting the life (number of loading cycles) of a structure undercyclical loading may be performed by using OptiStruct.

The stress-life method works well in predicting fatigue life when the stress level in thestructure falls mostly in the elastic range. Under such cyclical loading conditions, thestructure typically can withstand a large number of loading cycles; this is known as high-cycle fatigue. When the cyclical strains extend into plastic strain range, the fatigueendurance of the structure typically decreases significantly; this is characterized as low-cyclefatigue. The generally accepted transition point between high-cycle and low-cycle fatigue isaround 10,000 loading cycles. For low-cycle fatigue prediction, the strain-life (E-N) methodis applied, with plastic strains being considered as an important factor in the damagecalculation.

Sections of a model on which fatigue analysis is to be performed must be identified on a FATDEF bulk data entry. The appropriate FATDEF bulk data entry may be referenced from afatigue subcase definition through the FATDEF Subcase Information entry.

The Dang Van criterion is used to predict if a component will fail in its entire load history. Theconventional fatigue result that specifies the minimum fatigue cycles to failure is notapplicable in such cases. It is necessary to consider if any fatigue damage will occur duringthe entire load history of the component. If damage does occur, the component cannotexperience infinite life.

The Stress-Life (S-N) Approach

S-N Curve

The S-N curve, first developed by Wöhler, defines a relationship between stress and numberof cycles to failure. Typically, the S-N curve (and other fatigue properties) of a material isobtained from experiment; through fully reversed rotating bending tests. Due to the largeamount of scatter that usually accompanies test results, statistical characterization of thedata should also be provided (certainty of survival is used to modify the S-N curve accordingto the standard error of the curve and a higher reliability level requires a larger certainty ofsurvival).

Figure 1: S-N data from testing

When S-N testing data is presented in a log-log plot of alternating nominal stress amplitude



Sa or range SR versus cycles to failure N, the relationship between S and N can be described

by straight line segments. Normally, a one or two segment idealization is used.

Figure 2: One segment S-N curves in log-log scale

11

b

fS S Nfor segment 1 (1)

Where,

S is the nominal stress range

Nf are the fatigue cycles to failure

b1 is the first fatigue strength exponent

S1 is the fatigue strength coefficient

The S-N approach is based on elastic cyclic loading, inferring that the S-N curve should beconfined, on the life axis, to numbers greater than 1000 cycles. This ensures that nosignificant plasticity is occurring. This is commonly referred to as high-cycle fatigue.

S-N curve data is provided for a given material on a MATFAT bulk data entry. It is referencedthrough a Material ID (MID) which is shared by a structural material definition.

Damage Model

Palmgren-Miner's linear damage summation rule is used. Failure is predicted when:

1.0niDi Nif

(2)

Where,

Nif is the material’s fatigue life (number of cycles to failure) from its S-N curve at a

combination of stress amplitude and means stress level i



ni is the number of stress cycles at load level i

Di is the cumulative damage under ni load cycle

The linear damage summation rule does not take into account the effect of the load sequenceon the accumulation of damage due to cyclic fatigue loading. However, it has been proved towork well for many applications.

Cycle Counting

Cycle counting is used to extract discrete simple "equivalent" constant amplitude cycles froma random loading sequence. One way to understand “cycle counting” is as a changing stress-strain versus time signal. Cycle counting will count the number of stress-strain hysteresisloops and keep track of their range/mean or maximum/minimum values.

Rainflow cycle counting is the most widely used cycle counting method. It requires that thestress time history be rearranged so that it contains only the peaks and valleys and it startseither with the highest peak or the lowest valley (whichever is greater in absolutemagnitude). Then, three consecutive stress points (S1, S2, and S3) will define two

consecutive ranges as S1 = |S1 - S2| and S2 = |S2 - S3| . A cycle from S1 to S2 is only

extracted if S1 S2. Once a cycle is extracted, the two points forming the cycle are

discarded and the remaining points are connected to each other. This procedure is repeateduntil the remaining data points are exhausted.

Figure 3: Determine cycles using rainflow cycle counting method

Parameters affecting rainflow cycle counting may be defined on a FATPARM bulk data entry. The appropriate FATPARM bulk data entry may be referenced from a fatigue subcasedefinition through the FATPARM Subcase Information entry.

Equivalent Nominal Stress

Since S-N theory deals with uniaxial stress, the stress components need to be resolved intoone combined value for each calculation point, at each time step, and then used asequivalent nominal stress applied on the S-N curve.



Various stress combination types are available with the default being “Absolute maximumprinciple stress”. In general “Absolute maximum principle stress” is recommended for brittlematerials, while “Signed von Mises stress” is recommended for ductile material. The sign onthe signed parameters is taken from the sign of the Maximum Absolute Principal value.

Parameters affecting stress combination may be defined on a FATPARM bulk data entry. Theappropriate FATPARM bulk data entry may be referenced from a fatigue subcase definitionthrough the FATPARM Subcase Information entry.

Mean Stress Influence

Generally S-N curves are obtained from standard experiments with fully reversed cyclicloading. However, the real fatigue loading could not be fully reversed and the normal meanstresses have significant effect on fatigue performance of components. Tensile normal meanstresses are detrimental and compressive normal mean stresses are beneficial, in terms offatigue strength. Mean stress correction is used to take into account the effect of non-zeromean stresses.

The Gerber parabola and the Goodman line in Haigh's coordinates are widely used whenconsidering mean stress influence, and can be expressed as:

Gerber:

2

1

ae

m

u

SS

S

S(3)

Goodman:

1 m

u

ae

S

S

SS

(4)

Where,

Mean stress Sm = (Smax + Smin) / 2

Stress amplitude Sa = (Smax - Smin) / 2

Se is the stress range for fully reversed loading that is equivalent to the load case with a

stress range SR and a mean stress Sm

Su is ultimate strength

The Gerber method treats positive and negative mean stress correction in the same way thatmean stress always accelerates fatigue failure, while the Goodman method ignores thenegative means stress. Both methods give conservative result for compressive means stress. The Goodman method is recommended for brittle material while the Gerber method isrecommended for ductile material. For the Goodman method, if the tensile means stress isgreater than UTS, the damage will be greater than 1.0. For Gerber method, if the meanstress is greater than UTS, no matter tensile or compressive, the damage will be greater than1.0.



A Haigh diagram characterizes different combinations of stress amplitude and mean stress fora given number of cycles to failure.

Figure 4: Haigh diagram and mean stress correction methods

Parameters affecting mean stress influence may be defined on a FATPARM bulk data entry. The appropriate FATPARM bulk data entry may be referenced from a fatigue subcasedefinition through the FATPARM Subcase Information entry.

The Strain-Life (E-N) Approach

Monotonic Stress-Strain Behavior

Relative to the current configuration, the true stress and strain relationship can be definedas:

/P A (5)

(6)

Where, A is the current cross-section area, l is the current specimen length, l0 is the initial

specimen length, and and are the true stress and strain, respectively, Figure 5 showsthe monotonic stress-strain curve in true stress-strain space. In the whole process, thestress continues increasing to a large value until the specimen fails at C.



Figure 5: Monotonic stress-strain curve

The curve in Figure 5 is comprised of two typical segments, namely the elastic segment OAand plastic segment AC. The segment OA keeps the linear relationship between stress andelastic strain following Hooke Law:

eE(7)

Where, E is elastic modulus and e is elastic strain. The formula can also be rewritten as:

/e E(8)

by expressing elastic strain in terms of stress. For most of materials, the relationshipbetween the plastic strain and the stress can be represented by a simple power law of theform:

npK

(9)

Where, p is plastic strain, K is strength coefficient, and n is work hardening coefficient.

Similarly, the plastic strain can be expressed in terms of stress as:

1 n

p K(10)

The total strain induced by loading the specimen up to point B or D is the sum of plasticstrain and elastic strain:

1 n

e p E K(11)

Cyclic Stress-Strain Curve

Material exhibits different behavior under cyclic load compared with that of monotonic load. Generally, there are four kinds of response.



stable state

cyclically hardening

cyclically softening

softening or hardening depending on strain range

Which response will occur depends on its nature and initial condition of heat treatment. Figure 6 illustrates the effect of cyclic hardening and cyclic softening where the first twohysteresis loops of two different materials are plotted. In both cases, the strain isconstrained to change in fixed range, while the stress is allowed to change arbitrarily. If thestress range increases relative to the former cycle under fixed strain range, as shown in theupper part of Figure 6, it is called cyclic hardening; otherwise, it is called cyclic softening, asshown in the lower part of Figure 6. Cyclic response of material can also be described byspecifying the stress range and leaving strain unconstrained. If the strain range increasesrelative to the former cycle under fixed stress range, it is called cyclic softening; otherwise, itis called cyclic hardening. In fact, the cyclic behavior of material will reach a steady stateafter a short time which generally occupies less than 10 percent of the material total life. Through specifying different strain ranges, a series of hysteresis loops at steady state can beobtained. By placing these hysteresis loops in one coordinate system, as shown in Figure 7,the line connecting all the vertices of these hysteresis loops determine cyclic stress-straincurve which can be expressed in the similar form with monotonic stress-strain curve as:

Figure 6: Material cyclic response (a) Cyclic hardening; (b) Cyclic softening



Figure 7: Definition of stable stress-strain curve

1 '

'

n

e p E K(12)

Where, K' is cyclic strength coefficient, n' is strain cyclic hardening exponent.

Hysteresis Loop Shape

Bauschinger observed that after the initial load had caused plastic strain, load reversalcaused materials to exhibit anisotropic behavior. Based on experiment evidence, Massing putforward the hypothesis that a stress-strain hysteresis loop is geometrically similar to thecyclic stress strain curve, but with twice the magnitude. This implies that when the quantity

is two times of , the stress-strain cycle will lie on the hysteresis loop. This canbe expressed with formulas:

2 (13)

2 (14)

Expressing in terms of , in terms of , and substituting it into Eq. 12, thehysteresis loop formula can be deduced as:

1 '

22 '

n

E K(15)



Strain-Life Approach

Almost a century ago, Basquin observed the linear relationship between stress and fatiguelife in log scale when the stress is limited. He put forward the following fatigue formulacontrolled by stress:

' 2b

f fN(16)

Where, a is stress amplitude, fatigue strength coefficient, b fatigue strength exponent.

Later in the 1950s, Coffin and Manson independently proposed that plastic strain may also berelated with fatigue life by a simple power law:

' 2c

pa f fN(17)

Where, is plastic strain amplitude, fatigue ductility coefficient, c fatigue ductility

exponent. Morrow combined the work of Basquin, Coffin and Manson to consider both elasticstrain and plastic strain contribution to the fatigue life. He found out that the total strain hasmore direct correlation with fatigue life. By applying Hooke Law, Basquin rule can berewritten as:

'

2bfa

ea fNE E (18)

Where, is elastic strain amplitude. Total strain amplitude, which is the sum of the elasticstrain and plastic stain, therefore, can be described by applying Basquin formula and Coffin-Manson formula:

''2 2

b cfa ea pa f f fN N

E (19)

Where, is the total strain amplitude, the other variable is the same with above. Figure 8illustrates three methods in log scale in stress-life space. Two straight lines, which representBasquin formula and Coffin-Manson rule respectively, intersect at a point where elastic strainis equal to the plastic strain and the fatigue life predicted by the two methods is the same. The fatigue life at the intersection point is called transition life and can be calculated as:

1' '2 /

b c

t f fN E(20)

by combining Eq.17 and Eq.18, at the same time, applying the conditions:

ea pa (21)

ftN N(22)

Where, Nt is the transition life. When fatigue life is less than the transition life, plastic strain

plays the controlling role in life prediction; otherwise, elastic strain plays the key role.



Figure 8: Strain-life curve in log scale

Damage Accumulation Model

In the E-N approach, use the same damage accumulation model as the S-N approach, whichis Palmgren-Miner's linear damage summation rule.

Mean Stress Influence

The fatigue experiments carried out in the laboratory are always fully reversed, whereas inpractice, the mean stress is inevitable, thus the fatigue law established by the fully reversedexperiments must be corrected before applied to engineering problems. Morrow is the first toconsider the effect of mean stress through introducing the mean stress 0 in fatigue strength

coefficient by:

'0

2bf

ea fNE (23)

Thus the entire fatigue life formula becomes:

'0 '2 2

b cfa f f fN N

E (24)

Morrow's equation is consistent with the observation that mean stress effects are significantat low value of plastic strain and of little effect at high plastic strain.

Smith, Watson and Topper proposed a different method to account for the effect of meanstress by considering the maximum stress during one cycle (for convenience, this method iscalled SWT in the following). In this case, the damage parameter is modified as the productof the maximum stress and strain range in one cycle. For a fully reversed cycle, themaximum stress is given by:

'max 2

b

f fN(25)



By multiplying Eq.19 with Eq.25, it can be rewritten as:

' 2' '

max 2 2b b cf

a f f f fN NE (26)

The SWT method will predict that no damage will occur when the maximum stress is zero ornegative, which is not consistent with the reality.

When comparing the two methods, the SWT method predicted conservative life for loadspredominantly tensile, whereas, the Morrow approach provides more realistic results whenthe load is predominantly compressive.

Neuber Correction

Strain-life analysis is based on the fact that many critical locations such as notch roots havestress concentration, which will have obvious plastic deformation during the cyclic loadingbefore fatigue failure. Thus, the elastic-plastic strain results are essential for performingstrain-life analysis. Neuber correction is the most popular practice to correct elastic analysisresults into elastic-plastic results.

In order to derive the local stress from the nominal stress that is easier to obtain, the

concentration factors are introduced such as the local stress concentration factor K

, and

the local strain concentration factor K

.

/K S(27)

/K e(28)

Where, is the local stress, is the local strain, S is the nominal stress, and e is the nominal

strain. If nominal stress and local stress are both elastic, the local stress concentration factoris equal to the local strain concentration factor. However, if the plastic strain is present, the

relationship between K

and K

no long holds. Thereafter, focusing on this situation,Neuber introduced a theoretically elastic stress concentration factor Kt defined as:

2tK K K

(29)

Substitute Eq.27 and Eq.28 into Eq.29, the theoretical stress concentration factor Kt can be

rewritten as:

2tK

S e(30)

Through linear static FEA, the local stress instead of nominal stress is provided, which impliesthe effect of the geometry in Eq.30 is removed, thus you can set Kt as 1 and rewrite Eq.30

as:

e e (31)

Where, e , is locally elastic stress and locally elastic strain obtained from elastic analysis,

, the stress and strain at the presence of plastic strain. Both and can be calculated



from Eq.31 together with the equations for the cyclic stress-strain curve and hysteresis loop.

Dang Van Criterion (Factor of Safety)

The Dang Van criterion is used to predict if a component will fail in its entire load history. Incertain physical systems, components may be required to last infinitely long. For example,automobile components which undergo multiaxial cyclic loading at high rotational velocities(like propeller shafts) reach their high cycle fatigue limit within a short operating life. Theconventional fatigue result that specifies the minimum fatigue cycles to failure is notapplicable in such cases. It is not necessary to quantify the amount of fatigue damage, butjust to consider if any fatigue damage will occur during the entire load history of thecomponent. If damage does occur, the component cannot experience infinite life. Fatigueanalysis based on the Dang Van criterion is designed for this purpose.

Fatigue crack initiation usually occurs at zones of stress concentration such as geometricdiscontinuities, fillets, notches and so on. This phenomenon takes place in the microscopiclevel and is localized to certain regions like grains which have undergone local plasticdeformation in characteristic intra-crystalline bands. The Dang Van approach postulates afatigue criterion using microscopic variables in the apparent stabilization state; this is a stateof elastic shakedown if no damage occurs. The main principle of the criterion is that the usualcharacterization of the fatigue cycle is replaced by the local loading path and so damagingloads can be distinguished.

The general procedure of Dang Van fatigue analysis is:

1. Evaluate the macroscopic stresses ( )ij t

, for each location at a different point in time.

2. Split the macroscopic stress ( )ij t

into a hydrostatic part( )p t

and a deviatoric part( )ijS t

.

3. Calculate the stabilized microscopic residual stress *dev based on the following

equation:

*

2( ( ( ( ) )))ijdev Min Max J S t dev

The expression is minimized with respect to and maximized with respect to t.

4. Calculate the deviatoric part of microscopic stress.

*( ) ( )ij ijs t S t dev

5. Calculate factor of safety (FOS):

( ) ( )

bFOS Min

t ap t

( ) 0.5 ( ( ))ijt Tresca s t

Where, b and a are material constants.

If FOS is less than 1, the component cannot experience infinite life.



OptiStruct Factor of Safety setup

1. The torsion fatigue limit and hydrostatic stress sensitivity values required for an FOSanalysis can be set in the optional FOS continuation line on the MATFAT bulk data entry.

2. The Dang Van criterion type can be selected on the FATPARM bulk data entry.

3. Factor of Safety output can be requested using the FOS I/O options entry.

Other Factors Affecting Fatigue

Surface Condition (Finish and Treatment)

Surface condition is an extremely important factor influencing fatigue strength, as fatiguefailures nucleate at the surface. Surface finish and treatment factors are considered tocorrect the fatigue analysis results.

Surface finish correction factor Cfinish is used to characterize the roughness of the surface.

It's presented on diagrams that categorize finish by means of qualitative terms such aspolished, machined or forged.

Figure 9*: Surface finish correction factor for steels(* Source: Yung-Li Lee, Jwo. Pan, Richard B. Hathaway and Mark E. Barekey. Fatigue testing and analysis: Theoryand practice, Elsevier, 2005)

Surface treatment can improve the fatigue strength of components. NITRIDED, SHOT-PEENED, COLD-ROLLED are considered for surface treatment correction. It is also possible toinput a value to specify the surface treatment factor Ctreat.

In general cases, the total correction factor is Csur = Ctreat * Cfinish.

If treatment type is NITRIDED, then the total correction is Csur = 2.0 * Cfinish (Ctreat = 2.0).

If treatment type is SHOT-PEENED or COLD-ROLLED, then the total correction is Csur = 1.0.

It means you will ignore the effect of surface finish.

The fatigue endurance limit FL will be modified by Csur as: FL' = FL * Csur. For two segment

S-N curve, the stress at the transition point is also modified by multiplying by Csur.



Surface conditions may be defined on a PFAT bulk data entry. Surface conditions are thenassociated with sections of the model through the FATDEF bulk data entry.

Fatigue Strength Reduction Factor

In addition to the factors mentioned above, there are various others factors that could affectthe fatigue strength of a structure, e.g., notch effect, size effect, loading type. Fatiguestrength reduction factor Kf is introduced to account for the combined effect of all such

corrections. The fatigue endurance limit FL will be modified by Kf as: FL' = FL / Kf

The fatigue strength reduction factor may be defined on a PFAT bulk data entry. It may thenbe associated with sections of the model through the FATDEF bulk data entry.

If both Csur and Kf are specified, the fatigue endurance limit FL will be modified as: FL' = FL

* Csur / Kf.

Csur and Kf have similar influences on the E-N formula through its elastic part as on the S-N

formula. In the elastic part of the E-N formula, a nominal fatigue endurance limit FL iscalculated internally from the reversal limit of endurance Nc. FL will be corrected if Csur and

Kf are presented. The elastic part will be modified as well with the updated nominal fatigue

limit.

Setting Up a Fatigue Analysis

Linear Superposition of Multiple FEA/Load Time History Load Cases

When there are several load cases at the same time, all of which vary independently of oneanother, the principle of linear superposition will be used to combine all load cases togetherto determine the stress variation at each calculation point due to the combination of all loads. The formula is:

,

1 ,( ) ( )

nij k

ij kk FEA k

t P tP

(32)

Where,

n is the total number of load cases

Pk(t) and are, respectively, the time variation of the k-th load time history and the

total stress tensor

PFEA,k and are, respectively, the k-th load magnitude and stress tensor from FE

analysis

Load Time History Compression

This option is used to save calculation time. It will remove small cycles (defined by a gatevalue) and intermediate points.



Figure 10: Sample showing removal of small cycles

When removing small cycles, adjacent turning points, where the difference is less than themaximum range multiplied by relative gate value, will be removed from each channel. However, phase relationship will be maintained, when peaks and valleys occur on differentchannels at different times. This is shown by the sample above. In the first channel (top),the points at time 4 and 5 will be removed when the absolute gate equals one, while in thesecond channel (bottom), the points at time 1 and 2 will not be removed in order to keep thephase relationship between channels.

Figure 11: Sample showing removal of intermediate points

Removing intermediate points is another important mechanism to save computation time. Ifany point on the load-time history is neither a peak nor valley point, it will not contribute indetermining any stress cycle. Such points could be screened out in the fatigue computationwithout losing the accuracy, but the computation time could be saved significantly. Forexample, the left column in Fig 11 shows three load-time histories of three super-positioned



loadcases, respectively. After removing the intermediate points, the three load-time historiesare obtained as in the right column, which can produce the same fatigue results as the leftcolumn, but use much less time. This mechanism is built in OptiStruct and is effectiveautomatically.

Fatigue Loads, Events and Sequences

Fatigue loading is defined by scaling a static subcase with a load-time history.

A fatigue event consists of one or more static loadcases applied simultaneously in the sametime duration scaled by load-time histories. For fatigue events with more than one staticloadcase stress, linear superposition is used.

A fatigue sequence consists of a number of fatigue events and repeated instances of theseevents. A fatigue sequence can be made up of other sub fatigue sequences and/or fatigueevents. In this way, you can define very complex events and sequences for fatigue analysis.

In OptiStruct, fatigue sequences defined in fatigue subcases (referred by FATSEQ) are thebasic loading blocks. The fatigue life results of these fatigue subcases are calculated as thenumber of repeats of the loading block.

Below is an example of a "tree-like" fatigue sequence, which can be defined in OptiStruct,with FSEQ# identifying fatigue sequences and FEVN# identifying fatigue events:

Figure 12: Example of a "tree-like" fatigue sequence

Fatigue loading is defined by a FATLOAD bulk data entry, where a static subcase and a load-time history are associated.

A fatigue loading event is defined by a FATEVNT bulk data entry, where one or more fatigueloads (FATLOAD) are selected.

A fatigue loading sequence is defined by a FATSEQ bulk data entry, where a sequence of oneor more fatigue loading events or other fatigue loading sequences is given. The appropriateFATSEQ bulk data entry may be referenced from a fatigue subcase definition through the FATSEQ Subcase Information entry.



Multi-body Dynamics Simulation

A multi-body system is defined to be an assembly of sub-systems (bodies, components, orsub-structures). The motion of the sub-systems may be kinematically constrained and eachsub-system or component may undergo large translational and rotational displacements.

Bodies can be considered rigid or flexible. Rigid bodies do not undergo deformations. Rigidbody motion can be described completely by using six generalized coordinates. The resultingmathematical model is highly nonlinear. Neglecting the body deformations can lead toinaccurate results. Therefore, some of the bodies are considered flexible, that is they canundergo deformations. Modal reduction procedures are used to include flexible bodies inmulti-body dynamics simulations.

Joints, force elements, and controls connect the bodies. Initial velocities, forces, and motionsmay be applied to the system.

Different types of analysis can be performed on a multi-body system to determine itsbehavior under certain loading, applied motion, and initial velocity. Transient (kinematic,dynamic) analysis determines the response under time dependent loading. Static and quasi-static analyses determine the static equilibrium of a system. The multi-body solution isbased on an extended absolute coordinates formulation.

Multi-body system



This implementation is targeted at the typical finite-element user who wants to solve multi-body dynamics problems in the context of a finite element model, and is still somewhatlimited. HyperMesh is used for modeling. All geometry entities are defined in terms of afinite element mesh. Flexible body modeling is fully integrated.

HyperStudy can be used for optimization. Shape optimization of rigid and flexible bodies isavailable through the use of HyperMorph.



Transient Analysis for MBD

Transient analysis is used to calculate the response of a multi-body system to time-dependent loads and motions.

Forces and motions are time-dependent. Body initial conditions define the initial bodyvelocities, while joint initial conditions define the initial displacement of a particular joint.

The results of a transient analysis are displacements, velocities, accelerations, forces, as wellas modal contributions to stresses and strains in flexible bodies. The responses are usuallytime-dependent.

The equation of motion is given in the following form:

0

( )

( 0)

M q P t

q t v

&&

&

The matrix M is the mass matrix, the vector P is the vector of external forces, and the vector

q represents the generalized coordinates. Stiffness, damping, constraint forces, external

loads, and gravity are all included in the external force vector P. An initial and maximum

integration time step, an end time, and integrator tolerance need to be defined.

Two analyses, kinematic and dynamic, are defined depending on the degree of freedom ofthe system analysis.

A kinematic simulation is performed if all degrees of freedom are constrained throughappropriate joints and/or motions, making it a zero degree of freedom model. A kinematicssimulation finds a system configuration that satisfies all kinematic constraints and motionequations at any given time. The configuration is obtained by solving a system of nonlinearalgebraic equations representing constraints.

During a kinematic simulation, there is no need to integrate the differential equations ofmotion because the system configuration is fully determined by solving the constraint andmotion equations alone. Even though forces are not used to compute the kinematicssolution, joint reaction forces can be computed at any given time. The mass and inertiaproperties of bodies involved, and external forces acting on them, do not affect the resultantsystem configuration, but they do affect the joint reaction forces requested as outputs.

A dynamic simulation is employed whenever the model has one or more degrees of freedom. A dynamic simulation involves integrating the differential equations of motion subject tononlinear algebraic equations representing kinematics constraints. In other words, thesolution is obtained by solving a mixed system of differential-algebraic equations.

The resultant solution takes into account various dynamic effects and is dependent uponmass and inertia properties of bodies, damping within the system, and applied forces andmotions. Additional simulation parameters, such as the integration scheme, integration timestep, convergence tolerance, etc. could also affect the solution and; therefore, need to bespecified appropriately.

If a simulation type of transient is requested, the solver automatically determines whether torun a kinematic or dynamic solution from the degree of freedom.

The equation of motion is solved using one of the three different integrators that areavailable. The choice is based on the stiffness of the problem. A problem is stiff if thenumerical solution has its step size limited more severely by the stability of the numericaltechnique than by the accuracy of the technique. These are systems with high damping and



low transience.

VSTIFF (Default) – Implicit integrator that utilizes the Variable CoefficientDifferential Equation Solver (VODE). It is suited for stiff and non-stiffproblems.

MSTIFF – Implicit integrator that utilizes the Modified Extended BackwardDifferentiation Formula (MEBDF) to solve the nonlinear equations of motion. It is suited for stiff problems.

ABAM (Adams-Bashforth-Adams-Moulton) – Explicit integrator that uses afinite differences scheme to solve the nonlinear equations of motion. Thisintegrator is suitable for systems that are non-stiff.

A multi-body subcase needs to be defined in the input deck. Only one such subcase can beused in a model. The simulation type "transient" is defined on an MBSIM bulk data entrywhich must be referenced through a subcase statement MBSIM. The MBSIM bulk data entityalso defines the integrator, end time, and time step. A sequence of several simulations ofdifferent types can be defined by referring to an MBSEQ bulk data statement instead. Loadsand motions are referenced on MLOAD and MOTION subcase entries, respectively. Initialvelocity is referenced through INVEL. SPC type constraints in Multi-body Dynamics analysisare allowed only for MBD-ESL optimization of a flexible body if displacements are used asconstraints. Further information on loads and boundary conditions can be obtained from thesections Applied Forces and Motions and Initial Velocity.

The unit system for the simulation can be defined using a DTI, UNITS bulk data entry.



Static Analysis for MBD

A static simulation is also called an equilibrium simulation. The system must have at leastone degree of freedom to undergo a static simulation and an initial configuration must bespecified. A zero degree of freedom system is always considered to be in static equilibriumonce all of the kinematic constraints are satisfied.

Starting with the user-specified initial configuration, a final configuration is arrived atiteration-by-iteration, such that there are no unbalanced forces or torques on any of thebodies in the system and all of the kinematics constraints are satisfied. All of the velocitiesand accelerations are set to zero.

A multi-body subcase needs to be defined in the input deck. Only one such subcase can beused in a model. The simulation type "static" is defined on an MBSIM bulk data entry whichmust be referenced through a subcase statement MBSIM. The MBSIM bulk data entity alsodefines the integrator, end time, and time step. A sequence of several simulations ofdifferent types can be defined by referring to an MBSEQ bulk data statement instead. Loadsand motions are referenced on MLOAD and MOTION subcase entries, respectively. Initialvelocities do not apply here. SPC type constraints in Multi-body Dynamics analysis areallowed only for MBD-ESL optimization of a flexible body if displacements are used asconstraints. Further information on loads and boundary conditions can be obtained from thesections Applied Forces and Motions and Initial Velocity.




Quasi-static Analysis for MBD

A quasi-static simulation is a sequence of static simulation steps applied to a model over agiven duration at specified intervals. A quasi-static simulation is employed when you havetime-dependent forces or motions in the model and you want a static equilibriumconfiguration at every time step. The system must have at least one degree of freedom toundergo a quasi-static simulation and you must specify the initial configuration.

For the first time step, the user-specified initial configuration is used as a starting point,whereas for all other time-steps, a configuration from the previous time step is used as thestarting point for equilibrium simulation at that time step. A final configuration is arrived atiteration-by-iteration, such that there are no unbalanced forces or torques on any of thebodies in the system and all of the kinematic constraints are satisfied at that time step. Forevery step, all velocities and accelerations are set to zero.

A multi-body subcase needs to be defined in the input deck. Only one such subcase can beused in a model. The simulation type "quasi-static" is defined on an MBSIM bulk data entrywhich must be referenced through a subcase statement MBSIM. The MBSIM bulk data entityalso defines the integrator, end time, and time step. A sequence of several simulations ofdifferent types can be defined by referring to a MBSEQ bulk data statement instead. Loadsand motions are referenced on MLOAD and MOTION subcase entries, respectively. Initialvelocities do not apply here. SPC type constraints in Multi-body Dynamics analysis areallowed only for MBD-ESL optimization of a flexible body if displacements are used asconstraints. Further information on loads and boundary conditions can be obtained from thesections Applied Forces and Motions and Initial Velocity.




Linear Analysis for MBD

In linearization analysis, the nonlinear representations of force, motion, stiffness, or dampingare linearized. A linearization can be performed on these models to prepare a model for usewith Matlab or to obtain eigenmodes characteristics of the model. In the case of performinga linear analysis on the mechanical system, optional files of type eig_info, Simulink MDL,

and Matlab ABCD matrices are available to be exported.

A multi-body subcase needs to be defined in the input deck. Only one such subcase can beused in a model. A linear simulation is defined by referring an MBSIM subcase entry to aMBLIN bulk data statement. The MBLIN bulk data entity also selects linear analysis types,EIGEN or STMAT. A sequence of several simulations of different types can be defined byreferring to an MBSEQ bulk data statement instead. Loads and motions are referenced onMLOAD and MOTION subcase entries, respectively. SPC type constraints in Multi-bodyDynamics analysis are allowed only for MBD-ESL optimization of a flexible body ifdisplacements are used as constraints. Initial velocities do not apply here. Furtherinformation on loads and boundary conditions can be obtained from the sections AppliedForces and Motions and Initial Velocity.




Bodies

Bodies are the model elements that have mass and inertia. Bodies can be rigid or flexible.

A rigid body has only mass and inertia, and does not deform during the simulation. An initialvelocity can be assigned. Mass and inertia information can be omitted for kinematic, static,and quasi-static simulations. It does not affect displacement, velocity, and accelerationresults of kinematic simulation or displacement results of a static or a quasi-static simulation. Mass and inertia information must be correctly specified if joint-reaction forces are ofinterest in kinematic, static, or quasi-static simulations.

A flexible body deforms during the simulation. Mass and inertia are determined by thegeometry and material of the structure defining the body. An initial velocity and dampingcan be assigned. Flexible bodies are formulated using an orthogonal set of modes that

represent the displacements u of the flexible body such that

q

where, q are the modal coordinates which are to be determined by the multi-body dynamics

analysis. The set of orthogonal modes is determined in a Component Mode Synthesis (CMS). Depending on the model, CMS can be performed as a pre-processing step using a specialsimulation (see Direct Matrix Approach). Besides displacements, velocities, andaccelerations, stresses and strains can also be computed for flexible bodies.

One special rigid body is the ground body. It describes the reference environment, and doesnot add any degrees of freedom to the system. It is at absolute rest. Any grounded body ismerged into one.

Bodies are defined in terms of a finite element model. A body is formed by a group ofproperties, elastic, rigid, and mass elements as well as grid points.

Rigid bodies are defined on a PRBODY entry. Mass and inertia are either determined fromthe geometric entities or can be entered on PRBODY.

The ground body is defined using the GROUND bulk data entry.

Flexible bodies are defined using the PFBODY bulk data entry. The interface grid points areautomatically determined or are defined on PFBODY using the FLXNODE flag. The procedure,as described in Direct Matrix Approach, is applied to each PFBODY definition. The procedureis fully integrated in the multi-body dynamics solution sequence, where flexh3d files are

generated for multiple flexible bodies in the same model. The parameter PARAM, FLEXH3Dmay be used to control the regeneration of flexh3d files for subsequent runs.



Markers

A marker is a coordinate system attached to a body at a geometric point. Markers are usedas a reference for joints, compliant elements, applied loads, and output requests.

Markers are defined using a grid point and a coordinate system. The MARKER bulk dataentry is used.



Constraints

The multi-body system must be sufficiently constrained.

Typical types of constraints like joints, couplers, and high-pair joints can be defined. Higher-pair joints include point-to-curve, point-to-surface, and curve-to-curve constraints. They canconnect rigid bodies, flexible bodies, or a rigid and flexbody.

Before running the solver, any redundant constraints in the model are removed. Since theconstraint forces associated with redundant constraints are set to zero, it is important toreview all of the constraints in the model to make sure they are physically meaningful andthat there are no unintended redundant constraints.

Joints connect two grid points that belong to a body. They constrain the motion between thebodies. They are defined using the JOINT or JOINTM bulk data entries. SPC type constraintsin Multi-body Dynamics analysis are allowed only for MBD-ESL optimization of a flexible bodyif displacements are used as constraints.

Joint Type

Constrained Degrees ofFreedom Number of

GRIDsTranslation Rotation

Fixed 3 3 2

Revolute 3 2 3

Translational 2 3 3

Cylindrical 2 2 3

Universal(developmentsource only)

3 1 4

Planar 1 2 3

Ball 3 0 2

Perpendicular 0 1 4

Parallel axes 0 2 4

Orientation 0 3 2

In-plane 1 0 4

Inline 2 0 3

Constantvelocity

3 1 4



Couplers are constraints between the translational and/or the rotational motion of two orthree joints. They are defined using the COUPLER bulk data entries.

Higher-pair joints are connecting points, curves and surfaces. They can be rigid ordeformable.

Higher-pair JointType

Bulk DataEntry

Point-to-curve MBPTCV

Point-to-deformablecurve

MBPTDCV

Point-to-deformablesurface

MBPTDSF

Curve-to-curve MBCVCV

These entries refer to the parametric curve definition (MBPCRV), deformable curve definition(MBPTDCV), and deformable surface definition (MBDSRF).



Contact

The contact modeling capability for multi-body dynamics can handle complex contactscenarios between rigid bodies and rigid and flexible bodies. For the definition you have toidentify geometries on one body that can contact a different set of geometries on a secondbody. You also specify the contact material properties such as coefficient of restitution andfriction. The solver monitors the proximity of the specified geometries to each other. Whencontact between the two sets of geometry occurs, a force based on the defined physicalproperties is generated. This represents the contact force. Both normal and frictional forcesare modeled. When the bodies separate, the force becomes zero.

There are four key features to the contact capability:

Modeling the geometry of the bodies that are in contact

Detecting the onset of contact

Applying the contact force

Detecting the end of a contact "incident" and removing the contact force

Two contact types are available: Rigid body to rigid body (MBCNTR) which is defined as thecontact of two element sets (SET) and rigid to flexible body (MBCNTDS) which is defined asthe contact between a node set (SET) and a deformable surface. The deformable surfacemust be defined by the MBDSRF bulk data entry.

When the onset of a collision is detected, the collision detection algorithm returns a set ofinterfering polygons. From those the solver computes the following:

The point of contact and surface normal vector

The magnitude and direction of the normal and friction forces

Once the point of contact and surface normal vector are known, the normal and friction forcemagnitudes are computed using a penalty-based Poisson contact normal force model. Thetwo primary inputs to this model are the penalty and the coefficient of restitution (COR). COR is defined as the ratio of relative speed of separation to the relative speed of approach ofthe colliding bodies. A COR of 1.0 implies a perfectly elastic collision and a COR of 0.0represents a perfectly plastic collision. One may think of the COR as damping and penalty asstiffness. Too high of a penalty value may cause numerical difficulties, while too small of avalue may lead to excessive penetration. Some fine-tuning of these two parameters isusually required to reach stable and accurate results.

The frictional force is modeled as a viscous force according to the following law:

In the above equations:

is the current slip speed at the point of contact.

is the coefficient of static friction.

is the coefficient of dynamic friction.

is the stiction transition slip speed at which the full value of is used for thecoefficient of friction.



is the dynamic friction slip speed at which the full value of is used for thecoefficient of friction.

is the friction force that is to be applied. The friction force opposes the direction ofthe slip velocity.



Compliant Elements

Compliant elements are bushings, spring-dampers, and beams. For each, the relevantinformation such as stiffness, damping, preload, attachment markers, etc. needs to bedefined. Stiffness and damping value numbers should correctly represent the actual systemand must be physically meaningful. Otherwise, the system may inadvertently turn out to benumerically stiff, even though the physical system may not be.

Compliant elements can be defined with respect to grid points or with respect to markers.

CMBEAM and CMBEAMM bulk data entries define beam elements.

CMBUSH and CMBUSHM bulk data entries define bushing elements. A bushing element haslinear stiffness and damping properties.

CMSPDP and CMSPDPM bulk data entries define spring-damper elements.



Applied Forces and Motions

Forces and moments can be present in the system. There are action-only forces which areapplied to one point, and action-reaction forces which are applied to two points. Forcecomponents can be a constant value, a curve, an expression, or a user-written subroutine.

A special force is gravity. Acceleration is applied to a body and from mass and acceleration,the gravitational force is computed.

Motion is a scalar constraint to the system. Displacement, velocity, and acceleration-typemotions are possible. The motion must depend only on time and not on any other measuresin the model that could change during the simulation. In other words, at every time stepwith only time as the independent parameter, the solver should be able to evaluate theexpression completely without using any other information about the model. For example,the motion cannot depend upon displacement or velocity or acceleration between two pointsin the model.

Motion can be specified as a constant value, a curve, an expression, or user-writtensubroutine. Motion is either defined as motion between two points or joint motion. When amotion is applied on a joint, one joint degree of freedom is controlled as a function of time. When a motion is applied between two points, movement along a user-specified direction iscontrolled as a function of time.

Forces are always defined at grid points, and can be applied to one grid point (action-only) ortwo (action-reaction). The bulk data entry MBFRC defines constant force; the entry MBFRCCdefines force by a curve; and the entry MBFRCE defines a force by equation.

Moments are always defined at grid points, and can be applied to one grid point (action-only)or two (action-reaction). The bulk data entry MBMNT defines constant moment; the entryMBMNTC defines moment by a curve; and the entry MBMNTE defines a moment by equation.

GRAV defines the gravity acceleration.

The entry MLOAD can be used to derive force and moment set combinations.

Motion can be defined as grid point motion or as joint motion. Grid point motion can beapplied to one grid point or two (relative motion). The bulk data entry MOTNG definesconstant motion; the entry MOTNGC defines motion by a curve, and MOTNGE defines motionby an equation. Joint motion can be applied to translational or revolute joints only. The bulkdata entry MOTNJ defines constant motion; the entry MOTNJC defines motion by a curve, and MOTNJE defines motion by an equation. The entry MOTION can be used to derive motion setcombinations.



Initial Velocity

Initial velocity is part of the problem formulation of the equation of motion. It can be appliedto bodies or to cylindrical, translational, and rotational joints.

The INVELB bulk data entry defines body initial velocity. The entry INVEL can be used toderive initial velocity set combinations.



Function Expressions

Expressions can be used in many places. They formulate relationships as functions of time,displacements, velocities, acceleration, forces, etc. If geometric points are used in anequation, they are always related to markers.

The bulk data entry MBVAR is used to define equations.



Results of a Multi-body Dynamics Analysis

The primary results in a multi-body dynamics analysis are the motions of the bodies. Theyare written as nodal displacements, velocities, and accelerations. For flexible bodies, elementresults such as deformations, stresses, and strains are derived from those results. Theseresults can be displayed in an animation of the entire system in a graphical toll such as AltairHyperView (see figure). Aside from the full nodal results, the solver provides a morecompressed form of animation data only for multi-body dynamics analysis that can only bedisplayed in Altair HyperView, where HyperView does many of the typical transformationsand final computations.

See the Results of a Finite Element Analysis section to find more information on how to post-process nodal and elemental results.

Measures like body displacements, velocities, accelerations, joint forces, and user-definedexpressions are being written as time history. Marker time history can be written uponrequest. These results can be plotted in a graphical plotting tool such as Altair HyperGraph.

The definitions of the output options can be found in the I/O Options Section. An overview ofthe result files can be found in the Results Output by OptiStruct section.



Rotor Dynamics

Introduction

Rotor dynamics is the analysis of structures containing rotating components. The dynamic

behavior of such structures is influenced by the type and angular velocity of rotating

components and their locations within the model. Rotor dynamics is available in OptiStruct

for modal frequency response and complex eigenvalue analyses.

Motivation

When a component within the structure rotates, additional forces like the gyroscopic forceand circular damping force act on it. It is important to determine the effects of rotatingcomponents on the system as a whole. The natural frequencies of a system usually change, ifgyroscopic forces act on the model due to a rotating component. Circulating damping forcesdue to rotating components can lead to system instability. These forces are a function of thefrequency of rotating component. In OptiStruct, they are included in the calculation of theresponse of the structure of interest when required in applicable subcases.

Figure 1: Example illustration depicting an application of Rotor Dynamics analysis

In Figure 1, the rotating components of the structure are the shafts on which gears aremounted. The design of the rotors and their angular frequencies can affect the dynamicresponse of the structure. Any design will most likely lead to asymmetrical mass distributionabout the rotor axes. This unbalanced mass, even if it isn’t significant, can result in deflectionof the rotor depending on various factors. The magnitude of these deflections will beaugmented when the rotating speed of the shafts equals the natural frequency of thestructure (Resonance), and can lead to catastrophic failure of the system.

Implementation

The Rotor Dynamics functionality is activated in OptiStruct with the use of the RGYROsubcase information entry (RGYRO = ID). This RGYRO entry references the identificationnumber of a RGYRO bulk data entry. Related bulk data entries, RSPINR, UNBALNC, ROTORGand RSPEED are defined in the model for Rotor Dynamics. Parameters PARAM, GYROAVG,PARAM, WR3, and PARAM, WR4 are also used.



Whirl

A rotor is a structure that rotates about its own axis at a specific angular velocity. If a lateralforce is applied to the rotor, it will deform in the lateral direction. This deformation isdependent on various factors, such as, magnitude of the applied force, rotor materialproperties, stator stiffness, and damping within the system. Due to rotor rotation, thedeformed rotor will also whirl about an axis.

Synchronous and Asynchronous Analysis

The whirling speed can either be the same as rotor speed or it can be different from it. Thetype of analysis performed if the whirling speed and the rotor speed match is known assynchronous analysis. If the speeds don’t match, then asynchronous analysis is used todetermine the dynamic response of the model. In OptiStruct, the RGYRO bulk data entry canbe used to select synchronous/asynchronous analysis.

Figure 2: Illustration depicting the types of Whirl and the two analysis types that are dependent on the angularfrequency of a rotor.

Forward Whirl and Backward Whirl

The type of whirl depends on the spin direction of a rotor. If the rotor spin direction is thesame as that of its whirl direction, then it is termed as forward whirl. If the rotor spindirection is opposite to the whirl direction, it is termed as backward whirl. In complexeigenvalue analysis, you can determine and differentiate between the modes of a structureundergoing backward whirl and forward whirl.

Supported solution sequences

OptiStruct supports the Rotor dynamics functionality in the following solution sequences:


The response of a structure with rotating components to a specified external excitation canbe determined using the rotor dynamics functionality in frequency response analysis.

Asynchronous analysis (RGYRO = ASYNC)

If ASYNC is specified in the RGYRO bulk data entry, the rotors within the structure have user-defined spin rates. The excitation frequency (FREQi entries) is independent of the referencerotor speed defined in the RGYRO entry.

Synchronous analysis (RGYRO = SYNC)



If SYNC is specified in the RGYRO bulk data entry, the reference rotor spin rate is equal to (orsynchronous with) the excitation frequency. The reference rotor speed is not input via theRGYRO entry and the FREQi entry values are used in this analysis.


The eigenvalues and critical speeds of a structure with rotating components can bedetermined using the rotor dynamics functionality in complex eigenvalue analysis.

Asynchronous analysis (RGYRO = ASYNC)

If ASYNC is specified in the RGYRO bulk data entry, the rotors within the structure have user-defined spin rates via the RSPEED entry and the Campbell Diagram can be plotted to find thecritical speeds. Additionally, since the calculated eigenvalues are complex, you can determineunstable modes by studying the real parts of the calculated eigenvalues. If the real part of acomplex eigenvalue is positive, then the corresponding system mode is unstable.

Synchronous analysis (RGYRO = SYNC)

If SYNC is specified in the RGYRO bulk data entry, only the critical speeds are calculated asthe rotor speeds are equal to the whirl frequencies. These critical speeds can lead tostructural resonance and the design should be modified to change its whirl frequencies or theoperating rotor spin rate should be limited to avoid reaching the critical speeds.

Note: In a frequency response analysis, the synchronous

analysis (SYNC) option is generally used to model rotorswith an inherent unbalance. The rotor unbalance can bespecified as a force or via the UNBALNC entry. Theanalysis is synchronous because the unbalanced loadvibrates at the whirl frequency of the system which isequal to the rotor spin speed.

Implementation - Frequency Response Analysis (ASYNC)

Asynchronous analysis is activated using the RGYRO=ASYNC option. Frequency responseanalysis in rotor dynamics involves defining the excitation either as an external varying loadas a function of frequency or as a rotor unbalance via the UNBALNC entry (or as a force thatsimulates the effect of the rotor unbalance). Asynchronous frequency response analysis inOptiStruct is designed for an external varying force at a specific set of frequencies. Thefollowing equation implements the external loading functionality in OptiStruct. The rotorspeeds should be specified by you for Asynchronous frequency response analysis.

21 2

1 1 2

[ ] ([ ] [ ] [ ] [ ]) (1 )[ ] [ 4 ]

(1 )[ ] [ 4 ])( ) ( )

1( ) i [ ] [ ] [ ] [ ] [ ] [ 4 ]

S R R R R R S S

Rj RjjN

G C C C C Cj Rj ref Rj Rj R Rj R Rj Rj Rj

M i B B M K iG K i K

i GR K i Ku F

GRB B M K K K

The response of a system with rotating components to an external load in the frequencydomain is calculated based on the above equation.



Frequency Response Analysis (SYNC)

Synchronous analysis is activated using the RGYRO=SYNC option. Frequency responseanalysis in rotor dynamics involves defining the excitation either as an external varying loadas a function of frequency or as a rotor unbalance via the UNBALNC entry (or as a force thatsimulates the effect of the rotor unbalance). Synchronous frequency response analysis inOptiStruct is designed to calculate the response of a system with a rotor unbalance. Thefollowing equation implements the rotor unbalance functionality in OptiStruct. The rotorspeeds are determined from the FREQi entries for Synchronous frequency response analysis.

21 2

1 1 2

[ ] ([ ] [ ] [ ] [ ]) (1 )[ ] [ 4 ]

(1 )[ ] [ 4 ])

1( ) [ ] [ ] [ ] [ ] [ ] [ 4 ]

ref ref S R R R R R S S

Rj RjjN

G C C C C Cj Rj ref ref Rj Rj R Rj R Rj Rj Rj

ref ref


i GR K i K

GRi B B M K K K

( ) ( )ref refu F

The response of a system with rotating components to a rotor imbalance which is consideredas a force acting in the frequency domain is calculated based on the above equation.

Frequency Response Analysis with WR3 and WR4 (ASYNC)

Parameters PARAM, WR3 and PARAM, WR4 can be used to avoid frequency dependentcalculation of the rotor speeds in systems with multiple rotors. The frequency values in thecirculation damping terms are replaced with the values of the parameters as shown in theequation below.

21 2

1 1 2

[ ] ([ ] [ ] [ ] [ ]) (1 )[ ] [ 4 ]

(1 )[ ] [ 4 ])( ) (

1( ) i [ ] [ ] [ ] [ ] [ ] [ 4 ]

3 4

S R R R R R S S

Rj RjjN



i GR K i Ku F

GRB B M K K K

WR WR

)

Frequency Response Analysis with WR3 and WR4 (SYNC)

Parameters PARAM, WR3 and PARAM, WR4 can be used to avoid frequency dependentcalculation of the rotor speeds in systems with multiple rotors. The rotor speeds can becalculated as a linear function of the reference rotor spin rate (see description of termsbelow). The reference rotor spin rate values in the circulation damping terms are replacedwith the values of the parameters as shown in the equation below.

21 2

1 1 2

[ ] ([ ] [ ] [ ] [ ]) (1 )[ ] [ 4 ]

(1 )[ ] [ 4 ])

1( ) [ ] [ ] [ ] [ ] [ ] [ 4 ]

3 4


Rj RjjN



i GR K i K

GRi B B M K K K

WR WR

( ) ( )ref refu F



Complex Eigenvalue Analysis with WR3 and WR4 (ASYNC)

The eigenvalues and critical speeds of a structure with rotating components can bedetermined using the rotor dynamics functionality in complex eigenvalue analysis. Inasynchronous analysis the critical speeds can also be determined by plotting the Campbelldiagram for frequencies specified using the RSPEED entry. The parameters PARAM, WR3 andPARAM, WR4 can be used to replace the values of WR3 and WR4 in the equation below.

21 2

1 1 2

[ ] ([ ] [ ] [ ] [ ]) (1 )[ ] [ 4 ]

(1 )[ ] [ 4 ])( ) 0

1( ) i [ ] [ ] [ ] [ ] [ ] [ 4 ]

3 4

S R R R R R S S

Rj RjjN



i GR K i Ku

GRB B M K K K

WR WR

Complex Eigenvalue Analysis with WR3 and WR4 (SYNC)

Only the rotor speeds are required to perform the synchronous complex eigenvalue analysisas the whirl frequencies are equal to the reference rotor spin rates. Only the critical speedsare output as a result of this analysis. The parameters PARAM, WR3 and PARAM, WR4 can beused to replace the values of WR3 and WR4 in the equation below.

21 2

1 1 2

[ ] ([ ] [ ] [ ] [ ]) (1 )[ ] [ 4 ]

(1 )[ ] [ 4 ])

1( ) [ ] [ ] [ ] [ ] [ ] [ 4 ]

3 4


Rj RjjN



i GR K i K

GRi B B M K K K

WR WR

( ) 0refu

Where, ref is the reference rotor spin rate

( )Rj ref is the spin rate of rotor “j” as a function of the reference rotor spin rate. ( )Rj ref

can be determined for each excitation frequency or it can be calculated as a linear function ofthe reference rotor spin rate:

( )Rj ref j j ref

j and j are scaling factors calculated from the relative spin rates defined in the RSPINRbulk data entry.

[M] is the structural mass

[ ]SB is the viscous damping of the support

[ ]RB is the rotor viscous damping

[M ]R is the rotor mass

[K ]R is the rotor stiffness



[ 4 ]RK is the rotor material damping

[ ]CRB

is the circulation due to rotor viscous damping

[ ]CRM

is the circulation due to rotor ‘mass’

[ ]CRK

is the circulation due to rotor structural ‘stiffness’

[ 4 ]CRK

is the circulation due to rotor material damping

[K ]S is the stiffness of the support

[ 4 ]SK is the material damping of the support

N is the number of rotors in the model

( )uis the displacement as a function of frequency

( )refu is the displacement as a function of reference rotor spin rate

( )F is the external excitation as a function of frequency

( )refF is the unbalanced load as a function of reference rotor spin rate (via DAREA or

UNBALNC entries)

G is the structural damping value of the support defined using PARAM, G

GR is the structural damping value of the rotor defined using PARAM, G

1R and 2R are used to define the Rayleigh viscous damping as follows:

1 2[ ] [ ] [K ]R Rayleigh R R R RB Mand 1 2[ ] [ ] [K ]C C C

R Rayleigh R R R RB M

R and R are used to define the scale factors of the linear fit (between SPDLOW andSPDHIGH on the ROTORG entry) of the rotor speed to the reference rotor speed.

WR3 and WR4 are defined by the parameters PARAM, WR3, PARAM, WR4, respectively.

The general form of a circulation damping term is given as:

1[ ] [ ][ ] [ ][ ]

2CD T D D T

Where, [D] is the regular damping matrix and [T] is a rotation matrix defined as follows:



0 1 0 0 0 0

1 0 0 0 0 0

0 0 0 0 0 0[ ]

0 0 0 0 1 0

0 0 0 1 0 0

0 0 0 0 0 0

T

[ ]GRB

is the gyroscopic matrix defined in a rotor coordinate system as follows:

33

33

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0[ ]

0 0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

GRB

I

I

Model Restrictions

1D Rotor model

The OptiStruct rotor dynamics feature currently supports only 1D rotors. Rotor shaftsmodeled with 1D elements like CBEAM, CBAR, or CBUSH only can be used. CONM1 or CONM2entries should be used to define the mass and inertia of the rotors. Grid points are necessaryfor the definition of mass and inertia via CONM1 or CONM2. All grid points that belong torotors should be listed in the ROTORG entries and only grids listed in the ROTORG entries areincluded in the calculation of gyroscopic terms. The I33 field on CONM1/CONM2 entriesshould contain meaningful values as only the inertia about the local Z axis plays a role in thegyroscopic forces (see above description).

Detached Rotor model

The rotor should be detached from the rest of the structure. Only rigid elements (RBEi) canbe used to attach rotors to the ground or to flexible bearings. If any connection existsbetween the rotor and other parts of the structure using elements other than RBEi, then theprogram will error out.

Symmetric rotor in a fixed reference frame

Rotor dynamics analysis in OptiStruct is performed based on assumption that the rotor issymmetric. Therefore, the rotor model is required to be symmetric about the rotation axis.The implementation is based on equations of motion formulated in a fixed reference frame.Asymmetric rotors in a rotating reference frame is planned to be implemented in futureversions of OptiStruct.



Multiple Rotors

During synchronous analysis, the calculations are performed with respect to the referencerotor. In synchronous frequency response analysis, the reference rotor is rotating at thefrequency of the unbalanced load and in synchronous complex eigenvalue analysis, thereference rotor is rotating at the whirl frequency of the system. The interpretation of resultsin a multiple rotor system should always be done with respect to the reference rotor. Anydeduction of results from the behavior of rotors other than the reference rotor will beinaccurate and can lead to incorrect results. If the behavior of a rotor other than thereference rotor is to be studied, a different analysis should be run with the rotor of interest asthe reference rotor.

Campbell Diagram

The critical speeds of a rotating structure should be calculated and the design parameters canthen be altered if necessary to restrict the operating speeds of the structure from attainingthose resonant speeds. The structure may undergo excessive amplitude and phase changes ifits operating speeds reach critical speeds. The calculation of critical speeds in OptiStruct canbe undertaken in two ways:

1. Synchronous Complex Eigenvalue Analysis

The RGYRO=SYNC option in Complex Eigenvalue Analysis can be used to determine theexact critical speeds of the rotating structure. During a synchronous analysis, the rotorspeed is equal to the whirl frequency of the structure, which by definition, are the criticalspeeds of the structure that should be avoided during its operation.

Figure 3: An example Campbell Diagram to calculate the critical speeds.

2. Asynchronous Complex Eigenvalue Analysis

The RGYRO=ASYNC option and the RSPEED bulk data entry in Complex EigenvalueAnalysis can be used to determine the whirl frequencies (backward whirl and forwardwhirl) of the structure. These Whirl frequencies can be calculated for a sequence of rotorspin rates. Forward Whirl and Backward Whirl frequencies can then be plotted against therange of rotor spin rates (Figure 3). The critical speeds can be calculated bysuperimposing the “Rotor Spin Rate = Whirl Frequencies” line on the plot. The points ofintersection are the critical speeds.



