asas (non-linear) user manuals2.bitdownload.ir/engineering/all.ansys/ansys 12... · 2019. 5....

ASAS (Non-Linear)

User Manual

Version 12

© Copyright 2009. Century Dynamics Limited. All Rights Reserved. Century Dynamics is a subsidiary of ANSYS, Inc.

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Published in the U.S.A.

ASAS (Non-Linear) User Manual Update Sheet for Version 12

April 2009

Modifications:

The following modifications have been incorporated:

Section Page(s) Update/Addition Explanation

All All Update Conversion to Microsoft® Word format

Table 5.1 5-4 Update Changes for neutral RAO input

5.1.1 5-6 Update Allow 32 character hydrodynamic file name

5.1.6 5-11 Addition Add Note 4 on frequency analysis

5.1.11 5-16 Update Add HYDR command

Allow 32 character hydrodynamic file name

5.1.18 5-24 Update AP20 option replaced by APIW

App I.1 I-1 Update Delete references to legacy programs ASDIS, PICASO

App I.2 I-2 Update Delete references to legacy programs ASDIS, PICASO

App I.3 I-2 Update Delete Section I.3 (ASDIS Interface)

App I.6 I-15 Update Delete Section I.6 (PICASO Interface )

App M.3.2 M-3 Update AP20 option replaced by APIW

Table M.1 M-7 – M-8 Update AP20 option replaced by APIW




App M.6.45 M-58, M-59 Addition Add definition of phase offset data

App M.7 M-65 – M-66 Update AP20 option replaced by APIW

Contents ASAS (Non-Linear) User Manual

i Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Table of Contents

1. Introduction ............................................................................................................................. 1-1

1.1 General Capabilities ....................................................................................................... 1-1 1.2 Using this Manual .......................................................................................................... 1-1

2. Types of Analysis Available.................................................................................................... 2-1 2.1 General ........................................................................................................................... 2-1

2.1.1 Static Linear Elastic Solution .................................................................................. 2-1 2.1.2 Static Non-Linear Incremental Solution ................................................................. 2-2 2.1.3 Transient Non-Linear Incremental Solution ........................................................... 2-2 2.1.4 Eigenvalue Extraction ............................................................................................. 2-3 2.1.5 Steady State Heat Solution ...................................................................................... 2-4 2.1.6 General Field Analysis ............................................................................................ 2-4 2.1.7 Piezo-resistivity Analysis ........................................................................................ 2-4

3. Program Features ..................................................................................................................... 3-1 3.1 Types of Element ........................................................................................................... 3-1

3.1.1 Uniaxial Element ..................................................................................................... 3-1 3.1.2 Plane Stress/Strain Elements ................................................................................... 3-1 3.1.3 Axi-symmetric Solid Elements ............................................................................... 3-2 3.1.4 Three-Dimensional Solids ....................................................................................... 3-2 3.1.5 Gap/Interface Elements ........................................................................................... 3-3 3.1.6 Plates, Shells and Beams ......................................................................................... 3-3 3.1.7 Spring/Dashpot Elements ........................................................................................ 3-5 3.1.8 Linespring Elements................................................................................................ 3-5 3.1.9 Uniaxial Field Elements .......................................................................................... 3-5 3.1.10 Two Dimensional Plane Field Elements ............................................................... 3-6 3.1.11 Three Dimensional Solid Field Elements ............................................................. 3-6 3.1.12 Axisymmetric Solid Field Elements ..................................................................... 3-6

3.2 Material Model Types .................................................................................................... 3-6 3.2.1 Elasticity .................................................................................................................. 3-7 3.2.2 Plasticity .................................................................................................................. 3-7

3.2.2.1 Yield Criteria ................................................................................................... 3-8 3.2.2.2 Hardening Rules .............................................................................................. 3-9

3.2.3 Creep ....................................................................................................................... 3-9 3.2.4 Failure ................................................................................................................... 3-10 3.2.5 Field....................................................................................................................... 3-10 3.2.6 Piezo-Resistivity ................................................................................................... 3-10 3.2.7 Heat Convection .................................................................................................... 3-10 3.2.8 Heat Radiation ....................................................................................................... 3-10