Note: The rotor speeds specified on the RSPEED entry shouldbe input with sufficiently fine resolution to be able tocapture the critical speeds. If the specified rotor speedsare too far apart, the critical speeds may be missed.



NVH Applications and Techniques

The NVH Applications and Techniques section provides an overview of the following:

Transfer Path Analysis on an Automobile

Residual Runs using Super Elements

Basic OptiStruct NVH Output Files

Global Search Option

Create Door and Deck Lid Seals

Create a HyperGraph Template for Reading in Multiple Files

Using AMSES (Automatic Multi-Level Sub-Structuring Eigensolver Solution)

Poroelastic Materials (Biot theory)



Transfer Path Analysis on an Automobile

Transfer Function Body Analysis

The function of the transfer path analysis is to determine which body interface dominates thecritical NVH response in the interior of the body for a given type of vehicle loading.

The first step is to determine all the transfer functions at all the body interfaces, such as thefront and rear cradle mounts, front and rear suspension attachments, powertrain mounts,exhaust hangers and steering system. The major component file in this first run is the fullytrimmed body.

One issue that needs to be determined is whether or not the steering column and steeringwheel are part of the body model to start with. This would determine to which componentthese attachments belong. If one of the critical response points is the steering wheelresponse, then both the steering column and steering wheel must be included with the bodymodel.

The front cradle can also be included in the model and the paths from the front suspension tothe front cradle can also be evaluated.

Another requirement is that the body model is in its fully trimmed state and that it containsall bolt-on components that belong to the body, such as the doors, deck lid, hood, seats,instrument panel, etc.

Also the body model will need to include the air cavities, if the transfer path can determinethe critical paths causing interior noise problems in the vehicle.

Below is an example of how to set up the first deck to obtain the needed attachment results. The results from this run are used later to determine the transfer load paths for a full vehiclemodel subjected to a powertrain loading.

Example

OUTPUT, H3DOUTPUT, MASSPROPPARAM, AMLS, YESPARAM, AMLSNCPU, 4PARAM, AUTOSPC, YESPARAM, CHECKEL, NOTITLE = TRIM BODY MOBILITY ANALYSIS SUBTITLE = WITH CAVITY RESPONSE METHOD(FLUID) = 2METHOD(STRUCTURE) = 3FREQUENCY= 1$ DRIVER'S EAR ACOUSTIC RESPONSESET 2 = 80000000ACCELERATION(PUNCH,PHASE) = 1$$ UNIT INPUT LOAD AT EACH ATTACHEMENT POINT IN ALL 6 DOF'S$SUBCASE 2LABEL = 4003003:+X<>3003:+X<>Frt Susp.:LCA - Frt Bush:LHS:+XDLOAD = 101DISPLACEMENT (PUNCH,PHASE) = 2SET 3 = 4003003



VELOCITY (PUNCH,PHASE) = 3$SUBCASE 3LABEL = 4003003:+Y<>3003:+Y<>Frt Susp.:LCA - Frt Bush:LHS:+YDLOAD = 102DISPLACEMENT (PUNCH,PHASE) = 2SET 4 = 4003003VELOCITY (PUNCH,PHASE) = 4$SUBCASE 4LABEL = 4003003:+Z<>3003:+Z<>Frt Susp.:LCA - Frt Bush:LHS:+ZDLOAD = 103DISPLACEMENT (PUNCH,PHASE) = 2SET 5 = 4003003VELOCITY (PUNCH,PHASE) = 5$SUBCASE 5LABEL = 4003003:+RX<>3003:+RX<>Frt Susp.:LCA - Frt Bush:LHS:+RXDLOAD = 104DISPLACEMENT (PUNCH,PHASE) = 2SET 6 = 4003003VELOCITY (PUNCH,PHASE) = 6$SUBCASE 6LABEL = 4003003:+RY<>3003:+RY<>Frt Susp.:LCA - Frt Bush:LHS:+RYDLOAD = 105DISPLACEMENT (PUNCH,PHASE) = 2SET 7 = 4003003VELOCITY (PUNCH,PHASE) = 7$SUBCASE 7LABEL = 4003003:+RZ<>3003:+RZ<>Frt Susp.:LCA - Frt Bush:LHS:+RZDLOAD = 106DISPLACEMENT (PUNCH,PHASE) = 2SET 8 = 4003003VELOCITY (PUNCH,PHASE) = 8$ $ Not all subcases are shown in this example-------------------------------------------------------------------SUBCASE 273LABEL = 9005852:+RX<>9011999:+RX<>Frt Susp.:Int. Shaft to Col.::+RXDLOAD = 372DISPLACEMENT (PUNCH,PHASE) = 2SET 274 = 9005852VELOCITY (PUNCH,PHASE) = 274$SUBCASE 274LABEL = 9005852:+RY<>9011999:+RY<>Frt Susp.:Int. Shaft to Col.::+RYDLOAD = 373DISPLACEMENT (PUNCH,PHASE) = 2SET 275 = 9005852VELOCITY (PUNCH,PHASE) = 275$SUBCASE 275LABEL = 9005852:+RZ<>9011999:+RZ<>Frt Susp.:Int. Shaft to Col.::+RZDLOAD = 374DISPLACEMENT (PUNCH,PHASE) = 2SET 276 = 9005852VELOCITY (PUNCH,PHASE) = 276



$$BEGIN BULK$$ PARAM CARDS FOR ANALYSISPARAM WTMASS 1.$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>$FREQ1 1 5.0 1.0 195 $==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>EIGRL 2 600. EIGRL 3 300. ACMODL 4.0 1.0 1.0 1.0$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>$$ 4003003 +XDLOAD 101 1.0 1.0 401RLOAD1 401 1001 0 0 400 0DAREA 1001 4003003 1 1.0$ 4003003 +YDLOAD 102 1.0 1.0 402RLOAD1 402 1002 0 0 400 0DAREA 1002 4003003 2 1.0 $ 4003003 +ZDLOAD 103 1.0 1.0 403RLOAD1 403 1003 0 0 400 0DAREA 1003 4003003 3 1.0$ 4003003 +RXDLOAD 104 1.0 1.0 404RLOAD1 404 1004 0 0 400 0DAREA 1004 4003003 4 1.0$ 4003003 +RYDLOAD 105 1.0 1.0 405RLOAD1 405 1005 0 0 400 0DAREA 1005 4003003 5 1.0$ 4003003 +RZDLOAD 106 1.0 1.0 406RLOAD1 406 1006 0 0 400 0DAREA 1006 4003003 6 1.0$$ Not all load cards are shown in this example ----------------------------------------------------------------------------$$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>TABLED1 400 +400A+400A 20.0 1.0 400.0 1.0 ENDT$INCLUDE '/ANALYSIS/TRIM_BODY_CONNECTIONS.dat'INCLUDE '/MODELS/CAVITY/CAVITY.dat'INCLUDE '/ANALYSIS/TRIM_BODY_FILES.dat'INCLUDE '/MODELS/FRONT_CRADLE/FRONT_CRADLE.dat'INCLUDE '/MODELS/STEERING/STEERING_COLUMN.dat'INCLUDE '/MODELS/STEERING/STEERING_WHEEL.dat'ENDDATA



Note: Around 275 subcases were needed to define all theinterface point unit loads in all six degrees of freedom forthis example.

The label card: LABEL = 4003003:+X<>3003:+X<>Frt Susp.:LCA - Frt Bush:LHS:+X

The first parameter defines the input attachment point and its loading direction. The secondparameter defines a shortened version of this input attachment point. The third parameterdefines the attachment by its name and also includes the loading direction. The creation ofthe subcases and this labeling information will be automated in a future release of NVHDirector.

The major output from this analysis is the displacement and velocity output in the .pch file,which can be around 40 MB in size.

Full Vehicle Load Case

The second run is a full vehicle model analysis with a particular critical loading on one of thenon-body components. Below is an example of a P/T type of analysis. A torque loading isapplied to the crankshaft and the acoustic response at the driver’s ear is captured.

Example

OUTPUT, H3DOUTPUT, MASSPROPPARAM, AMLS, YESPARAM, AMLSNCPU, 4PARAM, AUTOSPC, YESPARAM, CHECKEL, NO$MODEL,100$TITLE = P/T FULL VEHICLE ANALYSISSUBTITLE = BASELINE COMPONENTSMPC = 406SPC = 1$ Acoustic response output setSET 1 = 80000000, 80000002, 80000004, 80000006$ Structural response output setSET 2 = 1006001,9106012$ Body attachment forcesSET 3 = 1002001,1002001,1002002,1002003,1002004,1003015,1003016, 1003521,1004503,1004507,1004515,1004523,1005003,1005004, 1005011,1005012,1005013,1005014,1005015,1005016,1005017, 1005018,2005807,2005809,2005810,4003003,4003004,4003005, 4003006,4003007,4003008,4003501,4003511,4003541,4005811, 4005812,9005852INCLUDE 'display_set.dat'$ This file contains set 200 that has the full vehicle plotel grid pointsidentified.$SUBCASE 1 $ MODAL DEFLECTION SHAPELABEL = P over T Modal



METHOD(FLUID) = 2METHOD(STRUCTURE) = 3DISPLACEMENT(H3D)= 200$SUBCASE 2 $ FREQUENCY RESPONSE ANALYSISLABEL = P over T BaselineMETHOD(FLUID) = 2METHOD(STRUCTURE) = 3DLOAD = 110FREQUENCY= 1GPFORCE (PUNCH,PHASE) = 3DISPLACEMENT(PUNCH,PHASE)= 1DISPLACEMENT(H3D,PHASE)= 1ACCELERATION (PUNCH,PHASE) = 2ACCELERATION (H3D,PHASE) = 2$SUBCASE 3 $ OPERATING DEFLECTION MODE SHAPELABEL = P over T PostMETHOD(FLUID) = 2METHOD(STRUCTURE) = 3$ Critical Frequencies specified in set 300SET 300 = 54.0,64.0,80.0,92.0,104.0,114.0,146.0OFREQ = 300DLOAD = 110FREQUENCY= 1DISPLACEMENT(H3D)= 200$BEGIN BULK$$ PARAM CARDS FOR ANALYSISPARAM WTMASS 1.$$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>FREQ1 1 5.0 1.0 195 EIGRL 2 600.EIGRL 3 300. ACMODL 4.0 1.0 1.0 1.0$ INCLUDE '/ANALYSIS/P_OVER_T/PT_LOADS.dat'$INCLUDE '/ANALYSIS/P_OVER_T/PT_CONNECTIONS_FULL.dat'$ INCLUDE '/ANALYSIS/FULL_VEHICLE_FILES_W_CAVITY.dat'ENDDATA

This run also puts out a large .pch file that includes the response and the body attachment

forces.

Once these two runs are completed, a transfer patch analysis can be performed inHyperView.



Transfer Path Analysis

To perform a transfer path analysis on this model, open up HyperView.

1. From the File menu, select Load > Preference File.

2. From the Preference dialog, select NVH Utilities and click Load.

3. From the NVH menu, select Transfer Path Analysis.

4. Click on the file browser icon to select a Transfer Function file.

This is the PCH from the first run.

5. Click on the file browser icon to select a Force file.

6. Select Load.



Residual Runs using Super Elements

Super Elements Only with No Structure in the Residual Run

To run an analysis on just a super element model with no residual structure, you mustinclude a dummy grid point or include the .seplot file generated with the super element.

OUTPUT, H3DASSIGN,H3DDMIG,BODY,/H3D/TRIMMED_BODY23_H3D.h3dTITLE = TRIM BODY MOBILITY ANALYSIS METHOD=1FREQUENCY=1$SET 2 = 1006001ACCELERATION (PUNCH,SORT1,PHASE) = 2$SUBCASE 2LABEL = 1002001: +XDLOAD = 101DISPLACEMENT = NONESET 3 = 1002001VELOCITY (PUNCH,SORT1,PHASE) = 3$SUBCASE 3LABEL = 1002001: +YDLOAD = 102DISPLACEMENT = NONESET 4 = 1002001VELOCITY (PUNCH,SORT1,PHASE) = 4$BEGIN BULKGRID, 1$FREQ1 1 10.0 1.0 490EIGRL 1 450.0$$ 1002001 +XDLOAD 101 1.0 1.0 401 RLOAD1 401 1001 0 0 400 0 DAREA 1001 1002001 1 1.0 $ 1002001 +YDLOAD 102 1.0 1.0 402 RLOAD1 402 1002 0 0 400 0 DAREA 1002 1002001 2 1.0 TABLED1 400 +400A +400A 10.0 1.0 500.0 1.0 ENDT $ INCLUDE '/MODELS/SEPLOTS/TRIMMED_BODY23_H3DFF.seplot'ENDDATA



Residual Run Containing Several Super Elements

An example to combine super elements in a residual run is shown in the following example.

OUTPUT, H3DOUTPUT, MASSCOMPPARAM, AUTOSPC, YESPARAM, CHECKEL, NOINCLUDE '/ANALYSIS/H3D_FILES_W_CAVITY.dat'TITLE = SUBTITLE = SPC = 1 SUBCASE 1LABEL = UNIT TORQUE INPUT DLOAD = 1000METHOD(FLUID) = 2METHOD(STRUCTURE) = 3FREQUENCY=1SET 1 = 80000000, 80000002, 80000004, 80000006DISPLACEMENT(PUNCH,SORT2,PHASE)= 1SET 2 = 1006001,9106012ACCELERATION (PUNCH,SORT2,PHASE) = 2$OUTPUT(XYPLOT)TCURVE = DRIVER'S ACOUSTIC RESPONSEXYPUNCH DISP RESPONSE / 80000000(T1RM)TCURVE = FRONT PASSENGER ACOUSTIC RESPONSEXYPUNCH DISP RESPONSE / 80000002(T1RM)TCURVE = RIGHT REAR PASSENGER ACOUSTIC RESPONSEXYPUNCH DISP RESPONSE / 80000004(T1RM)TCURVE = LEFT REAR PASSENGER ACOUSTIC RESPONSEXYPUNCH DISP RESPONSE / 80000006(T1RM)BEGIN BULK$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>FREQ1 1 50.0 2.0 49 EIGRL 2 600. EIGRL 3 300. $==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>ACMODL $ INCLUDE '/LOADS.dat'$INCLUDE '/CONNECTIONS_BETWEEN_COMPONENTS.dat'$ INCLUDE '/NON_H3D_FILES.dat'ENDDATA

Where the '/ANALYSIS/H3D_FILES_W_CAVITY.dat' looks like this.

ASSIGN,H3DDMIG,BODY,/H3D/TRIMMED_BODY23_W_CAVITY_H3DFF.h3dASSIGN,H3DDMIG,EXHAUS,/H3D/EXHAUST_H3DFF.h3dASSIGN,H3DDMIG,FRCALLS,/H3D/FRONT_CALIPHER_LS_H3DFF.h3dASSIGN,H3DDMIG,FRCALRS,/H3D/FRONT_CALIPHER_RS_H3DFF.h3dASSIGN,H3DDMIG,FRCRAD,/H3D/FRONT_CRADLE_H3DFF.h3dASSIGN,H3DDMIG,FRDILS,/H3D/FRONT_DISC_LS_H3DFF.h3dASSIGN,H3DDMIG,FRDIRS,/H3D/FRONT_DISC_RS_H3DFF.h3d



--------------------------------------------------ASSIGN,H3DDMIG,RRKNRS,/H3D/REAR_KNUCKLE_RS_H3DFF.h3dASSIGN,H3DDMIG,RRRLLS,/H3D/REAR_LAT_LINK_LS_H3DFF.h3dASSIGN,H3DDMIG,RRRLRS,/H3D/REAR_LAT_LINK_RS_H3DFF.h3dASSIGN,H3DDMIG,RRSTAB,/H3D/REAR_STAB_BAR_H3DFF.h3dASSIGN,H3DDMIG,RRSTLS,/H3D/REAR_STRUT_LS_H3DFF.h3dASSIGN,H3DDMIG,RRSTRS,/H3D/REAR_STRUT_RS_H3DFF.h3d

A unique name, six or less characters long, must be entered in the third field for eachcomponent.

Note: A residual run with a large Craig-Chang super elementshould be run in either Lanczos or the Direct method. Itwill be extremely slow with AMLS. AMLS is not neededsince the residual run is small in size.

Note that to get results for interior points in the super element response points that were notincluded in the list with the interface points, output using the PUNCH command; you mustalso include the DEBUG,SETDMIG,1 line in the file. It is the only output command thatrequires this extra line.



Basic OptiStruct NVH Output Files

For more detail information, refer to Files Created by OptiStruct.

From a Standard Modal or Frequency Response Analysis

*.h3d This file contains the super element information from a super elementcreation run, the modal information from a modal run, the response outputfrom a frequency response run, or the output from an optimization run. Information in this file can come from various types of analysis. This is abinary file that is used by HyperView.

*.html This file contains a problem summary and results summary of the run. Thisfile is created by default, but can be turned off using OUTPUT=HTML,NO. Open up this file in an internet browser like Internet Explorer or Firefox. Itis very useful in debugging modal problems.

*.interface This file contains the coupling between the cavity model and the structuralmodel. This file can be viewed by reading in both the cavity and structurefile first and then reading in the file through the standard file input selectionin HyperMesh. This file is created if there are both structural and fluidmeshes in the input data file.

*.mvw This file contains the information to quickly load in the requested outputinformation into HyperGraph. It references the .pch file information.

*.op2 Duplicates the standard Nastran .op2 file information. File is created by the

OUTPUT2 output format command. Binary file.

*.out This file contains the run information such as warning and error messages,mass information, memory requirements, and AMLS information. This file isalways created.

*.pch This file can contains output in both the XYPUNCH or PUNCH Nastranformat. This file is created when XYPEAK, XYPLOT, XYPUNCH or PUNCHoutput is requested. ASCII format.

*.peak This file contains the peak response information from a random responserun. It contains RMS value, the number of positive crossings, and the peakpower spectral density and responses. ASCII format.

*.res The .res file is a HyperMesh binary results file. Output results can be view

in HyperMesh Post capabilities. This file is created when the OUTPUT,HM,YES is turned on.

*.stat This file contains the module timing information. This file is created bydefault, but can be turned off with OUTPUT=STAT,NO. ASCII format.

*_frames.html This file is used by the *.html file to view the H3D results in the HyperView

Player browser plug-in.

*_menu.html This file is used by the *.html file to view the H3D results in the HyperView

Player browser plug-in.



From an Optimization Run

*.desvar Updated design variables at final iteration. ASCII format.

*.prop Update property values at final iteration. Output is for all property valueseven those not being optimized. Creation of this file is controlled by the PROPERTY I/O option. ASCII format.

*.slk This file contains the sensitivity information for the selected DESVARS. Thisoutput can be viewed in Excel. This file is created when the SENSITIVITYcommand is used.

*_noengl.slk This file is always generated if sensitivity information is requested. Non-English version of the .slk file.

*.hgdata This file contains the iteration history of the objective function, constraintfunctions, design variables, and response functions. Contents of this file arecontrolled by the I/O option HISOUT. This file can be read into HyperGraphto display its contents. ASCII format.

*.hist This file contains the iteration history of the objective function, maximumconstraint violation, design variables, DRESP1 type responses, and DRESP2type responses. Contents of this file are controlled by the I/O option HISOUT. ASCII format.

*.sh This file is created when an optimization is performed. Contains informationnecessary to restart the optimization from a given iteration. Output of thisfile is controlled by the I/O Option SHRES.

*_s#.h3d This file is a compressed binary file, containing both model and result data. It can be used to post-process results in HyperView or using the HyperViewPlayer. The _s#.h3d file is created when the H3D format is chosen.

*_des.h3d This file is a compressed binary file, containing both model and result data. It can be used to post-process results in HyperView or when using theHyperView Player. The _des.h3d file is created when the H3D format is

chosen (see I/O option FORMAT), and an optimization run is performed.

*_gauge.0.h3d This file is a compressed binary file containing both model and result data. It can be used to post-process shell thickness (gauge) sensitivity inHyperView. The *_gauge.0.h3d file is created when the H3D format is

chosen (see I/O option FORMAT), and an optimization run is performed.

*_hist.mvw This file is a HyperView session file and may be opened from the File menuin HyperView or HyperGraph. The file automatically creates individual plotsfor each of the results contained in the .hist file. Each plot occupies its

own page within HyperView (HyperGraph). This file is created when anoptimization is performed. Creation of this file is controlled by the I/Ooption DESHIS.



From PFMODE, PFGRID Analysis

*.pfmode.pch This file contains the output from PFMODE and PFPANEL requests. Thisinformation can be viewed in the HyperView NVH PFMODE-PFGRID module.In version 12.0, this file is only available when output=punch is requested

in PFMODE and PFPANEL. It is recommended to export the modal and panelparticipation data into a H3D file, due to the large volume of data.

*.h3d This file contains the output from PFMODE, PFPANEL, and PFGRID requests.Results of PFGRID is only available in H3D file.

From a Super Element Creation Analysis

*.seplot This file contains the exterior and interior grids, plotels and plate plotels,retained in the super element creation run. This file is created when the PARAM, SEPLOT,YES command is included in the run. ASCII format.

*.h3d This file contains the super element binary information to be included in afuture residual run. Always created for a super element run. This file iscreated by default, but can be turned off with OUTPUT,H3D, NO.




The global search option is incorporated directly in OptiStruct. It does not require an externalprogram to run with OptiStruct.

Below is an example on how it can be used to optimize engine mount locations in a fullvehicle model for a simple rough road shake input.

Initially here are the main cards for the global search option. Everything is controlled by the DGLOBAL card.

Now, this card might seem daunting and overloaded with parameters, but try running withdefault values first. Most parameters were implemented for advanced usage and for future-proofing the feature. Here's all you need for basic usage:

DGLOBAL = 10...BEGIN BULK...DGLOBAL 10

Engine Mount Optimization Example

PARAM, MASSPROPDGLOBAL = 10SENSITIVITY = ALLSENSOUT = FL $INCLUDE '/ANALYSIS/H3D_FILES.dat'TITLE = ENGINE MOUNT LOCATION OPTIMIZATION$ ENGINE MOUNT LOCATIONSSET 400 = 6966 6967 6968 6998 6999 7000DESVAR = 400DESOBJ = 1RANDOM = 2400SET 2 =1006001,9006002 ACCE(SORT1,PHASE,PLOT,PSDF) = 2SUBCASE 10 $RIGHT SIDE INPUT DLOAD=10 ANALYSIS = MFREQ FREQUENCY = 100 SPC = 1 MPC = 400 METHOD = 1SUBCASE 20 $LEFT SIDE INPUT DLOAD=20 FREQUENCY = 100 ANALYSIS = MFREQ SPC = 1 MPC = 400 METHOD = 1$OUTPUT(XYPLOT)XYPUNCH ACCE PSDF / 1006001(T1)XYPUNCH ACCE PSDF / 1006001(T2)XYPUNCH ACCE PSDF / 1006001(T3)



XYPUNCH ACCE PSDF / 9006002(T1)XYPUNCH ACCE PSDF / 9006002(T2)XYPUNCH ACCE PSDF / 9006002(T3)BEGIN BULK$-------------------------------------------------------------------------------$ PARAM CARDS FOR ANALYSISPARAM WTMASS 1.$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>$FREQ1 1 1.0 0.2 95EIGRL 1 45.0 $$-------------------------------------------------------------------------------$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>DOPTPRM DESMAX 50DGLOBAL 10$-------------------------------------------------------------------------------$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>$$-----------------------------------------------------------------------$$ Left Engine Mount Point of Action$GRID 4500 1250.0 -325.0 747.0 GRID 4505 1250.0 -325.0 747.0 GRID 4501 1260.0 -325.0 747.0 123456GRID 4503 1250.0 -325.0 757.0 123456CBUSH 5955 5964 4505 4500 5901CORD1R 5901 4500 4503 4501$--1---|---2---|---3---|---4---|---5---|---6---|---7---|---8---|---9---|-------|RBE2 5961 4004501 123456 4500RBE2 5962 6004501 123456 4505CONM2 5956 6004501 00.0035 0.0 0.0 0.0 CONM2 5957 4004501 00.0035 0.0 0.0 0.0 DESVAR 6966 EM4501X 10.0 -70.00 80.00 0.2DVGRID 6966 4505 1.0 1.0 0.0 0.0DVGRID 6966 4500 1.0 1.0 0.0 0.0DESVAR 6967 EM4501Y 10.0 -60.00 30.00 0.2DVGRID 6967 4505 1.0 0.0 1.0 0.0DVGRID 6967 4500 1.0 0.0 1.0 0.0DESVAR 6968 EM4501Z 10.0 -90.00 70.00 0.2DVGRID 6968 4505 1.0 0.0 0.0 1.0 DVGRID 6968 4500 1.0 0.0 0.0 1.0 $--1---|---2---|---3---|---4---|---5---|---6---|---7---|---8---|---9---|-------|PLOTEL 5977 6004501 4501 PLOTEL 5979 6004501 4503 $ PBUSH 5964 K 450.0 300.0 500.0 0.0 0.0 0.0 B 0.0 0.0 0.0 0.0 0.0 0.0 GE 0.040 0.040 0.040 0.0 0.0 0.0$-----------------------------------------------------------------------$$ Right Engine Mount Point of Action



$$GRID 4510 1250.0 325.0 747.0 GRID 4515 1250.0 325.0 747.0 GRID 4511 1260.0 325.0 747.0 123456GRID 4517 1250.0 325.0 757.0 123456CBUSH 5964 5964 4515 4510 6001CORD1R 6001 4510 4517 4511 $--1---|---2---|---3---|---4---|---5---|---6---|---7---|---8---|---9---|-------|RBE2 5994 4004511 123456 4510RBE2 5995 6004511 123456 4515CONM2 5996 6004511 00.0035 0.0 0.0 0.0CONM2 5997 4004511 00.0035 0.0 0.0 0.0DESVAR 6998 EM4511X 10.0 -75.00 80.00 0.2DVGRID 5998 4515 1.0 1.0 0.0 0.0DVGRID 5998 4510 1.0 1.0 0.0 0.0DESVAR 6999 EM4511Y 10.0 -20.00 80.00 0.2DVGRID 6999 4515 1.0 0.0 1.0 0.0DVGRID 6999 4510 1.0 0.0 1.0 0.0DESVAR 7000 EM4511Z 10.0 -65.00 60.00 0.2DVGRID 7000 4515 1.0 0.0 0.0 1.0DVGRID 7000 4510 1.0 0.0 0.0 1.0$--1---|---2---|---3---|---4---|---5---|---6---|---7---|---8---|---9---|-------|PLOTEL 6011 6004511 4511 PLOTEL 6013 6004511 4517 PLOTEL 24511 6004511 4004511INCLUDE '/ANALYSIS/OPTIMIZATION_CARDS.dat' INCLUDE '/ANALYSIS/SIMPLE_ROAD_INPUT.dat'INCLUDE '/ANALYSIS/CONNECTIONS_WO_ENGING_MOUNTS.dat' INCLUDE '/ANALYSIS/NON_H3D_FILES.dat'ENDDATA

In this model, the left and right mount locations are being optimized for improving thedriver’s seat track for a simple rough road shake input. Most of the component files are inthe CMS super element format. The simple component files are in OptiStruct. The superelements are required in order to make each optimization run faster.

This run will make several optimization runs from different starting points. Each optimizationoutput will be put into a separate directory. The .pch files from each directory can be viewed

in HyperGraph and the best results can be chosen.

The resulting .grid file for the best results can be included in the basic model file by the

ASSIGN UPDATE card. This will automatically update the engine mount locations for you.



Create Door and Deck Lid Seals

1. The first thing that needs to be done is to save this HyperMesh macro in one of yourdirectories. The best directory to use is the Work_dir_hw11. This is the default directory

for the HyperMesh command window. It orients the seal CBUSH elements properly.

2. The easiest way to create the door seals is to isolate both side of the structure that theseal is attached to. To do this, open up the body model in HyperMesh and save the outerdoor frame in a separate file. Do the same thing with the door inner panel to which thedoor seal contacts.

3. Open up both the body side frame and the door inner panel in HyperMesh.

4. Display only the body side frame.

5. Go to the Geom panel and select lines.

6. In the Lines panel, select node list and smooth as the two options displayed.

7. Start at one point on the door side frame where the seal is attached to the body. Donot select the edge point if the door seal is perpendicular to the door edge. For the decklid seal the deck lid edge is parallel to the seal and the edge points can be picked. Do notpick nodes that are shared by two components.

8. Continue around the perimeter selecting points. The points can be spaced far apart ifthey are in a straight line. Around the curve areas, select enough points to adequatelyfollow the curve surface. Select almost each point around a curve. If you select a wrongpoint, right-click on the last point to remove it. The right-click option can be performedseveral times to remove the last few points. Do not close the line. Select the last pointclose to the first point.

9. Click create. A line will be created along the path chosen.

10.Click return.

11.In the Geom panel, select Nodes.

12.Select on line.

Number of nodes =: around 200

bias style: linear

bias intensity: 0.0

13.Click the lines button and select the line just created.

14.Click create. The temporary nodes will be created equidistant from each other.

15.Display just these new nodes using the Model panel on the left side. Turn off the bodyside frame. Note the distance between nodes using the distance option in the Geompanel and selecting two sequential points.

Record this distance for future use.

16.Select the 1D panel at the bottom. Then click connectors > spot.

17.Select the spot selection.

Location: nodes



connect with: comps

type = sealing

fe file; <<econfig.cfg

prop file: <<sealing.tcl

diameter: 0.0

mesh: independent

no systems

Tolerance: 100

18.Click the nodes button and select displayed.

19.Bring up the body side frame and the door inner panel. Click comps and then select boththe body side frame and the door inner panel to which the door seal will attach to.

20.Click create.

The spot welds representing the door seals will be created. A message at the bottom lefthand corner appears reporting how many good spot welds have been created. Thereshould not be any bad spot welds.

21.Go to the Geom panel and select temp nodes.

22.Click nodes, then select all:

23.Click add and then clear all. This will remove the initial temporary nodes create with theline command.

24.Go to Mask by Config in the left hand panel. Select Springs/Gaps. To isolate just thespot welds, select 1. Just the CBUSH elements of the spot welds will appear.

25.Go to the Tool panel and select renumber. Select nodes.

26.Click nodes and select displayed.

27.Select a start with value that will move these nodes above all other nodes in the fullvehicle model.

Increment by 1 Offset 0.

28.Click renumber > return.

29.Go to the Properties selection on the top menu line. Select Edit > Prop and select thePBUSH0 property that represent the property for the spot weld CBUSH elements.

Note that there may be multiple PBUSH properties for the door seals. The Spot commandcreates a new property card when one of the components that the door seal attaches tochanges. The following needs to be performed for each door seal property card.

30.Click Select > update/edit.

This will bring up the PBUSH card. Enter your values for the door seal properties. Theseal stiffness properties will normally be given in stiffness per unit length for each of thethree translation directions. Multiply these numbers by the length distance recordedabove and enter the values into the K1, K2 and K3 locations. K1 will be the compressivedirection; K2 the direction along the seal length; and K3 the direction perpendicular tothe seal length.



31.For K4, K5 and K6, enter 0.0.

32.Click Return twice.

33.Go to the Model panel on the left hand side and turn on the spot welds auto1.

34.Select the Tool > renumber panel.

35.Select elems. Click the elems button and select displayed.

36.Enter a start with value that moves the element IDs above all the rest of the elements inthe full vehicle model.

37.Click the renumber button.

38.Go to Mask by Config in the left hand panel. Select the Springs/Gaps to isolate justthe spot welds. Just the CBUSH elements of the spot welds will appear.

39.Now select lines and click the “+” symbol. This will bring up the line created initially.

40.Now use the macro to align the CBUSH elements properly. Go to the top line in theHyperMesh window and select View; select command window, if it is not alreadypresent.

41.Enter the macro name source orient…tbc. in the white command window.

42.Click enter.

43.In the bottom window there is a button named nodes list, which is highlighted. Expandthe CBUSH elements. Select the node closest to the line on each CBUSH element. This isthe GA point for the CBUSH element. Click proceed at any time and the macro will alignjust those CBUSH’s that were selected. Vectors that are created pointing along the linedirection are shown. This defines the “XY” plane for the CBUSH elements. You canrestart the macro by moving the curser into the command window and hitting the uparrow button.

44.Click enter. Now proceed to do all the seal CBUSH elements.

45.Go to the Model panel on the left hand side and turn on the spot welds auto1.

46.Either keep the welds with the body or the door, or the seals can be put into a separatefile by going to the file output panel entering a new name for the file and set export to Displayed.

47.Click Export.

48.Presently in HyperMesh 10.0, the PBUSH ID cannot be renumbered initially. If the sealmodel is put in a separate file, close HyperMesh and reopen it and read this seal modelback in.

49.The PBUSH property can now be renumbered by clicking Tool > Renumber. Select propand click the prop button. Now select the PBUSH associated with the door seal CBUSHs.

50.Enter a start with value that moves the property ID above all the rest of the propertiesin the full vehicle model.

51.Click the renumber button. You will now need to resave the door seal file.

52.If you save the door seals in a separate file for use with your trim body model, the bodyand door seal grid points from the deck will need to be removed. You will also need toremove the control cards at the top of the deck and the enddata card at the end of thedeck, so that when it is included with the body and doors there will be no duplicate ID’s.



Create a HyperGraph Template for Reading in Multiple Files

All the .pch files should be in the same directory and the $label values should be the same.

1. Open HyperGraph.

2. Read in file number 1.

3. To read in multiple curves at one time, select one Y Type. Select multiple Y Request. Select multiple Y Components.

4. From the Layout menu, select One curve per plot.

5. Click Apply. Multiple plots will be created.

6. From the File menu, select Save as > Report Template. Save file as a .tpl in the

same directory as where the .pch files are located.

7. From the File menu, select New > Session. This will restart HyperGraph.

8. From the Tools toolbar, select Open Reports Panel.

9. In the Report definition list, the .tpl file will be listed.

10.Click Apply. The original curves will be shown.

11.Click Add to open another file to compare the results.

12.Select Overlay.

13.Once you have finished adding the files, Save the .tpl.

14.You can now open the .tpl file in HyperGraph and enter new file names for different

comparisons.



Using AMSES (Automatic Multi-Level Sub-StructuringEigensolver Solution)

For the solution of large eigenvalue problems, the AMSES solution can be used instead of theLanczos eigensolver. The resulting eigenvalues and eigenvectors are used in eigenvalueanalysis, CMS Super Element creation, Modal Frequency Response, and Modal TransientAnalysis. In addition, the AMSES solver can be used during topology, topography, shape,and sizing optimizations. The AMSES solver can be 2-100 times faster than Lanczos.

AMSES is a multi-threaded application and can use any number of processors. AMSES willuse the same number of processors that OptiStruct is using.

Activating AMSES

To use AMSES, one of the following must be defined:

1. Use of the EIGRA data, instead of EIGRL data.

2. Use of AMSES solver keyword on the CMSMETH data

AMSES Usage Guidelines

The following guidelines list the factors affecting AMSES usage:

1. The AMSES solution is, generally, much faster than Lanczos, but the results areapproximate. Accuracy of the lower modes is very high; therefore, AMSES is a goodcandidate for solutions with a large number of modes (greater than a few hundred) wherean approximated eigen-space is sufficient (as in Modal Frequency Response and ModalTransient Response Analysis). Although approximate, the large number of modes used formodal analysis will encompass the modal space and the resulting motion will match veryclosely with the Lanczos results. Lanczos is recommended in solutions where accuratemode shapes of a small number of modes are required.

2. AMSES is also recommended in cases where: 1) A low number of eigenvalues arerequested but the model consists of more than a million degrees of freedom, and/or; 2)The upper bound (V2) is specified or the number of modes (ND) is greater than 50 on theEIGRL entry. In such cases, it is likely that Lanczos runs are slower than AMSES runs.

3. For optimization runs, if accuracy of the eigenvector is important, normal modes analysiswith AMSES can be run first and then Lanczos can be run with precise lower and upperbounds to check the AMSES run for accuracy. The AMSES upper bound can then beadjusted to achieve acceptable accuracy of the desired eigenvectors. Now, AMSES can beused for all optimization runs in this analysis.

4. The AMSES solution is much faster for flexible body generation and modal solutions withmany residual vectors.

5. AMSES should be used cautiously in situations with very large RBE3’s (i.e., if the RBE3 isconnected to 1/4th of the structure). It may be better to eliminate such RBE3’s.

6. AMSES solution speeds depend on the number of eigenvector degrees of freedom (DOF)to be calculated. DISP=ALL will cause the entire eigenvector to be calculated and thespeedup will not be large. However, if results for only a few DOF are required (typical forNVH analysis), AMSES can be up to 100 times faster than Lanczos. To improve AMSES runtimes, it is recommended to request results only for the required DOF.



7. For an AMSES run with V1, V2 and ND specified on the EIGRA entry, AMSES calculates allthe modes up to the specified V2 (upper bound) regardless of the value of ND. Then “ND”number of requested modes is output. Therefore, reducing ND by keeping the upperbound (V2) the same will not significantly improve the AMSES run times, the upper boundmust also be correspondingly reduced to prevent the extraction of extra modes.

8. AMSES is also useful in checking for model irregularities. AMSES can be used to print thelist of grids associated with a massless mechanism or a singularity.

Parameters Affecting AMSES

AMSES controls the accuracy and the cost of a solution with the parameter AMPFFACT. The

“optimal” value of AMPFFACT for typical NVH analysis, 5.0, has been established through

extensive testing. AMPFFACT is set on the EIGRA and CMSMETH data.

In case of predominately solid models, such as engine blocks, AMPFACT should be set to 10.0.

PARAM,RBMEIG can be used to adjust the upper limit on eigenvalues associated with rigid

body modes. The default upper limit is 1.0 (equivalent to a natural frequency of 0.16 Hz) if PARAM,RBMEIG is not included in the deck.

Residual Vector Calculations

When the AMSES eigensolver is used, residual vectors for each of the following arecalculated:

USET U6 data

Frequency Response Dynamic Loads

Transient Response Dynamic Loads

Damping DOF from CBUSH, CDAMPi or CVISC data

One Residual Vector is calculated for each USET U6 degree of freedom, each DAREA degree offreedom, and each damping degree of freedom associated with the CBUSH, CDAMPi andCVISC data.

The Residual Vector calculations are controlled by the Solution Control data RESVEC. Tocontrol Residual Vector calculations with AMSES, the following commands can be used:

Use RESVEC=NO to turn off Residual Vector calculations with AMSES

Use RESVEC(NODAMP)=YES to turn off Residual Vectors associated with Damping DOF.

If the center of a large RBE3 is loaded, a residual vector will be created that includesterms for each of the independent DOF. If this number is large, say over 500, theAMSES run time will increase dramatically. For large loaded RBE3 it is recommended touse the RBE3 UM data to make the center GRID independent.



Modeling Techniques

The Modeling Techniques section provides an overview of the following:

Parts and Instances


Direct Matrix Input


Poroelastic Materials

Elements and Materials

Loads and Boundary Conditions

Virtual Fluid Mass

Modeling Errors



Parts and Instances

Introduction

The Parts and Instances functionality can be used to combine independently createdsubstructures (or, parts) into a single model. This feature allows you greater flexibility in thecreation of a finite element model. By following a few simple numbering requirements, youcan define independent substructures which in turn can be easily combined into a final biggermodel using simple translational and rotational transformations. Explicit instancing of partscan be achieved, as explained in the Instances section. This functionality is available for allanalysis solution sequences and is currently not supported for optimization runs. OptiStruct-Multi-body Dynamics (OS-MBD) and Geometric Nonlinear Analysis are not supported.

Motivation

There are various advantages to defining a large finite element model as a combination ofsubstructures or parts:

1. Model complexity is reduced as the structure is segregated into manageable substructureswhich are interconnected using simple transformations.

2. Individual part modules can be locally updated without having to make cascading edits tothe entire structure.

Figure 1: Illustration depicting a model created as a combination of multiple parts (substructures)

3. Each substructure can be independently developed in a modular environment and laterassembled into a single structure. This allows various departments working on a projectto focus on independent modules while following a few simple numbering requirements.

Numbering Requirements

In this implementation, specific ID control for grid points and elements (including rigidelements) is not required. Refer to ID Resolution Guidelines for a detailed explanation of partnumbering and how this influences the various other data entries in the model. The followingsimple numbering requirements should be enforced for any solver deck containing multipleparts:



1. Entities which are part specific, like grid points and elements, are numbered by part

based local numbering.

2. Global entities such as properties, materials, loads and boundary conditions are defined inthe global numbering system.

3. The individual parts forming the total structure can be combined without any changes informat if the numbering requirements (1) and (2) are met.

Parts

A part can be visualized as an independent entity which is connected to a global structureduring assembly (The global structure is also considered to be a part). Each part can bedefined as a section of the entire finite element model that is used for a specific purpose. Forexample, a door of an automobile can be defined as a part and multiple instances of this partcan be instantiated (refer to Instances for a detailed explanation of part instancing) to savetime during modeling.

Definition

A part is included in the global structure between BEGIN and END bulk data entriespotentially using the INCLUDE entry. The INCLUDE entry accepts a string that references thefile name (filename.fem) of a specific part. Parts are defined as separate solver decks and

could be included within the same working directory. Multiple INCLUDE entries can be usedwithin a single set of BEGIN and END entries to add multiple sections of a single part (referto Instances for a detailed explanation of part instancing). A part can also be split betweenseparate BEGIN and END entries with the same part name.

Format

BEGIN and END bulk data entries mark the start and end of the definition of a part in theglobal structure. A part is defined as a separate file which is included in the global structureusing the INCLUDE bulk data entry (The entire solver deck of the part can also be insertedbetween the BEGIN and END entries, instead of using the INCLUDE entry).

The format used to include a part in a global structure is as follows:

BEGIN, FEMODEL, name

INCLUDE “filename.fem”

END, FEMODEL, name

The second field of the BEGIN entry should be set to FEMODEL and the third field shouldcontain the name of the part. This part name will be used to define fully qualified referencesto local entries within the part from anywhere in the model. All part names in the modelshould be unique. Part names are not case sensitive and should start with a letter. They cancontain letters, digits, and underscores, only. filename.fem follows standard requirements

for INCLUDE, that is, it can refer to a local file or contain the full path. No other BEGIN orEND entries are allowed between BEGIN and END. All bulk data entries should be locatedbetween BEGIN, FEMODEL and END, FEMODEL. A full model consists of several parts. Onepart is designated as global. The other parts can be moved to arbitrary locations using the INSTNCE bulk data entry and connected to each other using connector elements or CONNECTbulk data entries.



Local and Global Entries

Local entries, as their name suggests, are data entries that can be defined locally within aspecific part. Local entries are currently limited to the following (refer to the Appendix for alist of all local entries).

Grid Point Definition

GRID Bulk Data Entry

Rigid Elements

RROD Bulk Data EntryRBAR Bulk Data EntryRBE1 Bulk Data EntryRBE2 Bulk Data Entry

Elements

CHEXA Bulk Data EntryCQUAD Bulk Data Entry CBUSH Bulk Data Entry and so on

All other data entries are considered global and should be defined in the global structure.Even if they are located within BEGIN – END entries in a different part, they are stillinterpreted as if they are in the global part. Some global data entries can reference local dataentries (see above list) using fully qualified references.

Fully Qualified References

The same ID number can be used for non-unique local data entries defined in multiple parts.Such ID’s cannot be referenced by entries in the global structure without the use of fullyqualified references. Fully qualified references contain information about both the local dataentry and its corresponding part.

Numeric Reference Fully Qualified Reference

A numeric reference on a local entryreferences another local entity withinthe same part, or a global entity. Anumeric reference can be used toreference a global entry only ifanother entry of the same type andwith the same ID does not existwithin the current part.

References a local entry definedwithin any part.

A numeric reference on a global entryreferences an entity within the globalpart only.

A fully qualified reference can beused to reference an entry whenanother entry of the same type andwith the same ID exists within themodel.



Numeric Reference Fully Qualified Reference

Format: A <number> equal to the

set ID of a non-local entry that is tobe referenced is input in thecorresponding field(s) of thereferencing entry.

Format: This is similar to the formatof a numeric reference. Thedifference is that<PartName.number> is input in the

corresponding field(s) of thereferencing entry. The PartName is

the name specified on the BEGIN

entry for the part that contains thereferenced entry.

Example:

RBE2, 16, 9, 123, 10

This connects grid points 9 and 10located in the same part as the RBE2entry (RBE2 is a local entry).

CHEXA, 5, 9, …

This references global material 9irrespective of where the MAT#, 9entry is located (Currently, allMaterial entries are global entries).

Example:

RBE2, 16, door.9, 123,bpillar.1

This connects grid points 9 and 10located in part “door” and part“bpillar”, respectively.

This RBE2 entry can be located inany part.

ID Resolution Guidelines

The following guidelines can be used to implement proper ID resolution in a model containingmultiple parts and instances.

1. Each part can be included only once within a specific set of BEGIN and END bulk dataentries. Inclusion of multiple copies of a single part is known as instancing (refer to Instances).

2. All references to properties and materials are resolved in a standard way. These entitiesare global and should be defined only once anywhere in the model.

3. Subcase information and I/O options entries are also handled similarly. These entriesrefer only to numeric ID of entries in the global part (for example, SPC = 5 will expectSPCADD, 5 or SPC, 5 within the global part). SPC’s, MPC’s, SPCADD and MPCADD arelocal entries and they allow fully qualified referencing of local entries anywhere in themodel. SPCADD, MPCADD entries in parts are allowed but will not be used in the solutionas they cannot be activated by subcase selectors.

4. Fully qualified references are allowed in some data entries (refer to the latest OptiStructReference Guide to check if a data entry accepts fully qualified references). Not all entriesand not all fields within these entries allow fully qualified references.

5. This generalized syntax is allowed in all four bulk formats – fixed small field, fixed largefield, free and free large field. As fully qualified references are usually longer than 8characters, free formats are more useful for this purpose.



6. As a general practice, all data entries using fully qualified references are placed inside theglobal part. This is not mandatory.

7. The own ID of each data entry (usually the second field after the card name) cannot be afully qualified reference.

8. As explained previously, for local entries, their own ID’s within a particular part cannot beequal. Whereas, similar data entries can be the same own ID if they are defined indifferent parts. In such cases they are completely independent entities and their ID’s areresolved by using fully qualified references. The same rules apply to set ID’s, for example,in SPC’s or MPC’s – the same SID in different parts represent completely independententities.

9. Any reference to a global entry must be a numeric reference regardless of whether it isbeing referred to from a global or a local part.

10.A fully qualified reference (if allowed) is resolved to a specific instance defined by partname and ID within that part.

11.If a local entry contains a numeric reference (instead of a fully qualified reference),OptiStruct resolves the reference to a local entry within the same part. If the part doesnot contain an entry (of the required type) with the ID equal to the numeric reference,OptiStruct looks in the global part for a possible match. If the entry is not available in theglobal part also, then the program errors out, regardless of whether the required entry(with same ID) is available locally in a different part. For example:

This entry is located in local part “grip”:

RBE2, 15, 5, 123, 7, 8

Grid points 1,3,5 are included in part “grip”

Grid points 1,3,5,7,8 are included in local part “frame”

Grid points 3,5,7 are included in global part “racquet”

In the above example, on the RBE2 element, grid point 5 refers to grid grip.5, grid point

7 refers to racquet.8 and grid point results in an error.

12.OptiStruct allows repetition of some global data entries, even if only unique ID’s areallowed, only if the content of such cards is identical (for example, material and propertyentries).

Logical Sets

The SET bulk data entry can be used in the global part to reference SET’s defined withindifferent parts. These SET entries in the global part can contain fully qualified references topart-specific SET data only if logical operators (OPERATOR field on the SET entry) are used.For example:

The following SET entry exists in part “A”:

BEGIN, FEMODEL, ASET, 29, ELEM, LIST 15 THRU 30…END, FEMODEL, A



Referencing SET, 29 in the global part “G”:

BEGIN, FEMODEL, GSET, 78, ELEM, OR A.29…END, FEMODEL, G

This process can be used to reference local sets in the global part on entries which do notsupport fully-qualified referencing of local sets (like, output entries). For example:

The following SET entry exists in part “A”:

BEGIN, FEMODEL, ASET, 3, GRID, LIST 15 THRU 30…END, FEMODEL, A

In the global part “G”:

Incorrect

BEGIN, FEMODEL, G

DISPLACEMENT(H3D)=part.3orDISPLACEMENT(H3D)=3 …END, FEMODEL, G

Correct

BEGIN, FEMODEL, G

DISPLACEMENT(H3D)=3

SET, 3, GRID, OR A.3…END, FEMODEL, G

Relocation

A full model in an OptiStruct Parts and Instances consists of a collection of parts. These partsare inserted into the global structure automatically (without relocation) or by using entrieswhich allow relocation (RELOC and INSTNCE). Relocation involves the positioning of partswithin the model relative to each other or the global structure. Currently relocation of partsincluded in the full structure can be accomplished using the INSTNCE and RELOC bulk dataentries. Relocation involves translational and rotational movement of parts relative to theirinitial position.

INSTNCE Bulk Data Entry

The full model consists of several parts. One part is designated as global and the rest of theincluded parts are relatively positioned with respect to the global part with the help of theINSTNCE entry. The INSTNCE entry references the RELOC bulk data entry that defines therelocation or mapping of grid points from one position to another.



Format

A INSTNCE bulk data entry can be specified only within the global part. No INSTNCE entrycan reference the global part. Each INSTNCE entry should reference a unique part name,however, it is not required that every part is positioned using an INSTNCE entry. Parts whichare not specified on the INSTNCE entry are included in the full model without any relocation.

INSTNCE, SID, name, NN

The third field “name” specifies the name of the part defined via the BEGIN, FEMODEL, name

entry and NN references the ID of the RELOC bulk data entry. The RELOC bulk data entry

defines the actual location of the part in the final model. Refer to the OptiStruct ReferenceGuide for detailed information.

RELOC Bulk Data Entry

The RELOC bulk data entry defines relocation or mapping of grid points from one position toanother. It can be used in conjunction with the INSTNCE entry to relocate parts relative toeach other or to the global structure.

Format

RELOC entries are used to relocate grid points within the full model. RELOC definesindependent transformation of each part, not the transformation of one part with respect toanother. In particular, it does define that two parts should be connected together and thenrelocated as an assembly. It can be specified in the global part and is referred to by partspecific entries like INSTNCE.

RELOC, ID, type, GID# …

The third field “type” specifies the type of relocation: MOVE, MATCH, ROTATE, or MIRROR. There

are multiple formats of the RELOC entry depending on the specified type. Refer to the OptiStruct Reference Guide for detailed information.

Connectivity

The final step in the part assembly process is connection. Connectivity between parts can beachieved in two different ways, the first involves using the CONNECT bulk data entry and theother is using connectors like rigid or bush elements that can explicitly reference grids in anypart.

Connectors can contain a mix of regular and fully qualified ID’s. Regular ID’s reference:

In a Local entry:

An entry with that ID in the same part, or to an entry with the same ID in the global part.

In a Global entry:

An entry with that ID in the global part.

Refer to comment 11 in the ID Resolution Guidelines section for information on how regularID references in localized entries are resolved. The Appendix contains a list of supportedLocal entries which can be defined within a part.

CONNECT Bulk Data Entry

The CONNECT bulk data entry defines equivalence for degrees of freedom between two parts.

Using two forms of the entry, you can equivalence all degrees of freedom for grids of both

parts within the specified tolerance distance from each other.



CONNECT always equivalences grid points located within two parts at the same location (X,Y, and Z) after all parts are moved to their final location using INSTNCE entries. If multiplegrid points exist in both parts at the same location (within the specified tolerance), then theywill be equivalenced together.

Format

The CONNECT entry can be used to define equivalence between two parts (name_a and

name_b) by searching for all grid points within a specified tolerance (tol). The alternate form

involves specifying a set of grid points at which to search for neighboring grids of either part“name_a” or part “name_b” within a specific tolerance (tol).

CONNECT, name_a, name_b, tol

The tolerance (tol) is a numeric value defining the maximum distance between two grid

points to allow equivalence. All grids in “part_a” are considered, if the search in “part_b”

finds a grid point matching the location (within the specified tolerance), then these two gridsare equivalenced. Refer to the OptiStruct Reference Guide for detailed information.

Instances

Instances are multiple copies of a part that are exactly the same as the part itself in allrespects. Currently, part instancing in OptiStruct is available as a logical extension to the partinclusion process. A direct approach to part instancing will be available in a future release.

Creating instances of a part

To create an additional instance of an existing part, the part inclusion process can berepeated.

For example, to create an additional instance of the part “CrankShaft”, the BEGIN FEMODEL

and END FEMODEL statements are repeated. The same set of include files (using the INCLUDE

entry) are repeated inside multiple part definitions.

BEGIN, FEMODEL, CrankShaft_1

include “CrankS_a.fem”

include “CrankS_b.fem”

END, FEMODEL, CrankShaft

BEGIN, FEMODEL, CrankShaft_2

include “CrankS_a.fem”

include “CrankS_b.fem”

END, FEMODEL, CrankShaft

Appendix

Local Data Entries

A list of data entries which can currently be defined as local entries in OptiStruct are listedbelow:

Miscellaneous

GRID, SPC, MPC, SET



Elements

CAABSF, CBAR, CBUSH1D, CBUSH, CDUM1, CELAS1, CELAS2, CELAS3, CELAS4, CFAST,CGAP, CGAPG, CGASK12, CGASK16, CGASK6, CGASK8, CHACAB, CHEXA, CONM1, CONM2,CONROD, CONV, CPENTA, CPYRA, CQUAD4, CQUAD8, CROD, CSEAM, CSHEAR, CTETRA,CTRIA3, CTRIA6, CTRIAX6, CTUBE, CVISC, CWELD, and PLOTEL

Rigid Elements

RBAR, RROD, RBE1, and RBE2

Entries which allow fully qualified references

TO GRID POINTS:

A list of data entries which currently allow fully qualified references to grid points inOptiStruct are listed below:

Local entries

CBUSH1D, CBUSH, RBAR, RROD, RBE1, RBE2, and RBE3

Global entries

SPC, MPC, FORCE, MOMENT, SPCD, and RELOC

TO OTHER ENTITIES:

A list of data entries which currently allow fully qualified references to other entities inOptiStruct are listed below:

SPCADD and MPCADD (allow fully qualified references to SPC and MPC, respectively)

SET (allow fully qualified references to other local SET entries only if logical operators areused)

Refer to the Release Notes for the latest list of all global/local entries and for entries whichallow fully qualified references to other entries. Analysis entries are available for Parts andInstances entries specific to optimization (for example, DVGRID, DESVAR) are not allowed.




Introduction

Subcase specific modeling in OptiStruct allows you to analyze multiple structures in a singlesolver run. The structures can be completely independent; can represent different regions ofthe same model, or different assemblies sharing common parts. Subcase specific modeling isalso known as submodeling. In a traditional modeling scenario without submodelingcapabilities, the entire model will be solved for each solver run, regardless of the boundaryconditions and multiple models will have to be created to solve structures with variablesections. Submodeling allows specific sections of the model to be solved independentlywithout affecting the rest of the structure.

Motivation

There are various advantages to subcase specific modeling for both analysis andoptimization. The primary motivation for submodeling is the ability to solve independentstructures with common parts. For example, if you consider the case of a pickup truck,various cabin shapes can be solved for, by allowing the bed and the chassis to remainunchanged. This is accomplished by assigning elements belonging to different cabin types todifferent sets. The constant chassis and bed can be a defined as another element set. Theseelement sets can now be combined to allow various structural submodels to be modeledwithout having to repeat the common parts of the structure for each solution.

Figure 1: Example illustration depicting an application of subcase specific modeling.

In Figure 1, each cabin body can be defined as a specific element set and the common partswill make up one element set. These can be independently combined under three differentsubcases with different boundary conditions and solved in one single solver run.

Implementation

The subcase specific modeling functionality is realized with the use of element sets and thesubcase selector entry SUBMODEL. The SUBMODEL entry can be used within a specificsubcase in the subcase information section to select a certain element set for the solution.

SUBMODEL subcase information entry

The full model consists of several common or shared sections which remain constant whileother sections are changed to find the best fit for a particular application. In such cases, the



SUBMODEL entry can be used to choose a set of elements for selective solution. The elementset identification number is the only input required for this entry.

Format

SUBMODEL, SID, SID_r

The fields “SID” and “SID_r” specify the identification numbers of the element and rigid

element sets, respectively defining the submodel that is solved within this subcase. The“SID_r” field is optional. Refer to the OptiStruct Reference Guide for detailed information.

Submodeling - Example OptiStruct input deck

$ Subcase Information Section

SUBCASE 1

$ Submodel specific SPC’s and LOAD’s can be defined here.

SUBMODEL, 11

SUBCASE 2


SUBMODEL, 12

$ Bulk Data Section

SET, 1, ELEM $ defines the shared/common part, for example, the chassis, bed and

wheels in Figure 1

SET, 2, ELEM $ defines the individual part, for example, cabin body 1 in Figure 1

SET, 3, ELEM $ defines the individual part, for example, cabin body 2 in Figure 2

SET, 11, ELEM, OR, 1, 2 $ defines the full truck model with cabin body 1 and the

common parts

SET, 12, ELEM, OR, 1, 3 $ defines the full truck model with cabin body 2 and the

common parts

Comments

1. Single Point Constraints (SPC), Loads (LOAD), Multi Point Constraints (MPC) and othersimilar subcase selectors should define attributes only applicable to the specific submodelor substructure. These attributes should apply exclusively to the subcase-specific modeldefined via SUBMODEL. The SUBMODEL entry does not trim the specified attributes(loads, constraints and so on) to the defined subcase.

2. This functionality is currently available for linear static analysis only. All optimizationtypes with responses from Linear Static analysis are supported (except SPCFORCE/residual force responses).

Global-Local Modeling

Global-local analysis is a technique in which a full model is solved using two (or more)submodels; one submodel represents the full structure but at a lower accuracy (for example,a larger mesh size) and the second submodel represents only a part of the structure (forexample, using a smaller mesh size). The global structure is solved first and thedisplacements from the selected zone are interpolated and applied to the local structure.



Global-local analysis is implemented with the use of the subcase specific modeling techniquedefined above.

Note that Global-local modeling is only an approximation, and its use depends on theassumption that a more accurate local model will not significantly affect the displacements ofthe global structure. This process should not be used whenever small stiffness changes in thelocal submodel may have a large impact on the solution outside of it.

Motivation

Global-local analysis may help improve results in models with local stress concentrations.Parts of the structure with small details which require relatively higher accuracy can bemodeled as local submodels with a fine mesh and the full structure can be modeled using acoarse mesh. This will allow for faster solution times as only a part of the structure is beingsolved with a fine mesh.

Figure 2: Example illustration depicting an application of global-local analysis.

In Figure 2, an example building is illustrated wherein sections containing the pillar-roof joint

are modeled as separate submodels with a refined mesh. The finer mesh allows for better

accuracy at regions with high stress concentrations. Using the global-local analysis capability,

the results from the coarser global model are interpolated and applied to the finer mesh of

the local model at the transfer region. This allows for the local model to be driven by the

results of the global model.

Implementation

The global-local modeling functionality is realized with the help of the subcase specificmodeling feature and the subcase selector entry GLOBSUB. This entry is defined in thesubcase which contains the local model definition. The GLOBSUB entry identifies the globalmodel which is used to drive the specific local model.

GLOBSUB subcase information entry

The full model consists of several sections with areas of high stress concentration or regionsof interest which require a higher accuracy. In such cases, the entire model can be solvedwith a coarser mesh and in each local subcase defining the submodel of interest, the globalstructure can be referenced using the GLOBSUB entry. The set of grids within the localstructure at the transfer zone is also specified.



Format

GLOBSUB, SUBID, SID

The field “SUBID” specifies the identification number of the subcase that contains the global

structure definition (via SUBMODEL) and the field “SID” specifies the set of grid points in the

local structure that defines the transfer zone. The displacements from the global structure areapplied to this set of grid points. Refer to the OptiStruct Reference Guide for detailedinformation.

Global-Local Analysis - Example OptiStruct input deck

$ Subcase Information Section

SUBCASE 1


SUBMODEL, 11

SUBCASE 2


SUBMODEL, 12

GLOBSUB, 1, 15

$ Bulk Data Section

SET, 11, ELEM $ defines the global structure, for example, the full building in Figure 2

SET, 12, ELEM $ defines the local structure, for example, the pillar-roof joint in Figure 2

SET, 15, GRID $ defines the transfer zone, for example, the interface grids of the pillar-

roof joint in Figure 2 at which the displacements are interpolated.

Comments

1. The transfer zone should contain only 3-dimensional elements in both the local and globalstructures. Second order elements (for example, CHEXA20) are allowed. There is nofurther restriction on element types elsewhere in the structure.

2. The transfer zone may represent single or multiple cuts (sections) through the structure.Multiple cuts should be separated from each other, that is, they should not exist closerthan the element size of the global model.

3. The GLOBSUB entry should always reference the subcase ID of a global subcase that isdefined above its corresponding local subcase.

4. This functionality is currently available for linear static analysis only. All optimizationtypes with responses from Linear Static analysis are supported.

Exceptions:

SPCFORCE/residual force responses are not supported.

Topology must lie outside the local part(s) and, any design variables affecting the localsubmodel should also be mapped to the global model.



Direct Matrix Input (Superelements)

Direct Matrix Input

Creating Superelements

Component Dynamic Analysis Super Element Generation



Direct Matrix Input

In the course of a finite element solution, matrix representations of a structure's stiffness,mass, damping, and loading are generated. The matrices are based on the informationprovided in the Bulk Data section of the input file. Depending on the analysis type, systemequations using these matrices are solved to simulate the structure’s behavior.

In a linear static analysis, for example, a system of linear equations Ku=f is solved. Here, Kis the stiffness matrix, f is the loading vector, and u is the vector of the unknown

displacements.

The time taken for these matrix solutions is about proportional to the square of the numberof degrees-of-freedom of the structure. The solution speed can be improved by representingsections of the structure (super element assemblies) with a smaller subset of degrees offreedom of those sections (boundary degrees of freedom of the super element assemblies)and a representative set of reduced matrices. In an optimization, for example, the solutionspeed can be improved dramatically by removing the non-design portion of the structure andkeeping only the design portion of the model.

For the purpose of deriving the matrices, the displacement vector may be partitioned intodisplacements of inner (OSET) and outer (ASET, interface) degrees of freedom.

(1)

Here, the subscript ‘o’ denotes the inner degrees of freedom, and ‘a’ the interface degrees of

freedom.

The static equilibrium is given as:

(2)

The eigenvalue problem for a normal modes analysis of the body using a diagonal massmatrix represents itself as:

(3)

Note: PARAM, WTMASS cannot be applied to superelements (.h3d or .pch) that are read

into the model. If the unit of mass is incorrect on the MAT# entries and PARAM,WTMASS is required to update the structural mass matrix; then this should be done inthe creation run.

There are two ways of obtaining the reduced matrices:

1. Static Condensation (or Guyan Reduction) reduces the linear matrix equation to theinterface degrees of freedom of the substructure through algebraic substitution. Theresult can be used as external matrices, representing a super element assembly, in afinite element analysis. This method is accurate for the stiffness matrix and approximatefor the mass matrix.



In addition, the load vectors are reduced to the ASET DOF. This includes the load vectorsfrom point and pressure loads as well as distributed loads due to acceleration (GRAV andRLOAD).

2. Component Mode Synthesis (CMS) reduces a finite element model of an elastic body tothe interface degrees of freedom and a set of normal modes. The result can either beused for inclusion as a flexible body in a multi-body dynamics analysis (see Flexible BodyGeneration) or as external matrices, representing a super element assembly, in a finiteelement analysis. It is always an approximation; however, it is the preferred method fordynamic analysis as it captures the mass matrix correctly.

Load vectors are not reduced during CMS Super Element creation.

Static Condensation

The first line of equation (2) reads as:

oo o oa a oK u K u P

The displacements of the inner degrees of freedom, therefore are:

1o oo o oa au K P K u (4)

Also from equation (2):

ao o aa a aK u K u P

Substituting equation (4) into this:

1ao oo o oa a aa a aK K P K u K u P

or

1 1oaKaa ao oo a a ao oo oK K K u P K K P

This is interpreted as:

areduced reducedK u P

So the reduced stiffness is:

1aa ao oo oareducedK K K K K

And the reduced loading is:

1a ao oo oreducedP P K K P



The reduced matrix can also be written as:

1Taa ao oo oareducedK S KS K K K K

Then, using the same transformation, you can obtain the reduced mass matrix:

1 1 1 1aa ao oo oa oo oa ao oo oa ao oo oareducedM M K K M K K K K M M K K

The solution of the reduced linear static problem provides an exact solution, whereas the

solution of the reduced eigen problem, a areduced reducedK u M u, only provides

approximations to the solution of the full eigenvalue problem as only vectors that satisfy the

constraint 1

o oo oa au K K u will be included in the solution.

Component Mode Synthesis (CMS)

The interface or boundary degrees of freedom (ASET) that are used in the construction ofmode shapes should be representative of the set of force-bearing degrees of freedom in thesubsequent analysis. For a finite element analysis, this refers to those nodes that connect toeither the residual structure or other super element assemblies.

The purpose of specifying the interface or boundary degrees of freedom for CMS is mainly toaccount for the static deformation due to constraint or applied forces acting on the interfacedegrees of freedom. A large number of eigenmodes is required if these static modes areomitted. The flexible deformations due to constraint forces, compared to the deformationdue to the body inertia forces, are often dominant in most constrained models. The inclusionof all force-bearing degrees of freedom as interface degrees of freedom is therefore anessential step to get accurate results from subsequent analyses.

The task of the component mode synthesis is to find a set of orthogonal modes thatrepresent the displacements u of the reduced structure such that:

q

Where, q is the matrix of modal participation factors or modal coordinates which are to be

determined by the analysis.

For creating external matrix representations of super element assemblies for use insubsequent finite element analyses, only the Craig-Bamption method of component modesynthesis is currently available.

Craig-Bampton Method

This method uses a system constrained in the interface degrees of freedom. Normal modes

analysis of the system yields the diagonal matrix of eigenvalue and the matrix of

eigenmodes . In this normal analysis, you can select the cut-off frequency or the number

of modes to be solved. This determines the column dimension of .

In addition, a static analysis is performed with a unit displacement in each interface degree



of freedom while all other interface degrees of freedom are fixed. The number of subcases inthis static analysis is six times the number of interface nodes. Note that it is important toconstrain each interface node with its neighboring nodes, if necessary, to ensure that it hasnon-zero stiffness along the direction of all six degree of freedom. This yields the

displacement matrix and the interface forces .

Reduced modal stiffness and mass matrices are now generated using,

which yields:

.

It follows an othogonalization step that transforms the original shapes X into a set of

orthogonal modes .

Eigenvector Normalization

First, a new eigenvalue problem using the reduced matrices above is solved.

The resulting diagonal matrix of eigenvalues D and the normal modes N are used to

transform the set of original shapes into the set of orthogonal modes .

It can be shown that the resulting modes are orthogonal with respect to the system stiffnessmatrix K and mass matrix M.

If the orthogonal modes are normalized with respect to the mass matrix M, the reduced

matrices for the subsequent analysis appear as:

Generating the Matrices

Through the inclusion of certain bulk data and I/O options entries described here, staticcondensation and component mode synthesis may be performed on a structure and thereduced matrices written to a file for use in subsequent analyses.

For static condensation, only stiffness, mass, and load matrices can be generated. If theSUBCASE is for static analysis, by default the reduced mass matrix will not be created. However, PARAM,DMIGMASS,YES can be used to create the reduces mass matrix for staticanalysis. For eigenvalue analysis, the mass and stiffness matrix will be reduced, but there is



no reduced load vector.

For component mode synthesis, stiffness, mass, structural and viscous damping, and fluid-structure coupling matrices can all be generated. No reduced load vector is created.

Matrix reduction is activated by the presence of ASET or ASET1 bulk data entries. These bulkdata entries indicate the interface or boundary degrees of freedom of a super elementassembly, i.e. the set of degrees-of-freedom where the component, being replaced by directmatrix input, connects to the modeled structure.

If ASET or ASET1 bulk data entries are present, and there is no CMSMETH I/O Option, thenthe static condensation method is used to generate the reduced matrices.

Component mode synthesis is activated by the presence of the I/O Option CMSMETH. The I/O Option references a CMSMETH bulk data entry, which defines the method of matrixreduction to be used (CBN or GUYAN methods apply to external super element generation). When CBN is the selected method, the frequency range or number of modes to be calculatedand the starting SPOINT ID for storing the modal data are also defined on CMSMETH. ForGUYAN, this additional information is ignored.

With component mode synthesis, no loads or SPC boundary conditions can be applied directlyto the portion of the structure that is being removed. For the definition of loads or SPCs,however, an ASET can be defined at the grid point of a load or SPC. Then, loads or SPCs canbe applied to that grid point in the assembled model.

Reduced matrices are automatically written to the .h3d output format, unless

OUTPUT,H3D,NONE is defined. The matrices can also be saved in the Nastran punch format(.pch file) or in a binary format (.dmg file) by using the PARAM, EXTOUT bulk data entry.

The matrices are written to the .pch file in the DMIG bulk data entry format. They are

defined by a single header entry and one or more column entries. The I/O option entry DMIGNAME provides you with control of the name of the matrices written to the .pch and

.dmg files. This is an optional entry and if not used matrices are given the suffix “AX.”

With static condensation, the stiffness matrix is always output when PARAM, EXTOUT ispresent in the input file; however, the load matrix is only output if a linear static subcase ispresent, and the mass matrix is only output if an eigenvalue subcase is present. All subcasesmust use the same boundary conditions (SPC set) and multi-point constraints (MPC set) oran error termination will occur.

With component mode synthesis, the orthogonal modes and the correspondingeigenvalues D are exported to the .h3d file by default. The export of the model to this file

can be controlled using the MODEL output statement. This allows for only a small portion ofthe model or a “display model” (a coarse representation of the structure consisting ofPLOTELs) to be exported.

For component modal synthesis super elements written to the .h3d file, there is no interior

grid or element data stored by default. However, the MODEL data can be used to specifyinterior grids for displacement, velocity, or acceleration results, and interior elements forstress and strain results in the residual run. The SEINTPNT data can be used to convert theinterior points to exterior points in the residual run, so that they can be used as connectionpoints, loading points, or response points in optimization.



Using the Matrices in a Finite Element Analysis

To use the reduced matrices that were written to an .h3d file, the ASSIGN I/O option must

be used to assign names to such matrices. Unlike matrices stored in .pch or .dmg formats,

those stored in the .h3d file are named on retrieval, rather than on creation. The ASSIGN,

H3DDMIG command provides a suffix “matrixname” for the matrices retrieved from that file. Once matrices in an .h3d file have been assigned a name they may be referenced using one

of the subcase information entries listed below. All of the matrices in the .h3d file are used in

the analysis by default. If only some of the matrices are to be used, then use the K2GG,M2GG, K42GG, and B2GG data to specify which matrices are to be used. The unreferencedmatrices will not be used in this case. The SEINTPNT can be used to convert the interiorpoints specified by the MODEL data in the creation run to exterior points in the residual run,so that they can be used as connection points, loading points, or response points inoptimization.

Reduced matrices that are written to .pch files are stored as DMIG bulk data input. As these

reduced matrices are already in a recognized input format, the files simply need to beincluded in the bulk data section by an INCLUDE statement.

Reduced matrices that are written to a .dmg file are stored in a binary format. Similar to the

.pch file, these reduced matrices simply need to be included in the bulk data section by an

INCLUDE statement.

As matrices are referred to by name, it is important to ensure that when multiple reducedmatrices are used that they have unique names. Matrices may be chosen through one of thefollowing subcase information entries as either stiffness, mass, damping, or load matrices.

The K2GG subcase information entry references a matrix by name, indicating that it is astiffness matrix. The stiffness matrix must be symmetric and it applies to all subcases.

The M2GG subcase information entry references a matrix by name, indicating that it is amass matrix. The mass matrix must be symmetric and it applies to all subcases. Gravityand centrifugal loads are not considered on the external mass matrix (M2GG). Gravity andcentrifugal loads must be included in generating the reduced loads (P2G). The P2G can thenbe used in DMIG input to get the exact static results.

The B2GG subcase information entry references a matrix by name, indicating that it is aviscous damping matrix. The viscous damping matrix must be symmetric and terms areadded to it before any constraints are applied.

The K42GG subcase information entry references a matrix by name, indicating that it is astructural element damping matrix. The structural element damping matrix must besymmetric and terms are added to it before any constraints are applied.

The P2G and P2GSUB subcase information entries reference a matrix by name, indicating thatit is a load matrix. The load matrix must be columnar and terms are added to it before anyconstraints are applied. Gravity and centrifugal loads are not considered on the externalmass matrix (M2GG). Gravity and centrifugal loads must be included in generating thereduced loads. The P2G and P2GSUB can then be used in DMIG input to get the exact staticresults. P2G must be used above the first SUBCASE. If there are multiple load vectors in theDMIG, then they will be applied in successive static SUBCASE until they are all used or untilevery static SUBCASE has a load vector. P2GSUB is used within a specific SUBCASE. If thereis more than one load vector in the DMIG, then P2GSUB can be used to specify which loadvector is to be used in that SUBCASE.



The A2GG subcase information entry references a matrix by name, indicating that it is afluid-structure coupling matrix. Only one instance of the fluid-structure coupling matrix isallowed.

Example

Figure 1 shows a finite element model composed of two components: a design componentand a non-design component. The structure is fully clamped along the left-hand edge andhas a downward vertical force applied along its right-hand edge. This example willdemonstrate how to replace the non-design component with a set of reduced matrices at theinterface nodes (the nodes which are common to both components) for both an analysisproblem and an optimization problem.

Figure 1: Example model indicating design and non-design components and boundary nodes.

First of all, a linear static analysis is performed on the complete structure. The displacementand von Mises stress results from this analysis are shown in Figure 3.

Next, a reduced stiffness matrix and a load vector are generated for the non-designcomponent. This is achieved by creating a new finite element model containing just the non-design component and the loads and boundary conditions directly applied to that component. This is shown in Figure 2.



Figure 2: Reducing out the non-design component.

All of the degrees of freedom at the interface nodes (see Figure 1) are selected as boundarydegrees of freedom. ASET or ASET1 bulk data entries are used to indicate this. The reducedmatrices output is requested through the inclusion of the PARAM, EXTOUT, DMIGPCH bulkdata entry. The model is submitted to OptiStruct, resulting in the creation of the file filename_AX.pch which contains the reduced matrices in ASCII format. (Had

PARAM,EXTOUT,DMIGBIN been used, the reduced matrices would be written in binary form tothe file filename_AX.dmg).

The non-design component can now be replaced in the original model by its reduced matrixrepresentation. This is done by manipulating the original model as follows:

1. Delete the bulk data entries for the nodes and elements of the non-design component.

2. Delete all loads and boundary conditions that were only applied to the non-designcomponent.

3. Include the file containing the reduced matrices in the bulk data section.

4. Select the reduced stiffness matrix with the subcase information entry K2GG. (In thisexample, the reduced stiffness matrix will have the default name KAAX).

5. Select the reduced load vector with the subcase information entry P2G. (In this example,the reduced load vector will have the default name PAX).

Figure 4 shows the displacement and von Mises Stress for the design component when thenon-design component was replaced by a reduced matrix representation. It can clearly beseen, they match perfectly with the original model's results.



(a) Displacements (b) von Mises Stress

Figure 3: Displacement and von Mises stress results for a linear static analysis on the complete structure.

(a) Displacements (b) von Mises Stress

Figure 4: Displacement and von Mises stress results for a linear static analysis with reduced matrix substitution.

Finally, for both the complete structural model and the reduced matrix model, a topologyoptimization was performed. For both models, the design component was identified asdesignable, the objective was to minimize the global compliance, and an upper limit of 50%was put on the volume fraction. The optimization results are shown in Figure 5.

(a) Complete Structure (b) Reduced Matrix Substitution

Figure 5: Density results for a topology optimization.

Compliance results not matching for reduced models.

If external forces are applied to the degrees of freedom that are reduced out of the model,then the strain energy or compliance values for the complete model will not match the strainenergy or compliance values for the reduced model.



The reduced loading is:

Therefore, strain energy for the reduced model is:

The strain energy for the complete model is:

So the compliance for the reduced model is missing the term:

But when no external forces are applied to the degrees of freedom that are reduced out ofthe model, then [f0] = 0, and the strain energy or compliance values for the reduced model

match the complete model.



Creating Superelements

There are three types of super elements that can be created in OptiStruct. The first is theCraig-Bampton in which the interface DOFs are fixed. These fixed interface DOF are specifiedusing ASET, BSET, or BNDFIX data. The second is the Craig-Chang in which the interfaceDOF is free. These free interface DOFs are specified using the CSET or BNDFREE data. Thethird is a combination of both, Craig-Bampton and Craig-Chang. This third version would beused for an automobile part such as the exhaust system where the fixed DOFs are couplingthe exhaust system to the powertrain; and the free DOFs are coupling the exhaust hangers tothe body. The other version that uses either form is a combination of a structure and fluidsuch as an automobile body and its interior cavity.

A super element can be a combination of a structure and fluid grids and elements to model atrimmed automobile body and its interior cavity. The fluid grids where the sound pressureresponse is to be calculated (microphone points) must be in the ASET list.

The interface points are where the component is attached to another component eitherthrough a rigid connection or a stiffness connection. These interface points must beindependent in all connection degrees of freedom. If they are the dependent DOF in an RBE3, the dependencies must be transferred to one of the independent grids referenced bythe RBE3 element. In the Bulk Data section on the RBE3 element, the UM parameter showshow to redefine the dependency on the initial grid. The RBE3 can also be changed to anRBE2 but this might stiffen up the local area as a result.

Interior points used in the super element to define the rough shape of the component usingPLOTEL elements do not need to be independent.

A component model has to be complete in order to be made into a super element. All gridsreferenced in the super element must be in the component model file, including localcoordinate systems grids. All properties and materials referenced in the components mustalso be included in the component. The component model must be able to be runsuccessfully in a modal analysis run.

Note: PARAM, WTMASS cannot be applied tosuperelements (.h3d or .pch) that are

read into the model. If the unit of mass isincorrect on the MAT# entries and PARAM,WTMASS is required to update thestructural mass matrix; then this shouldbe done in the creation run.

Craig-Bampton Approach

Initially, look at the Craig-Bampton input deck for an automobile body model without a bolton components referred to as a BODY-IN_WHITE (BIW).

MODEL = PLOTEL,,NORIGIDTITLE = BODY-IN-WHITE CMS MODEL SUBTITLE = DMIGNAME=BIW$-------------------------------------------------------------------------------SUBCASE 1CMSMETH = 1



BEGIN BULK$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>CMSMETH 1 CBN 300.0 1008000 AMSESASET1 123456 1000000 THRU 1006004INCLUDE '/MODELS/BODY/BODY.dat'ENDDATA

First, the Craig-Bampton approach can be run in either AMSES or in Lanczos. The resultsshould be the same. Use AMSES for large component models and Lanczos for smallcomponent models.

Second, the MODEL card will include all PLOTEL and the associated interior grids in the superelement. An alternate method to include extra grids can be accomplished by listing the gridsin a set and referencing the set in the MODEL card between the ,, in the MODEL card. ThePLOTEL generally are used to define a rough outline of the component for viewing its modeshapes.

The PLOTEL value will also now include the new plate PLOTEL that are available in OptiStruct.

Third, the PARAM, SEPLOT, YES will create a file including all the grids referenced in theMODEL card, plus the interface grids and the PLOTEL referenced in the MODEL card. This filecan be used later in residual runs, if desired, along with the super element H3D file, althoughit is not required. If a residual run on just this single component is to be made, such as amodal or mobility run, then the .seplot file should be created and used in the residual run.

Otherwise the runs will fail without having any other input besides the H3D file because noGRID data is in the input data.

The DMIGNAME is optional and can be specified later in the residual run. It creates a uniquename to the stiffness, mass and damping matrix and can only be a maximum of sixcharacters.

The CMSMETH case control card calls the new OptiStruct super element eigenvalue cardCMSMETH.

The CMSMETH bulk data card referenced in this case the CBN (Craig-Bampton Method). Thenext field is the upper frequency bound for the modes. The sixth field references the startingnumber for where the SPOINTS for the modes will be stored. This range of numbers must beunique for the full vehicle model and each super element will need its own numbering range. The seventh field is used to specify the eigensolver (Lanczos or AMSES).

The ASET1 lists the interface points of the super element model in the example above.

Only the connection and specific response points should be included in the ASET list. Theother points in the super element are called interior points. The interior points should not bein this ASET list, since the model size and run time will increase with the number of pointsincluded in the ASET list. If you have special response points in the component, they shouldbe included in the ASET list. Generally there are only a few critical response points. Thecritical response points must be independent points. The calculated responses will show upin the output files. If any type of random analysis is being performed, it is essential that theresponse points be included in the ASET list with the exterior points.

This file will generate an H3D binary file that includes all the information that is needed forthis super element. It can also create the optional .seplot ASCII file, if requested. The

H3D file will include matrices for the mass and stiffness and it will also include the matricesfor structural damping and viscous damping if these elements exist in the model. Look at thebottom of the .out file to see what matrices are created.



Below is an example. There were 274 modes found for this model. There were 166connection grids with six DOF each for a total of 996 connections DOF. The total number ofmodes (connection plus normal modes) is 1270.

OUTPUT DMIG MATRIX IN H3D FORMAT OUTPUT DMIG MATRIX: KA NCOL = 1270 OUTPUT DMIG MATRIX: MA NCOL = 1270 OUTPUT DMIG MATRIX: K4 NCOL = 1270

The .out file will show the modes for the fixed boundary condition. In general, it is desirable

to have at least 30 modes for each component model. For small items like a control arm, anupper limit of around 5,000 Hz may be needed.

Craig-Chang Approach

The following cards show the Craig-Chang approach.

PARAM, SEPLOT, YESPARAM, AUTOSPC, YESMODEL = PLOTEL,,NORIGIDTITLE = BODY-IN-WHITE CMS MODEL SUBTITLE = DMIGNAME=BIW$-------------------------------------------------------------------------------SUBCASE 1CMSMETH = 1BEGIN BULK$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>CMSMETH 1 GM 300.0 1008000 AMSESBNDFREE1 123456 1000000 THRU 1006016INCLUDE '/MODELS/BODY/BODY.dat'ENDDATA

For the Craig-Chang Approach, use AMSES to generate the super element. With AMSES youwill get the appropriate static modes. Static modes are additional modes created byperturbing each connection DOF. The number of static modes is the number of BNDFREEDOF. Since Lanczos does not generate the static modes for the Craig-Chang approach, theAMSES eigensolver must be used.

The only difference in the input data for creating Craig-Chang super elements from Craig-Bampton super elements is in the CMSMETH and the BNDFREE1 cards. The CMSMETH cardnow references the GM (General Method). This method is used for the Craig-Chang or thecombination of both methods. The BNDFIX or ASET data should be changed to BNDFREE orCSET data.

The BNDFREE1 card replaces the ASET1 card and has the same meaning for the inclusions ofthe interface points.



For this method, verify that the components have six good rigid body modes (that is below1.0E-02 Hz). This insures that the body model does not have any modeling problems. Having more than six rigid body modes or rigid body modes greater than 1.0E-2 indicatesthat the component has modeling problems that need to be identified and fixed.

To create a combination of both fixed and free modes, just add the ASET1 list to the GM andinclude in the list the interface points that you want to be fixed.

The superelements created by using the Craig-Chang method should not be used forsubsequent static analysis.

Craig-Bampton & Craig-Chang Approach

The following cards show an example of the combination approach for an automobile exhaustsystem.

MODEL = PLOTEL,,NORIGID$$--1---|---2---|---3---|---4---|---5---|---6---|---7---|---8---|---9---|-------|TITLE = EXHAUST H3D MODEL CREATIONSUBTITLE = FIXED AND FREE GM APPROACH $DMIGNAME=EXHAUST$-------------------------------------------------------------------------------SUBCASE 1CMSMETH = 1 $-------------------------------------------------------------------------------BEGIN BULK$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>CMSMETH 1 GM 400.0 7308000 $ EXHAUST ATTACHMENTS TO POWERTRAINASET1 123456 7304501 7304502$ EXHAUST HANGERS TO BODY BNDFREE1 123456 7304503 7304507 7304515 7304523$INCLUDE '/MODELS/EXHAUST/EXHAUST.dat'ENDDATA

The ASET1 list includes the two attachments of the exhaust system which are rigidlyconnected to the powertrain. The BNDFREE1 list includes the exhaust hangers which arerubber mounted to the body. In this case there will not be any rigid body modes.

Note that the Craig-Bampton approach can be used in either the CBN or GM process on theCMSMETH card. However, in the GM the underlying eigen space has additional rotation;which will make the residual run times with super elements longer if the Craig-Bamptonapproach is created with the GM method. GM with BNDFIX will be useful if you want to domore component level analysis in the residual run.



In summary:

1. CSET and BNDFREE are equivalent.

2. ASET, BSET/BNDFIX and CSET/BNDFREE; all three are not allowed in the same deck.

3. If CSET/BNDFREE and ASET are present, the DOFs associated with ASET would be inBSET; except the DOF assigned to CSET/BNDFREE.

4. If BSET/BNDFIX and ASET are present, the DOFs associated with ASET would be in CSET;except the DOF assigned to BSET/BNDFIX.

Automobile Body – Cavity Approach

Another special super element is an automobile body - cavity super element. Below is anexample of how this super element is created.

ANALYSISPARAM, CHECKEL NO PARAM, SEPLOT, YESMODEL = PLOTEL,,NORIGIDTITLE = FULLY TRIMMED BODY CMS MODEL WITH CAVITY MODEL SUBTITLE = DMIGNAME=TRIMBDY $-------------------------------------------------------------------------------SUBCASE 1CMSMETH = 1$------------------------------------------------------------------------------- BEGIN BULK$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>ACMODL CMSMETH 1 GM 300.0 1008000 AMSES 600.0 90000000BNDFREE1 123456 1002000 THRU 1006100BNDFREE1 123456 2005807 2005809 2005810 BNDFREE1 1 80000000 THRU 80000007$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>INCLUDE '/TRIM_BODY/TRIM_BODY_CONNECTIONS.dat'INCLUDE '/TRIM_BODY/TRIM_BODY_FILES.dat'INCLUDE '/MODELS/CAVITY/CAVITY.dat'ENDDATA

In this file, the BNDFREE1 connections contain the interface points for the BODY-IN-WHITEand the interface points for the instrument panel for the steering column connections. It alsoincludes the acoustic response points in the cavity model. Note only the one degree offreedom is referenced for the acoustic response points.

The CMSMETH card also contains a second line that references the upper frequency limit forthe cavity modes and the numbering starting point for the cavity modes.

The file also contains the ACMODL card that references the connections of the cavity to thetrim body parts.



The .out file shows the inclusion of the acoustic modes in the A matrix.

OUTPUT DMIG MATRIX IN H3D FORMAT OUTPUT DMIG MATRIX: KA NCOL = 1687 OUTPUT DMIG MATRIX: MA NCOL = 1687 OUTPUT DMIG MATRIX: K4 NCOL = 1402 OUTPUT DMIG MATRIX: A NCOL = 285



Component Dynamic Analysis Super Element Generation

The CDS super element should be used when it's anticipated that a large number of residualruns will be made on a very large model at the higher end of the frequency range of study. For example, this approach should be used when studying a variety of inputs on anautomobile model in the frequency range of 400 to 800 Hz. For the residual analysis to runas fast as possible, all components, except very small ones, should be converted into CDSsuper elements. The major limitation of this approach is that it takes longer to generate theCDS super elements than with the other super element creation methods. Also, the analysismust be performed at the fixed set of frequencies specified when the CDS supe element isformed. The major benefit of the CDS super element is that the residual run will be muchfaster than with super elements created by other methods.

For an example of the body CDS super element generation, see the input data for a body-in-white below. The special data for this input are the case control data: CDSMETH = 1; theFREQ card which restricts the residual analyses to just those frequencies; the CDSMETH data(see the CDSMETH card definition); and the BNDFREE data which defines the exterior pointson the component.

CDS Body Super Element Example

MODEL = NONETITLE = BODY-IN-WHITE CDS MODEL$-------------------------------------------------------------------------------SUBCASE 1FREQUENCY = 1METHOD = 2CDSMETH = 1BEGIN BULK$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>FREQ1 1 1.0 0.2 94FREQ1 1 20.0 0.5 159FREQ1 1 100.0 1.0 99FREQ1 1 200.0 2.0 200EIGRA 2 1000.0CDSMETH 1 CMSOUT 1008000BNDFREE1 123456 1000000 THRU 1006001INCLUDE '/MODELS/BODY/BODYNEW.dat'ENDDATA

This run will generate not only the CDS super element but also the GM method super elementbecause the CMSOUT keyword was present. The GM method super element is saved in thefile: XXX.h3d; while the CDS super element is saved in the file: XXX_CDS.h3d.

The interface points (exterior points) are where the component is attached to another superelement directly or to the residual structure. These interface points must be independent inall six degrees of freedom. If they are the dependent point of an RBE3, they must be madeindependent by transferring the dependencies to one of the independent grids referenced bythe RBE3 element using UM data on the RBE3 definition. In the Bulk Data section on theRBE3 element, the UM parameter shows how to redefine the dependency. The RBE3 can alsobe changed to an RBE2, but this could stiffen up the local area as a result.



In order to be formed into a super element, a component FEA model has to be complete. Allgrids referenced in the super element must be in the component model file. This includeslocal coordinate systems grids. All properties and material referenced in the componentsmust also be included in the component. The component model must be able to be runsuccessfully by itself in a modal analysis run.

The MODEL card includes all PLOTEL elements and the associated interior grids in the superelement. An alternate method of specifying interior GRID points is to use the GRID SET IDon the MODEL data. The PLOTEL elements generally are used to define a rough outline of thecomponent for viewing its mode shapes. The PLOTEL set can include the 3 and 4 nodePLOTEL elements.

Residual Run Using the CDS Super Elements

The residual run on the full model must be run with the direct analysis approach. Also, thesame or a subset of the frequencies specified in the CDS super element generation run mustbe used in the residual run.

$ THIS FILE CONTAIN ALL THE H3D FILES FOR THE CDS SUPER ELEMENTSINCLUDE '/CDS_FILES.dat'$TITLE = P/T FULL VEHICLE ANALYSISSUBTITLE = FVM DIR H3DSPC = 1MPC = 406SUBCASE 1LABEL = UNIT LOAD INPUT INTO CDS MODELDLOAD = 110FREQUENCY=1SET 2 = 1006001,9106012ACCELERATION (PUNCH,SORT2,PHASE) = 2$BEGIN BULK$$==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>FREQ1 1 1.0 0.2 94FREQ1 1 20.0 0.5 159FREQ1 1 100.0 1.0 99FREQ1 1 200.0 2.0 200EIGRL 1 800.0 $==01==><==02==><==03==><==04==><==05==><==06==><==07==><==08==><==09==><==10==>$ INCLUDE '/LOADS.dat'$INCLUDE '/CONNECTIONS_BETWEEN_COMPONENTS.dat'$ INCLUDE '/NON_CDS_COMPONENTS.dat'ENDDATA




Component Mode Synthesis (CMS) is used to reduce a finite element model of an elastic bodyto the interface degrees of freedom and a set of normal modes for inclusion as a flexible bodyin a multi-body dynamics analysis.

For the purpose of deriving the matrices, the displacement vector may be partitioned intodisplacements of inner (OSET) and outer (ASET, interface) degrees of freedom.

(1)

Here, the subscript ‘o’ denotes the inner degrees of freedom, and ‘a’ the interface degrees of

freedom.

The interface nodes that are used in the component mode synthesis process for theconstruction of mode shapes should be coincidental to the set of force-bearing nodes in thesubsequent multi-body dynamics analysis. In a multi-body dynamics model, the flexiblebody interacts with other components of the model through joints, constraints, or forceelements, which are connected or applied on the nodes of the flexible body. Except for bodyforces due to gravity or acceleration of the flexible body, all nodes that are subject toconstraint or applied forces in the multi-body dynamics analysis are denoted as force-bearingnodes.

The purpose of specifying the interface nodes for CMS is mainly to account for the staticdeformation due to constraints or applied forces acting on the interface nodes. A hugenumber of eigenmodes is required if these static modes are omitted. The flexibledeformations due to constraint forces, compared to the deformation due to the body inertiaforces, are often dominant in most constrained models; therefore, the inclusion of all force-bearing nodes as interface nodes is an essential step to get accurate results from subsequentflexible multi-body dynamics analysis.

The static equilibrium is given as:

(2)

The eigenvalue problem for a normal modes analysis of the body using a diagonal massmatrix represents itself as:

(3)

The task of the component mode synthesis is to find a set of orthogonal modes that

represent the displacements u of the reduced structure such that:

Where, q is the matrix of modal participation factors or modal coordinates which are to be

determined by the analysis.

The Craig-Bampton and Craig-Chang methods of component mode synthesis are available.



Craig-Bampton Method

Normal Modes Analysis with constrained Interface degrees of freedom

This method uses a system constrained in the interface degrees of freedom. Normal modes

analysis of the system yields the diagonal matrix of eigenvalue and the matrix of

eigenmodes . In this normal analysis, you can select the cut-off frequency or the number

of modes to be solved. This determines the column dimension of .

Static Analysis with alternately fixed Interface degrees of freedom

In addition, a static analysis is performed with a unit displacement in each interface degreeof freedom while all other interface degrees of freedom are fixed. The number of subcases inthis static analysis is six times the number of interface nodes. Note that it is important toconstrain each interface node with its neighboring nodes, if necessary, to ensure that it hasnon-zero stiffness along all six degrees of freedom directions. This process yields the

displacement matrix and the interface forces .

Reduced modal stiffness and mass matrices are now generated using:

Which yields:

And


orthogonal modes .

Craig-Chang Method

This method uses a system that is unconstrained (free-free) and therefore has six rigid body

modes. Normal modes analysis of the system yields the diagonal matrix of eigenvalue

and the matrix of eigenmodes . In this normal analysis, you can select the cut-offfrequency or the number of modes to be solved. This determines the column dimension of

. The eigenmodes associated with the rigid body modes will be normalized with respectto the mass matrix such that:

In addition, a static analysis is performed using an equilibrated load matrix .



The equilibrated load matrix is applied in an inertia relief static analysis without any SPCconstraints, but with proper support to remove the six rigid modes. The vector is acollection of the attachment force vectors which otherwise have all zero entries, except a unitforce along each degree of freedom of the interface nodes. The resulting modes are calledthe inertia relieve attachment modes.

Reduced modal stiffness and mass matrices are now generated using:

Which yields:

And


orthogonal modes .

Eigenvector Normalization

First, a new eigenvalue problem using the reduced matrices above is solved.

The resulting diagonal matrix of eigenvalues D and the normal modes N are used to

transform the set of original shapes into the set of orthogonal modes .

It can be shown that the resulting modes are orthogonal with respect to the system stiffnessmatrix K and mass matrix M.

If the orthogonal modes are normalized with respect to the mass matrix M, the reduced

matrices for the subsequent analysis appear as:



Distributed Loads

In MotionSolve, any arbitrary displacement field of the flexible body is approximated by:

x q

Where, q is the m by 1 modal participation vector.

Suppose pi is the i-th distributed load (pi is an n by 1 vector) defined in the FE model, xi is the

corresponding displacement field, and x is any arbitrary displacement field of the flexible

body. The virtual work due to pi is:

Taking the variation on both sides of the arbitrary displacement field equation and pluggingthe results into the above equation, results in:

Define modal distributed load as i, i=1,…,l , as:

Each modal distributed load is an m by 1 vector.

The above modal distributed loads, along with their load ID in the FE model, should be pre-computed in OS-Flexprep and written as new modal distributed loads blocks in the h3d file.

In addition, the corresponding displacement fields xi, i=1,…, l, should enter the mode shapes X

in the CMS process.

Input and Output

Component mode synthesis is activated by the presence of the I/O Option CMSMETH. The I/O Option references a CMSMETH bulk data entry which defines the method (only CC and CBmethods apply to flexible body generation), frequency range or number of modes to becalculated. Only one subcase is allowed per model. The interface degrees of freedom aredefined using ASET or ASET1 bulk data statements. An MPC reference is allowed. Whilesubcases are irrelevant for this run mode, if the model has multiple subcases, the MPCreference must match for all subcases. Subcase information entries other than MPC areignored.

In general, offsets should not be used in flexible body generation. However, PARAM,CMSOFST may be used to allow small offsets for shell elements.

The orthogonal modes and the corresponding eigenvalues D are exported to a flexh3d file

by default. The modal stresses and strains can be output optionally using the STRESS andSTRAIN output statements. Sets can be applied to reduce the amount of data. The export ofthe model to this file can be controlled using the MODEL output statement.



Recovering MBD Analysis results in OptiStruct

After MotionSolve is run, it is possible to recover displacements, velocities, accelerations,stresses, and strains for the flexbody in OptiStruct in order to create .op2 and .h3d results

files for fatigue analysis. The procedure is explained below.

After running MotionSolve, a residual run can be made to recover displacement, velocity,acceleration, stress, and strain results for interior grids and elements in the Flex Body basedon the modal participation results from MotionSolve. After running MotionSolve, a resulting <filename>.mrf file is created that contains MotionSolve results including the modal

participation factors at each time step for the Flex Body for transient analysis. In the residualrun, the Flex Body <filename>_recov.h3d file and the .mrf results file are specified using

the ASSIGN data:

ASSIGN,H3DMBD,30101,’pfbody_1_recov.h3d'

ASSIGN,H3DMBD,30102,’pfbody_2_recov.h3d'

ASSIGN,MBDINP,10,’pfbody.mrf'

Where the 10 in the ASSIGN,MBDINP data references the SUBCASE for which the MotionSolve

results will be used. In SUBCASE 10, instead of performing a transient analysis, OptiStruct

will just use the results from MotionSolve.

The 30101 and 30102 in the ASSIGN,H3DMBD data refer to the Flex Body ID’s in the .mrf file.

For transient analysis, the number of time steps in the transient analysis run must match thenumber of time steps used in the MotionSolve analysis. While the transient analysis data isignored, there must still be some dummy loading data (TLOAD, DAREA, and TABLED data). A sample of input data for a transient analysis run is shown below:

OUTPUT OP2OUTPUT H3DASSIGN,H3DMBD,30103,MBD_pfbody_BODY_2_PROP_6_recov.h3dASSIGN,H3DMBD,30102,MBD_pfbody_BODY_1_PROP_9_recov.h3dASSIGN,H3DMBD,30104,MBD_pfbody_BODY_3_PROP_10_recov.h3dASSIGN,MBDINP,1,MBD_pfbody_mbd.mrfSUBCASE 1 TSTEP(TIME) = 4 DLOAD = 3 DISPLACEMENT = ALL STRESS = ALL SPC = 1$BEGIN BULKGRID 9999999 $ Dummy GRID since at least one GRID is required$------+-------+-------+-------+-------+-------+-------+-------+-------TSTEP 4 300 .0003333 1 TLOAD1 3 3 DISP 2TABLED1 2 LINEAR LINEAR+ 0.0 1.0 10.0 1.0ENDT $$ Dummy load on the dummy gridSPC 1 9999999 1SPCD 3 9999999 1 -200.0 ENDDATA

A dummy grid and a dummy load have been added for the OptiStruct analysis run.



Poroelastic Materials (Biot theory)

Introduction

Poroelastic materials can be used to model coupled fluid-structure systems where the fluidexists within the interstitial spaces of a porous solid. The mechanical response of a porousmaterial varies, depending on the amount of fluid present within the pores, the type of fluid,the pressure of the interstitial fluid, and the structure of the porous material. In OptiStruct, aporoelastic material based on the Biot theory of poroelasticity can be modeled for use inrelevant applications.

Motivation

A porous material containing fluid within interstitial spaces cannot be accurately modeledwithout accounting for the influence of the fluid on the mechanical response of the structure.There are various physical applications for poroelastic material models; for example,trimmings of an automobile are porous and the cabin cavity is filled with air. The fluid (air)enters the interstitial spaces within these trimmings and the dynamic behavior of the systemis altered. This difference in dynamic behavior should be accurately accounted for in NoiseVibration and Harshness (NVH) studies of the automobile.

Figure 1: Difference in mechanical response between porous and non-porous materials.

For a possible application, the Biot poroelastic material implementation in OptiStruct can beused to model automobile trim components in frequency response analyses to generate amore accurate solution. Trim materials, carpets, foam pads, and other porous materials canbe modeled.

Implementation

Poroelastic materials in OptiStruct are implemented using the Biot poroelastic theory. Theycan be modeled using CTETRA, CHEXA, or CPENTA solid elements. The Biot u-p(displacement-pressure) formulation is used wherein each grid consists of three displacementdegrees of freedom (DOF) and one pressure component. The required material properties arelisted in detail on the MATPE1 entry in the Reference Guide. The MATPE1 entry can beselected on the PSOLID property entry with FCTN=PORO.


The Biot poroelastic material is frequency-dependent. The frequency-dependent elementmatrices are calculated at each frequency for each element. Direct and Modal Frequency



Response Analyses are supported. The frequency-dependent matrices are reduced to modalspaces for modal frequency response analysis. Panel participation calculation for the Biotmaterial is available similar to that of other panels. The fluid-structural grid participation isalso available for detailed interpretation of panel contributions.

Note

1. Coupling between the acoustic cavity (FLUID) and trim component (BIOT):

(a)A GRID to GRID match or Multi-point constraints (MPCs) are required to connect theacoustic cavity to fluid dof of the BIOT material.

(b)The ACMODL entry will be used to couple the fluid dof and the structural dof of theBIOT material.

(c) If a GRID to GRID match is used to couple the acoustic cavity to the BIOT material, thegrids on the fluid that are shared with the BIOT material should not have their CDfields set to -1. However, if Multi-point constraints (MPCs) are used, then the CD fieldsshould be set equal to -1.

2. Coupling between the trim component (BIOT) and the body structure:

(a) Coincident nodes (GRID to GRID match) can be used to achieve displacementcontinuity. However, if the nodes between the trim component and the body structureare not shared, TIE/CONTACT entries with the FREEZE option, rigids, MPC’s, or otherstructural elements can be used to ensure continuity.

Limitations

The pressure output for the trim component (poroelastic Biot material) is not currentlysupported. However, the pressure of the closest acoustic domain is available.



Elements and Materials

The following features can be found in this section

Elastic, Damper, and Mass Elements

Zero-dimensional Elements

Elements in this group only connect to grid points having a single degree of freedom ateach end. Elements also included in this group are those that connect to scalar points atone end and ground at the other, like the following:

CELAS1, CELAS2, CELAS3, and CELAS4 that are used to model elastic springs. Theproperties for CELAS1 and CELAS3 are defined on PELAS. CELAS2 and CELAS4define spring properties.

CDAMP1, CDAMP2, CDAMP3, and CDAMP4 that are used to model scalar dampers. The properties for CDAMP1 and CDAMP3 are defined on PDAMP. CDAMP2 andCDAMP4 define scalar damper properties.

CMASS1, CMASS2, CMASS3, and CMASS4 that are used to model point masses. Theproperties for CMASS1 and CMASS3 are defined on PMASS. CMASS2 and CMASS4define the mass.

CONM1 and CONM2, which are concentrated mass elements. CONM1 defines a 6x6mass matrix at a grid point. CONM2 defines mass and inertia properties at a gridpoint.

CVISC is used to model viscous dampers. The properties for CVISC are defined onPVISC.

One-dimensional Elements

Elements in this group are represented by a line connecting grid points at each end. Thefollowing actions involving forces (and displacements) at each end are possible:

Forces and displacements along the axis of the element.

Transverse shear forces (and displacements) in the two lateral directions.

Bending moments (and rotations) in two perpendicular, bending planes.

Torsional moments (and resulting rotations).

Twisting of the cross-section (or cross-sectional warping).

The elements in this category are:

CBEAM - a general beam element that supports all types of action listed above.

CBAR - a simple, prismatic beam element that supports all of the above types ofactions except cross-sectional warping.

CBUSH - a general spring-damper element that supports forces, moments, anddisplacements along the axis of the element.



CBUSH1D - a rod-type spring-damper element.

CGAP - a gap element that supports axial and friction forces.

CGAPG - a gap element that supports axial and friction forces. It does not have to beplaced between grid points. It can also connect surface patches.

CROD - a simple, axial bar element that supports only axial forces and torsionalmoments.

CWELD - a simple, axial bar element that supports forces, moments, and torsionalmoments. It does not have to be placed between grid points. It can also connectsurface patches.

The properties for these elements are defined on PBEAM, PBAR, PBUSH, PBUSH1D, PGAP,PROD, and PWELD, respectively.

CONROD - a simple, axial bar element that supports only axial forces and torsionalmoments. This element does not reference a property definition; the propertyinformation is provided with the element definition.

Two-dimensional Elements

Two-dimensional elements are used to model thin-shell behavior, which incorporates in-plane or membrane actions, plane strain, and bending action (including transverse shearcharacteristics and membrane-bending coupling actions). Reissner-Mindlin shell theory isused to model bending. A plane strain option is available for pure 2D applications. Theelement shapes may be triangular (CTRIA3) or quadrilateral (CQUAD4). Second ordertriangular (CTRIA6) and quadrilateral (CQUAD8) shell elements are also available. Theshell properties, including the behavior, are defined on the PSHELL entry.

The first order shell element formulation for CQUAD4 and CTRIA3 has the specialcharacteristic of using six degrees of freedom per grid. Hence, there is stiffness associatedto each degree of freedom. In some finite element codes, shell elements do not have adrilling stiffness normal to the mid-plane, which may cause singular stiffness matrix. Then, a user-defined artificial stiffness value is assigned to this degree of freedom to avoidthe singularity.

The second order shell elements (CTRIA6 and CQUAD8) have five degrees of freedom pergrid. Rotational degrees of freedom without stiffness are removed through SPC.

Another form of two-dimensional elements may also be used to model thin buckled plates. These elements support shear stress in their interior and extensional forces between theiradjacent grid points. These elements are used in situations where the bending stiffnessand axial membrane stiffness of a plate is negligible. The elements are quadrilateral andare defined as CSHEAR. Their properties are defined on the PSHEAR entry.

Three-dimensional Elements

The three-dimensional solid elements are used to model thick plates, solid structures. Ingeneral, structures in which the lateral dimensions are of the same order of magnitude asthe longitudinal dimensions can support the use of three-dimensional solid elements inmodeling. The elements in this category are the CHEXA, CPENTA, CPYRA, and CTETRAelements. The property definition associated with these elements is called PSOLID.



Offset for One-dimensional and Two-dimensional Elements

Some one-dimensional and two-dimensional elements can use offset to “shift” the elementstiffness relative to the location determined by the element’s nodes. For example, shellelements can be offset from the plane defined by element nodes by means of ZOFFS. Inthis case, all other information, such as material matrices or fiber locations for thecalculation of stresses, are given relative to the offset reference plane. Similarly, theresults, such as shell element forces, are output on the offset reference plane.

Offset is applied to all element matrices (stiffness, mass, and geometric stiffness), and torespective element loads (such as gravity). Hence, in principle, offset can be used in alltypes of analysis and optimization.

However, caution is advised when interpreting the results, especially in linear bucklinganalysis. Without offset, a typical simple structure will bifurcate and loose stability“instantly” at the critical load. With offset, though, the loss of stability is gradual andasymptotically reaches a limit load, as shown below in figure (b):

In practice then, the structure with offset can reach excessive deformation before the limitload is reached. (Note that more complex structures, such as frames or structuresexperiencing bending moments, buckle via limit load even in absence of ZOFFS on theelement card). Furthermore, in a fully nonlinear approach, additional instability pointsmay be present on the limit load path.

Elements for Geometric Nonlinear Analysis

Special element formulations are available for geometric nonlinear analysis. As a generalrule, property definitions that are only applicable in geometric nonlinear analysis aredefined on extensions to the original property. The extensions are grouped with the baseentry by sharing the same PID. In the case of a subcase that is not a geometric nonlinearanalysis, these extensions are ignored. The following extensions are available: PSHELLX,PSOLIDX, PBARX, and PBEAMX. Property defaults can be set for shells (XSHLPRM) andsolids (XSOLPRM) that may replace the use of property extensions. All other properties areused as they are.



Example:

PSHELL, 3, 7, 1.0, 7, , 7PSHELLX, 3, 24, , , 5

Non-structural Mass

Non-structural mass may be specified in two different ways.

1. Many property definitions (PSHELL, PCOMP, PBAR, PBARL, PBEAM, PBEAML, PROD,CONROD, PSHEAR, and PTUBE), have an NSM data field that allows a value of non-structural mass per unit area or non-structural mass per unit length to be defined.

When non-structural mass is defined in this way, it is considered in all analyses.

2. Non-structural mass may be defined via a number of non-structural mass bulk dataentries (NSM, NSM1, NSML, NSML1, and NSMADD) for a list of elements or properties. In the case of a list of properties, non-structural mass is applied to the elementsreferencing the properties in the list.

These non-structural mass definitions must be selected for use in an analysis throughthe NSM subcase information entry. Only one NSM subcase information entry can existin a model and it must occur before the first SUBCASE statement.

The bulk data entry NSM and its alternate form NSM1 allow you to define a value ofnon-structural mass per unit area or non-structural mass per unit length to be appliedto a selected list of elements.

The bulk data entry NSML and its alternate form NSML1 allow you to allocate andsmear a lumped non-structural mass value to be evenly distributed over a list ofelements. The non-structural mass value per unit area or per unit length to be appliedto the elements is computed as:

1

n

i

VALUENSM per unit area

area of element i

1

n

i

VALUENSM per unit length

length of element i

Where, n is the number of elements in the set and VALUE is the value of the lumpedmass. The NSML and NSML1 entries cannot mix "area" and "line" elements on thesame entry. The "area" elements are: CQUAD4, CQUAD8, CTRIA3, CTRIA6, andCSHEAR; "line" elements are: CBAR, CBEAM, CTUBE, CROD, and CONROD.

The bulk data entry NSMADD allows you to form combinations of NSM, NSM1, NSML,and NSML1.

An element can have more than one non-structural mass value specified for it. The actualnon-structural mass value will be the sum of all of the individual non-structural massvalues.



Virtual Fluid Mass

Virtual Fluid Mass mimics the mass effect of an incompressible inviscid fluid in contact witha structure. It does not represent the actual mass of the fluid. There is no mesh needed forthe fluid domain. The Virtual Fluid Mass represents the full coupling between accelerationand pressure at the fluid-structure interface. A dense mass matrix is generated amongdamp grids at the fluid-structure interface. This simulation is applicable to automobilecontainers, such as a fuel tank, which hold non-pressurized fluids.

Assumptions

1. The fluid is inviscid and incompressible. The fluid flow is a potential flow.

2. Because the fluid is nearly incompressible, the structural modes are below thecompressible fluid modes.

3. There is no gravity effect or sloshing effect.

4. There is no acoustic effect involved. The modes from the structural side do not couplewith the modes of the nearly incompressible fluid modes.

MFLUID Interface

If a fish can swim to every point inside fluid domain without leaving the fluid, the fluiddomain can be represented by a single MFLUID card in the bulk data section. Each MFLUIDcard in the bulk section can only be referred to by a single MFLUID card in the controlsection. Multiple bulk data MFLUID cards can be referred by a single MFLUID card in thecontrol section. Symmetry and anti-symmetry options can be applied to a MFLUID card.

If PARAM,VMOPT,1 is used (default), the virtual mass is included in the regular massmatrix and it can be applied to both direct and modal dynamic subcases. Because thevirtual mass matrix is dense for the damp grids, the computational time increasessignificantly. However, you have the option to use PARAM,VMOPT,2. Although,PARAM,VMOPT,2 can only be applied to modal dynamic subcases. In this case the virtualmass is added after the eigen solution, and the computational time is not increasedsignificantly. When PARAM,VMOPT,2 is used, the dry modes are computed without addingvirtual mass in the computation. Then the modes are modified based on the virtual massmatrix.

Theory

The elemental pressure and acceleration are calculated with respect to the source potentialof the element. The pressure is calculated based on displacement potential as:

If the source potential of element j is , then the pressure can be represented as:



An additional area integration is done to convert pressure into force.

Similarly, the acceleration vector can be represented as:

Using the force and acceleration, the effective mass matrix can be calculated.

Arbitrary Beam Section Definition

In addition to using predefined beam cross-sections selected by the TYPE field on the PBARL and PBEAML bulk data entries, defining arbitrary beam cross-sections. This isreferred to here as section definitions. To define an Arbitrary Beam Section, HYPRBEAMshould be entered into the GROUP field on the PBARL and PBEAML bulk data entries. Also,the ND field should specify the number of dimensions input during the definition of thearbitrary beam section in the DIMi fields of the PBARL and PBEAML bulk data entries.