3.3 Loading ........................................................................................................................ 3-10 3.3.1 Nodal Loads .......................................................................................................... 3-11 3.3.2 Prescribed Displacements ..................................................................................... 3-11 3.3.3 Pressure Loads ...................................................................................................... 3-11 3.3.4 Distributed Loads .................................................................................................. 3-11 3.3.5 Temperature Loads ................................................................................................ 3-11


ii Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

3.3.6 Face Temperature .................................................................................................. 3-12 3.3.7 Body Forces .......................................................................................................... 3-12 3.3.8 Centrifugal Loads .................................................................................................. 3-12 3.3.9 Angular Accelerations ........................................................................................... 3-13 3.3.10 Nodal Fluxes ....................................................................................................... 3-13 3.3.11 Prescribed Field Variables .................................................................................. 3-13 3.3.12 Flux Densities...................................................................................................... 3-13 3.3.13 Wave Load .......................................................................................................... 3-13 3.3.14 Tank Loads .......................................................................................................... 3-13 3.3.15 Load History........................................................................................................ 3-14

3.4 Node Numbers and Coordinates .................................................................................. 3-14 3.5 Element Numbering ..................................................................................................... 3-15 3.6 Global and Local Axis Systems ................................................................................... 3-15

3.6.1 Coordinate Local Axes .......................................................................................... 3-16 3.6.2 Element Local Axes .............................................................................................. 3-16 3.6.3 Skew Systems........................................................................................................ 3-16

3.7 Structural Suppressions and Constraints ...................................................................... 3-17 3.8 Solution Procedures ..................................................................................................... 3-17

3.8.1 Non-Linear Static Solution Procedures ................................................................. 3-17 3.8.2 Non-Linear Transient Solution Procedures ........................................................... 3-19 3.8.3 Contact Analysis Solution Procedures .................................................................. 3-19 3.8.4 Fracture Mechanics Solution Procedures .............................................................. 3-19

3.9 Program Organisation .................................................................................................. 3-19 3.10 Post-Processing ....................................................................................................... 3-20 3.11 Data Units ................................................................................................................ 3-20

4. Data Preparation ...................................................................................................................... 4-1 4.1 General ........................................................................................................................... 4-1

4.1.1 Data ......................................................................................................................... 4-1 4.1.2 Data Formats ........................................................................................................... 4-3

4.1.2.1 General Principles ........................................................................................... 4-3 4.1.3 Special Symbols ...................................................................................................... 4-6

4.2 Data Generation Facilities .............................................................................................. 4-8 4.2.1 Repeat Facilities ...................................................................................................... 4-8 4.2.2 Re-Repeat Facilities ................................................................................................ 4-9 4.2.3 List Generation in the Preliminary Data Section .................................................. 4-11

4.2.3.1 A Simple List ................................................................................................. 4-11 4.2.3.2 Generating a List with a Topological Variable ............................................. 4-11

4.3 Description of Each Data Block ................................................................................... 4-13 4.3.1 The Preliminary Data ............................................................................................ 4-13

4.3.1.1 General .......................................................................................................... 4-13 4.3.1.2 System Control .............................................................................................. 4-13 4.3.1.3 Solution Algorithm ........................................................................................ 4-14 4.3.1.4 Model Behaviour ........................................................................................... 4-15 4.3.1.5 Output Control ............................................................................................... 4-16

4.3.2 Structural Description Data - see Section 5.2 ....................................................... 4-16 4.3.3 Boundary Condition Data - see Section 5.3 .......................................................... 4-18


iii Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

4.3.4 Loading Data - see Section 5.4 ............................................................................. 4-19 4.3.4.1 Proportional Loading ..................................................................................... 4-19 4.3.4.2 Load Functions .............................................................................................. 4-20 4.3.4.3 Pseudo Times ................................................................................................ 4-20

4.3.5 Additional Mass Data - see Section 5.5 ................................................................ 4-21 4.3.6 Initial Conditions Data - see Section 5.6 ............................................................... 4-21

4.4 Description of Output ................................................................................................... 4-21 4.4.1 Data Input Echo and Checking ............................................................................. 4-21 4.4.2 Analysis Results .................................................................................................... 4-22 4.4.3 Analysis Summary ................................................................................................ 4-24 4.4.4 Journal Files .......................................................................................................... 4-24 4.4.5 ASASNL Output Markers ..................................................................................... 4-24

5. Data Formats ........................................................................................................................... 5-1 5.1 The Preliminary Data ..................................................................................................... 5-2