Section definitions are contained within the bulk data section of the input file. A sectiondefinition begins with the statement BEGIN and ends with the statement END. Section

definitions are referenced from a PBARL or PBEAML definition through the NAME field. TheNAME entered on the PBARL or PBEAML definition must match the NAME following the BEGIN,

statement.

The section is defined by a 2D finite element mesh. The finite element mesh is composedof nodes (denoted by GRIDS entries), which are connected by 2-node, 3-node, 4-node, 6-node or 8-node elements (denoted by CSEC2, CSEC3, CSEC4, CSEC6, or CSEC8 entries,respectively). These elements reference PSEC entries; these provide a material referencefor all elements and thickness information for the 2-noded CSEC2 elements.

The following is an example of a simple thin-walled section definition named SQUARE:

$BEGIN,HYPRBEAM,SQUARE$GRIDS,1,0.0,0.0GRIDS,2,1.0,0.0GRIDS,3,1.0,1.0GRIDS,4,0.0,1.0$CSEC2,10,100,1,2CSEC2,20,100,2,3CSEC2,30,100,3,4CSEC2,40,100,4,1$PSEC,100,1000,0.1$END,HYPRBEAM$



The following is an example of a solid section definition named CUTOUT:

$BEGIN,HYPRBEAM,CUTOUT$GRIDS,1,0.0,0.0GRIDS,2,0.05,0.0......GRIDS,895,0.35,1.18GRIDS,896,0.38,1.19$CSEC3,806,100,887,873,872CSEC3,809,100,868,820,885CSEC3,812,100,813,803,817$CSEC4,1,100,147,148,149,157CSEC4,2,100,157,149,150,158......CSEC4,813,100,648,712,895,896CSEC4,814,100,647,646,896,895$PSEC,100,1000$END,HYPRBEAM$

Rigid Elements and Multi-Point Constraints

Rigid elements and multi-point constraints are used to constrain one or more degrees offreedom to be equal to linear combinations of the values of other degrees of freedom.

Rigid elements are equations generated internally. You provide the connection data only. Rigid elements function as rigid bodies; therefore they are also known as rigid bodies orconstraint elements. Internally, they are treated the same way as multi-point constraints.

The RROD element can be used to model a pin-ended rod which is rigid in extension. Oneequation of constraint will be generated for this element. The RBAR element can be usedto model a rigid bar with six degrees of freedom at each end. From one to six (dependingon your input) equations of constraint will be generated for this element.

The RBE1 and RBE2 elements are rigid bodies connected to an arbitrary number of gridpoints. The number of equations of constraint generated is equal to or greater than one,depending on the dependent degrees of freedom selected by you. For the RBE1 element,the independent degrees of freedom are six components of motion that must be jointlycapable of representing any general rigid body motion of the element; whereas for theRBE2 element, the independent degrees of freedom are the six components of motion at asingle grid point.

The RBE3 element provides for specification from one to six equations of constraintdeveloped from the relation that the motion at a "reference grid point" is the least square



weighted average of the motion at other grid points. This element is generally used to"beam" loads and masses from a reference point to a set of grid points. Multi-pointconstraints are equations in which you explicitly provide the coefficients of the equations. Each multi-point constraint is described by a single equation that specifies a linearrelationship for two or more degrees of freedom. Multiple sets of multi-point constraintscan be provided in the bulk data section. In the subcase information section, the multi-point constraints are assigned to the specific load case using the MPC statement.

The bulk data entry MPC is the statement for defining multi-point constraints. The firstcoordinate mentioned on the card is taken as the dependent degree of freedom (that is,the degree of freedom that is removed from the equations of motion). Dependent degreesof freedom may appear as independent terms in other equations of the set; however, theymay appear as dependent terms in only a single equation.

Some uses of multi-point constraints are:

To enforce zero motion in directions other than those corresponding to componentsof the global coordinate system. In this case, the multi-point constraint will involveonly the degrees of freedom at a single grid point. The constraint equation relatesthe displacement in the direction of zero motion to the displacement components inthe global system at the grid point.

To describe rigid elements and mechanisms such as levers, pulleys, and gear trains. In this application, the degrees of freedom associated with the rigid element that arein excess of those needed to describe rigid body motion are eliminated with multi-point constraint equations. Treatment of very stiff members as being rigid elementseliminates the ill-conditioning associated with their treatment as ordinary elasticelements.

To be used with scalar elements to generate non-standard structural elements andother special effects.

When using rigid elements or multi-point constraints, you must make sure that thefollowing requirements are satisfied:

A dependent degree of freedom cannot be in the SPC.

A dependent degree of freedom in any rigid element or multi-point constraint cannotbe defined as a dependent degree of freedom in any other rigid element or multi-point constraint.

Materials

The different elastic material types provided by OptiStruct are: isotropic, orthotropic, andan-isotropic materials. The material property definition cards are used to define theproperties for each of the materials used in a structural model.

The MAT1 bulk data entry is used to define the properties for isotropic elastic materials. Itcan be referenced by any of the structural elements, and can also be referenced by anyproperty card.

The MAT2 entry is used to define the properties for an-isotropic materials. It applies onlyto triangular or quadrilateral membrane and bending elements, and can only be referencedby PSHELL, PCOMP, and PCOMPG property cards. This material type specifies therelationship between the in-plane stresses and strains. The angle between the materialcoordinate system and the element coordinate system is specified on the connection cards.



The MAT4 entry is used to define the properties for isotropic elastic materials. It can bereferenced by any of the structural elements, and can also be referenced by any propertycard.

The MAT5 entry is used to define the properties for an-isotropic elastic materials. It can bereferenced by any of the structural elements, and can also be referenced by any propertycard.

The MAT8 card is used to define the properties for planar orthotropic elastic materials intwo dimensions. Individual plys of a layered composite lay-up typically possess suchorthotropic properties. Since layered composite laminates are modeled using shellelements, MAT8 property data can only be referenced by PSHELL, PCOMP, and PCOMPGproperty cards.

The MAT9 bulk data entry can be used to define the properties for an-isotropic elasticmaterials for three dimensional solid elements. The general an-isotropic stress-strainrelationship linking the six independent stress components of the stress tensor at a pointand the six independent strain components of the tensor at the point contain 21independent constants in the elasticity matrix. These values are supplied using the MAT9bulk data card. The MAT9 bulk data card is used with the CHEXA, CPENTA, CPYRA, andCTETRA solid elements, and can only be referenced on the PSOLID property card. Theoptional coordinate system in which MAT9 data are specified is supplied via the PSOLIDbulk data entry.

The MAT10 bulk data entry is used to define material properties for fluid elements incoupled fluid-structural (acoustic) analysis. It may only be referenced on PSOLID entrieswith FCTN=’PFLUID’.

Temperature dependent material properties are defined using MATT1, MATT2, MATT8, andMATT9. All four have the same characteristics as described above. The temperaturedependency of each property is defined through TABLEM1, TABLEM2, TABLEM3, orTABLEM4 table entries.

Composite laminates are defined using the PCOMP and PCOMPG properties. They are notmaterial types; each ply in the laminate lay-up can reference a different material.

Nonlinear material properties are defined using MATS1. The nonlinear materialcharacteristics may need the table input TABLES1. MATS1 is defined as an extension to aMAT1 with the same MID. MATS1 is applicable to all nonlinear solutions.

For geometric nonlinear subcases, more nonlinear material laws are available. As ageneral rule, material definitions that are only applicable in geometric nonlinear analysisare defined on extensions to a MAT1 material that defines the basic elastic properties. Theextensions are grouped with the base entry by sharing the same MID. The table belowlists the MATXyz extensions available. If a law requires material curves, TABLES1 entriesare used.

Example

MAT1, 102, 60.4, , 0.33, 2.70e-6MATX02, 102, 0.09026, 0.22313, 0.3746, 100.0, 0.175



MATXy Description

MATX0 Void material

MATX02 Johnson-Cooke elastic-plastic material

MATX13 Rigid material

MATX21 Rock-Concrete material

MATX25 Composite shell material, TSAI-WU andCRASURV formulations

MATX27 Brittle elastic-plastic material

MATX28 Honeycomb material

MATX33 Visco-elastic foam material

MATX36 Piece-wise linear elastic-plastic material

MATX42 Ogden-Mooney and Rivlin material

MATX43 Hill orthotropic material

MATX44 Cowper-Symonds elastic-plasticmaterial

MATX60 Piece-wise nonlinear elastic-plasticmaterial

MATX62 Hyper-visco-elastic material

MATX65 Tabulated strain-rate dependentelastic-plastic material

MATX68 Honeycomb material

MATX70 Tabulated visco-elastic foam material

MATX82 Ogden material



Composite Laminates

Overview

Plates and shells can be made of layered composites in which several layers of differentmaterials (plies) are bonded together to form a cohesive structure. Typically, the plies aremade of unidirectional fibers or of woven fabrics and are joined together by a bondingmedium (matrix). In OptiStruct composite shells, the plies are assumed to be laid inlayers parallel to the middle plane of the shell. Each layer may have a different thicknessand different orientation of fiber directions.

Four-layer composite with ply angle shown.

Classical lamination theory is used to calculate effective stiffness and mass density of thecomposite shell. This is done automatically within the code using the properties ofindividual plies. The homogenized shell properties are then used in the analysis.

After the analysis, the stresses and strains in the individual layers and between the layerscan be calculated from the overall shell stresses and strains. These results may then beused to assess the failure indices of individual plies and of the bonding matrix.

Analysis of Composites

Analysis of composite shells is very similar to the solution of standard shell elements. Theprimary difference is the use of the PCOMP or PCOMPG property card, instead of PSHELL, tospecify shell element properties. From the ply information specified on the PCOMP entry,OptiStruct automatically calculates the effective properties of the shell element.

After the analysis, the available results include shell-type stresses as well as stresses,strains, and failure indices for individual plies and their bonding. These results arecontrolled by the results flags on the PCOMP or PCOMPG entry and the usual I/O controlcards.

PCOMP and PCOMPG define the composite lay-up in two different ways.

PCOMP defines the structure and properties of a composite lay-up which is then assignedto an element. The plies are only defined for that particular property and there is norelationship of plies that reach across several properties.



PCOMPG defines the structure and properties of a composite lay-up allowing for global plyidentification which is then assigned to an element. The plies of different PCOMPGdefinitions can have a relationship because of the use of global ply IDs.

Some remarks are in place regarding the specifics of composite analysis:

1. The most typical material type used for composite plies is MAT8, which is planarorthotropic material. The use of isotropic MAT1 or general anisotropic MAT2 for plyproperties is also supported.

2. While it is possible to specify ply angles relative to the element coordinate system, theresults become strongly dependent upon the node numbering in individual elements. Thus, it is advisable to prescribe a material coordinate system for composite elementsand specify ply angles relative to this system.

3. Depending on the specific lay-up structure, the composite may be offset from thereference plane of the shell element, i.e. have more material below than above thereference plane (or vice versa).

4. Stress results for composites include both shell-type stresses and individual plystresses. Importantly, shell-type stresses are calculated using homogenized propertiesand thus only represent the overall stress-state in the shell. To assess the actualstress-state in the composite, individual ply results need to be examined.

Interpretation of Results for Composites

A number of composite-specific results are calculated for composite shell elements. Due tothe specialized nature of these results, some explanation is required regarding theirmeaning.

Ply Stresses and Strains

Classical lamination theory assumes two-dimensional stress-state in individual plies(so-called membrane state). The values of stresses and strains are calculated at themid-plane of each ply, i.e. halfway between its upper and lower surface. Forsufficiently thin plies, these values can be interpreted as representing uniform stressin the ply.

Ply stresses and strains are calculated in coordinate systems aligned with plymaterial angles as specified on the PCOMP card. In particular, correspond to theprimary ply direction, is orthogonal to it, and represents in-plane shear stress.

Inter-laminar Stress

Inter-laminar bonding matrix usually has different material properties and stress-state than the individual plies. The primary stress that is of importance here is inter-laminar shear with two components:

Failure Indices

To facilitate prediction of potential failure of the laminate, failure indices arecalculated for plies and bonding material. While there are several theories availablefor such calculations, their common feature is that failure indices are scaled relativeto allowable stresses or strains, so that:

- the value of a failure index lower than 1.0 indicates that the stress/strain is withinthe allowable limits (as specified on the material data card), and

- a failure index above 1.0 indicates that the allowable stress/strain has been



exceeded.

- according to the formula, some failure criteria (for example, Tsai-Wu andHoffman) would produce the negative ply failure, depending on the problem.

Here, a brief summary of failure theories available is provided.

Hill's Theory of Ply Failure

According to Hill's theory, the ply failure index is calculated as:

Where, X is the allowable stress in the ply material direction (1), Y is the allowable

stress in the ply material direction (2), and S is the allowable in-plane shear stress. It

should be noted that Hill’s theory does not differentiate between tensile andcompressive stresses and it is strongly recommended to use the same values for bothallowable stresses, i.e. Xt = Xc and Yt = Yc. If this suggestion is not adopted, warning

messages will be output and the following rules will be applied: If > 0, X = Xt;

otherwise, X = Xc, and similarly for Y and . For the interaction term / X2, if >

0, X = Xt; otherwise, X = Xc.

Hoffman's Theory of Ply Failure

In Hoffman's theory, the ply failure index is calculated as:

Tsai-Wu Theory of Ply Failure

In Tsai-Wu theory, the ply failure index is calculated as:

Where, F12 is a factor to be determined experimentally.

Maximum Strain Theory of Ply Failure

In maximum strain theory, the ply failure index is calculated as the maximum ratio ofply strains to allowable strains:



Where, is the allowable strain in the ply material direction (1), is the allowable

strain in the ply material direction (2), and is the allowable in-plane engineering

shear strain. If you provide different values of and for tension and compression,the appropriate values are used depending on the signs of , respectively. Notethat if you prescribe allowable stresses rather than strains on the material data card,then the allowable strains are calculated via simple division by the relevant materialmodule.

Bonding Material Failure

The primary failure mode of the bonding material is due to inter-laminar shear. Thecorresponding failure index is calculated as:

Where, SB is the allowable shear in the bonding material.

Final Failure Index for Composite Element

After calculation of failure indices for individual plies, the potential failure index for thecomposite shell element is obtained. This is based on the premise that failure of asingle layer qualifies as failure of the composite. Thus, the failure index for compositeelement is calculated as the maximum of all computed ply and bonding failure indices(note that only plies with requested stress output are taken into account here).

Comparison of laminate modeled with PCOMP and PCOMPG



Loads and Boundary Conditions

The following boundary conditions are outlined here.

Static Loads and Boundary Conditions

Static loads are applied at grid points in a variety of ways, including:

Loads applied directly to grid points

Pressure on surfaces

Gravity loads

Centrifugal forces due to steady rotation

Equivalent loads resulting from:

thermal expansion

- enforced deformations of structural elements

- enforced displacements of grid points

Any number of load sets can be defined in the bulk data section of the input file. However,only those sets selected in the subcase information section (as described in the LinearStatic Analysis, Inertia Relief, and Nonlinear Quasi-Static Analysis sections) will be used inthe problem solution. The manner in which each type of load is selected is specified on theassociated bulk data statement description.

The FORCE statement is used to define a static load applied to a grid point in terms ofcomponents defined by a local coordinate system. The orientation of the load componentsdepends on the type of local coordinate system used to define the load.

The FORCE1 statement is used if the direction is determined by a vector connecting twogrid points.

The MOMENT and MOMENT1 statements are used to define the application of aconcentrated moment at a grid point.

Pressure loads on triangular and quadrilateral elements are defined with a PLOAD2 card. The positive direction of the loading is determined by the order of the grid points on theelement connection card (using the right-hand rule). The magnitude and direction of theload is automatically computed from the value of the pressure and the coordinates of theconnected grid points. The load is applied to the connected grid points.

PLOAD pressure loads are used in a similar fashion to define the loading of any three orfour grid points, regardless of whether or not they are connected with two-dimensionalelements.

Pressure loads on the HEXA, PENTA and TETRA solid elements are defined with the PLOAD4card. The pressure is defined positively outward from the element. The magnitude anddirection of the equivalent grid point forces are automatically computed using the iso-parametric shape functions of the element to which the load has been applied. Pressureloads on the QUAD4 and TRIA3 elements can also be applied using the PLOAD4 card.



The PLOAD1 card is used to describe concentrated, uniformly distributed or linearlydistributed loads on the CBAR or CBEAM elements.

The GRAV bulk data entry is used to specify a gravity load by providing the components ofthe gravity vector in any defined coordinate system. The gravity load is obtained from thegravity vector and the mass matrix of the structural model. Because the gravitationalacceleration is not calculated at scalar points, you are required to introduce gravity loadsat scalar points directly.

The RFORCE statement is used to define a static loading condition due to a centrifugalforce field. A centrifugal force load is specified by the designation of a grid point that lieson the axis of rotation and by the components of rotational velocity and acceleration in anydefined coordinate system. In the calculation of the centrifugal force, the mass matrixpertains to a set of distinct rigid bodies connected to grid points. Deviations from thisviewpoint, such as the use of scalar points or the use of mass coupling between gridpoints, can result in errors.

Temperature loads can only be defined at grid points. The temperatures of the connectedgrid points are given on the TEMP and TEMPD bulk data entries. The thermal expansioncoefficients are defined on the material definition cards. The mere presence of a thermalfield does not imply the application of a thermal load. A thermal load will not be appliedunless you make a specific request in the subcase information section.

The LOAD card in the bulk data section defines a static loading condition that is a linearcombination of load sets consisting of loads applied directly to grid points, pressure loads,gravity loads, and centrifugal forces. This card must be used if gravity loads are to beused in combination with loads applied directly to grid points, pressure loads, or centrifugalforces. The application of the combined loading condition is requested in the subcaseinformation section by selecting the set number of the LOAD combination.

It should be noted that the equivalent loads (thermal and enforced displacement) musthave unique set identification numbers and be selected separately in the subcaseinformation section. For any particular solution, the total load will be the sum of theapplied loads (grid point loading, pressure loading, gravity loading, and centrifugal forces)and the equivalent loads.

Zero enforced displacements may be specified on SPC or SPC1 cards. Zero displacementsresult in non-zero forces on the grid point constrained (SPC forces).

The SPCADD statement allows the combination of different SPC sets.

For inertia relief, the reaction degrees of freedom for the computation of the accelerationload are defined through SUPORT or SUPORT1 statements. Up to six degrees of freedomcan be defined per subcase.

Non-zero enforced displacements may be specified on SPC or SPCD cards. The SPC cardspecifies both the component to be constrained and the magnitude of the enforceddisplacement. The SPCD card only specifies the magnitude of the enforced displacement. When an SPCD card is used, the component to be constrained must be specified on eitheran SPC or an SPC1 card. The use of the SPCD card avoids the decomposition of thestiffness matrix when changes are only made in the magnitudes of the enforceddisplacements.

The equivalent loads resulting from enforced displacements of grid points are calculated bythe program and added to the other applied loads.

If the magnitudes of the enforced displacements are specified on SPC cards, the application



of the load is automatic when you select the associated SPC set in the subcase informationsection.

If the magnitude of the displacement is defined on an SPCD card, the load is applied if youselect the associated LOAD set in the subcase information section.

Prestressed Analysis

Preloaded or prestressed analysis is any type of structural analysis performed on astructure under prior loading (also termed preloading or prestressing). The response of astructure is affected by its initial state and this is in turn affected by the variouspreloading/prestressing applied to the structure, prior to the analysis of interest. Examples of prestressed analysis include analysis of rotorcraft blades under centrifugalpreloading, analysis of pillar-like structures under compressive preloading, etc. OptiStructcan be used to take into account such preloading or prestressing effects. The prestressing/preloading loadcase is a linear or nonlinear static loadcase. Prestressed/preloaded analysisis currently only supported for linear statics, eigenvalue analysis and direct frequencyresponse analysis. Specifying prestress in any other unsupported analysis will generate anappropriate user error. Prestressing is specified through the STATSUB(PRELOAD) CaseControl card, which refers to the preloading static loadcase ID. Nested preloading is notsupported and will generate an appropriate user error (that is: User error will be reported ifSubcase C has preloading from Subcase B, which in turn has preloading from Subcase A).

The preloading is captured or defined by a geometric stiffness matrix [KG] which is based

on the stresses of the preloading static subcase. In prestressed analysis, this geometricstiffness matrix is subtracted from the original stiffness matrix [K] of the (unloaded)structure. Depending on preloading conditions, the resulting effect could be a weakened orstiffened structure. If the preloading is compressive, it typically has a weakening effect onthe structure (example: column or pillar under compressive preloading). If the preloadingis tensile, it typically has a stiffening effect (for example: rotorcraft blade under centrifugalpreloading).

Prestressed Static Analysis

Prestressed static analysis is governed by the following equation (where, F is the loading

and U is the displacement).

GK K U F

While linear static subcases can have prestressing, nonlinear static subcases underprestressing are not supported.

Prestressed Eigenvalue Analysis

Prestressed eigenvalue analysis is governed by the following equation (where, M is the

mass matrix, F is the eigenvector and l is the eigenvalue).

0GK K lM F



Prestressed eigenvalue analysis is currently supported by AMSES, AMLS and the LanczosMethod. However, if the specified preload is greater than the first critical buckling load, anappropriate error will be reported for AMSES/AMLS runs.

Prestressed Direct Frequency Response Analysis

Prestressed direct FRF analysis is governed by the following equation.

2G G GEK K ig K K iK iwC w M U F

Where, M is the mass matrix, U is the complex displacement vector, KGE is the material

damping matrix, C is the viscous damping matrix that includes the Area Matrix for fluid-

structure coupling, w is the loading frequency and g is the structural damping coefficient.

Results

All results that are supported for regular structural analyses are also available in thecorresponding prestressed analyses. It is important to note that, while the prestressedanalysis includes the effects of preloading as a weakening or a stiffening of the structure,the results from the prestressed analysis do not include the preloading results. Forexample, the displacements from prestressed static analysis do not include the preloadingdisplacements. In order to get the overall deflection/stresses of the structure, thedisplacements/stresses from the prestressed analyses have to be carefully superposed withthe preloading displacements/stresses while post-processing. Particularly, while post-processing complex results from prestressed direct FRF, the correct approach would be tofirst obtain the complex results for a certain phase and then superpose the appropriatepreloading result. Any other superposing approach would lead to incorrect results.

Pretensioned Bolt Analysis

Overview

Many engineering assemblies are put together using bolts, which are usually pretensionedbefore application of working loads. A typical sequence is described below.



Figure 1: Step 1 of pretensioned assembly - application of pretensioning loads

In Step 1, upon preliminary assembly of the structure, the nuts on respective bolts aretightened, usually by applying prescribed torque (which translates into prescribed tensionforce according to the pitch of the thread).

As the result, the working part of the bolt becomes shorter by a distance L . This distancedepends upon the applied force, the compliance of the bolt and of the assembly beingpretensioned.

From the perspective of FEA analysis, it is important to recognize that:

Pretensioning actually shortens the working part of the bolt by removing a certainlength of the bolt from the active structure (in reality this segment slides through thenut, yet the net effect is the shortening of the working length of the bolt). At thesame time the bolt stretches, since now the smaller effective length of the boltmaterial has to span the distance from the bolt mount to the nut.

Calculation of each bolt’s shortening L , due to applied forces F, requires FEAsolution of the entire model with the pretensioning forces applied. This is because theamount of nut movement due to given force depends on the compliance of the bolts,of the assembly being bolted and is also affected by cross-interaction betweenmultiple bolts being pretensioned.

At the end of Step 1, the amount of shortening L for each bolt is established and“locked”, simply by leaving the nuts at the position that they reached during thepretensioning step.

In Step 2, with the shortening L of all the bolts “locked”, other loads are applied to theassembly (Figure 2). At this stage the stresses and strains in the bolts will usually change,

while the length of material removed L remains constant for each bolt.



Figure 2: Step 2 of pretensioned assembly – application of working loads with “locked” bolt shortening

Comments

In practice, there may be variations of the application of pretensioning loads and morecomplex pretensioning sequences than that presented above. For example:

In alternative assembly scenarios, instead of using a nut on top of the bolt, the bolt maybe screwed into a base and thus compress the assembly, as illustrated in Figure 3.

Figure 3: An alternative approach to application of pretensioning loads

In this case, the shortening (removal of material) of the working part of the bolt happensat the thread within the base, rather than at the bolt-nut interface. Yet the finalmechanical effect is the same.

Sometimes the pretensioning by torque/force is augmented by “tightening” via prescribed

number of turns. This means that on top of the L , due to pretensioning force, an



additional L ’ is added according to the number of turns and the pitch of the thread.

In an automated assembly process, usually all bolts are pretensioned simultaneously.Sometimes, however, the tensioning may happen in sequence or in groups. In such cases,

while L is “locked” for bolts that have already been pretensioned, consecutivepretensioning force is applied to the next batch of bolts, which then become “locked” forthe following step.

FEA Solution with Pretensioning

In analysis of structures, the FEA model is usually defined in material reference frame andthe amount of material is assumed to remain fixed, while the structure undergoesstretching and deformation. However, in the case of pretensioning, the actual working partof the model has some material removed by being driven through the nut (usually theprotruding part of the bolt is not included in the working FEA model, since it does notparticipate in the balance of forces on the structure).

The simulation of this phenomenon in Optistruct follows the approach described below:

First, it is recognized that for straight bolts, from the viewpoint of balance of forces it doesnot matter at what location the removal of the material happens in the bolt. Therefore,instead of simulating the precise interaction between the nut and the bolt, thepretensioning is handled within the length of the bolt. Pretensioning in OptiStruct isimplemented with the help of Multiple Point Constraints (MPC’s) via two differentprocesses:

1D Bolt Pretensioning


Multiple point constraints (MPC’s) are used in both 1D and 3D pretensioning, the differencebetween the two implementations is the number of duplicate grid points created andcontrolled via MPC’s.


In this process, the bolt or its selected section is represented by single or multiple 1Delement(s) (beam or rod).

Note: If a bolt is meshed with 3D (solid) elements, 1Dpretensioning can be applied by replacing a transversesection of the bolt with 1D beam/rod elements. In suchcases; however, 3D pretensioning is recommended sinceit is easier to implement and accuracy is improved. If abolt is constructed using 1D elements, 1D pretensioningcan be used effectively.

Step 1

The conceptual FEA handling of 1D bolt pretensioning is illustrated in Figure 4. A bolt ismodeled using 3D elements and a beam or rod element represents the selected section ofthe bolt where pretensioning will be applied.

1. First, an imaginary cut is introduced into the beam (This is automatically doneinternally for a subcase that includes a PRETENSION command) and two duplicate gridpoints are created at the location of the cut.



Figure 4: FEA implementation of Bolt Pretensioning applied to a 1D Bolt using a 1D element

Additionally, a scalar point (SPOINT) is automatically created to act as an independent gridpoint. A pair of self-balanced pretensioning forces is applied to both ends of the cut withthe help of the newly created SPOINT. The specified pretensioning force is internallyapplied on the SPOINT and this is transferred to the duplicated grid points via an MPC. TheMPC controls the movement of the newly created duplicate grid points and the scalar pointbased on the following equation:

int igspo dgu u u

Where,

spointu is the displacement of the independent scalar point (SPOINT)

dgu is the displacement of the dependent grid point

igu is the displacement of the independent grid point

The reaction force on the scalar point due to an enforced displacement of spointu on it can

be shown to be equal to the forces acting on the dependent or independent grid point.

int igspo dgF F F or spoint dg igF F F

depending on the direction of the forces.



Where,

spointF is the total reaction force on the independent scalar point (SPOINT) due to an

enforced displacement of spointu

dgF is the force acting on the dependent grid point

igF is the force acting on the independent grid point

2. With these forces (plus other loads referenced in this subcase) applied, static analysis isperformed to calculate deformation of the structure. Among the results of such analysis

is the “overlap” L across the cut portion of the beam, which is equivalent to thedistance that the bolt would move relative to the nut in Figure 1.

Figure 5: FEA implementation of Bolt Pretensioning applied to a 3D Bolt using a 1D element (Step 1)

Step 2

As shown in Figure 5, the amount of overlap L calculated in Step 1 is removed from thebolt length, and the bolt is reconnected at the cut location. This represents the shorterworking length of a pretensioned bolt on which the nut has been tightened (Mechanically,this is similar to the effect of the DEFORM command).

With bolt pretensioning “locked” in this way, additional working loads are applied and aFEA solution is performed.




As mentioned already, it is possible to construct more complex sequences of pretensioning,wherein some bolts have already been pretensioned (Step 2) while the next batch of boltsis being pretensioned (Step 1). (Note that a specific tensioning sequence has an effect onthe final result only in path-dependent problems, such as contact with friction or elasto-plastic materials.)


In 3D Bolt Pretensioning, the bolt is represented (meshed) using 3D solid elements. Atransverse surface in the beam is identified (cross-section) along which it is cut and theduplicate grids are then controlled by Multiple Point Constraints (MPC’s) and a SPOINT tosimulate the pretensioning effect.

Step 1

The first step in 3D pretensioning is to identify the transverse cross-sectional surface of thebolt. OptiStruct automatically cuts the bolt at the selected surface and duplicate grid pointsare created mirroring the existing grid points at the cut surface. This is automatically doneinternally for a subcase that includes a PRETENSION command.



Figure 7: FEA implementation of Bolt Pretensioning applied to a 3D Bolt using a 3D element (PretensionDirection)

Additionally, a scalar point (SPOINT) is automatically created to act as an independent gridpoint. A pair of self-balanced pretensioning forces is applied to both ends of the cut withthe help of the newly created SPOINT. The specified pretensioning force is internallyapplied on the SPOINT and this is transferred to the duplicated grid points via MPC’s. TheMPC’s controls the movement of the newly created duplicate grid points and the scalarpoint based on the following equations:

In the pretension direction:

Perpendicular to the pretension direction:

Where,

spointu is the displacement of the independent scalar point (SPOINT)

dgku is the displacement of the k’th dependent grid point

igku is the displacement of the k’th independent grid point

N is the displacement of the k’th independent grid point

dgks is the displacement of the k’th dependent grid point perpendicular to the

pretension direction



igks is the displacement of the k’th independent grid point perpendicular to the

pretension direction

Figure 8: FEA implementation of Bolt Pretensioning applied to a 3D Bolt using a 3D element (Perpendicular to thePretension Direction)

The reaction force on the scalar point due to an enforced displacement of spointu on it can

be shown to be equal to the sum of the magnitudes of the forces acting on either thedependent or independent grid points.

Where,

spointF is the total reaction force on the independent scalar point (SPOINT) due to an

enforced displacement of spointu

dgkF is the force acting on the k’th dependent grid point

igkF is the force acting on the k’th independent grid point

When these forces (including other loads referenced in this subcase) are applied, staticanalysis is performed to calculate deformation of the structure. Among the results of such

analysis is the “overlap” L across the cut portion of the bolt, which is equivalent to thedistance that the bolt would move relative to the nut.




Step 2

As shown in Figure 5, the amount of overlap L calculated in Step 1 is removed from thebolt length, and then the bolt is reconnected at the initial cut surface. This represents theshorter working length of a pretensioned bolt on which the nut has been tightened.(Mechanically, this is similar to the effect of the DEFORM command.)

With bolt pretensioning “locked” in this way, additional working loads are applied and FEAsolution is performed.


As mentioned earlier (in 1D pretensioning), it is possible to construct complexpretensioning sequences wherein some bolts have already been pretensioned (Step 2)while the next batch of bolts is being pretensioned (Step 1).

Note: A specific tensioning sequence has an effect on the final result only inpath-dependent problems, such as contact with friction or elasto-plastic



materials.

Analysis of Pretensioned Assemblies in OptiStruct

In OptiStruct, the solution of problems involving pretensioning fits into the standardsequences of static subcases, linear or nonlinear. (Step 2, analysis of pretensionedstructure, is also available in natural frequency, frequency response, buckling and transientsubcases).

Respective user’s input requires definition of pretensioning sections, loads and adjustmentsin the Bulk Data section, plus specification of tensioning sequences in the Subcase section.The available commands are outlined below – for more details, see individual carddescriptions.

Bulk Data Section

PRETENS Defines the pretension section. Presently this identifies therespective 1D element.

PTFORCE Defines the pretensioning force F (actually a pair of forces) andassigns it to the respective pretension section.

PTFORC1 A simplified format that allows assigning force to multiplepretension sections.

PTADJST Defines the tensioning adjustment L’ and assigns it to therespective pretension section.

PTADJS1 A simplified format that allows assigning one adjustmentamount to multiple pretension sections.

PTADD Combines multiple pretensioning forces or adjustments into asingle load ID.

Subcase Section

PRETENSION Identifies pretensioning forces / adjustments to be activatedin this static subcase. (Corresponds to Step 1 describedabove.)

STATSUB(PRETENS)

Identifies the static subcase that created pretensioned bolts,which are to be included in the present subcase.(Corresponds to Step 2 described above.)

It is allowed to have PRETENSION and STATSUB(PRETENS) in the same static subcase – this

can be used to emulate more complex pretensioning sequences.



A Simple Illustration

A simple illustration of typical flow of pretensioned analysis is shown below. This is not a

complete input deck, merely an illustration of a typical arrangement of respectivecommands. Refer to the tutorial OS-1390: 1D and 3D Pretensioned Bolt Analysis of an ICEngine Cylinder Head, Gasket and Engine Block System Connected Using Head Bolts formore information on setting up 1D and 3D pretensioned analysis.

Comments

Subcases that Support Pretensioning

Pretensioning Steps 1 and 2 require the solution of a static FEA problem. Therefore, PRETENSION and STATSUB(PRETENS) commands can appear only in linear or nonlinear

static subcases of the default NLSTAT type.

Referencing Pretensioning in Other Types of Subcases

Because pretensioning produces stresses in the FEA model, it can through nonlineargeometric stiffness effects, affect the static and vibrational response of the structure, suchas increase of natural frequency of a pretensioned bolt. Such geometric stiffness effects arecaptured by a STATSUB(PRELOAD) command, which is available in static, natural

frequencies and frequency response subcases. In problems with pretensioning, it is allowedfor STATSUB(PRELOAD) to point to a pretensioned subcase or any of the follow-on static

subcases that references pretension. The stresses created by pretension (and other loadsin such subcase) will be used as the respective preload.

Sequencing of Pretensioning Subcases

The subcases with PRETENSION and STATSUB(PRETENS) can be used to create various

sequences of pretensioning, such as tightening bolts in sequence or in groups.

A single pretension section (1D bolt) can receive consecutive cumulative pretensioningloads so as to model cases where bolt tightening with a force is followed up by an



additional adjustment by a prescribed distance (number of turns of the nut). Such astacked sequence is presented in the simple illustration above.

The specific rules for sequencing pretensioning subcases on the same section are asfollows:

1. Pretensioning force (PTFORCE) can only be activated in the new or “fresh”pretensioning subcase for a given section. In other words, subcase with PRETENSIONpointing to PTFORCE cannot also include STATSUB(PRETENS) referencing a subcasethat had already pretensioned this section.

2. Pretensioning adjustment (PTADJST) may be activated in any of the pretensioningsubcases for a given section. The effect of adjustment is cumulative relative to thepretensioning status reached in the respective previous subcase, as referenced by STATSUB(PRETENS).

In nonlinear path-dependent problems, this sequencing of pretensioning can be combinedwith continuation of nonlinear subcases, as controlled by subcase command CNTNLSUB, inquite arbitrary combination. STATSUB(PRETENS) controls the sequencing of pretensioning

steps and CNTNLSUB controls the sequencing of nonlinear aspects (plasticity, contact withfriction, and so on) for quite arbitrary loading scenarios.

Inertia Relief

Inertia relief allows the simulation of unconstrained structures. Typical applications are anairplane in flight, suspension parts of a car, or a satellite in space.

With inertia relief, the applied loads are balanced by a set of translational and rotationalaccelerations. These accelerations provide body forces, distributed over the structure insuch a way that the sum total of the applied forces on the structure is zero. This providesthe steady-state stress and deformed shape in the structure as if it were freely acceleratingdue to the applied loads. Boundary conditions are applied only to restrain rigid bodymotion. Because the external loads are balanced by the accelerations, the reaction forcescorresponding to these boundary conditions are zero.

This calculation is automated.

Inertia relief boundary conditions may be defined in the bulk data section of the input deckor they may be determined automatically by the solver.

The SUPORT and SUPORT1 bulk data entries are used to define up to six reactiondegrees of freedom of the free body.

SUPORT entries will be used in all relevant subcases and therefore do not need to bereferenced in the Subcase Information section.

SUPORT1 entries need to be referenced by a SUPORT1 data selector statement foruse within a subcase.

Inertia relief boundary conditions may be generated automatically by using PARAM,INREL, -2.

In OptiStruct, inertia relief can be applied to linear static, nonlinear gap, modal frequencyresponse (with residual vectors), and transient response (with residual vectors) analyses. A static case with inertia relief cannot be referenced in a linear buckling analysis. Inertiarelief is meaningless in normal modes analysis.



Geometric Nonlinear Analysis Loads and Boundary Conditions

Any number of load sets can be defined in the bulk data section of the input file. However,only those sets selected in the subcase information section (as described in the GeometricNonlinear Analysis section) will be used in the problem solution. The manner in whicheach type of load is selected is specified on the associated bulk data statement description.

Geometric nonlinear analysis, whether implicit or explicit, (quasi-)static or dynamic, isperformed as a time-dependent event with time-dependent loads. A termination time TTERM needs to be defined. Subcases can be combined to a successive load history usingthe CNYNLSUB subcase statement. Each continued subcases starts from the end time andfinal load of the previous (reference) subcase. TTERM is defined in terms of total time.

The NLOAD1 bulk data statement defines a time-dependent load of the form:

( ) * *t

f t A C FB

The load history function F is defined using TABLED1.

For both definitions, a DAREA or SPCD statement defines the force, displacement, velocity,or acceleration amplitude A, respectively. Aside from DAREA, FORCE, MOMENT, PLOAD,

and PLOAD4 entries can be used to define the load amplitude. The quantities B and C are

scale factors.

The NLOAD card in the bulk data section defines a loading condition that is a linearcombination of load sets consisting of loads applied directly to grid points. The applicationof the combined loading condition is requested in the subcase information section byselecting the set number of the NLOAD combination.

Rigid walls may be defined using RWALL. Multiple rigid wall sets can be combined into asingle set using RWALADD. The subcase selection is made by RWALL.

Zero enforced displacements may be specified on SPC or SPC1 cards. The SPCADDstatement allows the combination of different SPC sets.

In dynamic analysis (explicit and implicit), initial velocities can be defined using TIC andTICA bulk data entries. TIC defines an initial velocity on a grid point, while TICA definesthe initial velocities of a grid set along and/or about an axis. A subcase selection must bemade with IC.

In (quasi-)static analysis, static loads can also be defined by using FORCE, MOMENT,PLOAD, and PLOAD4 directly thru a LOAD reference in the subcase. These loads are thentreated as linear ramp-up. In this case, TTERM is not mandatory, but if defined the loadramps up from the end time of the previous subcase to TTERM. If TTERM is absent it willbe determined from the subcase identification number SID such that TTERM = SID.

Frequency Response Loads and Boundary Conditions

Frequency dependent dynamic loads are applied at grid points. There are two differentdefinitions available.

Any number of load sets can be defined in the bulk data section of the input file. However,



only those sets selected in the subcase information section (as described in the FrequencyResponse Analysis section) will be used in the problem solution. The manner in whicheach type of load is selected is specified on the associated bulk data statement description.

The RLOAD1 bulk data statement defines a frequency dependent excitation of the form:

The RLOAD2 bulk data statement defines a frequency dependent excitation of the form:

For both definitions, a combination of DAREA, FORCE, FORCE1, FORCE2, MOMENT,MOMENT1, MOMENT2, PLOAD, PLOAD1, PLOAD2, PLOAD4, and RLOAD, or SPCD define theamplitude A of an excitation force or motion, respectively. A DPHASE reference defines the

phase angle , and a DELAY reference defines the delay . The quantities B, C, D, and ,

are frequency dependent. They are defined using TABLED1, TABLED2, TABLED3, orTABLED4.

It is recommended that SPCD be used for enforced motion. If the old inferior Large MassMethod is used for modal frequency response analysis with EIGRA, use PARAM,AMSESLMfor better accuracy.

The range for the loading frequency is defined using the FREQ, FREQ1, FREQ2, FREQ3,FREQ4, or FREQ5 bulk data statements.

The DLOAD card in the bulk data section defines a static loading condition that is a linearcombination of load sets consisting of loads applied directly to grid points. The applicationof the combined loading condition is requested in the subcase information section byselecting the set number of the DLOAD combination.

Zero enforced displacements may be specified on SPC or SPC1 cards.


Combinations of dynamic loads (DAREA) with static loads (FORCE, FORCE1, FORCE2,MOMENT, MOMENT1, MOMENT2, PLOAD, PLOAD1, PLOAD2, PLOAD4, and RLOAD), issupported.

Transient Response Loads and Boundary Conditions

Transient dynamic loads are applied at grid points. Two different definitions are available.

Any number of load sets can be defined in the bulk data section of the input file. However,only those sets selected in the subcase information section (as described in the TransientResponse Analysis section) will be used in the problem solution. The manner in whicheach type of load is selected is specified on the associated bulk data statement description.

The TLOAD1 bulk data statement defines a time dependent load of the form:

( ) ( )f t AF t

where, F is defined using TABLED1, TABLED2, TABLED3, or TABLED4.



The TLOAD2 bulk data statement defines a time dependent load of the form:

The quantities T1, T2 are time constants, a frequency and a phase angle, C is an

exponential coefficient, and B is a growth coefficient.

For both definitions, a DAREA or SPCD statement defines the force or displacementamplitude A, respectively. A DELAY statement defines the delay .

The DLOAD card in the bulk data section defines a static loading condition that is a linearcombination of load sets consisting of loads applied directly to grid points. The applicationof the combined loading condition is requested in the subcase information section byselecting the set number of the DLOAD combination.

Transient initial conditions are defined using a TIC bulk data entry. Initial displacementsand initial velocities can be defined.

Zero enforced displacements may be specified on SPC or SPC1 cards.


Combinations of dynamic loads with static loads are not currently supported.

It is recommended that SPCD be used for enforced motion. If the old inferior Large MassMethod is used for modal transient analysis with EIGRA, use PARAM,AMSESLM for betteraccuracy.



Modeling Errors

Warning #340

RBE3 using 123456 DOF coupling at the independent GRID points can produced unexpectedresults.

OptiStruct will issue the following warning:

*** WARNING #340

RBE3 element 6300346 has nonzero weight at rotational (456) dofs of independentgrids.

This practice may result in undesirable load distribution - use with caution.

Warning #1265

Use of very thin plate elements (.001 thickness or less) on surfaces of solid elements willproduce near singularities, if MID2 and MID3 are specified on the PSHELL data. OptiStructwill issue the following warning.

*** WARNING #1265

PSHELL 10003383 has thickness 0.001 or less and bending properties defined. This can leadto matrix singularities, causing message 153.

If this element is intended to be only a membrane element, please leave MID2 and MID3blank on the PSHELL data.

For thin skin elements, leave MID2 and MID3 blank on the PSHELL data.

Warning #1942

Confirm that Field 9, CID is specified with either 0 (zero) or the appropriate local coordinatesystem on CELAS GRID points. Below is an example of the OptiStruct output for the twotypes of modeling errors:

For CELAS grids having different local coordinate systems.

*** WARNING # 1942

CELAS2 8820024 references GRID data with different CD.

This may constrain rigid body motion

Elements

Do not connect CBEAM or CBAR to skin elements that have MID2 and MID3 blank on thePSHELL data, as this will cause mechanisms. Use RBE2 elements instead with 123 DOFsspecified.



Rigid Body Modes

Welding Methods

Do not use welding methods that use MPC equations. This, in general, will give very poorrigid body modes that are not equal to zero. Use rigid elements instead.

Extra Rigid Body Modes

Do not use an RBE3 using 123456 DOF on the dependent GRID to only 1 or 2 GRID pointswith 123456 DOF on the independent points. Use of these types of elements can produceextra rigid body modes.

If you use just on independent GRID, OptiStruct will issue the following warning:

*** WARNING #341

RBE3 element 10159308 has only two nodes.

This practice may result in undesirable load distribution - use with caution.

Use at least 3 non co-linear grid points with only 123 DOF on the independent GRID.

Poor Rigid Body Modes

CELAS elements between two non-coincident points will produce poor rigid body modes. UseCBUSH elements instead. The use of GROUNDCHECK will catch misaligned CELAS elements.

Below is a list of elements that have non-zero rigid body strain energies:

These elements can cause GROUNDCHECK to FAIL

CELAS elements in this list are probably misaligned.

Elem no: 1 type: CELAS1 Six rigid mode energies and ratios:

energy - 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

ratio - 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 4.000E+00

Torsion Motion

When representing torsion motion through a ball joint connection, like the intermediate shaftto steering column using MPC equations, be sure to remove the rigid body reaction from theMPC equations. Otherwise, the model will have poor rigid body modes.



Results

The following features are outlined here.

Results of a Finite Element Analysis

The primary results in a finite element analysis are grid point displacements and rotations. Element results such as stresses, strains, and strain energy density are derived from thoseresults. Other results include element forces, MPC forces, SPC forces, and grid pointforces.

Results of a finite element analysis are post-processed using a graphical tool.

The definitions of the output options can be found in the I/O Options Section. An overviewof the result files can be found in the Results Output by OptiStruct section.

Information on stress, strain and force definitions regarding their coordinate systemdefinition can be found in the section Element Results Representation in OptiStruct and onthe respective element definitions.

Displacements

Displacements and rotations are computed in linear static, and frequency responseanalyses. In addition, in frequency response velocities and acceleration are computed.

Eigenvectors are the primary result in a normal modes and buckling analyses. In a normalmodes analysis, they are normalized with respect to the mass matrix or with respect to themaximum vector component. In a buckling analysis, the latter always applies.

Displacements, velocities, accelerations, and eigenvectors are grid point results. They areplotted as a deformed structure, or as a contour on the undeformed structure. Some post-processors, such as Altair HyperMesh and Altair HyperView, also allow the animation of thedisplacements.



Deformed displacement contour plot

Stresses

The stresses are secondary results in a static analysis.

Stresses near notches and other sharp corners, point loads and boundary conditions, andrigid elements are often unreliable due to the singularities in these points. This is not atrait unique to OptiStruct, but is inherent in the finite element method itself. A meshrefinement in such places can improve the stress prediction. A theoretically infinite stresscannot be predicted by finite elements.

Stresses are primarily calculated at the Gauss integration points. These give the mostaccurate prediction. However, element stresses, corner stresses, and grid point stressesare provided.

Element stresses are calculated at the centroid of the element. They should only be post-processed using an assign plot. Contouring of element stresses vastly underestimates theextreme values due to the smearing across element boundaries.

The stresses of interest are usually found on the surface of a structure. Mesh refinementwill actually not just improve the stress prediction but also change the location of the pointof stress evaluation. Therefore, it is common practice to use a skin of thin membraneelements in 3D modeling, or rod elements in 2D modeling, to evaluate the stresses onelement surfaces or edges, respectively. This method is accurate since it considers thecorrect condition of a stress-free boundary if no load is applied to the boundary. Themethod of skinning a model also has the advantage of much faster post-processing of solidmodels because only the membrane skin needs to be displayed.



Besides assign plots, elements stresses can be viewed in tensor plots that can help in theevaluation of the load path in a structure by evaluating the principal stress directions.

Corner stresses are computed by extrapolating the stresses from the Gauss points to theelement grid points. Corner stresses are plotted in a contour plot. Corner stresses forsolid elements are not available for normal modes analysis.

Grid point stresses are computed by averaging the corner stresses contributions of theelements meeting in a grid point. The averaging does not consider the condition of astress-free boundary. Further, interfaces between different materials, where a stress jumpnormally can be observed, are not considered correctly because of the smearing of thestress. Grid point stresses are plotted in a contour plot.

For first order elements, grid point stresses do not provide higher accuracy over elementstresses. For second order elements, the stress prediction might improve by using gridpoint stress over element stresses, considering the weaknesses mentioned above.

Assign plot of maximum principal element stress

Strains

Strains are secondary results.

They are calculated as elements strains. Remarks made above on element stresses applyhere too.

Strain Energy Densities

Strain energy densities are secondary results in static and normal modes analysis.



They are calculated as element strain energy densities. Remarks made above on elementstresses apply here too.

Forces

Element forces, MPC forces, SPC forces, and grid point forces are printed as tabulatedoutput.

Grid Point Stresses

The default method of calculating stresses in OptiStruct produces values of stresscomponents at the centroids of elements. (Typically a post-processor, such as HyperView,will then average these values to produce smooth contour plots). This method, whileuseful for viewing stress distribution, may underestimate stress maxima, especially on thesurface of the body.

To provide higher accuracy stresses, OptiStruct supports grid point stress calculation. Gridpoint stresses are computed using the following steps:

1. Calculate stress components at integration points of elements (these are generally themost accurate stress locations).

2. Extrapolate stress values to element nodes (grid points).

3. Calculate average at each grid point using values from surrounding elements.

4. Calculate derived quantities, such as von Mises stress or principal stresses, at each gridpoint (this assures that these values are consistent and make physical sense).

The above approach produces continuous stress field, typically in the entire domain. Since, however, stresses can be discontinuous between different materials, OptiStructsupports calculation of separate grid point stress field per each material sub domain. Thepresence of more than one material is detected automatically and then grid point stressesare calculated for the entire domain and as a separate field for each material region.

Grid point stress calculation is activated through the I/O subcase command GPSTRESS. When activated, grid point stresses are produced in addition to default stress results – theycan be found in a separate results subcase.

The present support for grid point stress capability has the following scope:

It is supported for nodes connected to three-dimensional solid elements

It is available for static load cases and non-design elements

Grid point stresses are always calculated in the basic coordinate system

Element Results Representation for Models in OptiStruct

Elemental results (namely stresses, strains and element forces) may be provided withreference to either the material system or the elemental system. For the HM, PUNCH, andOPTI output formats, results are provided with reference to the material system; for firstorder shell element results, PARAM, OMID may be used to output with eitherrepresentation. The H3D and OUTPUT2 output formats, to which these elemental results



are written as tensors, always contain results with reference to the elemental systems(unaffected by PARAM, OMID).

Since OptiStruct 10.0 optimization responses always match with the results written to theHM, PUNCH and OPTI formats and first order shell responses are consistent with thePARAM, OMID setting.

First Order Shell Elements

For first order shell elements (CQUAD4, CTRIA3), the material system is defined asfollows:

1. With blank MCID/THETA (default behavior), stresses, strains and plate forces arepresented in the default element material system, which has x-axis aligned with lineG1-G2, and other axis built accordingly to make an orthonormal triad.

2. With MCID > 0, results are presented in the material system CID projected onto theelement plane (projected material system).

3. With MCID = 0, results are presented in the basic coordinate system projected onto theelement plane (projected basic system).

4. With THETA specified (including zero), results are presented in a rotated elementmaterial system, which is rotated by angle THETA from the edge G1-G2.

The elemental system is the bi-sector system for CQUAD4 elements (see figure) and theG1-G2 system for CTRIA3 elements.

Bi-sector coordinate system

For the H3D and OUTPUT2 formats this representation allows HyperView to performcoordinate system transformations on stress and strain tensors.

Second Order Shell Elements

The results for second order shells (CQUAD8 and CTRIA6), including shell strains, stressesand forces, are always presented in the local material coordinate system, as described inthe manual for CQUAD8 and CTRIA6 elements.



Composite Shells

Shell-type strains and stresses for composite shells use the same representation ashomogeneous shells. By shell-type results, we mean strains and stresses calculated at Z1,Z2 using homogenized shell properties. Strains and stresses for individual plies are alwayspresented in the respective ply coordinate system.

Solid Elements

For solid elements (CHEXA, CTETRA, CPENTA and CPYRA), the results are always providedin the material coordinate system.

1. With blank CORDM on the PSOLID card (default behavior), strains and stresses arepresented in the basic coordinate system.

2. With CORDM > 0, strains and stresses are presented in the material system CID.

3. With CORDM = -1, stresses are presented in the local element coordinate system(described in detail on respective solid element manual pages).

Gap Elements

For gap elements, gap forces are represented in the gap coordinate system, as describedon respective gap element manual pages (CGAP and CGAPG). Compression is positive.

Saving and Retrieving Normal Modes Analysis Results

OptiStruct allows Normal Modes Analysis results to be retrieved for use in FrequencyResponse Analysis or Transient Response Analysis using the modal method. Thus, multipledynamic loading analyses can be performed using the eigenvalue results of a single normalmodes analysis.

The following input I/O options and subcase information section entries may be used forthis purpose:

EIGVSAVE

EIGVRETRIEVE

EIGVNAME

Saving Eigenvalues and Eigenvectors from a Normal Modes Analysis

EIGVSAVE is a subcase information entry that, if used within a normal modes analysissubcase, causes the eigenvalues and eigenvectors of that subcase to be written to anexternal data file. The external data file will use the default output file prefix unless theEIGVNAME I/O option is present, followed by an underscore, then followed by theEIGVSAVE integer argument and the .eigv extension.



For example, the input:

EIGVNAME = test_file$Subcase 10

spc = 1method = 20EIGVSAVE= 50

will save the eigenvector and eigenvalue results from a normal modes analysis to the file"test_file_50.eigv."

Retrieving Eigenvalues and Eigenvectors for a Modal Frequency Response Analysisor for a Modal Transient Analysis

EIGVRETRIEVE is a subcase information entry that, if used within a modal frequencyresponse analysis or a modal transient response analysis subcase, retrieves eigenvaluesand eigenvectors from external data files. EIGVRETRIEVE may have multiple integerarguments, each referring to a different external data file. The external data files musthave the default output file prefix unless EIGVNAME I/O option is present, followed by anunderscore, followed then by the EIGVRETRIEVE integer argument and the extension .eigv.

For example, the following input can be used in a frequency response analysis subcaseusing the modal method to retrieve the eigenvalues and eigenvectors that were saved inthe example above:


Spc = 1Dload = 30Method = 20EIGVRETRIEVE = 50

Combining Eigenvalues and Eigenvectors from Two or More Normal ModesAnalyses for a Single Modal Frequency Response or Modal Transient ResponseAnalysis

The results of two or more normal modes analyses can be retrieved in combination for amodal frequency response analysis.

For example, a normal modes analysis is performed with the real eigenvalue extraction(EIGRL) data:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

EIGRL 20 50.0

The results are written to an external data file as follows:


spc = 1



method = 20EIGVSAVE= 50

In this case, all of the eigenmodes up to 50 Hz have been calculated and written to the file"test_file_50.eigv."

In order to perform a modal frequency response analysis with all of the modes up to 70 Hz,another normal modes analysis can be performed with the real eigenvalue extraction data:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

EIGRL 20 50.0 70.0

This time, the results are written to an external data file as follows:

EIGVNAME = test_file$subcase 10

spc = 1method = 20EIGVSAVE= 70

All eigenmodes between 50 Hz and 70 Hz are written to the file "test_file_70.eigv."

You can now run a modal transient response analysis with:


spc = 1dload = 30method 20tstep(time) = 100EIGVRETRIEVE = 50, 70

The real eigenvalue extraction data referenced in the modal transient response analysissubcase must not request eigenvalue and eigenvector results outside of the range ofretrieved values. If it does, OptiStruct will terminate with an error. In this example, thefollowing EIGRL cards are valid:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

EIGRL 20 0.0 70.0

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

EIGRL 20 0.0 50.0

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

EIGRL 20 30.0 40.0



The following EIGRL cards would cause error terminations for this example:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

EIGRL 20 0 100.0

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

EIGRL 20 50.0 70.01

It is recommended to use a frequency range without the maximum number of modes onthe EIGRL bulk data entries referenced in normal modes analyses from which eigenvalueresults are saved. If the maximum number of modes is specified and these eigenvalueresults are retrieved by a modal frequency response analysis, and it cannot be determinedwhether all of the modes are obtained for the requested range, OptiStruct will terminatewith an error.

For example, assume there are exactly 300 modes in the frequency range 0.0 to 5.0.0 Hz. Now assume that a normal modes analysis is performed referencing the EIGRL bulk dataentry.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

EIGRL 20 0.0 50.0 300

The eigenvectors and eigenvalues are saved as follows:


spc = 1method = 20EIGVSAVE = 50

All 300 modes in the range of 0 to 50.0 Hz are extracted and saved to the file"test_file_50.eigv."

Now try to retrieve these results to use in a modal frequency response analysis, as follows:


spc = 1dload = 30method 20EIGVRETRIEVE = 50

where the referenced EIGRL definition is:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

EIGRL 20 0.0 50.0



This will cause an error termination because it is known (through the external data file)that there are 300 modes within the 0.0 to 50.0 Hz range, but do not know if this is all ofthe modes.

If the EIGRL definition referenced in the normal modes analysis were specified as:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

EIGRL 20 0.0 50.0 301

and only 300 modes were found, you would know that these are all of the modes withinthe 0.0 to 50.0 Hz range, and would retrieve the saved eigenvalue results in this case. OptiStruct would not terminate with an error.



Coupling OptiStruct with Third Party Software

The following features can be found in this section:

Using the AMLS (Automatic Multi-Level Sub-structuring) Eigensolvers

For the solution of large eigenvalue problems, the AMLS (Automatic Multi-Level Sub-structuring) eigensolver developed by the University of Texas can be used instead of theinternal OptiStruct Lanczos eigensolver. The AMLS eigensolver is a separate program fromOptiStruct and must be installed and licensed separately. OptiStruct interfaces with AMLSby writing AMLS input files, launching AMLS, and then reading the AMLS results back intoOptiStruct once the AMLS execution is complete. The resulting eigenvalues andeigenvectors can then be used by OptiStruct for eigenvalue analysis, modal frequencyresponse, and modal transient analysis. In addition, the AMLS solver can be used duringtopology and sizing optimizations.

OptiStruct only supports AMLS version 3.2.0128 or later. To use AMLS version 5 or later,OptiStruct version 13.0 or later must be used. To use AMLS, the following should bedefined:

1. The environment variable AMLS_EXE must be set by you to point to the AMLS

executable.

On UNIX and Linux platforms the script that is used to invoke OptiStruct (~altair/

scripts/invoke/optistruct) contains a "placeholder" where AMLS_EXE may be defined

(search for AMLS_EXE). The definition contained in the invoke script will only be used if

there is no pre-existing AMLS_EXE environment variable at invoke.

Example: setenv AMLS_EXE /share/ams/cdhopt/2005/AIX-5.3/3.2.r159_exe/amls.main_AIX.5

2. PARAM, AMLS must be set to YES in the OptiStruct input file. The run option –amls can

also be used to activate AMLS.

AMLS is a multithreaded application and can use 1, 2, or 4 processors. PARAM,AMLSNCPU may be defined in the OptiStruct input file to define the number ofprocessors that are to be used by AMLS. If PARAM, AMLSNCPU is not set, then theAMLS eignersolver will use only 1 CPU. Note that when PARAM, AMLSNCPU is defined,it is possible for OptiStruct and AMLS to use different numbers of processors.

Parameters Affecting AMLS

AMLS controls the accuracy and the cost of a solution primarily with three parameters. The “optimal” values of these parameters for typical NVH analysis have been establishedthrough extensive testing. The parameters and their values are:

PARAM,SS2GCR,5.0

PARAM,GMAR,1.1

PARAM,GMAR1,1.7

In case of predominately solid models, such as engine blocks, SS2GCR should be set to10.0 and GMAR1 should be set to 2.1. In case of typical shell models, such as car bodies,



a slight improvement in FRF accuracy can be obtained without large increases in elapsedtime by setting two of the parameters as follows:

PARAM,SS2GCR,7.5

PARAM,GMAR1,2.1

However, you are discouraged from adjusting these values unless the accuracyimprovement is known to be worth the increase in resource requirements.

The default upper limit on eigenvalues that are taken to be associated with rigid bodymodes is 1.0 (equivalent to a natural frequency of about 0.16 Hz). This parameter can beadjusted by parameter RBMEIG, which can be set by the command:

PARAM,RBMEIG,0.2

AMLS distinguishes between rigid body modes and flexible modes to improve the numericalconditioning, and hence accuracy, with which the flexible eigenvalues are computed.

Control of the singularity processing is performed using PARAM, AMLSMAXR. If AMLSMAXRis exceeded in the process of factoring a stiffness matrix, this indicates a singularity in K. If the mass of this DOF is also zero, there is a "massless mechanism", and an SPC isapplied and a message is written to the .out file. If there is mass, then this is a

mechanism, which is treated as a rigid body mode, and a message is written to the .out

file.

By default AMLS does not handle disconnected structures. There are two solutions forhandling disconnected structures:

PARAM,AMLSUCON,YES

PARAM,DISJOINT,n

If PARAM,AMLSUCON is set to YES then OptiStruct will SPC out the disconnected components

if there is a total of less than 4000 disconnected grids. This works with all versions ofAMLS.

When PARAM,DISJOINT is set to a value that is at least one larger than the number of

disconnected parts then AMLS will be able to solve the eigenvalue calculation problem. This feature is only available in AMLS versions 4.2r22 or newer.

For AMLS Versions 5 and later, the run option –amlsmem, the environment variable

AMLS_MEM or the parameter PARAM, AMLSMEM can be used to set the amount of memoryin Gigabytes used by AMLS. By default, AMLS will use the same amount of memory usedby OptiStruct. The run option –amlsmem, the environment variable AMLS_MEM or the

parameter PARAM, AMLSMEM can be used to override this default value. The run optionoverrides the value set by the environment variable and the parameter. If both AMLS_MEM and PARAM, AMLSMEM are set, then the value specified by the environmentvariable is used.

Residual Vector Calculations

When the AMLS eigensolver is used, OptiStruct’s Residual Vector calculations are ignored. The AMLS eigensolver calculates its own residual vectors for each of the following:

USET U6 data

Frequency Response Dynamic Loads



Transient Response Dynamic Loads

Damping DOF from CBUSH, CDAMPi or CVISC data

One Residual Vector is calculated for each USET U6 degree of freedom, each DAREA degreeof freedom, and each damping degree of freedom associated with the CBUSH, CDAMPi andCVISC data.

The Residual Vector calculations are controlled by the Solution Control data RESVEC. Tocontrol Residual Vector calculations with AMLS, use the following commands:

Use RESVEC=NO to turn off Residual Vector calculations with AMLS

Use RESVEC(NODAMP)=YES to turn off Residual Vectors associated with DampingDOF

Singularities

If AMLS detects a large number of singularities in the model this is most likely due to thinCQUAD4/CTRIA3 elements used to “skin” solid models. These singularities causenumerical ill-conditioning and increase run time. The singularities are caused by the verylow bending stiffness of these thin shell elements. To remove the singularities, convert thethin bending elements to membrane only elements by removing the MID2 and MID3 MID’sfrom the associated PSHELL data. The thin membrane elements will still calculate thecorrect surface stresses, but the singularities will not be present as the elements will haveno bending stiffness.

PARAM, AMLSMAXR is used to determine singularities in the stiffness matrix.

If the value of AMLSMAXR is exceeded in the process of factoring a stiffness matrix, thisindicates a singularity in K. If the mass of this degree-of-freedom is zero, there is a"massless mechanism"; an SPC is applied and a message is written to the .out file. If

there is mass, then this is a mechanism which is treated as a rigid body mode and amessage is written to the .out file.

The list of GRID identification numbers of singular grids during an AMLS run is output tothe .amls_singularity.cmf file.

Remote File Systems

If the execution directory is on a remote file system, long run times will result as the AMLSscratch files will have to be accessed over the NFS mounted file system. Use theenvironment variable TMPDIR to redefine the scratch directory to be on the local machine. Note that the environment variable TMPDIR is different from the scratch file directoryspecified by the command line argument –tmpdir.

The input and output files from AMLS (generic_real_file, generic_integer_file, and

generic_amls_output) are stored in the directory specified by the environment variable

AMLSDIR. In general, the environment variable AMLSDIR should be set to be the samedirectory as the environment variable TMPDIR.

Limitations

1. AMLS is designed for large problems. Problems less than a few hundred degrees offreedom cannot be solved by AMLS.



2. The model must consist of only one structure. Models of unconnected parts cannot besolved by AMLS. When the CBN method of creating CSM Super Elements is used onthe CMSMETH data, unconnected models can be generated if the center GRID of anRBE2 is an ASET GRID. If unconnected are found, a file named filename.unconnected.cmf is generated. This file can be used in HyperMesh to show

the unconnected parts. If the parts are small, PARAM, AMLSUCON,1 can be used toSPC out the unconnected structure and AMLS will run correctly. If the unconnectedpart is large, you can:

Remove one spider GRID of the RBE2 to make the structure connected

Use a small CBAR, CBEAM, or CROD to connect the two structures

FastFRS Usage (Fast Frequency Response Solver)

FastFRS is a solver developed by the University of Texas at Austin. It is very efficient for acertain class of large modal frequency response problems, such as NVH problems. OptiStruct has an interface to FastFRS. OptiStruct writes the file FastFRS_Gen.in as input

for FastFRS, and reads results from FastFRS_gen.out. FastFRS will run in the directory

specified by the environment variable AMLSDIR, or the current directory if AMSLDIR is notspecified.

The following parameters can be used within the OptiStruct to control the FastFRS solver.

1. Set the environment variable FASTFRS_EXE to point to the location of the FastFRS

executable.

2. The run option –ffrs yes or the parameter PARAM,FFRs,YES can be used to activate

FastFRS:

3. Add the following optional parameters to adjust the settings for FastFRS runs:

PARAM,FFRSLFRQ

PARAM,LOWRANK

PARAM,K4CUTOFF

PARAM,CSTOL

PARAM,FFRSNCPU (or the run option –ffrsncpu)

PARAM,FFRSMEM (or the run option –ffrsmem or the environment variable FFRS_MEM)

Note:

1. OptiStruct version 13.0 or above is required to run FastFRS version 2 or above.

2. If FFRSNCPU is not set (using either the parameter or the run option), and AMLSNCPU

is set, then FastFRS will use the number of CPU’s specified by AMLSNCPU.

3. For FastFRS versions 2 and later, the run option –ffrsmem, the environment variable

FFRS_MEM, or the parameter PARAM,FFRSMEM can be used to set the amount of memory

in Gigabytes used by FastFRS. By default, FastFRS will use the same amount ofmemory used by OptiStruct. The run option –ffrsmem, the environment variable,

FFRS_MEM, or the parameter PARAM, FFRSMEM can be used to override this defaultvalue. The run option overrides the environment variable and the parameter. If bothFFRS_MEM and PARAM, FFRSMEM are set, then the value specified by the environment



variable is used.

Creating Output for Third Party Software

The section describes how to create output from OptiStruct for third party programs forFatigue Analysis (FEMFAT, Design Life, and FE-SAFE), Multi-Body Dynamic Analysis (AVL/EXCITE, SIMPACK, ROMAX, ADAMS, RecurDyn and Virtual Lab), and Fluid StructureInteraction (AcuSolve).

Fatigue Analysis

The .op2 file from OptiStruct can be used directly by Third Party Fatigue Analysis software

programs FEMFAT, Design Life, FE-Fatigue, and FE-SAFE. Just request stress output tothe .op2 file:

STRESS(OP2) = SET or ALL

Multi-Body Dynamic Analysis

AVL/EXCITE

To create the condensed CMS Super Element information for AVL/EXCITE, use the CMSMETH CBN Method with ASET data for the connection DOF.

The MODEL data can used specify interior grid data to be included in the Super Element forviewing in AVL/EXCITE. The MODEL data format is:

MODEL=Element Set, Grid Set, RIGID/NORIGID.

All grids associated with elements in the element set and rigid elements, if RIGID isspecified, are combined with the grids in the Grid Set and output to AVL/EXCITE. Inaddition, the keyword PLOTEL can be used instead of an Element Set ID to specify all thegrids associated with all of the PLOTEL data in the model.

GPSTRESS is used to specify set of grids for which Grid Point Stresses are calculated forAVL/EXCITE.

The PARAM,EXCEXB data controls the output of the AVL/EXCITE .exb file directly from

OptiStruct.

The PARAM,EXCOUT data is used to specify what data is written out for AVL/EXCITE. TheEXCOUT values produce the information for AVL/EXCITE specified below:

$ EXCOUT - -1: no output$ 0: all output (default)$ 1: DOF, geometry, and elements tables$ (GEOM1,GEOM2,EQEXIN,USET),$ reduced mass and stiffness matrices (MAA and KMAA)$ 3: 1 + GOA transpose$ 4: 3 + unreduced mass matrix (MFF) (CON6) $ 5: 1 + eigenvectors of condensed system (PHA) and$ grid point stress table, SORT 1 (OGS1)$ 6: 4 + eigenvectors of condensed system (PHA) and$ grid point stress table, SORT 1 (OGS1)$ 7: 3 + eigenvectors of condensed system (PHA) and



$ grid point stress table, SORT 1 (OGS1)

After running AVL/EXCITE, a residual run can be made to recover displacement, velocity,acceleration, stress, and strain results for interior grids and elements in the CMS SuperElement based on the modal participation results from AVL/EXCITE. Note that the resultsare only calculated for GRID and elements specified by the MODEL data in the CMS SuperElement creation run. The residual run can be any combination of frequency response andtransient analysis SUBCASE’s. After running AVL/EXCITE, a resulting filename.INP4 file is

created that contains the modal participation factors for the modes of the CMS SuperElement for each loading frequency or transient analysis time step. In the residual run,the CMS Super Element .h3d file and the AVL/EXCITE modal results file are specified using

the ASSIGN data:

ASSIGN,H3DDMIG,AX,'Crank_split2h_all.h3d'ASSIGN,EXCINP,10,'Crankshaft_SOL109_time.INP4'

Where the 10 in the ASSIGN,EXCINP data corresponds to the SUBCASE for which the modal

participation results will be used. In SUBCASE 10, instead of performing a frequency

response or transient response analysis, OptiStruct will just use the modal participationresults from AVL/EXCITE. Note that since the analysis is skipped, it does not matter if theresidual run is modal or direct frequency response/transient analysis.

For transient analysis, the number of time steps in the transient analysis residual run mustmatch the number of time steps used in the AVL/EXCITE analysis. For frequency responseanalysis, the number of loading frequencies in the frequency response analysis residual runmust match number of loading frequencies used in the AVL/EXCITE analysis. While thefrequency response/transient analysis data is ignored, there must still be some dummyloading data (TLOAD/RLOAD, DAREA, and TABLED data). A sample of input data for atransient analysis residual run is shown below:

ASSIGN,H3DDMIG,AX,'Crank_split2h_all.h3d'ASSIGN,EXCINP,10,'Crankshaft_SOL109_time.INP4'$DISPLACEMENT = ALLSTRESS = ALL$SUBCASE 10 DLOAD = 10201 TSTEP = 10133$BEGIN BULK$GRID,80001,,0.,-62.,0.$ TLOAD1,10201,10202,,,10301DAREA,10202,80001,1,1.0TABLED1,10301,,0.0,1.0,0.1,1.0,0.2,1.0,0.3,1.0,ENDTTSTEP,10133,143,2.7778-4ENDDATA

SIMPACK

To create the condensed CMS Super Element information for SIMPACK, you must use the CMSMETH CBN Method with ASET or CSET data for the connection DOF. If CSET connectionDOF is used, then the AMSES solver must be specified on the CMSMETH data.



The PARAM,SIMPACK data is used to specify what data is written out for SIMPACK. TheSIMPACK values produce the information for SIMPACK.

Recover SIMPACK results in OptiStruct

ASSIGN, SIMPIMP identifies an external .unv file generated after running a multibody

dynamic analysis in SIMPACK. The resulting CMS flexbody modal participation factors inthe .unv file can be used by OptiStruct to recover the dynamic displacements, velocities,

accelerations, stresses and strains. The format is as follows:

ASSIGN, SIMPINP, Subcase ID, Filename

Subcase ID is used to specify which SUBCASE the modal participation factors should beused for.

RecurDyn

To create the modal CMS Super Element information for RecurDyn, you must use the CMSMETH CBN Method with ASET data for the connection DOF.

The PARAM,RFIOUT,YES data is used to turn on the generation of the .rfi file, which

contains the modal super element that is used by RecurDyn.

Note: This .rfi file can be created only by OptiStruct

executables running on 64-bit Windows machines. Thisfile cannot be created while using OptiStruct on Linux orMac OS X machines.

ROMAX

To create the condensed CMS Super Element information for ROMAX, use the CMSMETHCBN Method with ASET data for the connection DOF.

Use PARAM,EXTOUT,DMIGPCH to create a PUNCH file containing the Super Element data. This data can be read by any version of ROMAX after release R12.6.2.

ADAMS

To create the condensed Flex Body information for ADAMS, use the CMSMETH CC or CBMethod.

The MODEL data used can specify interior grid and element data to be included in the FlexBody for viewing in ADAMS. The MODEL data format is:

MODEL=Element Set, Grid Set, RIGID/NORIGID.

All grids associated with elements in the element set and rigid elements if RIGID isspecified are combined with the grids in the Grid Set and output to ADAMS. In addition,the keyword PLOTEL can be used instead of an Element Set ID to specify all the gridsassociated with all of the PLOTEL data in the model.

GPSTRESS is used to specify set of grids for which Grid Point Stresses are calculated forADAMS.



The OUTPUT command is used to generate the .mnf file for ADAMS. The command is:

OUTPUT=ADAMSMNF

Virtual Lab

To create the condensed Flex Body Modes and Full Diagonal Mass Matrix to the .op2 file for

Virtual Lab, use the CMSMETH CB or CC Methods.

The PARAM,LMSOUT data is to trigger the output of the condensed Flex Body Modes andfull Diagonal Mass Matrix to the .op2 file. PARAM,POST is not required. OUTPUT=OP2 is

not required.

Fluid Structure Interaction Analysis

The .op2 file from OptiStruct can be used directly by the AcuSolve CFD code.

Just request the eigenvector output to the .op2 file:

DISP(OP2) = ALL

Then run the Python script from ACUSIM called acuNASTRAN2pev.py:

python acuNastran2Pev.py problem.op2

This will create the nodes.dat, elems.dat, and modeXX.dat files. Be sure to use the latest

version of acuNASTRAN2pev.py from ACUSIM.



Design Optimization


Optimization Problem

Responses


Free-size Optimization


Size Optimization

Shape Optimization


Manufacturing Constraints

Reliability-based Design Optimization (Beta)

Optimization of Arbitrary Beam Sections

Optimization of Composite Structures

Equivalent Static Load Method (ESLM)

Gradient-based Optimization Method





Optimization Problem


Minimize Objective Function

OptiStruct solves the following structural optimization problem:

1 2, , , )min ( ) ( nx xf x f x K

Subject to:

( ) 0 1, ,

1, ,

j

L Uii i

g x j m

x x x i n

K

K

The objective function f(x) and the functions g(x) in the constraint function are structural

responses obtained from a finite element analysis. A constraint is considered active if it issatisfied exactly (g = 0); it is considered inactive if g < 0; it is considered violated if g > 0.

The selection of the vector of design variables x depends on the type of optimization beingperformed. In topology optimization, the design variables are element densities (see Design Variables for Topology Optimization). In size optimization (including free-size), thedesign variables are properties of structural elements (see Design Variables for SizeOptimization). In topography and shape (including free-shape) optimization, the designvariables are the factors in a linear combination of shape perturbations (see DesignVariables for Topography Optimization and Design Variables for Shape Optimization).

The objective function is defined using a DESOBJ entry in the subcase information section. DESOBJ references a response defined by either the DRESP1, DRESP2, or DRESP3 bulkdata entry. Depending on the type of response, DESOBJ is located inside or outside of aSUBCASE. The constraints are defined using a DESSUB or DESGLB entry in the subcaseinformation section, depending on if the type of response is subcase related or global,respectively. DESSUB and DESGLB refer to DCONSTR or DCONADD bulk data entries. DCONSTR relates the constraint value or bound to a response defined by DRESP1, DRESP2,or DRESP3.

Minmax Objective Function

The minmax optimization problem is given as:

1 1 2 2min max / , (x) / f , , ( ) / fK Kf x f f f xK

Subject to:

( ) 0 1, ,

1, ,

j

L Uii i

g x j m

x x x i n

K

K



Kf are the reference values

The reference values can take different values for positive or negative objective functions. These problems are solved using the Beta-method. In this method, the problem istransformed into a regular optimization problem through the introduction of an additional

design variable such that:

min

Subject to:

(x) / f 1, ,

( ) 0 1, ,

i i

j

f i k

g x j m

K

K

The functions fi(x) and the functions g(x) in the constraint function are structural responses

obtained from a finite element analysis. A constraint is considered active if it is satisfiedexactly (g = 0); it is considered inactive if g < 0; it is considered violated if g > 0.

The selection of the vector of design variables x depends on the type of optimization being

performed. In topology optimization, the design variables are element densities (see Design Variables for Topology Optimization). In size optimization (including free-size), thedesign variables are properties of structural elements (see Design Variables for SizeOptimization). In topography and shape (including free-shape) optimization, the designvariables are the factors in a linear combination of shape perturbations (see DesignVariables for Topography Optimization and Design Variables for Shape Optimization).

The objective function of a minmax problem is defined using MINMAX or MAXMINstatements in the subcase information section. MINMAX or MAXMIN references a DOBJREFstatement in the bulk data section, which again refers to a DRESP1, DRESP2, or DRESP3response definition. The reference values are defined on the DOBJREF entry. Theconstraints are defined as stated above. The constraints are defined using a DESSUB orDESGLB entry in the subcase information section, depending on if the type of response issubcase related or global, respectively. DESSUB and DESGLB refer to DCONSTR orDCONADD bulk data entries. DCONSTR relates the constraint value or bound to aresponse defined by DRESP1, DRESP2, or DRESP3.

System Identification

For system identification, OptiStruct solves the following two structural optimizationproblems:

2

1

( )min

(x) 0 1, ,

ni i

iii

j

f x TW

T

g j mK

or



11

( )min with W

(x) 0 1, ,

i

i

f x T

T

jg j mK

The functions fi(x) and the functions g(x) in the constraint function are structural responses

obtained from a finite element analysis. A constraint is considered active if it is satisfiedexactly (g = 0); it is considered inactive if g < 0; it is considered violated if g > 0. The

values Ti are the target value for the particular response, Wi is a weighting factor.

The selection of the vector of design variables x depends on the type of optimization being

performed. In topology optimization, the design variables are element densities (see Design Variables for Topology Optimization). In size optimization (including free-size), thedesign variables are properties of structural elements (see Design Variables for SizeOptimization). In topography and shape (including free-shape) optimization, the designvariables are the factors in a linear combination of shape perturbations (see DesignVariables for Topography Optimization and Design Variables for Shape Optimization).

The objective function is defined using a DESOBJ entry or a MINMAX, MAXMIN entry in thesubcase information section. DESOBJ, MINMAX, or MAXMIN reference a DSYSID entry thatdefines target values for responses defined by either a DRESP1, DRESP2, or DRESP3 bulkdata entry. The constraints are defined using a DESSUB or DESGLB entry in the subcaseinformation section, depending on if the type of response is subcase related or global,respectively. DESSUB and DESGLB refer to DCONSTR or DCONADD bulk data entries. DCONSTR relates the constraint value or bound to a response defined by DRESP1, DRESP2,or DRESP3.



Responses

The following responses can be found in this section:

Internal Responses

OptiStruct allows the use of numerous structural responses, calculated in a finite elementanalysis, or combinations of these responses to be used as objective and constraintfunctions in a structural optimization.

Responses are defined using DRESP1 bulk data entries. Combinations of responses aredefined using either DRESP2 entries, which reference an equation defined by a DEQATNbulk data entry, or DRESP3 entries, which make use of user-defined external routinesidentified by the LOADLIB I/O option. Responses are either global or subcase (loadstep,load case) related. The character of a response determines whether or not a constraint orobjective referencing that particular response needs to be referenced within a subcase.

Subcase Independent

Mass and Volume

Both are global responses that can be defined for the whole structure, for individualproperties (components) and materials, or for groups of properties (components) andmaterials.

It is not recommended to use mass and volume as constraints or objectives in atopography optimization. Neither is very sensitive towards design modifications made in atopography optimization.

In order to constrain the mass or volume for a region containing a number of properties(components), the SUM function can be used to sum the mass or volume of the selectedproperties (components), otherwise, the constraint is assumed to apply to each individualproperty (component) within the region. Alternatively, a DRESP2 equation needs to bedefined to sum the mass or volume of these properties (components). This can be avoidedby having all properties (components) use the same material and applying the mass orvolume constraint to that material.

Fraction of Mass and Fraction of Design Volume

Both are global responses with values between 0.0 and 1.0. They describe a fraction ofthe initial design space in a topology optimization. They can be defined for the wholestructure, for individual properties (components) and materials, or for groups of properties(components) and materials.

The difference between the mass fraction and the volume fraction is that the mass fractionincludes the non-design mass in the fraction calculation, whereas the volume fraction onlyconsiders the design volume.

Formulation for volume fraction:Volume fraction = (total volume at current iteration – initial non-design volume)/initialdesign volume

Formulation for mass fraction:



Mass fraction = total mass at current iteration/initial total mass

If, in addition to the topology optimization, a size and shape optimization is performed, thereference value for the volume fraction (the initial design volume) is not altered by sizeand shape changes. This can, on occasion, lead to negative values for this response. Therefore, if size and shape optimization is involved, it is recommended to use the Volumeresponses instead of the Volume Fraction response.

These responses can only be applied to topology design domains. OptiStruct will terminatewith an error if this is not the case.

Center of Gravity

This is a global response that may be defined for the whole structure, for individualproperties (components) and materials, or for groups of properties (components) andmaterials.

Moments of Inertia

This is a global response that may be defined for the whole structure, for individualproperties (components) and materials, or for groups of properties (components) andmaterials.

Weighted Compliance

The weighted compliance is a method used to consider multiple subcases (loadsteps, loadcases) in a classical topology optimization. The response is the weighted sum of thecompliance of each individual subcase (loadstep, load case).

12

Ti i i iW iC W C W u f

This is a global response that is defined for the whole structure.

Weighted Reciprocal Eigenvalue (Frequency)

The weighted reciprocal eigenvalue is a method to consider multiple frequencies in aclassical topology optimization. The response is the weighted sum of the reciprocaleigenvalues of each individual mode considered in the optimization.

0i i i iW withf W l K M u

This is done so that increasing the frequencies of the lower modes will have a larger effecton the objective function than increasing the frequencies of the higher modes. If thefrequencies of all modes were simply added together, OptiStruct would put more effort intoincreasing the higher modes than the lower modes. This is a global response that isdefined for the whole structure.

Combined Compliance Index

The combined compliance index is a method to consider multiple frequencies and staticsubcases (loadsteps, load cases) combined in a classical topology optimization. The indexis defined as follows:

j ji i

j

W lS W C NORM

W

This is a global response that is defined for the whole structure.



The normalization factor, NORM, is used for normalizing the contributions of compliancesand eigenvalues. A typical structural compliance value is of the order of 1.0e4 to 1.0e6. However, a typical inverse eigenvalue is on the order of 1.0e-5. If NORM is not used, thelinear static compliance requirements dominate the solution.

The quantity NORM is typically computed using the formula:

max minNF C

where, Cmax is the highest compliance value in all subcases (loadsteps, load cases) and

min is the lowest eigenvalue included in the index.

In a new design problem, you may not have a close estimate for NORM. If this happens,OptiStruct automatically computes the NORM value based on compliances and eigenvaluescomputed in the first iteration step.

von Mises Stress in a Topology or Free-Size Optimization

The von Mises stress constraints may be defined for topology and free-size optimizationthrough the STRESS optional continuation line on the DTPL or the DSIZE card. There are anumber of restrictions with this constraint:

The definition of stress constraints is limited to a single von Mises permissible stress. The phenomenon of singular topology is pronounced when different materials withdifferent permissible stresses exist in a structure. Singular topology refers to theproblem associated with the conditional nature of stress constraints, i.e. the stressconstraint of an element disappears when the element vanishes. This createsanother problem in that a huge number of reduced problems exist with solutions thatcannot usually be found by a gradient-based optimizer in the full design space.

Stress constraints for a partial domain of the structure are not allowed because theyoften create an ill-posed optimization problem since elimination of the partial domainwould remove all stress constraints. Consequently, the stress constraint applies tothe entire model when active, including both design and non-design regions, andstress constraint settings must be identical for all DSIZE and DTPL cards.

The capability has built-in intelligence to filter out artificial stress concentrationsaround point loads and point boundary conditions. Stress concentrations due toboundary geometry are also filtered to some extent as they can be improved moreeffectively with local shape optimization.

Due to the large number of elements with active stress constraints, no element stressreport is given in the table of retained constraints in the .out file. The iterative

history of the stress state of the model can be viewed in HyperView or HyperMesh.

Stress constraints do not apply to 1-D elements.

Stress constraints may not be used when enforced displacements are present in themodel.

Bead Discreteness Fraction

This is a global response for topography design domains. This response indicates theamount of shape variation for one or more topography design domains. The responsevaries in the range 0.0 to 1.0 (0.0 < BEADFRAC < 1.0), where 0.0 indicates that no shapevariation has occurred, and 1.0 indicates that the entire topography design domain hasassumed the maximum allowed shape variation.



Subcase Dependent


Static Compliance

The compliance C is calculated using the following relationship:

12

T withC u f Ku f

or

1 12 2

T TC u Ku dv

The compliance is the strain energy of the structure and can be considered a reciprocalmeasure for the stiffness of the structure. It can be defined for the whole structure, forindividual properties (components) and materials, or for groups of properties (components)and materials. The compliance must be assigned to a linear static subcase (loadstep, loadcase).

In order to constrain the compliance for a region containing a number of properties(components), the SUM function can be used to sum the compliance of the selectedproperties (components), otherwise, the constraint is assumed to apply to each individualproperty (component) within the region. Alternatively, a DRESP2 equation needs to bedefined to sum the compliance of these properties (components). This can be avoided byhaving all properties (components) use the same material and applying the complianceconstraint to that material.

Static Displacement

Displacements are the result of a linear static analysis. Nodal displacements can beselected as a response. They can be selected as vector components or as absolutemeasures. They must be assigned to a linear static subcase.

Static Stress of Homogeneous Material

Different stress types can be defined as responses. They are defined for components,properties, or elements. Element stresses are used, and constraint screening is applied. Itis also not possible to define static stress constraints in a topology design space (seeabove). This is a linear static subcase (loadstep, load case) related response.

Static Strain of Homogeneous Material

Different strain types can be defined as responses. They are defined for components,properties, or elements. Element strains are used, and constraint screening is applied. Itis also not possible to define strain constraints in a topology design space. This is a linearstatic subcase (loadstep, load case) related response.

Static Stress of Composite Lay-up

Different composite stress types can be defined as responses. They are defined forPCOMP(G) components or elements, or PLY type properties. Ply level results are used, andconstraint screening is applied. It is also not possible to define composite stressconstraints in a topology design space. This is a linear static subcase (loadstep, load case)related response.



Static Strain of Composite Lay-up

Different composite strain types can be defined as responses. They are defined forPCOMP(G) components or elements, or PLY type properties. Ply level results are used, andconstraint screening is applied. It is also not possible to define composite strainconstraints in a topology design space. This is a linear static subcase (loadstep, load case)related response.

Static Failure in a Composite Lay-up

Different composite failure criterion can be defined as responses. They are defined forPCOMP(G) components or elements, or PLY type properties. Ply level results are used, andconstraint screening is applied. It is also not possible to define composite failure criterionconstraints in a topology design space. This is a linear static subcase (loadstep, load case)related response.

Static Force

Different force types can be defined as responses. They are defined for components,properties, or elements. Constraint screening is applied. It is also not possible to defineforce constraints in a topology design space. This is a linear static subcase (loadstep, loadcase) related response.

Single Point Force at a constrained grid point

This response can be defined using the DRESP1 bulk data entry (with RTYPE=SPCFORCE). This response is defined for constrained grid points. Constraint screening is applied to thisresponse. This is a linear static subcase (loadstep, load case) related response.

Grid Point Force

This response can be defined using the DRESP1 bulk data entry (with RTYPE=GPFORCE). This response defines the contribution to a specific grid point force component from a non-rigid element (which is connected to that grid). Constraint screening is applied to thisresponse. If ATTi specify multiple elements, then multiple responses will be generated,where, each response calculates a specified element’s contribution to the grid point forcecomponent at the specified grid. This is a linear static subcase (loadstep, load case)related response.

Linear Heat Transfer Analysis

Temperature

Temperatures are the result of a heat transfer analysis, and must be assigned to a heattransfer subcase (loadstep, load case). Temperature response cannot be used in composite topology or free-size optimization.


Frequency

Natural frequencies are the result of a normal modes analysis, and must be assigned to thenormal modes subcase (loadstep, load case). It is recommended to constrain thefrequency for several of the lower modes, not just of the first mode.



Mode Shape

Mode shapes are the result of a normal modes analysis. Mode shapes can be selected as aresponse. They can be selected as vector components or as absolute measures. Theymust be assigned to a normal modes subcase.


Buckling Factor

The buckling factor is the result of a buckling analysis, and must be assigned to a bucklingsubcase (loadstep, load case). A typical buckling constraint is a lower bound of 1.0,indicating that the structure is not to buckle with the given static load. It is recommendedto constrain the buckling factor for several of the lower modes, not just of the first mode.

Frequency Response Function (FRF Analysis)

Frequency Response Displacement

Displacements are the result of a frequency response analysis. Nodal displacements, i.e.translational, rotational and normal*, can be selected as a response. They can be selectedas vector components in real/imaginary or magnitude/phase form. They must be assignedto a frequency response subcase (loadstep, load case).

*The normal at a grid point is calculated based on the normals of the surroundingelements. The normal frequency response displacement at a grid point can be selected as aresponse and it is the displacement in the normal’s direction. The normals are also updatedwhen shape changes occur during shape optimization.

Frequency Response Velocity

Velocities are the result of a frequency response analysis. Nodal velocities, i.e.translational, rotational and normal, can be selected as a response. They can be selectedas vector components in real/imaginary or magnitude/phase form. They must be assignedto a frequency response subcase (loadstep, load case).

*The normal at a grid point is calculated based on the normals of the surroundingelements. The normal frequency response velocity at a grid point can be selected as aresponse and it is the velocity in the normal’s direction. The normals are also updatedwhen shape changes occur during shape optimization.

Frequency Response Acceleration

Accelerations are the result of a frequency response analysis. Nodal accelerations, i.e.translational, rotational and normal, can be selected as a response. They can be selectedas vector components in real/imaginary or magnitude/phase form. They must be assignedto a frequency response subcase (loadstep, load case).

*The normal at a grid point is calculated based on the normals of the surroundingelements. The normal frequency response acceleration at a grid point can be selected as aresponse and it is the acceleration in the normal’s direction. The normals are also updatedwhen shape changes occur during shape optimization.



Frequency Response Stress

Different stress types can be defined as responses. They are defined for components,properties, or elements. Element stresses are not used in real/imaginary or magnitude/phase form, and constraint screening is applied. The von Mises stress for solids and shellscan also be defined as direct responses. It is not possible to define stress constraints in atopology design space. This is a frequency response subcase (loadstep, load case) relatedresponse.

Frequency Response Strain

Different strain types can be defined as responses. They are defined for components,properties, or elements. Element strains are used in real/imaginary or magnitude/phaseform, and constraint screening is applied. The von Mises strain for solids and shells canalso be defined as direct responses. It is not possible to define strain constraints in atopology design space. This is a frequency response subcase (loadstep, load case) relatedresponse.

Frequency Response Force

Different force types can be defined as responses. They are defined for components,properties, or elements in real/imaginary or magnitude/phase form. Constraint screeningis applied. It is also not possible to define force constraints in a topology design space. This is a frequency response subcase (loadstep, load case) related response.


PSD and RMS Responses

PSD displacement, PSD velocity, PSD acceleration, PSD acoustic pressure, PSD stress, PSDstrain, RMS displacement, RMS velocity, RMS acceleration, RMS acoustic pressure, RMSstress and RMS strain responses are available.

Coupled FRF Analysis on a Fluid-structure Model (Acoustic Analysis)

Acoustic Pressure

Acoustic pressures are the result of a coupled frequency response analysis on a fluid-structure model. This response is available for fluid grids. It must be assigned to acoupled frequency response subcase (loadstep, load case) on a fluid-structure model.

Multi-body Dynamics Analysis

Flexible Body Responses

For Multi-body Dynamics problems, the Mass, Center of gravity, and Moment of Inertia ofone or more flexible bodies are available as responses. This is in addition to other usualstructural responses.



MBD Displacement

MBD displacements are the result of a multi-body dynamics analysis. They must beassigned to a multi-body dynamics subcase (loadstep, load case).

MBD Velocity

MBD velocities are the result of a multi-body dynamics analysis. They must be assigned toa multi-body dynamics subcase (loadstep, load case).

MBD Acceleration

MBD acceleration are the result of a multi-body dynamics analysis. They must be assignedto a multi-body dynamics subcase (loadstep, load case).

MBD Force

MBD forces are the result of a multi-body dynamics analysis. They must be assigned to amulti-body dynamics subcase (loadstep, load case).

MBD Expression

MBD expression responses are the result of a multi-body dynamics analysis. They are theresult of the evaluation of an expression. They must be assigned to a multi-body dynamicssubcase (loadstep, load case).

Fatigue

Life/Damage

Life and Damage are results of a fatigue analysis. They must be assigned to a Fatiguesubcase.

Dynamic/Nonlinear Analysis

Equivalent Plastic Strain

Equivalent plastic strain can be used as an internal response when a nonlinear responseoptimization is run using the equivalent static load method. This is made possible throughthe use of an approximated correlation between linear strain and plastic strain, which arecalculated in the inner and outer loops respectively, of the ESL method.

User Responses

Function

A function response is one that uses a mathematical expression to combine designvariables, grid point locations, responses, and/or table entries. Whether the function issubcase (loadstep, load case) related or global, is dependent on the response types used inthe equation.



External

An external response is one that uses an external user-defined routine to combine designvariables, grid point locations, eigenvectors, responses, and/or table entries. Whether thefunction is subcase (loadstep, load case) related or global is dependent on the responsetypes used in the routine. Refer to External Responses below for more information.

External Responses

The DRESP3 bulk data entry, in combination with the LOADLIB I/O option entry, allows forthe definition of responses through user-defined external functions. The external functionsmay be written in HyperMath Language (HML), FORTRAN, C or a Microsoft Excel workbook. The resulting libraries and files should be accessible by OptiStruct regardless of the codinglanguage, providing that consistent function prototyping is respected, and adequatecompiling and linking options are used.

Writing External Functions

The OptiStruct installation provides "barebone" functions for FORTRAN(dresp3_barebone.F) and for C (dresp3_barebone.c) with proper function definition,

arguments, and compilation directives. These files can be used as starting points to writeyour own functions. Refer to Referencing External Files for information on responsedefinition through a user-defined Microsoft Excel workbook.

HyperMath Language (HML) functions are defined as follows:

integer function myfunct(iparam, rparam, iresp, rresp, userdata)

If sensitivities need to be requested, then the following external function can be used.

integer function myfunct(iparam, rparam, iresp, rresp, dresp, isens userdata)

FORTRAN functions are defined as follows:

integer function myfunct(iparam, rparam, nparam, iresp, rresp, nresp, userdata)


integer function myfunct(iparam, rparam, nparam, iresp, rresp, dresp, nresp, isens userdata)

character*32000 userdatainteger nparam, nrespinteger iparam(nparam), iresp(nresp)double precision param(nparam), rresp(nresp), dresp(nparam,nresp)



C functions are defined as follows:

int myfunct(int* iparam, double* rparam, int* nparam, int* iresp, double* rresp, int* nresp, char* userdata)


int myfunct(int* iparam, double* rparam, int* nparam,int* iresp, double* rresp, double* dresp, int* nresp, int* isens, char* userdata)

Note that the functions' arguments are identical in both languages so as to preservecompatibility. However, since FORTRAN always passes arguments by address, it isimportant to understand that external C functions receive pointers instead of variables.

In order to ensure portability, the following must be adhered to:

Function names should be written using either all lower-case or all upper-casecharacters.

Only alphanumeric characters should be used.

Underscore characters are prohibited.

Names cannot be longer than eight characters.

Regarding implementing of external, user-defined routines using HyperMath, refer to theonline documentation for writing scripts in HyperMath. HyperMath is supported on theWindows and Linux operating systems only.

Function Return Values

External functions should return 0 or 1 for successful completion, where 1 indicates that auser-defined information message should be output by OptiStruct. External functionsshould return -1 in case of fatal error, in which case OptiStruct will terminate afteroutputting a user-defined error message. See below for more information about error andinformation messages.

Function Arguments

The following table briefly describes the arguments which are passed from OptiStruct tothe external functions.

Argument TypeInput /Output

Description

iparam integer(table)

Input Input parameters types (optional use)

rparam double(table)

Input Input parameters values

nparam integer Input Number of parameters

iresp integer(table)

Input Output responses requests (optional use)



Argument TypeInput /Output

Description

rresp double(table)

Output Output responses values

dresp double(table)

Output Output sensitivity values

nresp integer Input Number of responses

isens integer Input Sensitivity output flag

userdata string Input / Output User data / Error or informationmessage

Parameters:

nparam is the number of input parameters that were defined on the DRESP3 card.

rparam(nparam) contains the values of the input parameters as evaluated byOptiStruct.

iparam(nparam) indicates the types of the input parameters as described below.

Parameter values are passed in the exact order in which they were defined on theDRESP3 card, regardless of their type. Using the parameter types table is optional,for instance to perform verifications or code-branching.

The following types are currently supported:

Parameter type iparam value

DESVAR 1

DTABLE 2

DGRID/DGRIDB 3

DRESP1 4

DRESP2 5

DRESP1L 6

DRESP2L 7

DVPREL1 8

DVPREL2 9

DVMREL1 10

DVMREL2 11

DVCREL1 12

DVCREL2 13

DVMBRL1 14



Parameter type iparam value

DVMBRL2 15

DEIGV 16

DGRIDB 18

Responses:

nresp is the maximum number of responses which the function is able to compute, asdefined on the MAXRESP field of the DRESP3 card.

rresp(nresp) returns the values of the responses as evaluated by the externalfunction.

iresp(nresp) contains the responses requests as described below.

The responses requests table indicates which of the available responses are actuallyneeded by OptiStruct. Entries in iresp(nresp) are flagged as 1 for requestedresponses and as 0 otherwise. Using that information is optional, and allows forsaving computational effort by not evaluating responses which OptiStruct does notneed.

Userdata String

Upon entering the function, the userdata string contains data as defined in the USRDATAfield of the DRESP3 card. It provides a convenient mechanism to pass constants or anyother relevant information to the function. There are no restrictions regarding the contentsof the string, but its length must be 32,000 characters at most.

Upon exiting the function, the string may contain a user-defined error or informationmessage. The updated string is then returned to OptiStruct, where it is printed to thestandard output (.out file and/or screen). Here again, the contents of the string are not

restricted as long as its length does not exceed 32,000 characters.

The error or information messages may be formatted by using the character "|" as a line-break indicator. Standard C escape sequences are supported as well. It is advised, butnot necessary, to format messages in such a way that each line does not exceed 80characters, since the same convention is used in OptiStruct's output files.

Sensitivity Flag

isens indicates whether sensitivities are requested in the code. It is recommended toskip the calculation of sensitivities when isens is turned off. This will avoidunnecessary computations.

Building External Libraries

Windows Systems with Microsoft Developer Studio

Creating dynamic libraries under Windows with Microsoft Developer Studio is an extremelyeasy task. Simply start a new project and select either "FORTRAN Dynamic Link Library"for FORTRAN, or "Win32 Dynamic-Link Library" for C.

For FORTRAN libraries, you need to change the argument passing conventions in the



project settings. Under the "FORTRAN" tab, select the category "External Procedures" andthen change the "Argument Passing Conventions" to "C, By Reference".

On Windows systems, %PATH% must be set correctly to ensure that the right compiler DLLs

are picked up at runtime.

UNIX Systems

Under UNIX, the general syntax to build a shared library starting from a FORTRAN or C fileis:

FC [options] -c myfile.F -omyfile.o

(for FORTRAN)

CC [options] -c myfile.c -omyfile.o

(for C)

LD [options] myfile.o -omylib.so

where, FC refers to the FORTRAN compiler (for instance f77), CC refers to the C compiler(for instance cc or gcc), and LD refers to the linker (for instance ld) installed on yourcomputer. Refer to your system's manuals for more information.

The compiler and linker options provide information about the platform you are buildingthe library for. The linker options also specify that you are building a shared library. Otheroptions, such as code optimization parameters, are left to your discretion and should notusually affect the compatibility with OptiStruct.

The following table defines options for each of OptiStruct's release platforms, which havebeen verified to work correctly on various systems. Keep in mind that these options mightchange depending on the compilers and linker installed on your computer, so refer to youroperating system manual for further information. In most cases GNU compilers can beused in place of Intel compilers. Use the appropriate compiler linker options to create ashared library with the compiler of your choice. The compilers and versions in thefollowing table are the ones used to build OptiStruct.

PlatformFORTRANCompiler Version

FORTRANCompiler Options

C Compiler Version

C Compiler Options

LinkerOptions

Win32 IntelFORTRAN12.1

/iface:default /libs:dll /threads

Intel C++ 12.1 /MD /LD

Win64 IntelFORTRAN12.1

/iface:default /libs:dll /threads

Intel C++ 12.1 /MD/LD

Macosx64 IntelFORTRAN10.1.006

-fPIC Intel C++10.1.006

-fPIC -dynamiclib



PlatformFORTRANCompiler Version

FORTRANCompiler Options

C Compiler Version

C Compiler Options

LinkerOptions

Linux64 IntelFORTRAN 12.1

–fPIC Intel C++ 12.1

-fPIC -shared

(If Compaq Visual Fortran is used to build the external response functions called byDRESP3, the following compiler directive is required to export the functions appropriately:

For a function – “myfunc”

integer function myfunc (iparam, rparam, nparam, iresp, rresp, dresp, nresp, isens, userdata)

cDEC$ ATTRIBUTES DLLEXPORT, C, REFERENCE :: myfunc

Compiler and linker options for Compaq Visual Fortran, similar to those given in the abovetable, will be required to build and use multithreaded dynamic runtime libraries).

Once your library has been built, you can verify that the functions have been exportedcorrectly by using nm mylib.so on UNIX systems and dumpbin /exports mylib.dll on

Windows systems with Microsoft Developer Studio. This command will display the list ofsymbols found in the library, among which you should recognize the function(s) which youhave written.

Note that some FORTRAN compilers convert function names to lower-case or upper-casesymbols, and some compilers also append an underscore to these names. However, inyour input decks, you do not have to worry about the exact symbol name. Simply use thefunction name as it is defined in your code, and OptiStruct will automatically locate theappropriate symbol.

Using External Libraries

All files referenced here are located in the HyperWorks installation directory under<install_directory>/demos/os/manual/.

To locate the HyperWorks installation directory, <install_directory>, use the following

approach:

From the permanent menu, select the global panel and review the path next to templatefile: <install_directory> is the portion of the path preceding the templates/ directory

on PC, and the hm/ directory on UNIX.

HyperMath Example

Refer to the OptiStruct tutorial, OS-4095 (Size Optimization using External Responses(DRESP3) through HyperMath), for information on using DRESP3 with HyperMath toimplement external, user-defined routines.

Simple Example

The files dresp3_simple.F and dresp3_simple.c contain source code for simple examples



of external functions written in FORTRAN and C, respectively. Both functions are named mysum and compute two responses – the sum of the parameters and the averaged sum ofthe parameters.

The input deck dresp3_simple.fem contains an example problem calling both of these

external functions. Two LOADLIB cards referring to the FORTRAN and C libraries aredefined:

LOADLIB DRESP3 FLIB dresp3_simple_f.dllLOADLIB DRESP3 CLIB dresp3_simple_c.dll

You have created four DRESP3 cards, which are pointing to the FORTRAN and C functionsand requesting the first and second responses in each of those functions. Two DRESP1responses are used as parameters:

DRESP3 6 SUMF FLIB MYSUM 1 2+ DRESP1 2 3DRESP3 7 AVGF FLIB MYSUM 2 2+ DRESP1 2 3DRESP3 8 SUMC CLIB MYSUM 1 2+ DRESP1 2 3DRESP3 9 AVGC CLIB MYSUM 2 2+ DRESP1 2 3

For verification purposes, you have also defined two DRESP2 cards that are pointing to twosimple equations which evaluate the sum and the averaged sum of their parameters:

DEQATN 1 F(x,y) = x+yDEQATN 2 F(x,y) = avg(x,y)

DRESP2 4 SUME 1+ DRESP1 2 3DRESP2 5 AVGE 2+ DRESP1 2 3

Running this input deck through OptiStruct shows that the FORTRAN external functions,the C external functions and the internal equations always return the same values, and areupdated simultaneously throughout the optimization process.

Advanced Example

The file dresp3_advanced.F contains the FORTRAN source code of the second example, in

which you are making use of advanced features of the DRESP3 functionality.

The external function is able to compute the von Mises and maximum principal stresses(strains) of an element based on its stress (strains) components. Either 3 or 6 componentscan be passed as parameters – 3 components for a shell element and 6 components for asolid element. The following features are used:

The USRDATA string is parsed to determine whether stresses or strains arerequested, and an error message is returned otherwise.

The number of parameters is used to determine whether a shell or solid element istreated, and an error message is returned if that number is not equal to 3 or 6.

An error message is returned if the parameters are not of type DRESP1 or DRESP1L,since stress or strain components are expected.

Even though the function is able to compute two different responses, only theresponse(s) actually requested by OptiStruct are computed when the function is



called.

An information message is returned indicating which responses were evaluated.

The input deck dresp3_advanced.fem gives a simple example of problem making use of

this external function, for analysis only.

The DRESP1 responses 10-12 and 13-18 correspond to the stress components of a 2-D anda 3-D element, respectively. The DRESP1 responses 20-23 evaluate the von Mises stressand the maximum principal stress of the same two elements:

DRESP1 10 SXX2D STRESS ELEM SX1 100DRESP1 11 SYY2D STRESS ELEM SY1 100DRESP1 12 SXY2D STRESS ELEM SXY1 100DRESP1 13 SXX3D STRESS ELEM SXX 50DRESP1 14 SYY3D STRESS ELEM SYY 50DRESP1 15 SZZ3D STRESS ELEM SZZ 50DRESP1 16 SXY3D STRESS ELEM SXY 50DRESP1 17 SXZ3D STRESS ELEM SXZ 50DRESP1 18 SYZ3D STRESS ELEM SYZ 50

DRESP1 20 SVM2D-1 STRESS ELEM SVM1 100DRESP1 21 SMP2D-1 STRESS ELEM SMP1 100DRESP1 22 SVM3D-1 STRESS ELEM SVM 50DRESP1 23 SMP3D-1 STRESS ELEM SMP 50

In addition, you have defined DRESP3 cards which compute the same stress resultsthrough our external library. You are also using the SLAVE feature to clone the parametersof similar cards:

DRESP3 30 SVM2D-3 STRLIB GETSTR 1 2+ DRESP1 10 11 12 + USRDATA STRESSDRESP3 31 SMP2D-3 STRLIB GETSTR 2 2+ SLAVE 30DRESP3 32 SVM3D-3 STRLIB GETSTR 1 2+ DRESP1 13 14 15 16 17 18+ USRDATA STRESSDRESP3 33 SMP3D-3 STRLIB GETSTR 2 2+ SLAVE 32

Referencing External Files

Microsoft Excel workbooks can be referenced via the LOADLIB entry to define user-definedresponses. Both Implicit and Explicit options are available and are defined as follows:

Implicit definition

This is a simple implementation wherein two columns in an Excel worksheet are used todefine the input and output parameters. Column 1 can be used to list input parametersand Column 2 can be used to list output parameters.

LOADLIB DRESP3 ELIB dresp3_excel.xlsx

DRESP3 10 SUM ELIB MYSUM+ DRESP1 5 6



Explicit definition

In this advanced implementation the cell input number is specified. Cells for input andoutput data are listed.

LOADLIB DRESP3 ELIB dresp3_excel.xlsx

DRESP3 20 FUNC ELIB MYFUNC+ DRESP1 5 6 7 8+ DESVAR 1+ CELLIN B3 THRU B6 + CELLIN C10+ CELLOUT E10




Topology Optimization is a mathematical technique that produces an optimized shape andmaterial distribution for a structure within a given package space. By discretizing the domaininto a finite element mesh, OptiStruct calculates material properties for each element. TheOptiStruct algorithm alters the material distribution to optimize the user-defined objectiveunder given constraints. Convergence occurs in line with the description provided on the Iterative Solution page.

The following responses (see Responses for a description) are currently available as theobjective or as constraint functions:

Mass Volume Volume or MassFraction

Center of Gravity Moment of Inertia Static Compliance

Static Displacement Natural Frequency von Mises Stress onEntire Model (only asconstraint)

Buckling Factor (specialcase)

FrequencyResponseDisplacement,Velocity,Acceleration

Temperature

Weighted Compliance WeightedFrequency

Combined ComplianceIndex

Function


The definition of stress constraints is limited to a single von Mises permissible stress. The phenomenon of singular topology is pronounced when different materials withdifferent permissible stresses exist in a structure. Singular topology refers to theproblem associated with the conditional nature of stress constraints, i.e. the stressconstraint of an element disappears when the element vanishes. This creates anotherproblem in that a huge number of reduced problems exist with solutions that cannotusually be found by a gradient-based optimizer in the full design space.

Stress constraints for a partial domain of the structure are not allowed because theyoften create an ill-posed optimization problem since elimination of the partial domainwould remove all stress constraints. Consequently, the stress constraint applies to theentire model when active, including both design and non-design regions, and stressconstraint settings must be identical for all DSIZE and DTPL cards.



The capability has built-in intelligence to filter out artificial stress concentrations aroundpoint loads and point boundary conditions. Stress concentrations due to boundarygeometry are also filtered to some extent as they can be improved more effectivelywith local shape optimization.

Due to the large number of elements with active stress constraints, no element stressreport is given in the table of retained constraints in the .out file. The iterative history

of the stress state of the model can be viewed in HyperView or HyperMesh.



The buckling factor can be constrained for shell topology optimization problems with a basethickness not equal to zero. Constraints on the buckling factor are not allowed in any othercases of topology optimization.

The following responses are currently available as the objective or as constraint functions forelements that do not form part of the design space:

Static Stress Static Strain Static Force

Composite Stress Composite Strain Composite Failure Criterion

Frequency ResponseStress

Frequency ResponseStrain

Frequency Response Force

If an element is in the topology design region, its individual stress/strain or force criterionvalue cannot be constrained.



Generating and Evaluating a Design using TopologyOptimization

The following example illustrates how OptiStruct is used to generate a design for a controlarm and how engineering analysis is used to evaluate the design.

1. The package space for the control arm is filled with a finite element mesh.

2. Parts of the mesh are designated as nondesign, and the elements that make up theseareas are placed in a nondesign component.

The darker elements represent attachment points for the frame, shock, spring seat,stabilizer bar, and spindle. Nondesign elements are placed where loads and constraintsare applied to the model.

Nondesign and design space of FEM model.

3. Loads and constraints are applied to the finite element model.

Three load cases are applied at the spindle and stabilizer bar attachment points.

Constraints are applied at the frame connections and shock point.

The model and parameters are submitted to OptiStruct for topology optimization.

4. Elements with material densities below 60% are masked out.



Density plot of control arm with elements below 60% material density removed from the display.

5. A finite element model of the control arm using the suggested layout as a guide isgenerated.

Finite element model of control arm design based on OptiStruct results.

6. Stress analysis is performed on the model using the loads and boundary conditions fromthe topology optimization run.



Stress contour plot of control arm model during braking load.

7. The performance of the part is evaluated.

Subsequent size and shape optimization is performed to minimize the mass while meetingstress and deflection criteria.

Final design with shape-optimized structural member.



Design Variables for Topology Optimization

OptiStruct solves topological optimization problems using the density method, also known asthe SIMP method in the research community.

Under topology optimization, the material density of each element should take a value ofeither 0 or 1, defining the element as being either void or solid, respectively. Unfortunately,optimization of a large number of discrete variables is computationally prohibitive. Therefore, representation of the material distribution problem in terms of continuousvariables has to be used.