5.1.1 AQWA Command ................................................................................................... 5-5 5.1.2 BLOCK Command.................................................................................................. 5-5 5.1.3 COMMENT Command ........................................................................................... 5-6 5.1.4 CONVERGENCE Command ................................................................................. 5-7 5.1.5 EGEN Command .................................................................................................... 5-8 5.1.6 EIGN Command...................................................................................................... 5-8 5.1.7 ELGROUP Command - (Group Section Only) ...................................................... 5-9 5.1.8 END Command ..................................................................................................... 5-10 5.1.9 FILE Command ..................................................................................................... 5-10 5.1.10 GROUP Command - (Group Section Only) ....................................................... 5-11 5.1.11 HYDR Command ................................................................................................ 5-12 5.1.12 INTEGRATION Rule Command ....................................................................... 5-14 5.1.13 ITERATION Command ...................................................................................... 5-15 5.1.14 JOB Command .................................................................................................... 5-16 5.1.15 LOCYCLE Load Cycle Command ..................................................................... 5-17 5.1.16 MONITOR Command ........................................................................................ 5-17 5.1.17 NEWSTRUCTURE Command ........................................................................... 5-20 5.1.18 OPTION Command ............................................................................................ 5-21 5.1.19 OUTPUT Command ........................................................................................... 5-23 5.1.20 PARAMETER Command ................................................................................... 5-25 5.1.21 PASS Command.................................................................................................. 5-27 5.1.22 PINO Pressure Interpolation Order Command ................................................... 5-27 5.1.23 PROBLEM and TITLE Command ..................................................................... 5-28 5.1.24 PROJECT Command .......................................................................................... 5-29 5.1.25 RESTART Command ......................................................................................... 5-30 5.1.26 RESU (or POST) Commands .............................................................................. 5-31 5.1.27 SAVE Command ................................................................................................. 5-33 5.1.28 SCALING Command .......................................................................................... 5-34 5.1.29 SKIP Command - (Group Section Only) ............................................................ 5-34 5.1.30 SLEEP Command ............................................................................................... 5-35 5.1.31 SOLUTION Command ....................................................................................... 5-36 5.1.32 SOLVE Command .............................................................................................. 5-39


iv Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

5.1.33 SPIT Command ................................................................................................... 5-40 5.1.34 SRESTART Special Solution Restart Command ............................................... 5-42 5.1.35 START Command .............................................................................................. 5-43 5.1.36 STRUCTURE Command .................................................................................... 5-43 5.1.37 SYSPAR Command ............................................................................................ 5-44 5.1.38 SYSTEM Command ........................................................................................... 5-45 5.1.39 TEMPORAL Command...................................................................................... 5-46 5.1.40 TEXT Command ................................................................................................. 5-47 5.1.41 TITLE Command ................................................................................................ 5-48 5.1.42 UNITS Command ............................................................................................... 5-48

5.1.42.1 Global UNITS Definition ............................................................................ 5-48 5.1.43 UPDATE Command ........................................................................................... 5-50 5.1.44 WAKE Command ............................................................................................... 5-51 5.1.45 WEIGHTS Command ......................................................................................... 5-52

5.2 Structural Description Data .......................................................................................... 5-53 5.2.1 UNITS Command ................................................................................................. 5-53 5.2.2 COORDINATE Data ............................................................................................ 5-56

5.2.2.1 Local Coordinate System Header .................................................................. 5-57 5.2.2.2 Local Coordinate System Orientation ........................................................... 5-57 5.2.2.3 Node Coordinates .......................................................................................... 5-60 5.2.2.4 Coordinate Imperfection Data ....................................................................... 5-62

5.2.3 Element Topology Data ........................................................................................ 5-65 5.2.4 Material Property Data .......................................................................................... 5-67

5.2.4.1 Elastic Material Properties ............................................................................ 5-70 5.2.4.1.1 Isotropic material properties .................................................................. 5-70 5.2.4.1.2 Orthotropic material properties.............................................................. 5-72 5.2.4.1.3 Woven material properties ..................................................................... 5-74 5.2.4.1.4 Anisotropic material properties ............................................................. 5-75 5.2.4.1.5 Hyper-elastic material properties ........................................................... 5-77 5.2.4.1.6 Laminated Material Properties .............................................................. 5-78 5.2.4.1.7 User Material Properties ........................................................................ 5-80 5.2.4.1.8 Field Material Properties ....................................................................... 5-81 5.2.4.1.9 Piezo-resistivity Material Properties...................................................... 5-81 5.2.4.1.10 Convective Heat Material Properties ................................................... 5-82 5.2.4.1.11 Radiant Heat Material Properties......................................................... 5-83

5.2.4.2 Plastic Material Properties ............................................................................. 5-84 5.2.4.3 Creep Material Properties .............................................................................. 5-89 5.2.4.4 Failure Material Properties ............................................................................ 5-91