With the density method, the material density of each element is directly used as the designvariable, and varies continuously between 0 and 1; these represent the state of void andsolid, respectively. Intermediate values of density represent fictitious material. The stiffnessof the material is assumed to be linearly dependent on the density. This material formulationis consistent with our understanding of common materials. For example, steel, which isdenser than aluminum, is stronger than aluminum. Following this logic, the representation offictitious material at intermediate densities does reflect engineering intuitions.

In general, the optimal solution of problems involves large gray areas of intermediatedensities in the structural domain. Such solutions are not meaningful when you are lookingfor the topology of a given material, and not meaningful when considering the use ofdifferent materials within the design space. Therefore, techniques need to be introduced topenalize intermediate densities and to force the final design to be represented by densities of0 or 1 for each element. The penalization technique used is the "power law representation ofelasticity properties," which can be expressed for any solid 3-D or 2-D element as follows:

pK K

Where, K and K represent the penalized and the real stiffness matrix of an element,

respectively, is the density and p is the penalization factor which is always greater than 1.

In OptiStruct, the DISCRETE parameter corresponds to (p - 1). DISCRETE can be defined on

the DOPTPRM bulk data entry. p usually takes a value between 2.0 and 4.0. For example,

compared to the non-penalized formulation (which is equivalent to p=1) at =0.3, p=2reduces the stiffness of the element from 0.3 to 0.09 times the stiffness of the fully denseelement. The default DISCRETE is 1.0 for shell dominant structures, and 2.0 for solids

dominant structures (the dominance is defined by the proportion of number of elements). Anadditional parameter, DISCRT1D, can also be defined on the DOPTPRM bulk data entry.

DISCRT1D allows 1-D elements to use a different penalization to 2-D or 3-D elements.

When minimum member size control is used, the penalty starts at 2 and is increased to 3 forthe second and third iterative phases. This is done in order to achieve a more discretesolution. For other manufacturing constraints such as draw direction, extrustion, patternrepetition, and pattern grouping, the penalty starts at 2 and increases to 3 and 4 for thesecond and third iterative phases, respectively. Obviously, due to the existence of semi-dense elements, the analysis results may change dramatically when the design processenters a new phase using a different penalization factor.

Three types of finite elements can be defined as topology design elements in OptiStruct:Solid elements, shell elements, and 1-D elements (including ROD, BAR/BEAM, BUSH, andWELD elements).



Design Elements

Solid Elements

The SIMP method (Solid Isotropic Material with Penalty) is used in OptiStruct. In the SIMPmethod, a pseudo material density is the design variable, and hence it is often called density method as well. The material density varies continuously between 0 and 1, with 0representing void state and 1 solid state. The SIMP method applies a power-lawpenalization for stiffness-density relationship in order to push density toward 0/1 (void/solid) distribution:

pK K

Where,

K is the penalized stiffness matrix of an element.

K is the real stiffness matrix of an element.

is the density.

p is the penalization factor (Always greater than 1, with default penalty at 3.0 if no

manufacturing constraints are applied).

Shell Elements

The SIMP method (Solid Isotropic Material with Penalty) is used in OptiStruct. In the SIMPmethod, a pseudo material density is the design variable, and hence it is often called density method as well. The material density varies continuously between 0 and 1., with 0representing void state and 1 solid state. The SIMP method applies a power-lawpenalization for stiffness-density relationship in order to push density toward 0/1 (void/solid) distribution.

pK K

Where,

K is the penalized stiffness matrix of an element.

K is the real stiffness matrix of an element.

is the density.

p is the penalization factor (Always greater than 1)

For isotropic material a non-zero base plate thickness can be defined. For a compositeplate or a plate with anisotropic material, the base plate thickness must be zero (thelimitation of the current development).

Topology optimization of composites has certain unique characteristics and is discussed in Composite Topology and Free-size Optimization.



1-D Elements

Only the density method is implemented for topology optimization of 1-D elements. Currently available elements include ROD, BAR/BEAM, BUSH, and WELD elements. Each

element is controlled by a single design variable that is the material density of thiselement that varies between 0 (numerically a small value is used) and 1.0. In essence, 0represents nonexistence and 1.0 represents full existence of the corresponding element. The following power law representation of elastic properties is used to penalizeintermediate density:

pK K

Where, K and K represent the penalized and the real stiffness matrix of an element,

respectively, p is the penalization factor which is always bigger than 1. The penalty is

controlled by the DISCRETE or DISCRT1D parameters, the value of these parameters

correspond to (p - 1).



Topology Optimization (Level Set Method)

A new topology optimization algorithm based on the level set method was implemented in

OptiStruct 12.0. In the level set method, the boundary of the design is implicitly represented

as the isosurface (the zero level set) of a function ( )x defined on the finite element mesh, asshown in Figure 1. In the level set model, the domain is defined based on the value of thelevel set function:

( ) 0 : /( ) 0 :( ) 0 : /

x xx xx x D

Where, D denotes the design domain; represents the material region, stands for the

boundary, and D/ denotes the region with no material. The dynamic motion of the

boundary is governed by the so-called, level set equation:

nVt

Where, Vn is the normal velocity and is the norm of the gradient of the level set function.

The basic idea of the level set equation is to map the boundary evolution into an evolution of

the level set function ( )x .

Figure 1: A 2-D Design and its corresponding Level Set representation

Level-set based topology optimization can be considered as advanced shape optimization. Itworks in a way like conventional shape optimization, where the design is changed by movingthe boundary, while at the same time topological changes such as boundary emerging andsplitting can be handled naturally.



Composite Topology and Free-size Optimization

Input Definition

For composite structures, topology and free-size optimization are defined through the DTPLand DSIZE bulk data entries, respectively. Both are supported in the HyperMeshoptimization panel. Features available include: minimum member size control, symmetry,pattern grouping and pattern repetition. Stress or failure constraints are not supported atthis stage.

Prior to OptiStruct 8.0, composite topology optimization was based on the notion that thehomogenized properties of an element remain unchanged. This construct does not allow thefreedom for material redefinition. However, if this is indeed a preferred assumption, theHOMO option can be set on the MAT line of the DTPL card. Otherwise, an individual ply-based formulation (discussed below) will be the default option.

Topology and free-size methods target a system level composite design where laminatefamily definition is the objective. Therefore, the PCOMP model should not reflect a detailedstacking of plies of the same orientation. For example, even though 10 layers of 0 degreegraphite cloth might be separated in the stacking of the final structure, the modeling for aconcept study using topology and free-size should group them together in one ply in thePCOMP so that the optimal total thickness distribution of a 0 degree ply is optimizedthroughout the structure.

Involving both topology and free-size in the same optimization problem is not recommendedsince the penalization on topology components creates a bias that could lead to sub-optimalsolutions.

Problem Formulation

For a composite shell element (shown in the figure below), the thickness ti of each ply is avariable between 0 and Ti defined on the PCOMP card.

Composite element

The only difference between topology and free-size here is that the former targets a discretefinal solution of 0 (or Ti) for ti, while free-size allows ti to vary freely between 0 and Ti. Thediscrete solution is achieved by penalizing intermediate thickness. Most generalcharacteristics of regular shell topology and free-size optimization also apply to composite. Itis recommended that you become familiar with free-size before proceeding. The majordifferences between topology optimization and free-size can be illustrated through a simpleexample.



Example: Cantilever Plate

The cantilever plate is shown in the following figure. A symmetric lay-up of (0, +45, -45,and 90) degree plies are used. The optimization problem is stated as:

Minimize ComplianceSubject to Volume fraction < 0.3

Composite cantilever plate

For topology optimization, the thickness distribution of individual plies in the final design isshown in the following figure.

Topology result – thickness of individual plies

The total thickness of the laminate is shown next.



Topology result – total thickness of the laminate

It can be seen that a rather discrete thickness for each ply is obtained. Note that while littleoverlapping of different orientations is shown in this result, it should be expected thatoverlapping of plies of different angles might be more pronounced when multiple load casesexist.

The thickness distribution of free-size optimization for this example is shown below.

Free-size result – thickness of individual plies



Free-size result – total thickness of the laminate

As expected, free-size created a design in which variable ply thickness appears in a largearea of the structure. The compliance of both designs are compared in the figure below. It isnot surprising to see that the free-size design outperforms the topology design in terms ofcompliance since a continuous variation of thickness offers more design freedom.

Compliance of topology and free-size results

While ply angles are not variables for topology and free-size optimization, thicknessoptimization of plies indirectly leads to a discrete optimization of angles. The availableangles in the PCOMP can be interpreted as discrete angle variables. Also, while free-sizeoften creates variable thickness distribution without extensive cavity, it does not preventcavity if the optimizer demands it. For this example, you can see cavity in the free-sizeresults in the 45 degree region, adjacent to the support, and in the upper and lower cornersof the free end.

Comparing Design Characteristics of Topology and Free-size

Most of the characteristics for general shell discussed in free-size section also apply tocomposite structures. One important exception is that the manufacturing cost is no longer arestrictive factor for composites. The reason for this is that a composite structure ismanufactured by laying very thin plies of fiber cloth over each other and binding them with amatrix material, like epoxy resin. Therefore, an almost continuous change of laminatethickness can be achieved seamlessly by dropping/adding plies freely.



Characteristics of Composite Topology vs. Free-size

Composite Topology Composite Free-size

Angle optimized indirectly. Angle optimized indirectly.

Goal – 0/Ti discrete thickness ofindividual plies

-> Restricted freedom

Goal – variable thickness ofindividual plies-> "Free" under upper bound Ti

Results – Truss-like designconcepts.

Variable thickness panel likely forin-plane loading, 0/1 thicknesslikely when bending is dominant.

Not useful compared to Free-size?

Always better design?

Manufacture – not a factor forcomposite unless pre-manufactured laminate is used.

Manufacture – naturally achievedwith no additional cost.

Concentrated full thick membersare stronger against out of planebuckling.

Spread thin shell could be prone tobuckling.

Functionality may need holes forother non-structural components orfor passing lines/pipes.

Cavity is controlled by optimality,and is usually not extensive underin-plane loading.

Interpreting Topology and Free-size Results

Interpretation of topology results is rather straight-forward. For free-size, the change inthickness of individual plies provides insight for ply dropping/adding zones. The thickness ofeach ply in each individual zone can then be defined as a design variable in a detailed sizeoptimization. At this stage, discrete variables can be used to reflect the discrete nature of plythickness change. Overlapping all zones of individual plies can than help to generate PCOMPzones, where a ply traveling through different zones can be defined using PCOMPG.



Free-size Optimization

Input Definition

Free-size optimization is defined through the DSIZE bulk data entry that is supported in theHyperMesh Optimization panel. Features available for free-size include: minimum membersize control, symmetry, pattern grouping and pattern repetition, and stress constraintsapplied to von Mises stresses of the entire structure.

Involving both topology and free-size in the same optimization problem is not recommendedsince penalization on topology components creates a bias that could lead to sub-optimalsolutions.

Problem Formulation

For a shell cross-section (shown below), free-size optimization allows thickness t to varyfreely between T and T0 for each element; this is in contrast to topology optimization whichtargets a discrete thickness of either T or T0. The differences of topology optimization andfree-size can be illustrated through a simple example.

Shell cross-section

Example: Cantilever Plate

The cantilever plate is shown in the following figure. Base-plate thickness T0 is zero. Theoptimization problem is stated as:

Minimize ComplianceSubject to Volume fraction < 0.3

Cantilever plate



The next figure shows the final results of topology and free-size optimization as performed onthis plate, side by side. As expected, the topology result created a design with 70% cavity,while the free-size optimization arrived at a result with a zone of variable thickness panel.

Topology result Free-size result

The compliance of both designs are compared in the following figure.

It is not surprising to see that the free-size design outperforms the topology design in termsof compliance since continuous variation of thickness offers more design freedom.

It should be emphasized that free-size offers a concept design tool alternative to topologyoptimization for structures modeled with 2-D elements. It does not replace a detailed sizeoptimization that would fine tune the size parameters of an FEA model of the final product. To illustrate the close relationship between free-size and topology formulation, consider a 3-Dmodel of the same cantilever plate shown previously. The thickness of the plate is modeledin 10 layers of 3-D elements.

Cantilever plate – 3-D model



3-D topology result

The topology design of the 3-D model shown above looks similar to the free-size resultsshown previously. This should not be surprising because when the plate is modeled in 3-D, avariable thickness distribution becomes possible under the topology formulation that seeks adiscrete density value of either 0 or 1 for each element. If infinitely fine 3-D elements areused, a continuous variable thickness of the plate can be achieved via topology optimization. The motivation for the introduction of free-size is based on the conviction that limitationsdue to 2-D modeling should not become a barrier for optimization formulation. In regards tothe 3-D modeling of shell, topology optimization is equivalent to the application of extrusionconstraint(s) in the thickness direction of a 3-D modeled shell.

It is important to point out that while free-size often creates variable thickness shells withoutextensive cavity, it does not prevent cavity if the optimizer demands it. For the examplealready shown, you can see cavity in the free-size result in the 45 degree region, adjacent tothe support, and in the upper and lower corners of the free end.

If a plate is predominantly under a bending load, free-size design can converge to a discrete0/1 thickness distribution similar, or even identical to, the result of a topology optimization. The reason is that bending stiffness is a function of t3 and, therefore, maximum thickness isheavily favored. In other words, intermediate thickness is naturally penalized for bendingperformance. In the following figure, the free-size result of a plate under bending clearlydemonstrates this behavior.

Free-size result of a plate under bending



Stress Constraints for Free-size Optimization


The definition of stress constraints is limited to a single von Mises permissible stress. The phenomenon of singular topology is pronounced when different materials withdifferent permissible stresses exist in a structure. Singular topology refers to theproblem associated with the conditional nature of stress constraints, i.e. the stressconstraint of an element disappears when the element vanishes. This creates anotherproblem in that a huge number of reduced problems exist with solutions that cannotusually be found by a gradient-based optimizer in the full design space.

Stress constraints for a partial domain of the structure are not allowed because theyoften create an ill-posed optimization problem since elimination of the partial domainwould remove all stress constraints. Consequently, the stress constraint applies to theentire model when active, including both design and non-design regions, and stressconstraint settings must be identical for all DSIZE and DTPL cards.

The capability has built-in intelligence to filter out artificial stress concentrations aroundpoint loads and point boundary conditions. Stress concentrations due to boundarygeometry are also filtered to some extent as they can be improved more effectivelywith local shape optimization.

Due to the large number of elements with active stress constraints, no element stressreport is given in the table of retained constraints in the .out file. The iterative history

of the stress state of the model can be viewed in HyperView or HyperMesh.



Comparing Design Characteristics of Topology and Free-size

The differences in the characteristics of topology and free-size are summarized in thefollowing table. It is important to note that while the free-size design concept generallyachieves better performance when buckling constraints are ignored, the topology conceptcould outperform free-size if buckling constraints become the driving criteria during the sizeand/or shape optimization stage. The reason for this is that topology optimization eliminatesintermediate thicknesses, which leads to a more concentrated material distribution and ashell that is stronger against out-of-plane buckling. The performance of topology and free-size is compared in the next practical example. Since it is usually not possible to know whatcriteria are most critical for a given structure, it is recommended to follow both designconcepts until detailed size and shape optimization is complete and can be evaluated. If it isnot possible to derive two designs for every structural component, a benchmark of therelative performance of both concepts for every type of commonly evaluated structure shouldbe established so that general guidelines can be used for reference.

Manufacturing and functional considerations may favor topology optimization. Two cases inwhich free-size may not be the best choice from the start include those in which:



(1) A variable thickness shell is typically far more expensive to manufacture and may not bea viable choice; as with most shell structures of an automobile that are manufactured usingstandard sheet metal, for example. (2) The functionality of the structure might require extensive cavity in the design; as with anairplane fuselage floor supporting beam which may need a significant amount of cavity toallow for the pass-through of wires, pipes or other equipment.

Characteristics of Shell Topology vs. Free-size

Shell Topology Optimization Free-size

GOAL: 0/1 thickness-> Restricted freedom

GOAL: variable thickness-> "Free" under upper bound T

Results: Truss-like designconcepts.

Variable thickness panel likely forin-plane loading, 0/1 thicknesslikely when bending is dominant.

Equivalent to extrusion constraintswhen shell is modeled in infinitelyfine 3-D elements.

Equivalent to model with infinitelyfine 3-D elements.

Not useful compared to free-size?

Always better design?

Manufacturing constraint –punched sheet metal of constantthickness.

Manufacture – expensive and onlyused in industries less sensitive tocost.

Concentrated full thick membersare stronger against out of planebuckling.

Spread thin shell could be prone tobuckling.

Functionality may need holes forother non-structural components orfor passing lines/pipes.

Cavity is controlled by optimality,and is usually not extensive underin-plane loading.

Interpreting Free-size Results

In most cases, variable thickness of a shell structure is achieved through step-wise change ofthickness. Free-size results provide a different concept about how the zones of differentthicknesses should be designed. Detailed size optimization can then be performed to finetune the final design. This process is illustrated in the following example.



Example: Supporting Beam of an Airplane Door Structure

This example was discussed in a paper by Cervellera, Zhou and Schramm in 2005(Proceedings of 6th World Congresses of Structural and Multidisciplinary Optimization, Rio deJaneiro, 30 May - 03 June 2005, Brazil). Free-size optimization is applied to improve thetraditional beam design consisting of an "I" cross section with circular cut-outs. A modelrepresenting the design space of a beam component has been generated, in which a portionof outer skin and vertical frames is included (shown in following image).

Supporting beam of an airplane door structure

The design areas include the upper flange and the web, while the lower flange and theattachment ribs of vertical frames remain unchanged. Free-size optimization allows elementthickness to vary between 0.05 mm and 10.0 mm. The design problem is to minimize themass subject to a beam center deflection of 3 mm. The free-size result is shown on the leftin the figure below. This result is interpreted into zones of different thicknesses as shownwith the different colors on the right in the figure.

Left: Free-size result; Right: Interpreted zones of constant thickness

For comparison, topology optimization is applied to the same problem for shell thickness of 5mm in the design area. The result and its interpretation is shown below.



Left: Topology result; Right: Interpreted zones of constant thicknesses

Detailed size optimization is then carried out for both concepts, allowing all shell thickness tovary between 1.6 mm and 20 mm. The optimization problem is formulated as minimizationof the beam mass subject to the following constraints:

Maximum deflection of the beam < 3.0 mm.Maximum von Mises stress in the beam design area < 300 MPa.Buckling load factors > 1.0.

In order to study the behavior of the design concepts under different design criteria, sizeoptimization is carried out for different permissible deflection constraints (1.5 mm, 2.0 mm, 3mm, 4.0 mm, and 5.0 mm). The results are summarized with the figure below, in whichcritical constraints are highlighted in red numbers. The figure also shows the optimum massof the two concepts with respect to the maximum displacement. Note that the plate design ismore efficient than the truss-like concept if high stiffness is required, while it is less efficientif stability and strength requirements dominate the final designs. More details of thisexample and additional discussions about free-size can be found in the paper by Cervellera,Zhou and Schramm in 2005.

Comparison of results for different deflection constraints




Topography optimization is an advanced form of shape optimization in which a design regionfor a given part is defined and a pattern of shape variable-based reinforcements within thatregion is generated using OptiStruct. The approach in topography optimization is similar tothe approach used in topology optimization, except that shape variables are used rather thandensity variables. The design region is subdivided into a large number of separate variableswhose influence on the structure is calculated and optimized over a series of iterations. Thelarge number of shape variables allows you to create any reinforcement pattern within thedesign domain instead of being restricted to a few.


Mass* Volume* Center of Gravity

Moment of Inertia Static Compliance StaticDisplacement

Natural Frequency Buckling Factor Static Stress,Strain, Forces

Static CompositeStress, Strain, Failure Index

Frequency ResponseDisplacement, Velocity,Acceleration

FrequencyResponse Stress,Strain, Forces

Weighted Compliance Weighted Frequency CombinedCompliance Index

Function Bead discretenessfraction

Temperature

* Mass and Volume are not recommended for use as objectives or constraints since

mass and volume are not very sensitive to design changes in topography

optimization.

Design Variables for Topography Optimization

OptiStruct solves topography optimization problems using shape optimization withinternally generated shape variables. One or more design domains are defined using the DTPG card. These cards must, in turn, reference PSHELL, PCOMP or DESVAR definitions. If a DESVAR definition is referenced, it must be a shape design variable, meaning that itmust, in turn, be referenced by one or more DVGRID cards. If a PSHELL or PCOMPdefinition is referenced, OptiStruct generates shape variables using the parameters definedon the DTPG card, creating internal DVGRID data for the nodes associated with the PSHELLor PCOMP definitions. In both cases, the end result is that each DTPG card references asingle shape variable. This shape variable then gets converted into topography shapevariables.



Basic topography shape variables follow the user-defined parameters on the DTPG card(minimum bead width, and draw angle), they are circular in shape, and they are laid outacross the design domain in a roughly hexagonal distribution. Each topography shapevariable has a circular central region of diameter equal to the minimum bead width. Gridswithin this region are perturbed as a group, which prevents the formation of anyreinforcement bead of less than the minimum bead width. Grids outside of the centralcircular region of the topographical variables are perturbed as the average of the variablesto which they are nearest. This results in smooth transitions between neighboringvariables. If two adjacent variables are fully perturbed, all of the nodes between them willbe fully perturbed. If one variable is fully perturbed and its neighbor is unperturbed, thenodes in between will form a smooth slope connecting them at an angle equal to the drawangle. The spacing of the variables is determined by the minimum bead width and thedraw angle in such a way that no part of the bead reinforcement pattern forms an anglegreater than the draw angle.

Pattern grouping options link topographical variables together in such a way that thedesired reinforcement patterns are formed. Linear, planar, circular, radial, etc. shapedreinforcements are controlled by single variables, ensuring that the reinforcements followthe desired pattern. One-plane, two-plane, three-plane and cyclical symmetry patterngrouping options also use a similar approach to ensure that symmetry is created in thesolution.

Although topography optimization is primarily a tool for creating bead type reinforcementsin shell elements, it can accommodate solid models as well. Many pattern groupingoptions (such as planar and cylindrical) are intended to be used with solid models sincethey effectively reduce 3-D problems into 2-D ones.

Variable Generation

There are three methods of automatically generating shape variables for topographyoptimization using the DTPG card. The first two, element normal and draw vector, areperformed entirely in OptiStruct. The third (user-defined) requires that the input datacontain one or more shape design variables that are used as the design domain.

Method Description

Elementnormal

This method is the easiest one to use. When norm isentered for the draw direction, the normal vectors ofthe elements are used to define the draw vector forthe shape variables. This method is especiallyeffective for curved surfaces and enclosed volumeswhere the beads are intended to be drawn normal tothe surface.



Method Description

Beads created using the element normal method of determiningdraw vector.

Draw vector This method allows you to define the draw vector thatis used for generating the shape variables. The X, Y,and Z components of the draw vector in the nodalcoordinate system are entered. This method is usefulwhen all beads must be drawn in the same direction. Note that the draw angle may not be maintainedwhile using this method.

Beads created using the Draw vector method of determining drawvector.

User-defined This method allows you to set up the vectors andheights for the topography optimization. A DESVARcard is referenced in place of a PSHELL or PCOMPcard. All of the grids with DVGRID cards associatedwith that DESVAR card are considered part of thedesign domain. The DESVAR and DVGRID entries areredefined to reflect the minimum bead width anddraw angle parameters that have been set by you. The vectors and magnitudes of the displacementvectors on each DVGRID card for each grid are



Method Description

retained, so these entries must be left blank on theDTPG card. This allows you to create a design domainin which each node can have its own draw vector anddraw height.

Multiple Topography Design Regions

OptiStruct generates topography shape variables for each design domain defined by a DTPG card. It allows for overlapping of design domains. A grid that is in more than onedesign domain will be a part of shape variables for each design domain. For automaticallygenerated bead variables, the draw height is divided by the number of bead variablesacting on that grid. Thus, if a grid is a part of two DTPG cards that have draw heights of3.0mm and 5.0mm, the draw heights become 1.5mm and 2.5mm. If this is not desired,simply make sure that no grid is in more than one design domain. In cases where twodesign components touch each other and the design domains are not user-defined (i.e.PSHELL or PCOMP definitions are referenced), a row of non-design elements needs to beinserted between them to prevent averaging. If the bead variables are user-defined (i.e.DESVAR definition is referenced), no averaging will be performed. It is assumed that youintend to have the shape variables overlap, which will result in the grid deflection beingcumulative between multiple influencing bead cards.

Bead Discreteness Fraction

The bead discreteness fraction is a response that can be used to control the amount ofshape variation for topography design domains. This response indicates the amount ofshape variation for one or more topography design domains. The response varies in therange 0.0 to 1.0 (0.0 < BEADFRAC < 1.0), where 0.0 indicates that no shape variation hasoccurred, and 1.0 indicates that the entire topography design domain has assumed themaximum allowed shape variation.



Size Optimization

OptiStruct has the capability of performing size optimization. Size optimization can beperformed simultaneously with the other types of optimization.

In size optimization, the properties of structural elements such as shell thickness, beamcross-sectional properties, spring stiffness, and mass are modified to solve the optimizationproblem.

Defining size variables in OptiStruct is done very similarly to other size optimization codes. Each size variable is defined using a DESVAR bulk data entry. If a discrete design variable isdesired, a DDVAL bulk data entry needs to be referenced for the design variable values. TheDESVAR cards are related to size properties in the model using a DVPREL1 or DVPREL2 bulkdata entry. Each DVPREL bulk data entry must reference at least one DESVAR bulk dataentry to be active during the optimization. HyperWorks includes a pre-processor calledHyperMesh that can be used to set up any number of size variables for the properties.


Mass Volume Center of Gravity

Moment of Inertia Static Compliance Static Displacement

Natural Frequency Buckling Factor Static Stress, Strain,Forces

Static CompositeStress, Strain, Failure Index

FrequencyResponseDisplacement,Velocity,Acceleration

Frequency ResponseStress, Strain, Forces

Weighted Compliance WeightedFrequency

Combined ComplianceIndex

Function Temperature

Design Variables for Size Optimization

In finite elements, the behavior of structural elements (as opposed to continuumelements), such as shells, beams, rods, springs, and concentrated masses, are defined byinput parameters, such as shell thickness, cross-sectional properties, and stiffness. Thoseparameters are modified in a size optimization. Some structural elements have severalparameters depending on each other; like beams in which the area, moments of inertia,and torsional constants depend on the geometry of the cross-section.

The property itself is not the design variable in size optimization, but the property isdefined as a function of design variables. The simplest definition, as defined by thedesign-variable-to-property relationship DVPREL1, is a linear combination of design



variables defined on a DESVAR statement such that

0 i ip C DV C

Where, p is the property to be optimized, and Ci are linear factors associated to the design

variable DVi.

Using the equation utility DEQATN, more complicated functional dependencies using eventrigonometric functions can be established. Such design-variable-to-property relations arethen defined using the DVPREL2 statement.

For a simple gage optimization of a shell structure, the design-variable-to-propertyrelationship turns into:

iT DV

Where, the gage thickness, T is identical to the design variable.

If a discrete design variable is desired, a DDVAL bulk data entry needs to be referenced onthe DESVAR bulk data entry for the design variable values.



Shape Optimization

OptiStruct has the capability of performing shape optimization. In shape optimization, theouter boundary of the structure is modified to solve the optimization problem. Using finiteelement models, the shape is defined by the grid point locations. Hence, shape modificationschange those locations.

Shape variables are defined in OptiStruct in a way very similar to that of other shapeoptimization codes. Each shape variable is defined by using a DESVAR bulk data entry. If adiscrete design variable is desired, a DDVAL bulk data entry needs to be referenced for thedesign variable values. DVGRID bulk data entries define how much a particular grid pointlocation is changed by the design variable. Any number of DVGRID bulk data entries can beadded to the model. Each DVGRID bulk data entry must reference an existing DESVAR bulkdata entry if it is to be a part of the optimization. The DVGRID data in OptiStruct containsgrid location perturbations, not basis shapes.

The generation of the design variables and of the DVGRID bulk data entries is facilitated bythe HyperMorph utility, which is part of the HyperMesh software.


Mass Volume Center of Gravity

Moment of Inertia Static Compliance Static Displacement

Natural Frequency Buckling Factor Static Stress, Strain,Forces

Static CompositeStress, Strain, FailureIndex

Frequency ResponseDisplacement,Velocity,Acceleration

Frequency ResponseStress, Strain, Forces

Weighted Compliance Weighted Frequency Combined ComplianceIndex

Function Temperature

Design Variables for Shape Optimization

In finite elements, the shape of a structure is defined by the vector of nodal coordinates(x). In order to avoid mesh distortions due to shape changes, changes of the shape of the

structural boundary must be translated into changes of the interior of the mesh.

The two most commonly used approaches to account for mesh changes during a shapeoptimization are the basis vector approach and the perturbation vector approach. Bothapproaches refer to the definition of the structural shape as a linear combination ofvectors.



Using the basis vector approach, the structural shape is defined as a linear combinationof basis vectors. The basis vectors define nodal locations.

i ix DV BV

Where, x is the vector of nodal coordinates, BVi is the basis vector associated to the design

variable DVi.

Using the perturbation vector approach, the structural shape change is defined as alinear combination of perturbation vectors. The perturbation vectors define changes ofnodal locations with respect to the original finite element mesh.

0 i ix X DV PV

Where, x is the vector of nodal coordinates, X0 is the vector of nodal coordinates of the

initial design, PVi is the perturbation vector associated to the design variable DVi.

The initial nodal coordinates are those defined with the GRID entity. The perturbationvectors are defined on the DVGRID statement, which is referenced by the design variableentity DESVAR.

If a discrete design variable is desired, a DDVAL bulk data entry needs to be referenced onthe DESVAR bulk data entry for the design variable values.

Note: In OptiStruct, only the perturbation vector approach isavailable. The DVGRID cards must contain perturbationvectors.




Free-shape optimization uses a proprietary optimization technique developed by AltairEngineering Inc., wherein the outer boundary of a structure is altered to meet with pre-defined objectives and constraints. The essential idea of free-shape optimization, and whereit differs from other shape optimization techniques, is that the allowable movement of theouter boundary is automatically determined, thus relieving you of the burden of definingshape perturbations.

Free-shape design regions are defined through the DSHAPE bulk data entry. Design regionsare identified by the grids on the outer boundary of the structure (the edge of a shellstructure or the surface of a solid structure). These grids are listed on the DSHAPE entry.

Free-shape optimization allows these design grids to move in one of two ways:

1. For shell structures; grids move normal to the surface edge in the tangential plane.

2. For solid structures; grids move normal to the surface.

During free-shape optimization, the normal directions change with the change in shape of thestructure, thus, for each iteration, the design grids move along the updated normals.

Defining Free-shape Design Regions

Ideally, free-shape design regions should be selected where it can be assumed that theshape of the structure is most sensitive to the concerned responses. For example, it wouldbe appropriate to select grids in a high stress region when the objective is to reducestress.

Free-shape design regions should be defined at different locations on the structure where itis desired for the shape to change independently. For solid structures, feature lines oftendefine natural boundaries for free-shape design regions. Containing any feature linesinside a free-shape design region should be avoided unless the intention is to smooth thefeature lines during an optimization. Likewise for a shell structure, sharp corners shouldnot be contained inside a free-shape design region unless the intention is to smooth outsuch corners.

The DSHAPE card identifies the design region through the GRID continuation card, shownhere:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

GRID GID1 GID2 GID3 GID4 GID5 GID6 GID7

GID8 GID9 … …



A free-shape design region is defined on thecurved edge of the plate by selecting theedge grids; the grids are free to move in thenormal direction on the tangential plane.

A free-shape design region is defined on asurface of the solid structure by selectingthe face surface grids; the grids are free tomove normal to the surface.

Free-shape Parameters

The five parameters that affect the way in which the free-shape design region deforms arethe direction type, the move factor, the number of layers for mesh smoothing, themaximum shrinkage, and the maximum growth.

Direction Type

This provides a general constraint on the direction of the movement of the free-shapedesign region. It is defined on the PERT continuation line of the DSHAPE entry in theDTYPE field, as shown:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

PERT DTYPE

MVFACTOR NSMOOTH MXSHRK MXGROW SMETHOD

NTRANS

DTYPE has three distinct options:

1. GROW – grids cannot move inside of the initial part boundary.

2. SHRINK – grids cannot move outside of the initial part boundary.

3. BOTH – grids are unconstrained.



GROW SHRINK BOTH

Undeformed

Deformed

Move Factor

The maximum allowable movement in one iteration of the grids defining a free-shapedesign region is specified as:

MVFACTOR* mesh_size

where "mesh_size" is the average mesh size of the design region defined in the sameDSHAPE card.

MVFACTOR is defined on the PERT continuation line of the DSHAPE entry.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

PERT DTYPE MVFACTOR

NSMOOTH

MXSHRK

MXGROW SMETHOD

NTRANS

The default value of MVFACTOR is 0.5. A smaller MVFACTOR will make free-shapeoptimization run slower but with more stability. Conversely, a larger MVFACTOR will makefree-shape optimization run faster but with less stability.



MVFACTOR affects the maximum movement in one iteration.

Undeformed shape

Shape at iteration 1 with MVFACTOR = 0.5 (default)

Shape at iteration 1 with MVFACTOR = 1.0

Number of Layers for Mesh Smoothing

With free-shape optimization, internal grids adjacent to those grids defining the designregion are moved to avoid mesh distortion. The number of layers of grids to be included inthe mesh smoothing buffer may be defined by the NSMOOTH field on the PERTcontinuation line of the DSHAPE entry.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

PERT DTYPE MVFACTOR

NSMOOTH

MXSHRK

MXGROW

SMETHOD

NTRANS

The default value of NSMOOTH is 10. A larger NSMOOTH will give a larger smoothingbuffer, and consequently will work better in avoiding mesh distortion; however, it willresult in a slower optimization.

NSMOOTH=5, 5 layers of grids move alongwith the design boundary.

NSMOOTH=1, only 1 layer of grids movealong with the design boundary.

Maximum Shrinkage and Growth

The maximum shrinkage and growth provide a simple way to limit the total amount ofdeformation of the free-shape design region. These parameters are defined on the PERTcontinuation line of the DSHAPE entry.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

PERT DTYPE

MVFACTOR

NSMOOTH

MXSHRK

MXGROW

SMETHOD

NTRANS



The design region is offset to form two barriers; MXSHRK is the offset in the shrinkagedirection and MXGROW is the offset in the growth direction. The design region is thenconstrained to deform between these two barriers.

Deformation space defined by the maximum growing/shrinking distance

For more details and an example, refer to the section on the Mesh Barrier Constraintbelow.

Additional treatment to grids in the Transition Zone

When the entire surface or edge of a system is not a design zone and both design and non-design regions exist adjacent to one another, a transition zone can be defined usingNTRANS which helps to smooth out the transition. Sharp changes can occur in the designregion during optimization and the sections of the design region closest to the non-designregion are designated as a transition zone where the corresponding location of theadjacent non-design region is taken into consideration allowing for a smoother transitionfrom the design to non-design region.

NTRANS defines the number of design grid layers in the transition zone to non-design area,where additional treatment will be applied to produce smooth transition.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

PERT DTYPE

MVFACTOR

NSMOOTH

MXSHRK

MXGROW

SMETHOD

NTRANS



Defining the Transition Zone grid points for a smooth transition between Design and Non-Design regions(NTRANS=3)

The resulting optimized design will incorporate the effect of non-design regions whilemoving the transition zone grid points to achieve a smoother final design. The threeregions illustrated in the figure above consist of the following highlighted nodes:

The non-design nodes (marked by yellow circles), which do not move duringFreeshape optimization.

The design nodes are separated into two groups:

- Design nodes in transition zone (highlighted nodes enclosed by red circles, definedby NTRANS=3)

- Design nodes that are NOT in the transition zone (highlighted nodes enclosed by ablack circle)

The design nodes in the transition zone will be adjusted during Free-shape optimization tobuild a smooth transition between “(1) non-design nodes” and “(3) Design nodes that areNOT in the transition zone”. Otherwise, you may get discontinuous or sharp sections, whichcan be explained in the illustration below.



Defining the Transition Zone grid points for a smooth transition between Design and Non-Design regions(NTRANS=3)

Constraints on Grids in the Design Region

It is possible to identify additional constraints on certain grids in free-shape design regions. Three types of constraints are available for specified grids as defined by CTYPE# on theGRIDCON continuation line of the DSHAPE entry:

1. FIXED – grid cannot move due to free-shape optimization.

2. VECTOR – grid is forced to move along the specified vector.

3. PLANAR – grid is forced to remain on a plane for which the specified vector defines thenormal direction.

Note: VECTOR is used to constrain a grid to move along aline, thus it makes no difference by rotating the vectorby 180 degrees.

Constraints are defined on the GRIDCON continuation line as follows:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

GRIDCON

GCMETH GCSETID1 / GDID1

CTYPE1 CID1 X1 Y1 Z1

GCMETH GCSETID2 / GDID2

CTYPE2 CID2 X2 Y2 Z2



Example Showing CTYPE = VECTOR

This example demonstrates a simple case where it is necessary to use the "DIR" constrainttype to force grids to move in a predefined direction.

A free-shape optimization is performed on a quarter model of a rectangular plate with ahole, shown here:

The curved edge is the free-shape design region. Without any constraints on the free-shape design region, the grids at the ends of the curved edge do not move exactly alongthe line of the straight edge, but move slightly outward, as shown here:

In order to prevent this phenomenon, the grids at the ends of the curved edge (shown inyellow below) are both constrained to move along the vector indicated by the red arrows.



Using these constraints - corner grids moving along the constrained direction - the grids atthe ends of the curved edge now move as desired, along the line of the straight edge, asshown here:

Example showing CTYPE = PLANAR

In this example, the total volume of a cantilever beam is to be minimized subject to adisplacement constraint in the loading direction at the free-end of the beam. The model isshown here:

Two free-shape design regions are defined in this example. Both of the vertical sides ofthe beam are selected as design regions and a free-shape optimization is performed.



Without any constraints on the free-shape design region, the top and bottom surfaces ofthe beam do not remain strictly on the X-Z plane.

To ensure that the top and bottom surfaces remain on the X-Z plane, the grids along theedges of the design regions DSHAPE1 and DSHAPE2 are constrained to move only on theX-Z plane.



Using these constraints – constrained grids moving only on the X-Z plane – the top andbottom surfaces of the beam remain on the X-Z plane as desired.

1-plane Symmetry Constraint

It is often desirable to produce a symmetric design. Even if the loads and boundaryconditions are perfectly symmetric, there is no guarantee that the resulting design will beperfectly symmetric. In order to ensure a symmetric design, a symmetry constraint mustbe defined. An additional advantage of this constraint is that it will produce symmetricdesigns regardless of the initial mesh, loads or boundary conditions.

The 1-plane symmetry constraint is defined on the PATRN continuation line:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

PATRN TYP AID/XA YA ZA FID/XF YF ZF



Example Showing 1-plane Symmetry Constraints in 2-dimensions

In this example, the objective is to minimize the total volume subject to a stress constraintusing free-shape optimization. Results are shown with and without symmetry constraints.

2-D model showing free-shape design grids

Result without symmetry constraint Result with symmetry constraint (XZ plane)

Example Showing 1-plane Symmetry Constraints in 3-dimensions

In this example, the objective is to minimize the compliance subject to a volume constraintusing free-shape optimization. Results are shown with and without symmetry constraints.

3-D Model showing free-shape design grids



Result without symmetry constraint Result with symmetry constraint (XZ plane)

Extrusion Constraint

It is often desirable to produce a design with a constant cross-section along a given path,particularly in the case of parts manufactured by an extrusion process. By using extrusionmanufacturing constraints with free-shape optimization, constant cross-section designs canbe attained for solid models (regardless of the initial mesh, loads or boundary conditions).

The extrusion constraint is defined on the EXTR continuation line:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

EXTR ECID XE YE ZE

Two types of extrusion path are available for free-shape optimization – straight line andcircular.

Example Showing Extrusion Constraint Along a Straight Line

The FE model, optimization problem and design variables definition are the same as in theprevious example, so the result without the extrusion constraint is the same as shownabove. The result with the extrusion constraint (straight line) is shown here.

Result with extrusion path (along x-axis)



Example Showing Extrusion Constraint Along a Circular Path

In this example, the objective is to minimize the von Mises stress subject to a volumeconstraint using free-shape optimization. A circular extrusion path is defined using acylindrical coordinate system ( direction). Results are shown with and without extrusionconstraints (circular).

Model showing free-shape design grids

Result without extrusion pathResult with extrusion path (circular)

Draw Direction Constraint

In the casting process, cavities that are not open and lined up with the sliding direction ofthe die are not feasible. Draw direction constraints may be defined for the design regionso that the optimized shape will allow the die to slide in a prescribed direction. Only asingle die is considered for each design region (defined in each DSHAPE card), and non-design regions will not be considered for this constraint.

The draw direction constraint is defined on the DRAW continuation line:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

DRAW DTYP DAID/XDA

YDA ZDA DFID/XDF

YDF ZDF



Example Showing Draw Direction Constraint

The FE model, optimization problem and design grids definition are the same as those inthe example showing 1-plane symmetry constraints in 3 dimensions. Results with drawdirection constraint are shown here.

Result with draw direction constraint (along Y-axis)

Example Showing Combination of 1-plane Symmetry and Draw DirectionConstraints

The FE model, optimization problem and design grids definition are the same as those inthe example showing 1-plane symmetry constraints in 3 dimensions. Results with 1-planesymmetry and draw direction constraints are shown here.

Result with both draw direction constraint (Y-axis) and 1-plane symmetry constraint (XY-plane)

Side Constraints

Similar to the maximum shrinkage and growth parameters as defined on the PERTcontinuation line, it is possible to limit the extent of the total deformation of the designregion by way of side constraints. Side constraints allow the deformation space to bedefined as a coordinate range; i.e. between (x1, y1, z1) and (x2, y2, z2). These ranges

may be with reference to rectangular, cylindrical or spherical systems.



Example Showing Side Constraints

In this example, the objective is to minimize the von Mises stress subject to a volumeconstraint using free-shape optimization. Results are shown with and without sideconstraints.

Model showing side constraints defined by the radii R1 and R2 (1-direction of cylindrical system)

Result without side constraints Result with side constraints

Mesh Barrier Constraints

Aside from shrinkage and growth parameters and side constraints, a more generalcapability to limit the extent of the total deformation of the design region is available byway of defining a mesh barrier constraint. The mesh barrier is composed of special shellelements (BMFACE), and in order to keep computational effort to a minimum, as fewelements as possible should be used in its definition.

The mesh barrier is defined on the BMESH continuation line.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

BMESH BMID



Example Showing Mesh Barrier Constraint

The FE model, optimization problem and design grids definition are the same as those inthe example showing 1-plane symmetry constraints in 3 dimensions. A mesh barrier isadded (large red tria elements).

Model with mesh barrier

Result without mesh barrier constraint Result with mesh barrier constraint

Result combining mesh barrier constraint and 1-plane symmetry constraint

From the results, you can see how the mesh barrier constrains the model deformation, butif the mesh barrier is not big enough, the design region deformation is unconstrainedbeyond its limits.



Example Showing Maximum Shrinkage and Growth Parameters

The FE model, optimization problem and design grids definition are the same as those inthe example showing 1-plane symmetry constraints in 3 dimensions. In addition,maximum shrinkage and growth parameters (2.0) and a 1-plane symmetry constraint (XZ-plane), are defined.

Result with shrinkage and growth parameters.Max. growth distance = 2.0Max. shrinkage distance = 2.0

Result with shrinkage and growth parameters and 1-plane symmetry constraint (XZ-plane).Max. growth distance = 2.0Max. shrinkage distance = 2.0

Additional Comments

1. In the case where multiple constraints are defined for the same design region, while theoptimizer tries its best to satisfy all the different constraints, it is possible that it maynot be able to coordinate all these constraints.

2. It should be pointed out that if constraints like mesh barrier, maximum growth andshrinkage, or side constraints are applied to avoid of interference between structuralparts, you should define the constraints in such a way that clearance is guaranteedunder manufacturing tolerance and structural deformation. In other words, the barriersurface should contain an offset from the potentially interfering parts.



Manufacturing Constraints

The following optimization features can be found in this section:

Manufacturability for Topology Optimization

Manufacturability for Topography Optimization

Manufacturability for Free-size Optimization




Manufacturability for Topology Optimization

A concern in topology optimization is that the design concepts developed are very often notmanufacturable. Another problem is that the solution of a topology optimization problem canbe mesh dependent, if no appropriate measure is taken.

OptiStruct offers a number of different methods to account for manufacturability whenperforming topology optimization:

Member Size Control

Draw Direction Constraints

Extrusion Constraints

Pattern Repetition

Pattern Grouping



Member Size Control for Topology Optimization

Member size control allows you some control over the member size in the final topology andthe resulting degree of simplicity of the final design. This feature may be added one of thetwo ways described below.

1. The DOPTPRM card:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

DOPTPRM MINDIM VALUE

Here, only the preferred minimum diameter (width in 2-D) of members may be defined asthe VALUE field, following the MINDIM keyword. A global minimum member size isdefined in this way.

2. The DTPL card:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

DTPL ID PTYPE PID1 PID2 PID3 PID4 PID5 PID6

PID7 … … …

MEMBSIZ MINDIM MAXDIM

MINGAP

Here, both the preferred minimum, MINDIM, and the maximum, MAXDIM, diameter ofmembers may be defined on the MEMBSIZ continuation line. Member size dimensions canbe defined differently for each DTPL in this way.

Minimum Member Size Control

Although minimum member size control penalizes the formation of small members, resultsthat contain members significantly under the prescribed minimum member size can still beobtained. This is because a small member in the structure can be very important to the loadtransmission and may not be removed by penalization. Minimum member size controlfunctions more as a quality control than a quantity control.

A discrete solution is achieved in two iterative steps. The first step converges to a solutionwith a large number of semi-dense elements. The second step tries to refine this solution toa solution with fully dense members. Each step consists of a number of iterations. The firststep consists of two entire convergence phases - the first run with the initial discretenessvalues (defined by DISCRETE and DISCRT1D parameters on the DOPTPRM bulk data entry),followed by a run with the discreteness values increased by 1.0. This procedure isimplemented in order to achieve a solution with clearly defined members. If this step couldnot create a solution with clearly defined members, the preferred minimum member size willnot be preserved in the second step. In which case, you need to increase the discretenessparameters and/or reduce the convergence tolerance (defined by the OBJTOL parameter onthe DOPTPRM bulk data entry) to improve the solution of the first phase. The defaultdiscreteness is set to 1.0 for 1-D elements, plates and shells, and 2.0 for 3-D solids.



In general, once MINDIM is activated, checkerboarding is controlled by the methods appliedfor this feature, eliminating the need for the CHECKER parameter. In rare circumstances,checkerboards may still be introduced in the second phase described above for 3-D solids. Ifthis happens, an additional checkerboard control algorithm can be activated with theMMCHECK parameter. (The CHECKER and MMCHECK parameters are defined using theDOPTPRM bulk data entry).

The use of this card will assure a checkerboard-free solution, although with the undesiredside effect of achieving a solution that involves a large number of semi-dense elements,similar to the result of setting CHECKER equal to 1. Therefore, use this card only when it isnecessary.

It is recommended that MINDIM be at least 3 times, and no greater than 12 times, theaverage element size for all elements referenced by that DTPL (or all designable elementswhen defined on DOPTPRM). The average element size for 2-D elements is calculated as theaverage of the square root of the area of the elements, and for 3-D elements, as the averageof the cubic root of the volume of the elements.

This recommendation is enforced when combined with other manufacturing constraints, andif the defined MINDIM is less than this value, it will be reset to a default value equal to 3times the average element size. Similarly, if the defined MINDIM is larger than 12 times theaverage element size, it will be reset to a value equal to 12 times the average element size. This limit has been set to trim memory requirements that can become too large as a result ofhaving to keep track of a much larger number of elements needed to satisfy the MINDIMconstraint. In structures where the mesh is aligned with the draw or extrusion direction,setting MTYP as ALIGN on the MESH continuation line of the DTPL card may circumvent thisconstraint.

The following examples demonstrate significant improvement in the manufacturability ofresults through the use of minimum member size control:

Michell-truss Example

MBB-Beam Example

Arch Example

3-D Bridge Model Example

Maximum Member Size Control

Maximum member size control penalizes the formation of large members. The control is notdirectional, meaning that if the thickness of a member is less than MAXDIM in any direction,this constraint is satisfied. This reflects the need to control the rib thickness of castingparts.

MAXDIM must be at least twice MINDIM, and hence the minimum mesh requirement is thatMAXDIM has to be at least 6 times the average element size for all elements referenced bythat DTPL. This constraint is strongly enforced and an error termination will occur when thiscriteria is not met. In addition, MAXDIM should be less than half the width of the thinnestpart of the design region.

Based on the constraints mentioned above, a fine mesh is required to achieve good resultswith this manufacturing constraint.



It is to be noted that use of the maximum member size control induces further restriction ofthe feasible design space and should therefore only be used when it is truly desirable. Alsonote that this feature is a new research development, and the techniques are still undergoingimprovement. An undesired side effect that has been noticed for some examples is that itmight result in more intermediate density in the final solution. Therefore, it is recommendedthat this feature be used sparingly until the technology becomes more robust.

While MAXDIM also enforces a spacing of members of the same dimension, the maximumreachable volume fraction is 0.5. For problems involving constraints on structural responses,this could interfere with constraint satisfaction. It is strongly recommended that the behaviorof the design problem be studied without MAXDIM first in order to determine if the use ofMAXDIM would be advantageous, and if the target volume allows for it to be applied.

The following examples demonstrate the impact of maximum member size control to thedesign outcome.

Example 1: Engine Bracket

Engine Bracket Design with Draw Direction Constraint



Engine Bracket Design with Draw Direction and Maximum Member Size Constraints

Example 2: Steering Wheel Bracket

Steering Wheel Bracket Design with Draw Direction Constraint



Steering Wheel Bracket Design with Draw Direction and Maximum Member Size Constraints



Draw Direction Constraints for Topology Optimization

In the casting process, cavities that are not open and lined up with the sliding direction of thedie are not feasible. Designs obtained by topology optimization often contain cavities thatare not viable for casting. Transformation of such a design proposal to a manufacturabledesign could be extremely difficult, if not impossible. In some cases where thistransformation is made, the likelihood of severely affecting the design optimality is high.

OptiStruct allows you to impose draw direction constraints so that the topology determinedwill allow the die to slide in a given direction. These constraints are defined using the DTPLcard. Different constraints can be applied to different structural parts, specified by PSOLIDIDs. There are two DRAW options available. The option 'SINGLE' assumes that a single diewill be used and it slides in the given drawing direction. The bottom surface of theconsidered casting part is the predefined contra part for the die. The option 'SPLIT' impliesthat two dies splitting apart in the given draw direction will be used to cast the part describedin this DTPL card. The splitting surface of the two dies is optimized during the optimizationprocess.

It is often a requirement of certain designs that no through – holes exist. These holes can beprevented from forming in the direction of the draw through use of the ‘NO HOLE’ option. This parameter is also defined on the DTPL card. With ‘NO HOLE,’ the topology can onlyevolve gradually from the boundary one layer at a time, and in certain cases, it may takeseveral iterations to remove one layer.

Available with the ‘SINGLE’ draw option is a stamping or sheet metal manufacturingconstraint. This option forces the evolution of 3-D shell interpretable structure from a 3-Ddesign domain. This allows the design of 2-D shell or stamped parts from a 3-D designdomain allowing greater design flexibility. The ‘STAMP’ option is also specified on the DTPLcard along with a thickness value that represents the desired thickness of the resulting shellor stamped part.

A casting may contain a non-designable region in addition to a designable region. Thesenon-designable regions must be defined as obstacles for the casting process on the sameDTPL card. This preserves the casting feasibility of the final structure.

Also note that there is a default minimum member size for use with draw directionconstraints. This is determined internally to be three times the average mesh size of therelevant components. Therefore, the mesh density of the model and the target volumefraction should be chosen so that enough material is available to fill members of the defaultminimum size. You can specify a desired minimum member size for each design part definedby a DTPL card. This value must be bigger than the default value or else it will be replacedby the default value.

Example 1: Beam under Torsion

The considered beam is clamped on one end and loaded with a pair of twisting forces onthe free end. The finite element model is shown in Figure 1.1. The design problem is tominimize the compliance with a volume fraction constraint of 0.3. The final design withoutdraw direction constraints is shown in Figure 1.2. The chosen draw direction is along theZ-axis. The designs with the options 'SINGLE’ and 'SPLIT' for draw direction constraint areshown in Figures 1.3 and 1.4, respectively.



Figure 1.1: Finite element model of the beam under torsion

Figure 1.2: Design without draw direction manufacturing constraint



Figure 1.3: Design with draw direction Z and die option 'SINGLE'

Figure 1.4: Design with draw direction Z and die option 'SPLIT'

As expected, the result without manufacturing constraints is a tube-like structure that isindeed the optimal topology for torsion load. However, this design does not permit thesliding of the die in the Z direction. The result that allows the sliding of the die for castingis not very intuitive, it forms a periodical X pattern to cross the pair of twist loads untilthey reach the supported end. Significantly more material at the crossing point reflectsthe doubled shear force at this point. Compared to an upward facing C channel solution,the cross pattern has the advantage that the stress is periodical in every X cell, thuseliminating higher order influence of the span of the beam for any solution that has systemlevel bending action.

Example 2: Engine Bracket

The example shown below is an engine bracket model of a car. The finite element modelof the design domain is shown in Figure 2.1, in which 9046 elements are used and thedesign domain is shown in blue color. Six load cases were considered, which reflect thefollowing driving and service status: 1) start; 2) backwards; 3) into a pothole; 4) out of a



pothole; 5) loads from an attaching part; and 6) loads during engine transport. The finaltopology that allows a single die sliding upwards is shown in Figure 2.2. The design thatallows two dies to slide up and down, respectively, is shown in Figure 2.3.

Figure 2.1: Finite element model of a engine bracket

Figure 2.2: Design with draw direction Z and die option 'SINGLE'

Figure 2.3: Design with draw direction Z and die option 'SPLIT'



Example 3: Compressor Mounting Bracket

In this example, a topology optimization is run on a compressor mounting bracket, and theeffects of the ‘NO HOLE’ manufacturing constraint will be showcased. The finite elementmodel is shown in Figure 3.1. Regions in red indicate non-design space and the region inblue indicates design space. Four different loading conditions were consideredrepresenting operating conditions, and the model was built up with approximately 90,000elements. The design problem was formulated to minimize the compliance as theobjective function, with a constraint on the design volume fraction.

Figure 3.2 shows the design proposal for the compressor mounting bracket without the useof the ‘NO HOLE’ manufacturing constraint. As seen in the image, the design containsthrough-holes.

Figure 3.3 on the other hand, shows the design proposal of the bracket with the use of the‘NO HOLE’ constraint. In this case now, the resulting design proposal does not contain anythrough-holes.

Figure 3.1: Finite element model representing the design and non-design spaces of the compressor mountingbracket

Figure 3.2: Design proposal without the ‘NO HOLE’ option



Figure 3.3: Design proposal with the ‘NO HOLE’ option

Example 4: Automotive Bracket

The bracket in this example was designed incorporating the ‘NO HOLE’ constraint alongwith the ‘STAMP’ constraint. The goal of the study was to generate a design proposalwithout any through-holes, while at the same time being interpretable as a sheet metaldesign. The ‘STAMP’ constraint here forces the formation of a 3-D shell interpretablestructure representing a sheet metal design. Four subcases representing four differentloading conditions were considered and the model was comprised of approximately 20,000elements. The optimization problem was formulated to minimize the weighted compliance(one compliance value per subcase) for a constrained design volume fraction. Thisessentially results in evolving the stiffest design for a given amount of material.

Figure 4.1 represents the finite element model of the design and non-design spaces of thebracket. The regions in red are the non-design regions and the region in blue is the designspace.

Figure 4.2 is the design proposal without the consideration of the ‘STAMP’ and ‘NO HOLE’manufacturing requirements. While it is possible to cast such a design, stamping such apart is not feasible.

Figures 4.3 and 4.4 showcase the design proposal after incorporating the ‘STAMP’ and ‘NOHOLE’ manufacturing constraints. The ‘NO HOLE’ constraint prevents the formation of anythrough-holes in the design space and helps keep a continuous shell layout, while the‘STAMP’ constraint leads to the formation of a uniform thickness design proposal. Thethickness is defined along with the ‘STAMP’ constraint and represents the desired thicknessof the sheet metal part. From this proposal, it is now possible to interpret the design as asheet metal or stamped part.



Figure 4.1: Finite element model representing the design and non-design spaces of the bracket

Figure 4.2: Design proposal without ‘STAMP’ and ‘NO HOLE’

Figure 4.3: Design proposal with ‘STAMP’ and ‘NO HOLE’ (view 1)



Figure 4.4: Design proposal with ‘STAMP’ and ‘NO HOLE’ (view 2)



Extrusion Constraints for Topology Optimization

In some cases, it is desirable to produce a design characterized by a constant cross-sectionalong a given path, particularly in the case of parts manufactured through an extrusionprocess. By using extrusion manufacturing constraints in topology optimization, constantcross-section designs can be attained for solid models – regardless of the initial mesh,boundary conditions or loads.

Extrusion constraints can also be used for the conceptual design study of structures that donot specifically need to be manufactured using an extrusion procedure. Those requirementscan be regarded as specific geometric constraints and can be used for any design that desiressuch characteristics. For instance, it might be desirable to have ribs going through the entiredepth of a solid domain.

As with other manufacturing constraints, extrusion constraints can be applied on acomponent level, and can be defined in conjunction with minimum member size control usingthe DTPL card.

Setting up the Problem

Extrusion constraints can be applied to domains characterized by non-twisted cross-sections(left figure) or twisted cross-sections (right figure) by using the NOTWIST or TWISTparameters respectively in the ETYP field. The structure is non-twisted when the localcoordinates systems associated with each cross-section, projected onto a reference plane,remain parallel to each other.

Defining the Extrusion Path

It is necessary to define a ‘discrete’ extrusion path by entering a series of grids in the EPATH1field. The curve between these grids is then interpolated using parametric splines. Theminimum amount of grids depends on the complexity of the extrusion path. Only two gridsare required for a linear path, but it is recommended to use at least 5-10 grids for morecomplex curves.



In the example above, four grids are used to define the extrusion path (left figure). As youcan see, the path computed by OptiStruct is inaccurate. To obtain a more accurateapproximation, more grids are included in the extrusion path (right figure).

For twisted cross-sections, a secondary extrusion path needs to be defined in a similarmanner through the EPATH2 field.

Example 1

In this example, a curved beam is considered to be a rail over which a vehicle is moving. Both ends of the beam are simply supported. A point load applied over the length of therail as five independent load cases simulates the movement of the vehicle. The objectiveis to minimize the sum of the compliances, and the material volume fraction is constrainedat 0.3. The rail should be manufactured through extrusion. The 13 grids represented asblack dots on the right figure define the extrusion path.

The optimized topologies without and with extrusion constraints are shown below. Reanalyzing the final designs without penalty for intermediate density, the compliances forthese two designs are 29.9396 and 37.4377 respectively, which implies a 20% loss inperformance due to extrusion constraints. The extruded design represents a cleanproposal that requires little refinement. On the other hand, the design obtained withoutmanufacturing constraints may require significant modifications that could cause efficiencyloss in performance.



Example 2

In this example, a "stairs" shaped structure is submitted to two lateral pressure loadsdefined in two separate subcases. The objective is to minimize the sum of the compliancesunder both load cases. The extrusion path is defined as a straight line parallel to theglobal Y-axis. The cross-section of the finite elements model along that path is notconstant.

Clearly, this type of structure is not suitable to be manufactured through an extrusionprocess. However, extrusion constraints can be applied to obtain a manufacturable designcharacterized by ribs going through the entire depth of the structure. The optimizeddesign gives a good idea of the layout of the resulting stiffening panels.



Example 3

This example illustrates how extrusion constraints can be used to develop commoncomponents in different areas of a structure. The extrusion path can be defined through asolid mesh that is not continuous.



Pattern Repetition for Topology Optimization

Pattern repetition is a technique that allows different structural components to be linkedtogether so as to produce similar topological layouts.

To achieve this goal, a master DTPL card needs to be defined, followed by any number ofslave DTPL cards which reference the master. The master and slave components are relatedto each other through local coordinate systems, which are required, and through scalingfactors, which are optional.

Other manufacturing constraints, such as minimum or maximum member size, draw directionconstraints or extrusion constraints, can be applied to the master DTPL card. Theseconstraints will then automatically be applied to the slave DTPL card(s) as described in thenext sections.

The following procedure should be followed to set up pattern repetition:

1. Create a master DTPL card.

2. Apply other manufacturing constraints as needed.

3. Define the local coordinate system associated to the master DTPL card.

4. Create a slave DTPL card.

5. Define the local coordinate systems associated to the slave DTPL card.

6. Apply scaling factors as needed.

7. Repeat steps 4-6 for any number of slave DTPL cards.

Local Coordinates Systems

Local coordinates systems are generated by providing four points. These points can bedefined either by entering explicit coordinates or by referencing existing grids, as follows:

1. CAID defines the anchor point for the local coordinates system.

2. CFID defines the direction of the X-axis.

3. CSID defines the XY plane and indicates the positive sense of the Y-axis.

4. CTID indicates the positive sense of the Z-axis.

The definition of the fourth point allows for both right-handed and left-handed coordinatesystems, which facilitates the creation of reflection patterns.

Right-handed coordinates system Left-handed coordinates system



Alternatively, local coordinate systems can be defined by referencing an existing rectangularcoordinate system in the CID field, and by defining an anchor point in the CAID field.

Note that if the fields defining CFID, CSID, CTID, and CID are left blank, then the globalcoordinates system is used by default. The anchor point CAID, however, is always required.

Scaling Factors

Scaling factors in the X, Y, and Z directions can be defined for each slave DTPL card. Thesefactors are always related to the local coordinate system. By playing with the localcoordinate systems and the scaling factors, a wide range of effects can be obtained asillustrated with the figure below.

Pattern Repetition with Draw Direction Constraints

Draw direction constraints can be applied simultaneously with pattern repetition. To achievethis, simply define the draw direction for the master DTPL card, and the draw direction forthe slave(s) will automatically be generated based on the local coordinate system.

Even if some components are not naturally identical, the optimized design for eachcomponent will still satisfy the draw direction constraints. In particular, if differentcomponents contain different obstacles, the combination of all obstacles will always beconsidered.

Pattern Repetition with Extrusion Constraints

Extrusion constraints can also be used in conjunction with pattern repetition. This allows forcreating parts which have identical cross-sections. The components do not need to beidentical in a three-dimensional sense; each part can have its own extrusion path.

If the components have different extrusion paths, these paths have to be defined explicitly oneach DTPL card. However, if the components have identical extrusion paths, the paths forthe slave(s) will automatically be computed based on the master's extrusion path.



Example 1

This example shows how pattern repetition may be used to generate the same topology indifferent parts. The first figure shows two similar blocks loaded in two different ways. Theoptimization problem is to minimize the compliance with 30 percent volume fraction.

If pattern repetition is not used, you can clearly see that the optimized topologies aredifferent, as shown in the figures below:

Same view as in the first figure.



Viewed from behind showing that the turquoise block is hollowed out.

Using pattern repetition, both of the loads on the master (the left hand block in first figure)and the loads on the slave are taken into account, and the optimized topology is repeatedfor both blocks, as shown below:

Example 2

This example shows a simplified wing model.



The internal wing structure consists of 2 spars and 11 ribs. In this example, each rib issubdivided into three sections; the nose section, the center section and the tail section,and each of these sections is chosen as a topology design region.

The optimization problem is to minimize compliance for 30 percent of the design volumefraction. Here you see the optimized topology when each region is independent.



Pattern repetition is used to group all of the noses together, all of the centers together andall of the tails together, resulting in 3 master pattern definitions, each with 10 slavedefinitions. Notice how different meshes are used for each rib; pattern repetition is meshindependent. Also the wing tapers, so the outboard ribs are shorter and thinner than theinboard ribs, scaling is defined for the slaves so that the pattern fits in the design space.

The optimized topology achieved using pattern repetition is shown below, and you canclearly see how the same topological layout is repeated for each rib.



Pattern Grouping for Topology Optimization

Pattern grouping is a feature that allows you to define a single part of the domain that shouldbe designed in a certain pattern.

Planar Symmetry

It is often desirable to produce a design that has symmetry. Unfortunately, even if thedesign space and boundary conditions are symmetric, conventional topology optimizationmethods do not guarantee a perfectly symmetric design.

By using symmetry constraints in topology optimization, symmetric designs can be attainedregardless of the initial mesh, boundary conditions, or loads. Symmetry can be enforcedacross one plane, two orthogonal planes, or three orthogonal planes. A symmetric mesh isnot necessary, as OptiStruct will create variables that are very close to identical across theplane(s) of symmetry.

To define symmetry across one plane, it is necessary to provide an anchor grid and areference grid. The first vector runs from the anchor grid to the reference grid. The plane ofsymmetry is normal to that vector and passes through the anchor grid.

To define symmetry across two planes, a second reference grid needs to be provided. Thesecond vector runs from the anchor grid to the projection of the second reference grid ontothe first plane of symmetry. The second plane of symmetry is normal to that vector andpasses through the anchor grid.



To define symmetry across three planes, no additional information is required, other than toindicate that a third plane of symmetry is to be used. The third plane of symmetry isperpendicular to the first two planes of symmetry, and also passes through the anchor grid.

Uniform Element Density

Pattern grouping also provides the possibility to request a uniform element densitythroughout selected components.

This pattern group ensures that all elements of selected components maintain the sameelement density with respect to one another.

Cyclical Symmetry

Cyclical symmetry can also be defined through the use of pattern grouping.

With cyclical pattern grouping, the design is repeated about a central axis a number of timesdetermined by you. Furthermore, the cyclical repetitions can be symmetric within



themselves. If that option is selected, OptiStruct will force each wedge to be symmetricabout its centerline.

To define cyclical symmetry, it is necessary to provide an anchor grid and a reference grid. The axis of symmetry runs from the anchor grid to the reference grid. It is also necessary tospecify the number of cycles; the repetition angle will be automatically computed.

To add planar symmetry within each wedge, a second reference grid needs to be provided. The plane of symmetry is determined by the anchor grid and the two reference grids.

Pattern Grouping with Draw Direction Constraints

Draw direction constraints can be combined with pattern grouping.

As illustrated below for one-plane symmetry, the sense of the vector defining the symmetryalso determines the primary side of the design space to which the draw direction applies. The draw direction for the secondary side of the design space is automatically computed.



Vector defining the symmetry Vector defining the draw direction Primary domain Plane of symmetry Secondary domain Vector defining the draw direction for the secondary domain (automatically created)

The same reasoning applies for two-plane and three-plane symmetries, as well as for cyclicalsymmetry.

Caution should be used in order to achieve manufacturable designs. With cyclical symmetry,for instance, the draw direction should be parallel to the axis of symmetry.

Pattern Grouping with Extrusion Constraints

Currently extrusion constraints cannot be used simultaneously with pattern grouping.

Example 1

In this example, a solid block of material is used. The grids located on the rear of theblock (in the YZ plane) are fully constrained. Axial loading is applied to the block's upperedge in the direction of the negative Y-axis. The objective is to minimize the compliancewith a constraint on the volume fraction. Single-die draw direction constraints are appliedin the direction of the positive Z-axis.



The figures below illustrate the results obtained for various symmetry combinations. Asthe loading is not symmetric with respect to the XY and YZ planes, the design is notsymmetrical about these planes when symmetry constraints are not prescribed. Enforcingsymmetry conditions about the XY or YZ planes yields significantly different results.



Example 2

Here, solid elements are used to model a car wheel. The outer layers as well as the boltsare non-designable. Twenty load cases are considered. The objective is to minimize theweighted compliance with a constraint on the volume fraction. Split-die draw directionconstraints are applied in the direction of the X-axis. Cyclical pattern grouping is definedwith planar symmetry within each cycle.



As the results show, a clean and reasonably manufacturable design is achieved. Cyclicalsymmetry is obtained even though the loading is not symmetric.



Combining Pattern Repetition and Pattern Grouping withother Manufacturing Constraints for

Pattern repetition is a feature that allows you to define multiple parts of the model thatshould be characterized by identical or similar designs. Pattern grouping is a feature thatallows you to define a single part of the model that should be designed in a certain pattern.

Pattern repetition and pattern grouping can be used with solid and shell elements. They canalso be applied in conjunction with minimum and maximum member size constraints, withdraw direction constraints, and (to some extent) with extrusion constraints. The followingcombinations are allowed:

Shells

Solids

Simple Draw Extrusion

Patternrepetition

Withoutscaling

Yes Yes Yes Yes

With scaling Yes Yes Yes No

Patterngrouping

1-planesymmetry

Yes Yes Yes No

2-planessymmetry

Yes Yes Yes No

3-planessymmetry

Yes Yes Yes No

Cyclicalsymmetry

Yes Yes Yes No

Pattern grouping can be combined with draw direction constraints, but you should usecaution in order to achieve manufacturable designs.

For extrusion, pattern repetition generates identical cross-sections for differentcomponents. Therefore, scaling is not supported for this combination.



Manufacturability for Topography Optimization

Manufacturing methods can place constraints on the types of reinforcement patternsavailable for a given part. Some examples of this are: channels, which must have acontinuous cross-section; discs, which must be turned on a lathe; and stampings, whichcannot have the die lock conditions.

These constraints can be accounted for in topography optimization by using Pattern GroupingOptions, and a design with a manufacturable reinforcement pattern can be generated.



Pattern Repetition for Topography Optimization

Pattern repetition is a technique that allows different structural components to be linkedtogether so as to produce similar topographical layouts.

To achieve this goal, a master DTPG card needs to be defined, followed by any number ofslave DTPG cards which reference the master. The master and slave components are relatedto each other through local coordinate systems, which are required, and through scalingfactors, which are optional.

Other manufacturing constraints, such as pattern grouping, can be applied to the masterDTPG card. These constraints will then automatically be applied to the slave DTPG card(s).


1. Create a master DTPG card.


3. Define the local coordinate system associated to the master DTPG card.

4. Create a slave DTPG card.

5. Define the local coordinate systems associated to the slave DTPG card.


7. Repeat steps 4-6 for any number of slave DTPG cards.







The definition of the fourth point allows for both right-handed and left-handed coordinatesystems, which facilitates the creation of reflected patterns.

Alternatively, local coordinate systems can be defined by referencing an existing rectangularcoordinate system in the CID field, and by defining an anchor point in the CAID field.



Note that if the fields defining CFID, CSID, CTID, and CID are left blank, then the globalcoordinates system is used by default. The anchor point CAID, however, is always required.

Scaling Factors

Scaling factors in the X, Y, and Z directions can be defined for each slave DTPG card. Thesefactors are always related to the local coordinate system. By playing with the localcoordinate systems and the scaling factors, a wide range of effects can be obtained asillustrated with the figure below.



Pattern Grouping Options for Topography Optimization

There are over 70 pattern grouping options and variations available for topographyoptimization. A summary of the major categories is shown below:

Variablegroupingpattern

PatternOption

Type#

RequiredVectorDefinitions

Description

None - 0 - Variables grouped as points.

One planesymmetry

- 10 One Reflection of variables across one planenormal to first vector.

Two planesymmetry

- 20 Two Reflection of variables across two planes,one normal to the first vector and onenormal to second vector.

Threeplanesymmetry

- 30 Two Reflection of variables across three planes,one normal to first vector, one normal tothe second vector and one perpendicularto both vectors.

Linear - 1 One Variables grouped as lines extending indirection of first vector.

+1 plane 21 Two Reflection of variables across one planenormal to second vector.

+2 planes 31 Two Reflection of variables across two planes,one normal to second vector and oneperpendicular to both vectors.

Circular - 2 One Variables grouped as circles around anchornode lying in a plane normal to firstvector.

+1 plane 12 One Reflection of variables across one planenormal to first vector.

Planar - 3 One Variables grouped as planes extendingnormal to first vector.

+1 plane 13 One Reflection of planes across plane normal tofirst vector.

Radial 2-D - 4 One Variables grouped as rays extendingradially and normal to first vector.




PatternOption

Type#


Description

+1 plane 14 One Reflection of rays across plane normal tofirst vector.

+2 planes 24 Two Reflection of rays across two planes, onenormal to the first vector and one normalto second vector.

+3 planes 34 Two Reflection of rays across three planes, onenormal to first vector, one normal to thesecond vector and one perpendicular toboth vectors.

Cylindrical - 5 One Variables grouped as endless cylindersextending along and centered around firstvector.

Radial 2-D& Linear

- 6 One Variables grouped as a combination ofradial and linear patterns.

+1 plane 26 Two Reflection of radial planes across planenormal to second vector.

+2 planes 36 Two Reflection of radial planes across planenormal to both first and second vectors.

Radial 3-D - 7 - Variables grouped as rays extendingradially outward from anchor node.

+1 plane 17 One Reflection of rays across plane normal tofirst vector.

+2 planes 27 Two Reflection of rays across two planes, onenormal to the first vector and one normalto second vector.

+3 planes 37 Two Reflection of rays across three planes, onenormal to first vector, one normal to thesecond vector and one perpendicular toboth vectors.

Vectordefined

- 8 - Variables grouped along vectors defined bythe draw vectors of the individual nodes.




PatternOption

Type#


Description

+1 plane 18 One Reflection of variables across plane normalto first vector.

+2 planes 28 Two Reflection of variables across two planes,one normal to the first vector and onenormal to second vector.

+3 planes 38 Two Reflection of variables across three planes,one normal to first vector, one normal tothe second vector and one perpendicularto both vectors.

Cyclical* - 40,41 Two Cyclical repetition of variables about axisdefined by first vector.

+1 plane 50,51 Two Reflection of variables across one planenormal to first vector.

+ linear 60,61 Two Cyclically repeated variables grouped aslines extending in direction of first vector.

+ radial 70,71 Two Cyclically repeated variables grouped asrays extending radially and normal to firstvector.

+ radial &linear

80,81 Two Cyclically repeated variables grouped as acombination of radial and linear patterns.

* For cyclical symmetry, the UCYC parameter (field 30) controls the number of repetitions(and thus the repetition angle) for the cycles. If the TYP option selected for cyclicalsymmetry is 40, 50, 60, 70, or 80, the cyclical repetition pattern will be non-reflective. If theTYP option selected for cyclical symmetry is 41, 51, 61, 71, or 81, the cyclical repetitionpattern will be reflective.

These options can be used with shell and solid models to create reinforcement patterns thatobey manufacturing constraints and which conform to the shapes of the parts. Examples ofpattern grouping options are given in the following sections:

Cross-section Optimization of a Spot Welded Tube

Optimization of the Modal Frequencies of a Disc Using Constrained Beading Patterns

Multi-plane Symmetric Reinforcement Optimization for a Pressure Vessel

Shape Optimization of a Stamped Hat Section

Shape Optimization of a Solid Control Arm

Using Topography Optimization to Forge a Design Concept Out of a Solid Block



None

If no variable grouping pattern is selected, OptiStruct will automatically generate circularbead variable definitions throughout the design variable domain as shown below:

TYP = 0: No symmetry



Two Planes

For two planes of symmetry (TYP = 20), the planes of symmetry are defined normal to boththe first and second vectors as shown below. Note that the second grid does not have to bein the plane defined by the first vector, OptiStruct will calculate the second vector byprojecting the second grid (or vector) onto the plane defined by the first vector.

TYP = 20: Two planes of symmetry



Three Planes

For three planes of symmetry (TYP = 30), the symmetry plane definitions are identical tothose for two planes of symmetry with the third plane being placed perpendicular to the firsttwo and located at the anchor node as shown below:

TYP = 30: Three planes of symmetry



One Plane - Simple Symmetry Options

For a single plane of symmetry (TYP = 10), the plane is defined normal to the first vector andis located at the anchor node as shown below:

TYP = 10: One plane of symmetry



Linear Pattern Grouping

Linear pattern grouping allows you to force OptiStruct to create beads in a given directionalong the entire length of the part. This can be very useful for optimizing the shape ofextruded parts which must maintain a constant cross section. It is also very useful whenoptimizing the side walls of stamped plates whose beads must run from the top to the bottomso that the part can be drawn from the die. In solid models, where the variable needs tocontrol the movement of all grids through the thickness, linear pattern grouping is also veryuseful.

For linear pattern grouping (TYP = 1, 21, or 31), OptiStruct generates shape variables thatrun along a line parallel to the first vector. These shape variables have a width equal to theminimum bead width parameter but have no limit on length. For simple linear patterngrouping, the anchor point and first vector can be located anywhere as shown below:

TYP = 1: Linear pattern grouping

For one and two plane linear symmetry, the anchor point locates the plane(s) of symmetry. For one plane linear symmetry (TYP = 21), the second vector defines the symmetry plane(since the first vector has been used to define the direction of the pattern).

TYP = 21: One plane linear symmetry

For two plane symmetry (TYP = 31), the symmetry planes are defined by the second vectorand the cross product of the first and second vectors as shown below. There is no threeplane linear pattern grouping since the pattern is automatically symmetric in the direction ofthe first vector.



TYP = 31: Two plane linear symmetry



Circular Pattern Grouping

Circular pattern grouping allows you to force OptiStruct to create beads that form concentriccircles around a user-defined axis. This can be very useful for optimizing the shape ofcircular parts that must have a circular reinforcement pattern such as a part turned on alathe.

For circular pattern grouping (TYP = 2 or 12), OptiStruct generates shape variables that formcircles about an axis defined by the first vector. These circular beads have a width equal tothe minimum bead width parameter. The anchor point can be located anywhere, but the firstvector must be collinear with the desired central axis for the circular beads. The simplecircular pattern grouping (TYP = 2) is shown below:

TYP = 2: Circular pattern grouping

For one plane circular pattern grouping (TYP = 12), the circular patterns are reflected about aplane located at the anchor node and defined by the first vector. One plane circularsymmetry ensures that nodes equal distances above and below the plane of symmetry will begrouped into the same variables. See below:

TYP = 12: One plane circular symmetry



Planar Pattern Grouping

Planar pattern grouping allows you to force OptiStruct to create variables that consolidate theperturbations of active grids in a given plane. This can be very useful in forming beads thatrun in a fixed direction across an uneven part or in solid models to control the changes in theshape of a cross section.

For a planar pattern grouping (TYP = 3 or 13), OptiStruct generates a series of parallel planarshape variables that are defined by the first vector. These shape variables have a widthequal to the minimum bead width parameter, but have no limit on length. Beads formedusing planar pattern grouping can turn vertical corners. For simple planar pattern grouping,the anchor point and first vector can be located anywhere as shown below:

TYP = 3: Simple planar pattern grouping

For one plane planar symmetry (TYP = 13), the planes are symmetric about a plane locatedat the anchor point as shown below. There is no need for two and three plane planarsymmetry.

TYP = 13: One plane planar symmetry



Radial (2-D) Pattern Grouping

Radial (2-D) pattern grouping allows you to force OptiStruct to create beads in a radialdirection extending outward from a central axis. This can be very useful for optimizingcircular parts in which radial reinforcements are desired.

For radial (2-D) pattern grouping (TYP = 4 , 14, 24, and 34), OptiStruct generates shapevariables that run radially away from a central axis defined by the first vector. Radial beads,at their closest point to the central axis, have a width equal to the minimum bead widthparameter. The width of the beads increases with distance from the center. There is no limiton the bead length. The anchor point can be located anywhere, but the first vector must becollinear with the desired central axis for the radial beads. The simple radial (2-D) patterngrouping (TYP = 4) is shown below:

TYP = 4: Simple radial (2-D) pattern grouping

For one plane radial (2-D) pattern grouping (TYP = 14), the radial patterns are reflectedabout a plane located at the anchor node and defined by the first vector. One plane radialsymmetry ensures that nodes equal distances above and below the plane of symmetry will begrouped into the same variables. See below:

TYP = 14: One plane radial pattern grouping

For two and three plane radial (2-D) pattern grouping (TYP = 24 and 34), two symmetryplanes are determined by the first and second vectors as shown below.



TYP = 24: Two plane radial (2-D) pattern grouping

TYP = 34: Three plane radial (2-D) pattern grouping



Cylindrical Pattern Grouping

Cylindrical pattern grouping allows you to force OptiStruct to create variables thatconsolidate the perturbations of active grids along the surface of a cylinder. This can beuseful in assigning a circular pattern grouping through the thickness of a solid model.

For a cylindrical pattern grouping (TYP = 5), OptiStruct generates a series of concentriccylinders that run parallel to and are positioned about the first vector. The cylindrical patterngrouping is essentially the linear pattern grouping combined with the circular patterngrouping. The anchor point can be located anywhere, but the first vector must be collinearwith the desired central axis for the cylinders.



Radial 2-D and Linear Pattern Grouping

Radial linear pattern grouping allows you to force OptiStruct to create variables thatconsolidate the perturbations of active grids along planes running radially from a central axis. This can be useful for assigning radial pattern groupings through the thickness of a solidmodel.

For a radial linear pattern grouping (TYP = 6), OptiStruct generates a series of planes thatrun radially away from, and in the same plane as, the first vector. The radial linear patterngrouping is essentially the linear pattern grouping combined with the radial pattern grouping. The anchor point can be located anywhere, but the first vector must be collinear with thedesired central axis for the radial planes.

One and two planes of radial linear pattern grouping (TYP = 26 and 36) can be created byusing the second vector to define the planes of symmetry. The symmetry planes areassigned in a manner similar to that for two and three plane radial symmetry.



Vector Defined Pattern Grouping

Vector defined pattern grouping allows you to force OptiStruct to create variables which aregrouped according to the direction and magnitude of the individual draw vectors of the grids. This pattern grouping option is similar to the linear pattern grouping option except that thelinear vector is not constant for the entire model. Instead, the direction of the draw vectorfor each grid is used to determine the variable groupings in place of a global linear vector. Additionally, unlike the linear pattern grouping option, the lengths of the beads are notinfinite. The lengths of the beads are equal to the magnitude of the draw vectors for thegrids. This pattern grouping option can be very effective for optimizing the shape ofamorphous solid models.

For vector defined pattern grouping (TYP = 8, 18, 28, and 38), OptiStruct generates shapevariables by consolidating the perturbations of active grids that are within a cylindrical regionabout evenly spaced grids in the model. For a selected grid, a cylindrical zone of influence iscreated around it which has a radius defined by the minimum bead width and draw angleparameters, a length defined by twice the draw vector for the selected grid, and is oriented inthe direction of the draw vector. See the figure below:

Note that for solid models, the internal grids will move along with the surface grids providedthat the internal grids have draw vectors associated with them. This allows for large scaleperturbations both inward and outward from the surface of a solid part while maintaining anacceptable mesh quality.

You must create perturbations for all of the grids in the model to effectively use vectordefined pattern grouping. If perturbations are defined for the surface grids only, those gridsmay end up passing through the second layer of grids if the variables are perturbed inward. The best way to use this pattern grouping option is to create a single shape variable byuniformly collapsing all of the grids in a solid model towards the center and then creating aDTPG card which points at the DESVAR for that shape variable.



Radial (3-D) Pattern Grouping

Radial (3-D) pattern grouping allows you to force OptiStruct to create variables thatconsolidate the perturbations of active grids in a radial direction away from a central point. This can be very useful for optimizing spherical models with solid elements.

For radial (3-D) pattern grouping (TYP = 7, 17, 27, and 37), OptiStruct generates shapevariables that run radially away from a central point defined by the anchor node. Radialbeads, at their closest point to the central axis, have a width equal to the minimum beadwidth parameter. The width of the beads increases with distance from the center. There isno limit on the bead length. The anchor point can be located anywhere, but is ideally locatedat the center of a sphere.

The planes for one, two, and three plane radial (3-D) symmetry are established in a manneridentically to one, two and three plane symmetry without radial (3-D) pattern grouping (TYP= 10, 20, and 30).



Cyclical Pattern Grouping

The cyclical pattern grouping allows you to force OptiStruct to create a series of symmetricshape variables about a central axis that repeat a number of times determined by you (withthe UCYC field). This can be useful in assigning a reinforcement pattern in a circular platethat matches an angularly repeated load in a symmetric fashion.

For cyclical pattern groupings (TYP = 40 and 41), OptiStruct generates a series of symmetricshape variables about an axis defined by the cross product of the first and second vectors. The axis of rotation is positioned at the anchor point. The first vector defines a planeestablishing one side of the cyclical wedge. The other side of the cyclical wedge is defined bythe angle of repetition. The figure below shows cyclical pattern grouping for three "wedges".

TYP = 40: Cyclical pattern grouping for 3 repetitions

OptiStruct allows any number of repeated cyclical wedges. You enter the number of desiredwedges into field 30 (UCYC). OptiStruct internally calculates the repetition angle accordingto the formula 360.0 / UCYC. For example, setting UCYC to three results in three wedges of120.0 each, and setting UCYC to 6 results in six wedges of 60.0 each.

You can also control whether the cyclical repetitions will be symmetric within themselves. This is done by choosing one of the cyclical TYP options ending in ‘1’ (41, 51, 61, 71, and81). If the symmetric wedge option is selected, OptiStruct will force each wedge to besymmetric about its centerline. Selecting one of the cyclical options ending in ‘0’ (40, 50, 60,70, and 80) will result in the wedges being non-symmetric. See the figures below:

TYP = 40 (non-symmetric) with UCYC = 5

TYP = 41 (symmetric) with UCYC = 3



Other Forms of Cyclical Pattern Grouping

OptiStruct supports the combination of cyclical pattern grouping with one plane symmetry,linear pattern grouping, radial pattern grouping, and radial linear pattern grouping. Eachoption is specified with a different base TYP number to which the number denoting therepetition angle is added.

For one plane cyclical pattern grouping (TYP = 50 and 51), the cyclical patterns are reflectedabout a plane located at the anchor node and defined by the cross product of the first andsecond vectors. One plane cyclical symmetry ensures that nodes equal distances above andbelow the plane of symmetry will be grouped into the same variables. See below:

TYP = 50: One plane cyclical symmetry with 3 wedges

For linear cyclical symmetry (TYP = 60 and 61), OptiStruct generates shape variables thatrun along a line parallel to the cross product of the first and second vectors. These shapevariables have a width equal to the minimum bead width parameter but have no limit onlength. The full lengths of the linearly drawn shape variables will be cyclically symmetric:

TYP = 60: Linear cyclical pattern grouping with 3 wedges

For radial cyclical pattern grouping (TYP = 70 and 71), OptiStruct generates shape variablesthat run radially away from a central axis defined by the cross product of the first and secondvector. Radial beads have a width equal to the minimum bead width parameter but have nolimit on length. The width of the beads does not change depending on the distance from thecenter. The full lengths of the radially drawn shape variables will be cyclically symmetric:



TYP = 70: Radial cyclical pattern grouping with 3 wedges

For radial linear cyclical pattern grouping (TYP = 80 and 81), OptiStruct generates a series ofplanes that run radially away from and in the same plane as the first vector. The radial linearcyclical pattern grouping is essentially the linear cyclical pattern grouping combined with theradial pattern grouping. The full lengths of the radially drawn shape variables will becyclically symmetric.



Manufacturability for Free-size Optimization

A concern in free-size optimization is that the design concepts developed are very often notmanufacturable. Another problem is that the solution of a free-size optimization problem canbe mesh dependent, if no appropriate measure is taken.

OptiStruct offers a number of different methods to account for manufacturability whenperforming free-size optimization:

Member Size Control

Member size control allows you some control over the member size in the final free-sizedesign and the resulting degree of simplicity therein. This feature may be added one ofthe two ways described below.

1. The DOPTPRM card:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

DOPTPRM MINDIM VALUE

Here, only the preferred minimum diameter (width in 2-D) of members may be definedas the VALUE field, following the MINDIM keyword. A global minimum member size isdefined in this way.

2. The DSIZE card:

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

MEMBSIZ

MINDIM

Here, the preferred minimum, MINDIM member may be defined on the MEMBSIZcontinuation line. Member size dimensions can be defined differently for each DSIZEentry in this way.

Minimum Member Size Control

Although minimum member size control penalizes the formation of small members, resultsthat contain members significantly under the prescribed minimum member size can still beobtained. This is because a small member in the structure can be very important to theload transmission and may not be removed by penalization. Minimum member size controlfunctions more as a quality control than a quantity control.

A discrete solution is achieved in two iterative steps. The first step converges to a solutionwith a large number of semi-dense elements. The second step tries to refine this solutionto a solution with fully dense members. Each step consists of a number of iterations. Thefirst step consists of two entire convergence phases - the first run with the initialdiscreteness values (defined by DISCRETE and DISCRT1D parameters on the DOPTPRMbulk data entry), followed by a run with the discreteness values increased by 1.0. This



procedure is implemented in order to achieve a solution with clearly defined members. Ifthis step could not create a solution with clearly defined members, the preferred minimummember size will not be preserved in the second step. In which case, you need to increasethe discreteness parameters and/or reduce the convergence tolerance (defined by theOBJTOL parameter on the DOPTPRM bulk data entry) to improve the solution of the firstphase. The default discreteness is set to 1.0 for 1-D elements, plates and shells, and 2.0for 3-D solids.

In general, once MINDIM is activated, checkerboarding is controlled by the methodsapplied for this feature, eliminating the need for the CHECKER parameter. In rarecircumstances, checkerboards may still be introduced in the second phase described abovefor 3-D solids. If this happens, an additional checkerboard control algorithm can beactivated with the MMCHECK parameter. (The CHECKER and MMCHECK parameters aredefined using the DOPTPRM bulk data entry).

The use of this card will assure a checkerboard-free solution, although with the undesiredside effect of achieving a solution that involves a large number of semi-dense elements,similar to the result of setting CHECKER equal to 1. Therefore, use this card only when itis necessary.

It is recommended that MINDIM be at least 3 times the average element size for allelements referenced by that DSIZE (or all designable elements when defined onDOPTPRM). The average element size for 2-D elements is calculated as the average of thesquare root of the area of the elements, and for 3-D elements, as the average of the cubicroot of the volume of the elements.

This recommendation is enforced when combined with other manufacturing constraints,and if the defined MINDIM is less than this value, it will be reset to a default value equal to3 times the average element size.

Pattern Repetition

Pattern repetition is a technique that allows different structural components to be linkedtogether so as to produce similar topological layouts.

To achieve this goal, a master DSIZE card needs to be defined, followed by any number ofslave DSIZE cards which reference the master. The master and slave components arerelated to each other through local coordinate systems, which are required, and throughscaling factors, which are optional.

Other manufacturing constraints, such as minimum or maximum member size, can beapplied to the master DSIZE card. These constraints will then automatically be applied tothe slave DSIZE card(s) as described in the next sections.


1. Create a master DSIZE card.


3. Define the local coordinate system associated to the master DSIZE card.

4. Create a slave DSIZE card.

5. Define the local coordinate systems associated to the slave DSIZE card.




7. Repeat steps 4-6 for any number of slave DSIZE cards.







The definition of the fourth point allows for both right-handed and left-handed coordinatesystems, which facilitates the creation of reflected patterns.

Alternatively, local coordinate systems can be defined by referencing an existingrectangular coordinate system in the CID field, and by defining an anchor point in the CAIDfield.

Note that if the fields defining CFID, CSID, CTID, and CID are left blank, then the globalcoordinates system is used by default. The anchor point CAID, however, is alwaysrequired.

Scaling Factors

Scaling factors in the X, Y, and Z directions can be defined for each slave DSIZE card. These factors are always related to the local coordinate system. By playing with the localcoordinate systems and the scaling factors, a wide range of effects can be obtained asillustrated with the figure below.



Pattern Grouping

Pattern grouping is a feature that allows you to define a single part of the domain thatshould be designed in a certain pattern.

Planar Symmetry

It is often desirable to produce a design that has symmetry. Unfortunately, even if thedesign space and boundary conditions are symmetric, conventional free-size optimizationmethods do not guarantee a perfectly symmetric design.

By using symmetry constraints in free-size optimization, symmetric designs can beattained regardless of the initial mesh, boundary conditions, or loads. Symmetry can beenforced across one plane, two orthogonal planes, or three orthogonal planes. Asymmetric mesh is not necessary, as OptiStruct will create variables that are very close toidentical across the plane(s) of symmetry.

To define symmetry across one plane, it is necessary to provide an anchor grid and areference grid. The first vector runs from the anchor grid to the reference grid. The planeof symmetry is normal to that vector and passes through the anchor grid.



To define symmetry across two planes, a second reference grid needs to be provided. Thesecond vector runs from the anchor grid to the projection of the second reference grid ontothe first plane of symmetry. The second plane of symmetry is normal to that vector andpasses through the anchor grid.

To define symmetry across three planes, no additional information is required, other thanto indicate that a third plane of symmetry is to be used. The third plane of symmetry isperpendicular to the first two planes of symmetry, and also passes through the anchorgrid.



Uniform Element Thickness

Pattern grouping also provides the possibility to request a uniform element thicknessthroughout selected components.

This pattern group ensures that all elements of selected components maintain the sameelement thickness with respect to one another.

Cyclical Symmetry

Cyclical symmetry can also be defined through the use of pattern grouping.

With cyclical pattern grouping, the design is repeated about a central axis a number oftimes determined by you. Furthermore, the cyclical repetitions can be symmetric withinthemselves. If that option is selected, OptiStruct will force each wedge to be symmetricabout its centerline.

To define cyclical symmetry, it is necessary to provide an anchor grid and a reference grid. The axis of symmetry runs from the anchor grid to the reference grid. It is also necessaryto specify the number of cycles; the repetition angle will be automatically computed.



To add planar symmetry within each wedge, a second reference grid needs to be provided. The plane of symmetry is determined by the anchor grid and the two reference grids.



Reliability-based Design Optimization (Beta)

Introduction

Reliability-based Design Optimization (RBDO) is an optimization method that can be used toprovide optimum designs in the presence of uncertainty. A gradient-based localapproximation of responses is used to perform reliability analysis. The design variables,constraints, and objective are tested for reliability based on user-defined reliabilityrequirements.

Deterministic and Random design variables can be selected for a design optimization run,while a Random parameter is also available to check for Robustness of a particular designwithin specified bounds. Similarly, Design Constraints and Objectives can also be specified asDeterministic (mean) or Percentile values.

Implementation

The Single Loop Approach (SLA) is used to optimize structures using Reliability-based DesignOptimization in OptiStruct. Reliability-based optimization methods test the reliability ofdesigns for each optimization iteration. The traditional, double-loop RBDO algorithm requiresnested optimization loops, where the design optimization (outer) loop repeatedly calls aseries of reliability (inner) loops.

The computational time can be prohibitive for practical problems due to the nestedoptimization-reliability loops. The SLA converts the nested loops into a single loop usingKarush-Kuhn-Tucker (KKT) conditions of the inner reliability loops in the outer optimizationloop. The probabilistic optimization problem is converted into a deterministic optimizationproblem. SLA is highly efficient compared to the traditional double-loop RBDO process.

The Single Loop Approach (SLA) is terminated if one of the following conditions is met:

1. The Sequential Quadratic Programming (SQP) convergence criterion is achieved.

2. Design variable convergence criterion is achieved.

3. Maximum number of allowable iterations is attained.

Variables

The following design variables and parameters can be used to define the structural designspace in OptiStruct:

Random Design Variables

Random design variables are defined via the RAND continuation lines on the DESVAR bulkdata entry. Various random distribution types can be selected and their parameters aredefined accordingly. In an RBDO process, during reliability and/or robustness analysis, thedesign should satisfy optimality based on the specified distributions.

Random parameters

The definition of Random parameters is similar to that of Random Design Variables, usingRANP definition. However, the important difference is that, while the mean values of randomvariables are changed to improve the design, the mean values of random parameters remainconstant. For example, typically sheet metal thickness can be a random variable, due to



fabrication variance, while the Young’s modulus of a material would typically be a randomparameter, if its variance is accounted for.

Deterministic Design Variables

The deterministic design variables are the regular design variables used in an OptiStructoptimization run.

Note: Due to the deviation of the random distribution, thedesign region should be defined carefully. For example, ifa design variable value is intended to be positive, then itslower bound should not be defined lower than n*σ;where, σ is the standard deviation of the variable; n is aconstant multiplier (a value of n=6 is recommended).

Objective

The following design objective types are available in OptiStruct:

Percentile value (RBDO)

The minimum or maximum of the percentile based objective function can be defined on the DESOBJ subcase information entry. The MINP/MAXP options and the PROB argument can beused to define the required parameters.

Figure 1: Illustration depicting Percentile Value based Objective

The percentile value based objective is defined as follows:

min or max

Where, is the objective function, and r is the probability level (for example, 95%). The

right and left percentile values are available. MINP minimizes the right percentile value andMAXP maximizes the left percentile value.

Deterministic (mean) value

The deterministic value based objective is the regular objective used in an OptiStructoptimization run. The mean value based objective is defined as follows:

min or max

Where, is the objective function.



Constraints

The following design constraint types are available in OptiStruct:

Percentile value (RBDO)

The probability of one constraint satisfying its bounds should not be less than the predefinedreliability value. The reliability value is defined via the PROB field on the DCONSTR bulk dataentry.

The reliability-based constraints are defined as follows:

Where,

c(x) is the constraint value

ub is the upper bound of the constraint

lb is the lower bound of the constraint

r is the probability level (for example, 95%)

For the “ ” constraint, the right percentile value of c(x) is forced to be

less than or equal to the upper bound “ub”. For the “ ” constraint, the

left percentile value of c(x) is forced to be greater than or equal to the lower bound “lb”.

Deterministic (mean) value

The deterministic value based constraint is the regular constraint definition used in anOptiStruct optimization run. The mean value based constraint is defined as follows:

c(x) < ub

c(x) > lb

Where, c(x) is the constraint value, ub is the upper bound of the constraint, and lb is the

lower bound of the constraint.

OptiStruct RBDO

The RBDO process is illustrated in Figure 2.



Figure 2: Flowchart depicting the OptiStruct RBDO implementation

Note that while all deterministic optimization capabilities in OptiStruct use the sameapproximation approach, design requirements are accurately evaluated after each FEAanalysis. This premise does not hold for RBDO as accurate reliability analysis would needmore FEA analyses for a given design. Therefore, it is important to assess the usability of theimplemented algorithm. Seventeen examples are tested to verify the reliability of thisapproach. In these examples, distribution types of random design variables are normaldistribution and constraints have a reliability requirement of 99%. A Monte Carlo simulationwith 1000 sampling points based on accurate FEA analysis is used to check the reliabilitystatus (Table 1).

Example

NME

Start Design Status Optimized Design Status

T N M Objective Reliability Objective Reliability

1 5 28 3 40.4 98.0% 27.6 98.5%

2 2 26 7 4.51 0.0% 3.24 100.0%

3 3 4 4 3.84e-5 70.4% 3.99e-5 98.8%

4 4 159 5 9.0e-4 100.0% 4.47e-4 98.9%

5 3 2 4 1.98 0.0% 0.472 98.1%

6 3 4 13 0.5 0.0% 2.98e-4 99.0%



Example

NME

Start Design Status Optimized Design Status

T N M Objective Reliability Objective Reliability

7 2 20 8 4.83 100.0% 3.41 98.8%

8 8 170 13 661.4 0.0% 552.8 98.5%

9 3 316 8 5.785 0.0% 6.825 98.8%

10 2 1 6 26.07 100.0% 21.03 100.0%

11 8 2 7 3.9e-5 0.0% 1.229e-4 99.0%

12 6 16 8 0.01 0.0% 3.45e-3 96.4%

13 2 3 8 232.4 0.0% 240.1 100.0%

14 5 3 4 40.0 0.0% 39.3 98.1%

15 10 168 3 49.4 100.0% 71.9 97.3%

16 3 22 11 4.83 0.0% 2.70 98.8%

17 2 1060 6 232.5 0.0% 61.5 100.0%

T: test number of the example

N: number of random design variables

M: number of reliability constraints

NME: number of model evaluations

Objective: the objective value of the design; in these examples, objective value is to beminimized

Reliability: the probability of the design that satisfies the constraint requirement

The following conclusions can be drawn from the results in Table 1:

1. The OptiStruct RBDO approach is very efficient, since it consumes just a few modelevaluations.

2. The reliability of the optimized design is close to the predefined requirement in mostcases. Error does exist, however, and can be quite significant as observed in examples 12and 15.

The OptiStruct RBDO approach (based on local approximation) offers an efficient tool toconsider uncertainty involved in design. For most problems this approximate reliabilityanalysis yields reasonable estimates. Local approximation based reliability analysis does,



however, contain some error of varying degree. Accurate reliability analysis should be carriedout if accurate satisfaction of reliability requirements is critical. Also note that for theapproximation-based OptiStruct RBDO approach, reliability analysis is performed only forretained constraints for which sensitivity is available. You can adjust the screening criteriausing the DSCREEN bulk data entry, if required.



Optimization of Arbitrary Beam Sections

Optimization of Thin-walled Sections

Optimization of thin-walled sections is facilitated through the use of the dimension fields onthe PBARL and PBEAML bulk data entries and the DIM entry within the section definition.

The DIM entry is used in the section definition to link either the thickness of a PSEC entry orthe Y or Z coordinate of a GRIDS entry to the value of the corresponding DIM field of thereferencing PBARL or PBEAML. Should the DIM field on the referencing PBARL or PBEAML bereferenced by a DVPREL, the thickness or grid coordinate in the section definition will beaffected by changes in the design variable.

Solid sections are not designable at this time.

The following is an example of a thin-walled section, where the wall thickness and the ycoordinate of G2 are designable:

$DESVAR,1,THK,0.1,0.05,0.15DESVAR,2,G2Y,1.0,0.5,1.5$DVPREL1,1,PBARL,1,DIM1,,,0.0,1,1.0DVPREL1,2,PBARL,1,DIM2,,,0.0,2,1.0$PBARL,1,1000,HYPRBEAM,SQUARE,0.1,1.0$MAT1,1000,2e5,,0.33,7.85e-9$BEGIN,HYPRBEAM,SQUARE$GRIDS,1,0.0,0.0GRIDS,2,1.0,0.0GRIDS,3,1.0,1.0GRIDS,4,0.0,1.0$CSEC2,10,100,1,2CSEC2,20,100,2,3CSEC2,30,100,3,4CSEC2,40,100,4,1$PSEC,100,1000,0.1$DIM,1,T,100DIM,2,G,2,Y$END,HYPRBEAM$



Optimization of Composite Structures

OptiStruct offers a comprehensive optimization solution aimed at guiding and simplifying thedesign of laminate composite structures. The solution includes the following optimizationphases and associated techniques:

Phase I – Concept. Free-sizing optimization is used to generate design concepts, while considering globalresponses and optional manufacturing constraints.

Phase II – System. Sizing optimization – with ply-based modeling – is performed to control the thickness ofeach ply bundle, while considering all design responses and optional manufacturingconstraints.

Phase III – Detail. Ply-stacking optimization is applied to determine the detailed stacking sequence, againwhile considering all behavioral responses, manufacturing constraints and various plybook rules.

While these techniques can be applied independently, it is recommended to use themtogether as a three-phase integrated process guiding the design from concept to completion. This is particularly important when manufacturing constraints are involved. In order tosatisfy such constraints at the finishing stage, they should be incorporated at the beginningso that the design concept can be carried forward. Automated tools are provided to facilitatethe transition between the design optimization phases.

Composite Structures - Free-sizing Optimization

The purpose of composite free-sizing optimization is to create design concepts that utilizeall the potential of a composite structure where both structure and material can bedesigned simultaneously. By varying the thickness of each ply with a particular fiberorientation for every element, the total laminate thickness can change ‘continuously’throughout the structure, and at the same time, the optimal composition of the compositelaminate at every point (element) is achieved simultaneously. At this stage, a super-plyconcept should be adopted, in which each available fiber orientation is assigned a super-ply whose thickness is free-sized. In other words, a super-ply is the total designablethickness of a particular fiber orientation. In addition, in order to neutralize the effect ofply stacking sequence, the SMEAR option is usually a good choice for this design phaseunless it is intended to follow through with the stacking preference of the super-plylaminate model.

In OptiStruct, additional manufacturing constraints can be defined for free-sizingoptimization. As a composite laminate is typically manufactured through a stacking andcuring process, certain manufacturing requirements are necessary in order to limitundesired side effects emerging during this curing process. For example, one such typicalconstraint for carbon fiber reinforced composites is that plies of a given orientation cannotbe stacked successively for more than 3 or 4 plies. This implies that a design concept thatcontains areas of predominantly a single fiber orientation would never satisfy thisrequirement. Therefore, to achieve a manufacturable design concept, manufacturingrequirements for the final product need to be reflected during the concept design stage. For the particular constraint mentioned above, for instance, the design concept would offerenough alternative ply orientations to break the succession of plies of the same orientation



if the percentage of each fiber orientation is controlled (for example, no ply orientationshould drop below 15%). In addition, balancing of a pair of ply orientations could beuseful for practical reasons. For example, balancing 45° and -45° plies would eliminatetwisting of a plate under bending along the 0 axis. In order to address these needs, thefollowing manufacturing constraints are made available for composite free-sizing:

Lower and upper bounds on the total thickness of the laminate.

Lower and upper bounds on the thickness of individual orientations.

Lower and upper bounds on the thickness percentage of individual orientations.

Constant thickness of individual orientations.

Thickness balancing between two given orientations.

As for the constraints on laminate thickness, ply thickness and thickness percentage, thesecan be applied locally through the definition of element sets. Therefore, multiple instancesof these constraints are supported. Advantages include being able to allow differentconstraints in different regions while preserving the continuity of plies. For example,different thickness requirements in critical regions, such as bolted areas, can be factoredinto the design process. Additionally, zone based free-sizing optimization can beperformed. Zones are defined through groups of elements and there can be elements thatdo not belong to any zone. Zones are typically defined to simplify the designinterpretation process and improve manufacturability. Instead of having to interpretmanufacturable zones from the solution of a free-sizing optimization, the optimization isrun based on pre-defined zones. While the interpretation process is simplified, there is aloss in design freedom as now the optimization is restricted to some extent due to thedefined zones.

Refer to the DSIZE card for detailed information regarding composite free-sizingoptimization and its associated manufacturing constraints. Note also that other genericmanufacturing constraints, such as pattern grouping or member size control, can beactivated for composite free-sizing as well.

The standard result from a free-sizing optimization is the thickness contribution of eachorientation defined on the PCOMP(G) or STACK card referenced by the DSIZE card in theoptimal laminate design. But, using free-sizing as part of the three-phase compositedesign and optimization process, and the mechanism to automatically generate an inputfile for phase two of this process, an additional level of detail/results can be drilled down toin terms of the thickness contributions per orientation. The automatically generated inputfile for phase two contains ply bundle data that can be reviewed in HyperMesh.

A ply bundle is a continuous stack of plies of the same shape (or coverage area). Eachsuper-ply results in the formation of 4 ply bundles. This is the default behavior and can bechanged, that is a different number of ply bundles can be requested from the super-plies. However, in most cases, it is recommended to use the default approach.

As described above, multiple ply shapes per orientation (through ply bundles) can bedetermined and generated from a free-sizing optimization.

Note: Automatic offset control is available in composite free-size and sizingoptimization wherein the specified offset values are automaticallyupdated based on thickness changes. The offset values can bespecified on the PCOMP(P/G) property entries or the CTRIA3/6,CQUAD4/8 element entries using the Z0 or ZOFFS fields.



Composite Structures - Ply-based Sizing Optimization

Ply-based Laminate Modeling

Complimentary to the conventional property-based composite definition, a new ply-basedmodeling technique was introduced in OptiStruct 9.0. In this format, laminates are definedin terms of ply entities and stacking sequences, which reflect the native language of ‘ply-book’ standards to composite laminate modeling and manufacturing. This is alsoanalogous with how a laminate composite is manufactured. The PLY card specifies thethickness, orientation and material data for each ply, as well as its layout in the structure. The STACK card ‘glues’ the PLYs together to produce the laminate structure. Properties ofevery zone of unique laminate lay-ups are uniquely, albeit implicitly, defined. This allowsyou to simply focus on the physical buildup of the composite structure and eliminates theburden associated with identifying patches (PCOMPs) of unique lay-ups, which can beespecially complicated for a free-sizing generated design.

Ply-based Optimization

In property-based sizing optimization, the designable entities are the ply thicknessesassociated with the PCOMP(G) properties. In ply-based sizing optimization, the PLYthicknesses are directly selected as designable entities. This approach greatly simplifiesthe design variables definition, since ply continuity across patches is automatically takeninto account.

As with free-sizing optimization, several composite manufacturing constraints are availableto control the thickness of the laminate or the thicknesses of specific orientations. Theseconstraints are defined on the DCOMP card and should generally be inherited from theconcept phase. A mechanism exists whereby the composite manufacturing constraintsdefined in the free-sizing phase are automatically carried over into the ply sizingoptimization phase. This is part of the same mechanism that also generates the input filefor the ply based sizing optimization (phase 2), containing ply bundles as explained in thesection on Phase 1: Free-Sizing Optimization. Through this, the ply bundles areautomatically set up for optimization with the necessary DESVAR and DVPREL cardsdefined. The ply bundles are now ready to be sized to determine the optimum thicknessper bundle per fiber orientation.

In addition, discrete optimization is automatically activated when TMANUF, the thickness ofthe basic manufacturable ply, is specified for the PLY associated with a given designvariable. This feature forces ply bundles to reach thicknesses reflecting a discrete numberof physical plies.

Therefore, from a ply bundle sizing optimization, the number of plies required perorientation can be established.

Typically, additional behavioral constraints such as failure, strain, etc. are added to theproblem formulation at this stage.

To proceed to the final phase, an input file for phase 3 can be automatically generatedfrom running phase 2, i.e. ply bundle sizing optimization.



Note: Automatic offset control is available in composite free-size and sizingoptimization wherein the specified offset values are automaticallyupdated based on thickness changes. The offset values can bespecified on the PCOMP(P/G) property entries or the CTRIA3/6,CQUAD4/8 element entries using the Z0 or ZOFFS fields.

Composite Structures - Stacking Sequence Optimization

Composite plies are shuffled to determine the optimal stacking sequence for the givendesign optimization problem while also satisfying additional manufacturing constraints,defined on the DSHUFFLE card, such as:

The stacking sequence should not contain any section with more than a givennumber of successive plies of same orientation.

The 45° and -45° orientations should be paired together.

The cover and/or core sections should follow a predefined stacking sequence.

Using the three-phase process, composite plies are generated from running a discrete plybundle sizing optimization (through TMANUF) in phase 2. Additionally, an input file forphase 3, i.e. stacking sequence optimization, is automatically generated from phase 2.

An efficient proprietary technique is developed to allow the process to evaluate a hugenumber of stacking combinations from both performance and manufacturabilityperspectives.

Phase Transitions in the Optimization of Composite Structures

In order to simplify the transition between the three design phases, OptiStruct is able toautomatically generate input decks after the free-sizing optimization or the sizingoptimization stages have converged.

OUTPUT,FSTOSZ (free-sizing to sizing) is an output request that can be used during thefree-sizing optimization phase to write a ply-based sizing optimization input deck. Foreach orientation, the composite interpreter identifies regions of similar thickness andcreates PLYs for these regions. The resulting deck contains PCOMPP, STACK, PLY, and SETcards describing the ply-based composite model, as well as DCOMP, DESVAR, and DVPRELcards defining the optimization data. Manufacturing constraints are transferred from theDSIZE card to the DCOMP card. Typically, additional design responses such as stress/failure constraints would be introduced at this optimization stage.

OUTPUT,SZTOSH (sizing to shuffling) is an output request that can be used during the ply-based sizing optimization stage to write a ply stacking optimization input deck. Each PLYbundle is divided into multiple PLYs whose thickness is equal to the manufacturablethickness TMANUF, and the STACK card is updated accordingly. The DESVAR and DVPRELcards from the previous stage are removed, and a bare DSHUFFLE card is introduced. Asrequired by the design, additional ply-book rules or manufacturing constraints can bedefined on the DSHUFFLE card.



Example of Composite Structure Optimization - RectangularComposite Panel

In this example, a rectangular composite panel is clamped on one side and subjected to atip load on the other side. This simple model can be used to demonstrate how the threephases of the composite optimization package interact with each other to ultimatelygenerate a manufacturable design.

Free-sizing Optimization

During the concept phase, the composite panel is modeled with four orientations (0°, 90°,45° and -45°) of uniform thickness, and the SMEAR option is applied to eliminate stackbiasing. At this stage, you are minimizing the compliance of the structure whilemaintaining its volume fraction below 30%. Manufacturing constraints are introduced tolimit the total thickness of the panel and to ensure that each orientation accounts for atleast 10% of the total thickness. In addition, the thicknesses of the 45° and -45°orientations should be balanced. The resulting DSIZE card is:

DSIZE 1 PCOMP 1

+ COMP LAMTHK 3.2

+ COMP PLYPCT ALL 0.10

+ COMP BALANCE 45.0 -45.0

The optimization converges in seven iterations, after which the ply-based interpreteridentifies thickness zones and generates a ply-based input deck. As illustrated by thefollowing image (Figure 1), four ply bundles are created for each orientation. Figure 2shows the thickness of each orientation after free-sizing optimization, while Figure 3 showsthe equivalent thicknesses after going through the ply-based interpreter. As expected, thethickness zones are considerably more discrete in the interpreted design.

Figure 1: Ply bundles after ply-based interpretation



Figure 2: Thicknesses after free-sizing optimization

Figure 3:Thicknesses after ply-based interpretation

Ply-based Sizing Optimization

Once a concept design has been established, additional performance measures should beintroduced. In this example, you are changing the formulation to minimize the volumewhile constraining the maximum principal stress in every ply. Also, the compositemanufacturing constraints from the previous stage are preserved and transferred to theDCOMP card.

The optimization converges in 19 iterations, at which point the objective function has beenslightly reduced while satisfying the design constraints and the manufacturing constraints. Figure 4 shows the thickness of each orientation after convergence has been achieved. Note that, due to the implicit discrete variables formulation, each ply bundle’s thickness is



equal to a multiple of TMANUF=0.05.

Figure 4: Thicknesses after ply-based sizing optimization

Ply Stacking Optimization

At this stage, you are keeping the formulation that was introduced in the previous phase,while adding detailed stacking constraints. Specifically, you are requesting that no morethan four successive plies of same orientation be present in the stack, and that -45° and45° orientations be paired together in the reverse manner to minimize angle changes. Theresulting DSHUFFLE card is:

DSHUFFLE 1 STACK 1

+ MAXSUCC ALL 4

+ PAIR 45.0 -45.0 REVERSE

The optimization converges in seven iterations, and the resulting stacking sequence strictlysatisfies all constraints.

The image below illustrates how the ply-based sizing optimization and the ply stackingoptimization phases work together once free-sizing optimization has been performed. Figure (a) shows the initial stack for the sizing optimization phase; it consists of four plybundles for each orientation as determined by the ply-based interpreter. Figure (b) showsthe optimized stack; the thickness of each ply bundle has changed, and the total thicknesshas been slightly reduced to satisfy the manufacturing constraints. Figure (c) shows theinitial stacking sequence for the shuffling optimization phase, where the ply bundles havebeen converted to actual plies. Figure (d) shows the optimized stacking sequence, whichnow satisfies the detailed manufacturing constraints as well as the design constraints.



Figure 5: Stacking sequences during sizing and shuffling optimization

Note that, because most plies only cover part of the laminate structure, the stackingsequence for each zone of unique lay-ups is different from the one illustrated above. However, the manufacturing feasibility is evaluated for every individual zone.



Equivalent Static Load Method (ESLM)

The equivalent static load method, originally published by Dr. Park, Hanyang University, is atechnique suitable for optimization of designs undergoing dynamic loads. The method hasbeen implemented for the optimization of the following solutions:

Multi-body dynamics problems including flexible bodies.

Nonlinear responses from implicit static analysis, implicit dynamic analysis and explicitdynamic analysis.

The equivalent static load method takes advantage of the well established static responseoptimization capabilities of OptiStruct.

Equivalent Static Load

Figure 1.1: Displacement – time history response

The equivalent static load is that load which creates the same response field as that of thedynamic/nonlinear analysis at a given time step. From Figure 1.1, an equivalent static load iscalculated corresponding to each time step in the time history of the solution, therebyreplicating the dynamic/nonlinear behavior of the system in a static environment.

The calculated equivalent static loads from the analysis (as explained above) are consideredas separate load cases, and these multiple load cases are used in the linear responseoptimization loop. An updated design from the optimization loop is then passed back to theanalysis for validation and overall convergence. The design is validated against the originaldynamic/nonlinear analysis. Based on the outcome of this validation, the solution convergesor an updated set of equivalent static loads is calculated for the updated geometry, and theentire process is repeated till convergence. Figure 1.2 is a graphic description of theequivalent static load method for optimization.

Figure 1.2: Equivalent static load method

The equivalent static load method is completely automated in OptiStruct and is an efficientapproach for the optimization of responses from transient, dynamic and nonlinear solutions.

Apart from others, the equivalent static load method offers the following benefits:



It can be applied at the concept design phase as well as design fine tuning phase, i.e. itcan be used with topology, free-sizing, topography, size, shape and free-shapeoptimization.

A design is optimized for updated loads due to an updated design during theoptimization process.



ESLM for MBD

The equivalent static load method has been implemented for the solution of multi-bodydynamics problems that include flexible bodies. Size, shape, free-shape, topology,topography, free-size, and material optimization can be applied to flexible bodies. Responsesare mass, volume, center of gravity, moment of inertia, stress, strain, compliance (strainenergy), and displacement of the flexible bodies. Displacement responses are taken intoaccount with respect to local boundary conditions defined on the flexible body (see definitionbelow). The optimization problem setup follows the setup typical for size, shape, free-shape,topology, topography, free-size, and material optimizations in OptiStruct. Responses aredefined using DRESP1, DRESP2, and DRESP3 bulk data entries. Responses can only bedefined on flexible bodies (PFBODY) using the properties, elements and grid points includedin such bodies as reference. Design variables are defined using DESVAR, DVPREL1,DVPREL2, DVMREL1, DVMREL2, DSHAPE, DTPL, DTPG, DSIZE, and DVGRID bulk data entries. Free-size optimization is currently only available when PTYPE=PSHELL on the DSIZE card. Design variables can only be defined on flexible bodies (PFBODY) using the propertiesincluded in such bodies as reference. Constraints are defined using DCONSTR, DCONADDand DOBJREF bulk data entries. Constraints and objectives are referenced in the multi-bodydynamics subcase or globally through DESOBJ, DESSUB, DESGLB, and MINMAX, respectively.

ESLM specific parameters can be set through the DOPTPRM bulk data entry (see Parametersfor the ESLM).

The Method

An optimum solution can be found through a series of static response optimizations with theequivalent static load set, that is:

eqf Ku f Ma Cv

Where, feq, u, a, v, and f are the equivalent static load, deformation, acceleration, velocity, and

external load, respectively. The steps involved in the ESLM can be summarized as:

Step 1 Initial design.

Step 2 Dynamic analysis.

Step 3 Static response optimization with the multiple subcasesthat consist of multiple equivalent static load sets.

Step 4 If design converged, Stop. Otherwise go to Step 2.

The iteration at the third step is referred to as an inner iteration; Steps 2 through 4 form theouter loop. The converged solution at Step 3 is the starting point of the next outer loop (ifthe design does not converge at the current outer loop). Note that if there are time steps inthe multi-body dynamics analysis at Step 2, subcases in static response optimization aregenerated at Step 3 (provided that the time step screening option is deactivated). See Parameters for the ESLM.



Boundary Conditions for Structural Analysis and Optimization

To perform structural optimization with ESL, you must specify boundary conditions for eachflexible body. In the solution of the dynamic analysis, the flexible and rigid bodies areconnected by joints to form a multi-body system. When performing ESLM on the flexiblebodies, these joints are not included in this static subcase based structural optimization. Thismeans that each flexible body will have 6 rigid body modes. The 6 rigid body modes of eachflexible body must be removed for structural analysis. Exactly 6 degrees of freedom (DOF) ofeach flexible body must be fixed to remove the 6 rigid body modes. If more than 6 DOF arefixed in a flexible body, the additional fixed DOF become the constraint of the flexible body,which may not result in an optimal solution and consequently increases the required ESLMouter loops.

Due to the way ESL is calculated, each flexible body is in its equilibrium at the 0-th inneriteration of each outer loop. This is why you can fix an arbitrary 6DOF (usually single node)to get rid of rigid body modes in order to do static analysis with ESL. Reaction force at thefixed node is zero at the 0-th inner iteration. Thus, no additional load is applied to a flexiblebody although 6DOF of the flexible body are fixed. However, design changes occur as theinner iteration goes on. This means the original configuration that maintains equilibrium alsochanges. As a result, the equilibrium status does not hold true anymore from the 1st inneriteration in each outer loop. An undesirable effect caused by a broken equilibrium status(disequilibrium status) is the reaction force at the fixed point is not zero anymore, whichmeans additional load is applied to that fixed point. This effect, due to shape/sizechanges, can be minimized by fixing a proper node, as explained below.

A common way to remove the 6 rigid body modes is to fix all 6 DOF of a node. When lookingfor a node to fix, choose one that is not in a high stress region. If the fixed point is located ina high stress region, the optimization can be very slow. It is highly recommended that the 6DOF of an independent node of a spider or rigid element (usually used to model joints) beselected to be fixed. On solid models, where the nodes do not have rotational stiffness; if asolid model does not have a rigid element to represent a joint, the next best way to removethe 6 rigid body modes is to fix 3 translational DOF (123) of one node, 2 translational DOF(23) of another node, and 1 translational DOF (3) of a third node. However, still make surethat the 3 nodes are not in a high stress region, otherwise this method of removing 6 rigidbody modes does not work. One way or another, all of the 6 rigid body modes of eachflexible body must be removed. SPC, SPC1, or SPCADD (referenced in the subcaseinformation section) can define the fixed DOF.

The example that follows shows a solid model with joints at the centers of two holes.



Stress contours of this model at two time steps are shown in the following images.

Nodes A and B are the locations of joints. The best option here is to fix 6 DOF of either node(A or B) in order to remove 6 rigid body motions in this model. To fix alternative nodes otherthan node A or B, it would work to fix 3 DOF (123) of node E1, 2 DOF (23) of node E2, and 1DOF (3) of node E3. These three nodes are located in a relatively low stress region. In thismodel, nodes C1, C2, and C3 or nodes D1, D2, and D3 would take a long time to converge iffixed. Again, the best and simplest way to remove 6 rigid body modes of eachflexible body is to fix one of the joint locations in each flexible body.

When the boundary conditions are properly defined, displacement constraints in anoptimization can be applied to limit the deformation of the flexible body. An example is tooptimize a rotating cantilever. You could fix either the left end or the middle point to retrievedeformation as long as the point has nothing or little to do with the shape perturbationvectors. If a relative displacement at the right end with respect to the left end is to beconstrained, it would be most convenient to fix the 6 DOF of the left end to measure therelative displacement. Constraining a relative displacement of the left end with respect tothe middle point of the cantilever, it would be best to fix the 6 DOF of the middle point. Regardless of whether the left end or the middle point (or even the right end) is fixed, the



stress is the same. If the optimization problem is simply to constrain stress or minimize themaximum stress of a flexible body, all that is needed is to fix one proper node of the flexiblebody.

Rotating cantilever

Deformation when the left end is fixed

Deformation when the middle point is fixed

Output Files Generated by the Optimization Process

Once ESL optimization converges, the following output files are available:

.eslout This text file contains brief and useful information about theoptimization process. Open this file first to find out whatoccurred during the ESL optimization. This file is oftenenough to understand the overall optimization process. Thefollowing information is stored in this file:

Involved time steps and corresponding subcases.

The number of involved time steps.

Design results.

The number of inner iterations.

CPU time.

_mbd_#.h3d This binary output file contains the MBD analysis results ofthe #-th outer loop. Displacement, stress, and deformation

are available in this file. This file is a modal h3d format(PARAM,MBDH3D,MODAL), which is only available format in ESL

optimization. HyperView can display this file.

_des_#.h3d This binary output file contains design change of the #-th

outer loop. By selecting the contour button, you can see thedesign change. HyperView can display this file.

_mbd_#.abf This binary output file contains information about rigid bodydynamics and modal participation factors of the #-th outerloop. HyperGraph can display the data stored in this file.

Other than above output files, .desvar, .prop, .grid, .fsthick, and .oss will be found, if

available.



Convergence Enhancement for the ESLM

It is important to catch the critical responses of a structure properly when optimizing thestructure. Generally, it is a good practice to define many time steps in the time intervalswhere the critical responses of interest show up. By doing this, the optimizer can considermore precise responses at the critical time intervals, resulting in a decreased probability thatthe optimizer will go in the wrong direction in the current outer loop.

Here is an example that shows how to refine specific time intervals. Suppose the analysistime interval is from 0 seconds to 1.0 seconds. In order to find out at which steps the criticalresponses of interest show up, you could use equi-spaced time steps first.

MBSIM 4 TRANS END 1.0 NSTEPS 100

The above card divides the time interval from 0 seconds to 1.0 seconds into 100 time steps,which is an equi-spaced time step. After analyzing with the above card, you can obtain thefollowing time history for stress: At the time interval of around 0 seconds to 0.02 secondsand 0.60 seconds to 0.63 seconds, critical values of the stress show up. Generally speaking,these critical responses are dominant responses that control the optimization process. It isdesirable to consider more critical responses at around these time intervals. In order toconsider more critical responses at around these time intervals, increase the number of timessteps at these time intervals.

$more time steps from 0.0 sec to 0.02 sec.MBSIM 1 TRANS END 0.02 NSTEPS 200 + VSTIFF MBSIM 2 TRANS END 0.61 NSTEPS 200 + VSTIFF $more time steps from 0.61 sec to 0.63 sec.MBSIM 3 TRANS END 0.63 NSTEPS 200 + VSTIFF MBSIM 4 TRANS END 1.0 NSTEPS 100 $MBSEQ 10 1 2 3 4

Time history of a response

In the above MBSIM cards, time steps in the time interval 0 to 0.02 seconds and timeinterval 0.61 and 0.63 seconds have been increased. Generally, the more information theoptimizer knows, the better the solution it can provide. It is beneficial to define many time



steps; enough to catch precisely the critical responses in the time intervals where criticalresponse of interest show up. This will enhance convergence of the optimization process.



Parameters for the ESLM

Control the maximum number of outer loops executed in the ESLM by using the followingparameter:

DOPTPRM, ESLMAX

In this case, the ESLMAX is an integer value, greater than or equal to 0. If the ESLMAX is

equal to 0, then optimization process is not activated. The default value for the ESLMAX is 30.

The ESLM has a feature that screens out the time steps that are not dominant during theoptimization. In the most cases, this feature is very helpful to improve the efficiency of theESL optimization process in terms of CPU time. This feature can be activated or deactivatedby using:

DOPTPRM, ESLSOPT

The ESLSOPT can be either 0 or 1. If ESLSOPT is 0, then the screening is deactivated. If

ESLSOPT is 1, then this screening is activated. The default value is 1. Unless deactivated by

DOPTPRM, ESLSOPT, 0, this feature is always activated.

The time step screening feature is different from the constraint screening of the staticresponse optimization in Step 3, although the concepts of both screening capabilities aresimilar. The time step screening is performed at time Step 2, which is right before enteringthe static response optimization phase. By performing the time step screening beforeentering the static response optimization phase, the huge amounts of CPU time required forstructural analysis and subsequent constraint screening strategy can be saved at the 0-thiteration in the static response optimization phase.

Once ESLSOPT is activated, the number of time steps that should be screened out can be

controlled by using:

DOPTPRM, ESLSTOL

ESLSTOL is a real number between 0.0 and 1.0. The smaller the value of ESLSTOL, the fewer

the number of time steps involved in the optimization process. If ESLSTOL is 1.0, all of the

time steps in multi-body dynamic analysis will be involved in the optimization process. Obviously, the smaller the ESLSTOL value, the less total CPU time will be used. Note,

however, that assigning too small a value to the ESLSTOL could cause the optimization

process to diverge. Therefore, if the number of time steps retained by ESLSTOL is less than

10, the 10 most dominant time steps will be involved in the optimization process. Thedefault value for the ESLSTOL is 0.3.



Output Requests and ESLM

Users are not allowed to control analysis output in ESL optimization. All information from theMBD analysis is already available in _mbd_#.h3d, including displacement, stress, and

deformation. All analysis output requests are invalidated during ESL optimization except thatOutput Request = option is allowed above the first subcase. For example, STRESS = ALL or

DISPLACEMENT = SID is allowed above the first subcase.

Optimization output is not controllable in ESL optimization. See Equivalent Static LoadMethod (ESLM) for more details.

Output and format in output format controls are not controllable in ESL optimization. Allrequests on output and format are invalidated during ESL optimization, except for FSTHICKand OSS.



MBD System Level Response Optimization

The original ESLM implemented in OptiStruct is for the optimization of flexible bodies in MBDsystems through the control of structural responses, such as stress or deformation. Theoriginal ESLM is not capable of handling system level responses, such as joint force of a jointor velocity of a node of a body. System-level responses referred to in this section can bedisplacement, velocities, acceleration, joint force, and functions of those 4 quantities definedby MBVAR. In addition to the original ESLM, MBD system level response optimization is alsoavailable in OptiStruct. ESLM and MBD system level optimization can be combined togetherto optimize MBD systems. One of typical optimization formulations that can be solved byOptiStruct could be:

Minimize joint force of a joint

subject to stress < allowable value

deformation < allowable value

velocities of a node < allowable value

MBD system level responses can be controlled by the properties of PRBODY, CMBUSH(M),CMBEAM(M), and CMSPDP(M) as well as usual design variables in structural optimizationsuch as thickness of bodies, shape of bodies, etc. DVMBRL1 and DVMBRL2 are available todefine relationships between design variables and properties of PRBODY, CMBUSH(M),CMBEAM(M), and CMSPDP(M).

Large Number of Design Variables

MBD system level responses are approximated by adaptive response surfaces. The basicsolution strategy for MBD system level optimization is the same as that implemented inHyperStudy. In general, response surface based optimization cannot handle large number ofdesign variables. This issue has been resolved in OptiStruct through the introduction ofintermediate design variables for bodies. All the design variables defined on rigid/flexiblebodies are converted to some predefined intermediate design variables. Adaptive responsesurfaces are built based on those intermediate design variables. As a result, even if there arehundreds of design variables defined on bodies, adaptive response surfaces for MBD systemlevel responses can be built with only several intermediate design variables. This way,OptiStruct can handle MBD system level responses with large number of design variables.

Change of Length of Bodies as Shape Optimization

When you try to achieve a specific velocity value less than an allowed value, changing thelength of bodies is an efficient way to achieve it. You can set up shape optimization problemto change the length of bodies. The designable bodies can be either rigid bodies or flexiblebodies. When defining shape perturbation vectors with DVGRID, you have to make sure thateach perturbation vector does not break down the original joint configuration as the designchanges. For example, a revolute joint must have two coincident nodes attached to twodifferent bodies. Be aware while defining shape perturbation vectors, that the perturbationvector could cause a location change for only one of the two coincident nodes so that therevolute joint definition would not be valid after one design iteration.



Limitations of MBD System Level Response Optimization

Design variables associated with PRBODY, CMBUSH(M), CMBEAM(M), and CMSPDP(M) cannotcontrol structural responses, such as deformation or stress. They can only control MBDsystem level responses such as MBDIS, MBVEL, MBACC, MBFRC, and MBEXPR. Designvariables associated with structures such as length, shape, and thickness can control MBDsystem level responses. Thus, if interaction between structural responses and MBD systemlevel responses are mutually strong, this feature is not applicable.

Rigid bodies cannot have structural design variables (shape, properties, thickness, etc.) andthe design variables associated with DVMBRL1/2 with TYPE=PRBODY at the same time.

Currently, system level responses must be scalar values. OptiStruct provides an option topick up the maximum, minimum, maximum absolute, or minimum absolute value ofdisplacement/velocity/acceleration/ joint force when defining MBD system level responsesusing the DRESP1 card. If a system level response is an objective function, and the timewhen the objective function is picked up jumps around during the optimization process,convergence could be slow or even diverge in some cases.



ESLM for Nonlinear Response Optimization

The equivalent static load method has been extended to support nonlinear responseoptimization. The following geometric nonlinear analyses are supported for optimization inOptiStruct:

Implicit (quasi-) static analysis (NLGEOM)

Implicit dynamic analysis (IMPDYN)

Explicit dynamic analysis (EXPDYN)

Refer to the Geometric Nonlinear Analysis section for more details on the supported analysistypes.

This method is implemented to support various types of responses that are available in ausual static response optimization problem, i.e. displacement, strain, stress, etc., forexample. Only responses defined by DRESP1 are currently supported.

Concept level design techniques such as topology, free-sizing and topography optimization,and design fine tuning techniques such as size, shape and free-shape optimization aresupported for nonlinear response optimization using ESLM. In the current implementation,for topology optimization, PSHELL and PSOLID are supported and PSHELL is supported forfree-size optimization.

The optimization setup using ESLM for nonlinear response optimization in terms of designvariables, responses, constraints and objective function is the same as the setup for a typicalstatic response optimization problem for topology, topography, free-size, size, shape andfree-shape optimization.

Output Files Generated by the Optimization Process

In addition to the standard optimization outputs, the following files are output:

[model]_#.h3d: Analysis results for each #th outer loop.

[model].eslout: Outer loop iteration history summary.

Parameters of ESLM

Several parameters are available to control the optimization process:

DOPTPRM, ESLMAX

This parameter controls the maximum number of outer loops.

DOPTPRM, DESMAX

This parameter controls the maximum number of inner loop iterations.

DOPTPRM, NESLNLGM

This parameter controls the number of ESLs generated for each NLGEOM subcase.

DOPTPRM, NESLIMPD

This parameter controls the number of ESLs generated for each IMPDYN subcase.



DOPTPRM, NESLEXPD

This parameter controls the number of ESLs generated for each EXPDYN subcase.

For more details, refer to DOPTPRM parameters.



Gradient-based Optimization Method


Iterative Solution

OptiStruct uses an iterative procedure known as the local approximation method to solvethe optimization problem. This method determines the solution of the optimizationproblem using the following steps:

1. Analysis of the physical problem using finite elements.

2. Convergence test; whether or not the convergence is achieved.

3. Response screening to retain potentially active responses for the current iteration.

4. Design sensitivity analysis for retained responses.

5. Optimization of an explicit approximate problem formulated using the sensitivityinformation. Back to 1.

To achieve a stable convergence, design variable changes during each iteration are limitedto a narrow range within their bounds, called move limits. The biggest design variablechanges occur within the first few iterations and, due to an advanced formulation andother stabilizing measures, convergence for practical applications is typically reached withonly a small number of FE analyses.

The design sensitivity analysis calculates derivatives of structural responses with respect tothe design variables. This is one of the most important ingredients for taking FEA from asimple design validation tool to an automated design optimization framework.

The design update is generated by solving the explicit approximate optimization problem,based on sensitivity information. OptiStruct has two classes of optimization methodsimplemented: dual method and primal method. The dual method solves the optimizationproblem in the dual space of Largrange multipliers associated with active constraints. It ishighly efficient for design problems involving a very large number of design variables butmuch fewer constraints (common to topology and topography optimization). The primalmethod searches the optimum in the original design variable space. It is used forproblems that involve equally as many design constraints as design variables, which iscommon for size and shape optimizations. The choice of optimizer is made automaticallyby OptiStruct, based on the characteristics of the optimization problem.

Regular or Soft Convergence

Two convergence tests are used in OptiStruct and satisfaction of only one of these tests isrequired.

Regular convergence (design is feasible) is achieved when the convergence criteria aresatisfied for two consecutive iterations. This means that for two consecutive iterations, thechange in the objective function is less than the objective tolerance and constraintviolations are less than 1%. At least three analyses are required for regular convergence,as the convergence is based on the comparison of true objective values (values obtainedfrom an analysis at the latest design point). An exception (design is infeasible) is whenthe constraints remain violated by more than 1%, and for three consecutive iterations thechange in the objective function is less than the objective tolerance and the change in the



constraint violations is less than 0.2%. In this case, the iterative process will beterminated with a conclusion ‘No feasible design can be obtained.’

Soft convergence is achieved when there is little or no change in the design variables fortwo consecutive iterations. It is not necessary to evaluate the objective (or constraints) forthe final design point, as the model is unchanged from the previous iteration. Therefore,soft convergence requires one less iteration than regular convergence.

OptiStruct Optimization Algorithms

OptiStruct utilizes gradient-based optimization algorithms to solve the optimizationproblem. The default optimization algorithm is known as the Method of Feasible Directions(MFD). You can select a different algorithm using the DOPTPRM, OPTMETH parameter. Thefollowing algorithms are available in OptiStruct:

Method of feasible directions (MFD)

Sequential quadratic programming (SQP)

Dual Optimizer based on separate convex approximation (DUAL)

Large scale optimization algorithm (BIGOPT)

MFD, SQP, and DUAL are standard optimization algorithms. For further information, referto relevant books and papers in the OptiStruct References section.

Large Scale Optimization Algorithm (BIGOPT)

The Large scale optimization algorithm (BIGOPT) is a gradient-based method. It consumesless memory and is relatively more computationally efficient, compared to MFD and SQP.

Implementation

Consider an optimization problem that involves minimizing f(X) based on a set of

constraints. It is described as follows:

Where,

f(X) is the objective function,

gi(X) is the i’th constraint function,

me is the number of equality constraints,

m is the total number of constraints,

X is the design variable vector,

X L and XU are the lower and upper bound vectors of design variables, respectively.



If BIGOPT is selected, OptiStruct converts this problem to an equivalent problem using thepenalty method, as follows:

Where, r and qi are penalty multipliers.

BIGOPT considers the bound constraints separately. So the original problem is converted toan unconstrained problem. Polak-Ribiere conjugate gradient method is used to generatesearch direction. After the search direction is calculated, a one-dimensional search can beaccomplished by parabolic interpolation (Brent’s method).

Terminating Conditions

Optimization runs, based on the BIGOPT algorithm, will be terminated if one of thefollowing conditions is met:

1. and the design is feasible.

2. and the design is feasible.

3. The number of iteration steps exceeds Nmax.

Where,

is the gradient of

k is the k’th iteration step

is the convergence parameter

Nmax is the allowed maximum iterations

Sensitivity Analysis

The response quantity, g, is calculated from the displacements as:

Tg q u

The sensitivity of this response with respect to the design variable x, or the gradient of the

response, is:

TTg q u

u qx x x

Two approaches to sensitivity analysis, the direct and adjoint variable method, arepossible. Given the equation of motion:

Ku f



and its derivative with respect to design variable x,

fK uu K

x x x

one can calculate the sensitivity of the displacement vector u as:

fu KK u

x x x

Using this equation, the largest cost in the calculation of the response gradient is theforward-backward substitution required for the calculation of the derivative of thedisplacement vector with respect to the design variable. This is called the direct method. One forward-backward substitution is required for each design variable.

If constraints are active in more than one load case, and the load is a function of thedesign variable (say body force or pressure loads for shape optimization), then the set offorward-backward substitutions must be performed for each active load case. If the loadsare not a function of the design variables, but there are active load cases with multipleboundary conditions, then the set of forward-backward substitutions must be performed foreach active boundary condition.

For the adjoint variable method of sensitivity analysis, the vector (adjoint variable) a is

introduced, which is calculated as:

Ka q

Then the derivative of the constraint can be calculated as:

TTg q f K

u a ux x x x

When the adjoint variable method for sensitivity analysis is used, a single forward-backward substitution is needed for each retained constraint. This forward-backwardsubstitution is needed to calculate the vector a.

There are typically a small number of design variables in shape and size optimization (say5 to 50) and a large number of constraints. The large number of constraints comes fromstress constraints. If there are 20,000 elements, each with a single stress constraint, and10 load cases, there are a total of 200,000 possible stress constraints.

There are typically a large number of design variables in topology optimization (between 1and 3 per element) and a small number of constraints. Because stress constraints are notusually considered in topology optimization, it makes sense that the adjoint variablemethod of sensitivity analysis be used for topology optimization (in order to reducecomputational costs).

For shape and sizing optimization, it is often beneficial to use the direct method forsensitivity analysis. However, in some cases, when there are a large number of designvariables and a small number of constraints, the adjoint variable method should be used. For example, in a topography optimization, the number of constraints that gradients needto be calculated for can be reduced using constraint screening. With constraint screening,constraints that are not close to being violated are ignored. Only constraints that areviolated, or nearly violated, are retained. Also, if there are many stress constraints thatare retained in a small region of the structure, say at a stress concentration, only a few ofthe most critical need to be retained.



The sensitivities of responses with respect to design variables can be exported to an Excelspreadsheet (see OUTPUT, MSSENS) or plotted in HyperGraph (see OUTPUT, HGSENS). For contouring in HyperView, the sensitivities of topology, free-sizing and gauge designvariables can be exported to H3D format (see OUTPUT, H3DTOPOL and OUTPUT,H3DGAUGE, respectively). Sensitivity output in ASCII format for topology and free-sizingvariables can be requested through OUTPUT, ASCSENS.

The Excel spreadsheet allows the modification of design variables and then computesapproximated responses. This can be used to make design studies without runningOptiStruct again. See the image below.

Example spreadsheet output showing that modification of field C10 yields approximate results in the lower rightof the spreadsheet, identified by a border surround here.

Move Limit Adjustments

As the design moves away from its initial point in the approximate optimization problem,the approximate values become less accurate. This can lead to slow overall convergence,as the approximate optimum designs are not near the actual optimum design. Move limitson the design variables, and/or intermediate design variables, are used to protect theaccuracy of the approximations. They appear as:

mmX X X X X

Small move limits lead to smoother convergence. Many iterations may be required due tothe small design changes at each iteration. Large move limits may lead to oscillationsbetween infeasible designs as critical constraints are calculated inaccurately. If theapproximations themselves are accurate, large move limits can be used. Typical movelimits in the approximate optimization problem are 20% of the current design variablevalue. If advanced approximation concepts are used, move limits up to 50% are possible.

Even with advanced approximation concepts, it is possible to have poor approximations ofthe actual response behavior with respect to the design variables. It is best to use largermove limits for accurate approximations and smaller move limits for those that are not so



accurate.

Note that the same set of design variable move limits must be used for all of the responseapproximations. It is important to look at the approximations of the responses that aredriving the design. These are the objective function and most critical constraints. If theobjective function moves in the wrong direction, or critical constraints become even moreviolated, it is a sign that the approximations are not accurate. In this case, all of thedesign variable move limits are reduced. However, if the move limits become too small,convergence may be slowed, as design variables that are a long way from the optimumdesign are forced to change slowly. Therefore, the move limits on the individual designvariables that keep hitting the same upper or lower move limit bound are increased. Movelimits are automatically adjusted by OptiStruct.

Constraint Screening

At each iteration of the optimization process, the objective function(s) and all constraintsof the design problem are evaluated. Retaining all of these responses in the optimizationproblem has two potential disadvantages:

1. This can result in a big optimization problem with a large number of responses anddesign variables. Most optimization algorithms are designed to handle either a largenumber of responses or a large number of design variables, but not both.

2. For gradient-based optimization, the design sensitivities of these responses need to becalculated. The design sensitivity calculation can be very computationally expensivewhen there are a large number of responses and a large number of design variables.

Constraint screening is the process by which the number of responses in the optimizationproblem is trimmed to a representative set. This set of retained responses captures theessence of the original design problem while keeping the size of the optimization problemat an acceptable level. Constraint screening utilizes the fact that constrained responsesthat are a long way from their bounding values (on the satisfactory side) or which are lesscritical (i.e. for an upper bound more negative and for a lower bound more positive) than agiven number of constrained responses of the same type, within the same designatedregion and for the same subcase, will not affect the direction of the optimization problemand therefore can be removed from the problem for the current design iteration.

Consider the optimization problem where the objective is to minimize the mass of a finiteelement model composed of 100,000 elements, while keeping the elemental stresses belowtheir associated material's yield stress. In this problem, you have 100,000 constraints (thestress for every element must be below its associated material's yield stress) for eachsubcase. For every design variable, 100,000 sensitivity calculations must be performed foreach subcase, at every iteration. Because design variable changes are restricted by movelimits, stresses are not expected to change drastically from one iteration to the next. Therefore, it is wasteful to calculate the sensitivities for those elements whose stresses areconsiderably lower than their associated material's yield stress. Also the direction of theoptimization will be driven primarily by the highest elemental stresses. Therefore, thenumber of required calculations can be further reduced by only considering an arbitrarynumber of the highest elemental stresses.

Of course there is trade-off involved in using constraint screening. By not considering allof the constrained responses, it may take more iterations to reach a converged solution. Iftoo many constrained responses are screened, it may take considerably longer to reach aconverged solution or, in the worst case, it may not be able to converge on a solution if the



number of retained responses is less than the number of active constraints for the givenproblem.

Through extensive testing it has been found that, for the majority of problems, usingconstraint screening saves a lot of time and computational effort. Therefore, constraintscreening is active in OptiStruct by default. The default settings consider only the 20 mostcritical (i.e. for an upper bound most positive and for a lower bound most negative)constraints that come within 50 percent of their bound value (on the satisfactory side) foreach response type, for each region, for each subcase.

The DSCREEN bulk data entry controls both the screening threshold and number ofretained constraints. Different DSCREEN settings are allowed for all of the response typessupported by the DRESP1 bulk data entry. Responses defined by the DRESP2 bulk dataentry are controlled by a single DSCREEN entry with RTYPE = EQUA. Likewise, responsesdefined by the DRESP3 bulk data entry are controlled by a single DSCREEN entry withRTYPE = EXTERNAL. It is important to ensure that DRESP2 and DRESP3 definitions thatuse the same region identifier use similar equations. (In order for constraint screening towork effectively, responses within the same region should be of similar magnitudes anddemonstrate similar sensitivities, the easiest way to ensure that is through the use ofsimilar variable combinations).

In order to reduce the burden on the user, it is possible to allow the screening criteria to beautomatically and adaptively adjusted in an effort to retain the least number of responsesnecessary for stable convergence. Setting RTYPE=AUTO on the DSCREEN bulk data entrywill enable this feature. Region definition is also automated with this setting. This settingis useful for less experienced users and can be particularly useful when there are manylocal constraints. However, there are some drawbacks; experienced users may be able toachieve better performance through manual definition of screening criteria, more memorymay be required to run with RTYPE=AUTO, and manual under-retention of constraints willrequire less memory and may, therefore, be desirable for very large problems (even withcompromised convergence stability and optimality).

Regions and Their Purpose

In OptiStruct, a region is a group of responses of the same type.

Regions are defined by the region identifier field on the DRESP1, DRESP2, and DRESP3bulk data entries used to define the responses. If the region identifier field is left blank,then each property associated with the response forms its own region. The same regionidentifier may be used for responses of different types, but remember that because theyare not of the same type they cannot form the same region.

Example 1

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

DRESP1 1 label STRESS PSHELL SMP1 1

2 3

DRESP1 with ID 1 defines stress responses for all the elements that reference thePSHELL definitions with PID 1, 2, or 3. As no region identifier is defined, the stress



responses for each PSHELL form their own regions. So, all of the stress responses forelements referencing PSHELL with PID1 are in a different region than all of the stressresponses for elements referencing PSHELL with PID2, which in turn are in a differentregion than all of the stress responses for elements referencing PSHELL with PID3. Ifthis response definition is constrained in an optimization problem, and the defaultsettings for constraint screening are assumed, then 20 elemental stresses are consideredfor each of the three PSHELL definitions, i.e. 20 for each region, giving a total of 60retained responses.

Example 2

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

DRESP1 2 label STRESS PSHELL 1 SMP1 1

2

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

DRESP1 3 label STRESS PSHELL 1 SMP1 3

All of the stress responses defined in the DRESP1 entries above form a single region -notice the entries (not blank) in field 6. Now, if these response definitions which are ofthe same type (STRESS) with the same entry (not blank) in field 6 are constrained in anoptimization problem (assuming the default settings for constraint screening), then 20elemental stresses are considered in total for the three PSHELL definitions because theyform a single region.

Discrete Design Variables

OptiStruct uses a gradient-based optimization approach for size and shape optimization. This method does not work well for truly discrete design variables, such as those thatwould be encountered when optimizing composite stacking sequences. However, themethod has been adopted for discrete design variables where the discrete values have acontinuous trend, such as when a sheet material is provided with a range of thicknesses. The adopted method works best when the discrete intervals are small. In other words, themore continuous-like the design problem behaves, the more reliable the discrete solutionwill be. For example, satisfactory performance should not be expected if a thicknessvariable is given two discrete values 0 and T.

It is known that rigorous methods such as branch and bound are very time consumingcomputationally. Therefore, we developed a semi-intuitive method that is targeted atsolving relatively large size problems efficiently. It is recommended to benchmark thediscrete design against the baseline continuous solution. This helps to quantify the trade-off due to discrete variables and to understand whether the discrete solution is reasonable. As local optima are always a barrier for none convex optimization problems, and discretevariables tend to increase the severity of this phenomenon, it could be helpful to run thesame design problem from several starting points, especially when the optimality of a



solution is in doubt.

It is also possible to mix these discrete variables with continuous variables in anoptimization problem.

Discrete design variables are activated by referencing a DDVAL entry on a DESVAR card.

The DDVOPT parameter on the DOPTPRM card allows you to choose between a fullydiscrete optimization or a two phased approach where a continuous optimization isperformed first, and a discrete optimization is started from the continuous optimum.




A common discussion that arises when an optimization problem is solved is whether or notthe obtained optimum is a local or global optimum. Local approximation based methods(gradient-based optimizations) are more susceptible to finding a local optimum, while globalapproximation methods (response surface methods) and exploratory techniques (geneticalgorithms) are less susceptible than local approximation based methods to finding a localoptimum. In other words, these techniques improve the chances of finding a more globaloptimum. However, no algorithm can guarantee that the optimum found is in fact the globaloptimum. An optimum can be guaranteed to be the global optimum only if the optimizationproblem is convex. For a convex optimization problem, the objective function and feasibledomain need to be convex. Unfortunately, in reality, most engineering problems beingsolved cannot be shown to be convex. Therefore, for practical problems, a global optimumremains elusive. Different algorithm types simply alter one’s chances of finding a moreglobal optimum, not guarantee it. With that consideration, it is important to keep in mindthat algorithms which improve the chances come at a computational cost. And most oftenthis can be significant.

The following image illustrates the concept of a convex problem as discussed above. Aconvex optimization problem has just one minimum (or maximum). This minimum (Point Ain the image) is the global minimum.

Convex function, f(x)

In the case of non-convex problems solved using gradient-based techniques, the inherentbehavior is that the optimized result obtained is dependent on the initial design startingpoint. This makes these types of algorithms all the more susceptible to finding localoptimum. Recently implemented in OptiStruct version 11.0, is a new global search algorithm– an extension to the gradient-based optimization approach. The approach is called MultipleStarting Points Optimization. This global search algorithm performs an extensive search ofthe design space for multiple starting points to improve the chances of finding a more globaloptimum. Being dependant on the initial design starting point, n different design startingpoints could potentially result in n different optimum solutions. It is also highly likely thatdifferent design starting points could result in the same optimum solution. However, this



does not mean that the optimum solution found is the global optimum. This concept isillustrated in the following image.

Non-convex function, f(x)

Consider the non-convex function, f(x), bounded by –a < x < b. Optimizing a design from

design starting point A will result in the optimum solution, P. Similarly, optimizing a designfrom starting point B will result in the same optimum solution, P. On the other hand,optimizing a design from initial design starting point C will result in the optimum solution, Q. From this, it can be seen that through the multiple starting points approach, a globaloptimum cannot be guaranteed (as with any other algorithm), but at the same time, thechances of finding a more global optimum are improved.

As of version 11.0, the Global Search Option (GSO) in OptiStruct supports those optimizationdisciplines with user-defined variables.

Identifying a global search optimization study is done through the DGLOBAL entry in the I/Osection of the input deck, and the parameters required to setup and run a GSO are definedon the DGLOBAL bulk data entry.



Design Interpretation - OSSmooth

OSSmooth is a semi-automated design interpretation software, facilitating the recovery of amodified geometry resulting from a structural optimization, for further use in the designprocess and FEA reanalysis. The tool has two incarnations: a standalone version that comeswith the OptiStruct installation, and a dependent version that is embedded in HyperMesh.

OSSmooth can be used in three different ways: OSSmooth for geometry, FEA topologyreanalysis, and FEA topography reanalysis.

Note: FEA topology reanalysis and FEA topography reanalysisare features which are available only in the version ofOSSmooth that is embedded within HyperMesh, they arenot supported by the standalone OSSmooth software.

OSSmooth (for geometry) has several uses and can be used to:

Interpret topology optimization results, creating an iso-density boundary surface (Iso-surface).

Interpret topography optimization results, creating beads or swages on the designsurface.

Recover and smooth geometry resulting from a shape optimization.

Reduce the amount of surface data from a given set of triangular patches by combiningsmaller patches.

Smooth surface data given as triangular patches.

For FEA topology reanalysis and FEA topography reanalysis, OSSmooth can be used to:

Preserve component boundaries for multiple design components.

Recover geometry with or without an artificial layer of elements around a non-designspace optionally.

Tetramesh Iso-surfaces ‘by property’.

Preserve boundary conditions upon geometry recovery to enable quick reanalysis.

The following flowchart provides an overview of how OSSmooth works to interpretoptimization results from OptiStruct:



Each of the three applications of OSSmooth has a corresponding sub-panel in the OSSmoothpanel in HyperMesh. OSSmooth (for geometry) is generally used to recover geometry byinterpreting topology, topography, and shape optimization results, while FEA topology andFEA topography are used to generate recovered geometry with boundary conditions for FEAreanalysis.

OSSmooth (for geometry) requires a parameter file (generally has the file extension .oss) to

run. This parameter file may be generated from the OSSmooth panel in HyperMesh, or itmay be generated manually through a text editor. At the completion of an optimization run,OptiStruct automatically exports an OSSmooth parameter file <prefix>.oss with certain

default settings depending on the type of optimization run.

In addition to the parameter file, OSSmooth (for geometry) also requires the input file(<prefix>.fem), the shape file (<prefix>.sh), and/or the grid file (<prefix>.grid) from an

OptiStruct run. The grid file <prefix>.grid contains the grid point locations after a

topography or shape optimization and is output at the end of a topography or shapeoptimization run. The shape file, <prefix>.sh, contains the element density information of a

topology optimization and is output at the end of a topology optimization run.

FEA topology requires the input model (<prefix>.fem) to be loaded into HyperMesh before

running, which is different from OSSmooth (for geometry). It also requires the shape file(<prefix>.sh) generated by a topology optimization. For processing of the non-design

elements, two options (Keep smooth narrow layer around and Split all quads) areprovided to recover geometry.



FEA topography requires a grid file (<prefix>.grid) to run. Similar to FEA topology, it also

requires that the input model (<prefix>.fem) be loaded into HyperMesh first, with the option

for iso-surface that performs the same functionality as FEA topology.

Note: OSSmooth currently does not recognize OptiStruct long-format input data. A possible work-around for thisproblem is to import the long-format input file intoHyperMesh and export it using the regular OptiStructtemplate before running OSSmooth.

The interpreted design from OSSmooth can be exportedas a finite element mesh in the bulk data format, as IGESsurfaces, as a stereolithography file, or as a Hyper3D file.



OSSmooth Parameter File

The OSSmooth parameter file is composed of a number of parameter statements, each ofwhich has the following format:

parameter_name arg1,arg2,...,argn

The parameter_name and arguments can be separated either by spaces or commas. The file

is not case sensitive.

Comment lines in the OSSmooth parameter file should start with either ‘#’ or ‘$’.

The following is a list of allowable parameters and their respective arguments:

Parameter Description

input_file Identifies the files to be interpreted by OSSmooth.

arg1 The file name (without extension) of the OptiStruct .fem, .sh, and/or .grid files to be interpreted by

OSSmooth.

output_file Name of the file to be output by OSSmooth.

arg1 Full name of the file output by OSSmooth.

output_code Identifies the type of output.

Argument Description

arg1 Output format for iso-surface:

1 – Bulk data trias2 – IGES patches3 – STL trias [default]4 – H3D trias

arg2 Output control for tet-meshing of volume enclosed by theiso-surface.

[Default: no tet-meshing]

1 – Tetra4 + Tria3 elements2 – Tetra10 + Tria6 elements3 – Tetra4 elements4 – Tetra10 elements

The tet-mesh is written in OptiStruct input format to a file <input_file>_mesh.fem. In this file, the design space of

the file <input_file>.fem is replaced with a tet-mesh for

immediate reanalysis. Loads, boundary conditions, andnon-design elements are carried over from the input file.




units Defines output units for IGES format. This information gets written tothe header of the IGES file and may be recognized by your CAD system.

1 – inch [default]2 – mm4 – foot6 – m10 – cm

autobead Improves the recovered geometry from a topography optimization byapplying automatic geometry creation.


arg1 Operation flag [integer]:

0 – autobead off1 – autobead on [default]

arg2 Threshold value for creating autobead.

[real, between 0.0 and 1.0, default = 0.3]

arg3 Bead layer [integer]:

1 – create 1 layer bead [default]2 – create 2 layers bead

isosurface Generate threshold surface from a topology optimization by applyingautomatic geometry creation.


arg1 Operation flag [integer]:

0 – isosurface off1 – isosurface on [default]

arg2 Type of surface created [integer]:

0 – isosurface only1 – isosurface with Optimization-based smoothing2 – Element threshold surface3 – isosurface with Laplacian smoothing [default]

For topology results, smoothing maintains the topology assuggested by OptiStruct, but it can deviate from the givendensity distribution. If option 1 or 3 is used, check themaximum and average smoothing error output byOSSmooth.

arg3 Density threshold for creating isosurface.

[real, between 0.0 and 1.0, default = 0.3]




opti_smoothing Optimization-based smoothing [Only used if isosurface C2=1].


arg1 Unit-less surface distance coefficient

[real, default = 0.0]

Defines closeness of the smooth surface from the thresholdsurface. The effect of this coefficient varies for differentinput meshes. Higher magnitudes (both positive andnegative) give smoother results, but the surface deviatesmore from the original density distribution. Therecommended range is from -50 to 50. When thecoefficient is set between 0 and 50, the surface usuallytends to smooth and shrink. When the coefficient is setbetween 0 and -50, the surface usually tends to smooth andexpand.

arg2 Smooth isosurface boundary flag [integer]:

0 – boundary not included in smoothing [default]1 – boundary included in smoothing

laplacian_smoothing

Laplacian smoothing [Only used if isosurface C2=3].


arg1 Number of iteration for Laplacian smoothing

[integer > 0, default = 10]

arg2 Feature angle threshold in degrees


The feature angle is defined as the angle of normal betweentwo intersected element planes. All corners with a featureangle larger than the threshold will be preserved in thesmoothing process.

arg3 Smooth isosurface boundary flag [integer]:

0 – boundary not included in smoothing1 – boundary included in smoothing [default]

remesh Remesh autobead surface and/or isosurface flag [integer]:

0 – remesh off [default]1 – remesh on

Remesh detects 2-layer elements around bead shape and/or boundaryof isosurface. Use mixed type remesh if input mesh contains any QUADelements, otherwise remesh with TRIA elements.




surface_reduction

Reduces the number of surfaces representing the geometry. Can reducethe number of surfaces by up to 80%.


arg1 Surface reduction flag [integer]:

0 – no surface reduction [default]1 – do surface reduction



The feature angle is defined as the angle formed by thesurface normal of two adjacent elements. The surfacereduction will be performed on any two adjacent elementsin which the feature angle between the two elements issmaller than the threshold. The greater the threshold, themore surface reduction will be conducted. The valid rangeof the threshold is [1.0, 80.0].

pure_surf_smoothing

Surface smoothing only.


arg1 Pure surface smoothing flag [integer]:

0 – no surface smoothing [default]1 – Optimization-based smoothing2 – Laplacian smoothing

arg2 Number of iteration [Only used if G1=2]

[integer > 0, default = 10]

arg3 Feature angle threshold in degrees [Only used if G1=2]


The feature angle is defined as the angle of normal betweentwo intersected element planes. All corners with a featureangle larger than the threshold will be preserved in thesmoothing process.

pure_surf_reduction

Surface reduction only.


arg1 Pure surface reduction flag [integer]:

0 – no surface reduction [default]1 – do surface reduction






The feature angle is defined as the angle formed by thesurface normal of two adjacent elements. The surfacereduction will be performed on any two adjacent elementsin which the feature angle between the two elements issmaller than the threshold. The greater the threshold, themore surface reduction will be conducted. The valid rangeof the threshold is [1.0, 80.0].

OSS Example Input File


input_file example Identifies the root of the input files as example, soOSSmooth will look for the files example.fem,

example.grid, and example.sh.

output_file example.stl The resulting output will be example.stl.

output_code 3 The output will be in stereolithography format.

Autobead 1 0.3 1 Topography results will be interpreted using theautobead feature with a threshold value of 30%creating single depth beads.

Isosurface 1 3 0.3 Topology results will be interpreted by creating aniso-density boundary surface with at a density valueof 30% and smooth using laplacian smoothing.

laplacian_smoothing 10 30 1 The Laplacian smoothing will run for 10 iterations,consider a feature angle of 30-degrees andincluding the boundary in the smoothing.

Remesh 1 The two rows of elements around the recoveredgeometry will be remeshed in an attempt to smooththe mesh transition.



Running OSSmooth

To run OSSmooth from the command line, type:

ossmooth <prefix>.oss

To run OSSmooth from the HyperMesh solver panel:

1. Select Solver from the Tools menu.

2. Click the switch and select OSSmooth.

3. After input file=, enter <prefix>.oss.

4. Click solve.

Note: OSSmooth standalone, which can also be invokedfrom the solver panel in HyperMesh, checks out 50HyperWorks Units.

To run OSSmooth from the HyperMesh ossmooth panel:

1. Select the ossmooth panel on the post page.

2. Choose either OSSmooth (for geometry), FEA topology or FEA topography.

3. Select the OptiStruct input file (<prefix.fem> and/or <prefix.sh> and/or <prefix.

grid>) using the file= browser.

4. Edit the OSSmooth input data by making selections on the screen.

5. Click ossmooth.

6. OSSmooth (for geometry) will write a new <prefix.oss> file with the screen settings

and load the geometry recovered into HyperMesh if the data format is IGES, STL, orNastran. FEA topology and FEA topography will update the model in HyperMesh withoutoutputting the result; if required, data can be exported from HyperMesh.

Note: OSSmooth invoked from the ossmooth panel inHyperMesh checks out 42 HyperWorks Units (21 leveledand 21 stacked).

To run OSSmooth from the HyperWorks Run Manager:

1. Select the .oss file using the Input file(s) browser.

2. The Options field must be empty.

3. Click Run.



Interpretation of Topology Optimization Results

The purpose of this functionality is to provide an iso-density surface based on the volumetricdensity information of a topology optimization, which is conducted using OptiStruct.

OSSmooth can handle both shell and solid elements with the same parameter setting. Oneexample of post-processing of shell element topology optimization is shown below with thefollowing parameter setting in the OSSmooth parameter file:

#general parameters

input_file mattel

output_file mattel.stl

output_code 3

#specific parameters

isosurface 1 3 0.300

laplacian_smoothing 10 30.000 1

surface_reduction 1 10.000

Surface reconstruction of shell element topology optimization.

The parameter laplacian_smoothing is used for additional smoothing. In most cases, the

threshold surface (isosurface with second argument 0) already creates a smooth shape.

Additional smoothing (isosurface with second argument 3) maintains the topology as

suggested by OptiStruct, but it can deviate from the given density distribution. If this optionis used, the maximum and average smoothing error output by OSSmooth should be checked. The surface_reduction parameter is used to reduce the number of elements.



Laplacian Smoothing

Laplacian smoothing can be used in the smoothing of the results of topology optimization. The laplacian_smoothing statement controls the iteration number of when the Laplacian

smoothing will be performed and the feature angle threshold to preserve normal discontinuityat corners. One smoothing result is shown below with the following parameter setting in theOSSmooth parameter file.

#general parameters

input_file surf

output_file surf.stl

output_code 3

isosurface 1 3 0.300


laplacian_smoothing 10 30.000 1

Laplacian smoothing creates smooth boundary iso-surface by entering 1 as the 3rd argumentof the laplacian_smoothing parameter statement. The comparison of the following two

figures shows that the second figure is almost ready for casting.

Fix boundary of iso-surface.



Smooth boundary of iso-surface.

The advantages of the laplacian_smoothing statement in OSSmooth include:

The flexibility of controlling the number of smoothing iterations to obtain differentdegrees of smoothing (possibly a smoothing quality ready for casting). Normally, theiteration number ranges from 5 to 20.

Smooth boundary of iso-surface with feature angle constrain are seamlesslyincorporated into the smoothing process, which is more challenging in a pure CADsystem.



Interpretation of Topography Optimization Results

The autobead feature of OSSmooth allows OptiStruct topography optimization results to beinterpreted as one or two level beads. The following figure shows the level of detail capturedin both cases; while the 2-level approach captures more details, it is more complicated tomanufacture than the 1-level interpretation, often without significant performance gain.

Autobead interpretation of topography optimization result.

One example of post-processing of topography optimization is shown below with the followingparameter setting in the OSSmooth parameter file:

#general parameters

input_file decklid

output_file decklid.fem

output_code 1


autobead 1 0.300 1

remesh 1

Autobead result from topography optimization.



Some topography performances are relying on the half translation part. OSSmooth caninterpolate topography optimization results to 2-layer autobead (autobead third argument 2). Here is one example of creating 2-layer autobead with the following parameter setting in theOSSmooth parameter file:

#general parameters

input_file decklid

output_file decklid.nas

output_code 1


autobead 1 0.300 2

2-layer autobead result from topography optimization.



Shape Optimization Results, Surface Reduction and SurfaceSmoothing

OSSmooth may also be used to reduce and smooth surfaces or the surfaces of a domain. Theparameter statements pure_surf_reduction and pure_surf_smoothing may be used for

this purpose.

The file defined by input_file must be in OptiStruct, and OSSmooth can smooth the surface

or the surfaces of a domain of the model.

The usage of in the OSSmooth parameter file is as follows:

#general parameters

input_file surf

output_file surf.stl

output_code 3


pure_surf_smoothing 2 10 30.000

pure_surf_reduction 1 10.000



FEA Topology for Reanalysis

Note: This feature is available only in the version of OSSmooth that isembedded within HyperMesh, it is not supported by the standaloneOSSmooth software.

The purpose of this functionality is to provide an iso-density surface based on the volumetricdensity information from a topology optimization. Through tetrameshing for 3-D models andinheriting boundary conditions, the results from FEA topology can be used for quickreanalysis.

FEA topology support is available for first and second order shell and solid elements. For 3-Dmodels, the recovered iso-surface can be tetrameshed-by-property automatically. FEAtopology provides two options for the processing of non-design elements: Keep smoothnarrow layer around and Split all quads. Keep smooth narrow layer around will retainan artificial layer of elements around the non-design space in the interpretation, and Split allquads will split quad elements in the non-design space, if present, to generate a tetraconnection between design and non-design regions. Finally, FEA topology preservesboundary conditions by inheriting them from the original model (<prefix>.fem). Those

boundary conditions unattached to nodes/elements after geometry recovery are deleted toensure reanalysis.

An example of FEA topology for reanalysis is shown below with the following input datadefinition:

file block

density threshold 0.300

Keep smooth narrow layer around off

Split all quads on

Result of FEA topology for reanalysis



The same model is run, this time with Keep smooth narrow layer around on, and Split allquads off. This approach creates a layer of elements around the non-design region andpyramids around the quad elements, if quads exist, to connect to the design spacetetrahedral elements.

Result of FEA topology with a layer of elements around non-design space

Tetramesh will be applied on the iso-surface result if there is one close volume at least. Theadvantages of the tetramesh in FEA topology include:

Tetramesh can be performed by property.

The flexibility of controlling the number of tetramesh retries by perturbing the densitythreshold value, in cases where tetramesh sometimes fails.



FEA Topography for Reanalysis

Note: This feature is available only in the version of OSSmooththat is embedded within HyperMesh, it is not supported bythe standalone OSSmooth software.

The FEA topography option in OSSmooth allows the results from an OptiStruct topographyoptimization to be interpreted as one or two level beads and recover boundary conditionsupon geometry extraction. An option for iso surface is also provided for combined use, whichperforms the same functionality as FEA topology, with FEA topography. The following figureshows the level of detail captured in a 1-level bead and 2-level bead case while preservingboundary conditions for quick reanalysis. FEA topography support is available for first andsecond order elements.

The input data definition for a 1-level Autobead extraction is as follows:

Grid file brkt

Threshold 0.300

Layers 1

1-level autobead result from FEA Topography

A 2-level Autobead extraction is activated with the following input data:

Grid file brkt

Threshold 0.300

Layers 2



2-level autobead result from FEA Topography



OptiStruct References

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Multi-body Dynamics – Books

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Powerflow – Papers

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