5.2.4.4.1 Lamina Failure Values ........................................................................... 5-92 5.2.4.4.2 Plastic Lamina Failure FLW1 Values .................................................... 5-93 5.2.4.4.3 Plastic Lamina Failure FLW2 Values .................................................... 5-94 5.2.4.4.4 Laminate Failure Values ........................................................................ 5-95

5.2.5 Geometric Properties Data .................................................................................... 5-98 5.2.5.1 Geometric Properties - (WST4 and SST4) .................................................... 5-99 5.2.5.2 Geometric Properties - (SPR1 and SPR2) ................................................... 5-101 5.2.5.3 Geometric Properties - (Laminated Construction) ...................................... 5-103


v Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

5.2.5.4 Geometric Properties - (Rigid Surface Elements) ....................................... 5-106 5.2.5.5 Definition of geometric properties for beam elements having local axes definition and/or rigid offsets ..................................................................................... 5-108

5.2.6 Section Data ........................................................................................................ 5-114 5.2.6.1 Section Types and Dimensions ................................................................... 5-116 5.2.6.2 Fabricated Plate Sections ............................................................................. 5-120

5.2.7 Skew System Data............................................................................................... 5-123 5.2.7.1 Skew Systems - Direction Cosines .............................................................. 5-123 5.2.7.2 Skew Systems - Nodal Definition ............................................................... 5-125

5.3 BOUNDARY Conditions Data .................................................................................. 5-126 5.3.1 UNITS Command ............................................................................................... 5-126 5.3.2 FREEDOM Release Data .................................................................................... 5-126 5.3.3 SUPPRESSED Freedoms Data ........................................................................... 5-129 5.3.4 Prescribed Freedom Data .................................................................................... 5-131 5.3.5 CONSTRAINT Equation Data ........................................................................... 5-133 5.3.6 RIGID Constraints Data ...................................................................................... 5-137

5.4 Loading Data .............................................................................................................. 5-140 5.4.1 UNITS Command ............................................................................................... 5-140 5.4.2 LOADING Data .................................................................................................. 5-142 5.4.3 NODAL LOADS Data ........................................................................................ 5-143 5.4.4 PRESCRIBED Displacements, Velocities and Accelerations Data ................... 5-145 5.4.5 PRESSURE Load Data ....................................................................................... 5-146

5.4.5.1 UNIFORM Pressure Load Data .................................................................. 5-148 5.4.5.2 NON-UNIFORM Pressure Load Data ........................................................ 5-149

5.4.6 DISTRIBUTED Load Data ................................................................................. 5-154 5.4.6.1 Local Beam Distributed Loads .................................................................... 5-158

5.4.6.1.1 BL1 and BL2 Load Patterns ................................................................ 5-161 5.4.6.1.2 BL3 Load Pattern ................................................................................. 5-162 5.4.6.1.3 BL4 Load Pattern ................................................................................. 5-163 5.4.6.1.4 BL5 Load Pattern ................................................................................. 5-164 5.4.6.1.5 BL6 Load Pattern ................................................................................. 5-165 5.4.6.1.6 BL7 Load Pattern ................................................................................. 5-166 5.4.6.1.7 BL8 Load Pattern ................................................................................. 5-167

5.4.6.2 Global Beam Distributed Loads .................................................................. 5-168 5.4.6.2.1 GL1 and GP1 Load Patterns ................................................................ 5-171 5.4.6.2.2 GL4 and GP4 Load Patterns ................................................................ 5-173 5.4.6.2.3 GL5 Load Pattern ................................................................................ 5-174 5.4.6.2.4 GL6 and GP6 Load Patterns ................................................................ 5-175 5.4.6.2.5 GL7 and GP7 Load Patterns ................................................................ 5-176

5.4.6.3 Panel Edge Distributed Loads ..................................................................... 5-178 5.4.6.4 Curved Beam Distributed Loads ................................................................. 5-181

5.4.7 TEMPERATURE Load Data .............................................................................. 5-183 5.4.7.1 NODAL Temperature Data ......................................................................... 5-183 5.4.7.2 ELEMENT Temperature Data .................................................................... 5-185 5.4.7.3 UNIFORM Element Temperature Data ...................................................... 5-186 5.4.7.4 NON-UNIFORM Element Temperature Data ............................................ 5-187


vi Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

5.4.8 FACE TEMPERATURE Data ............................................................................ 5-191 5.4.8.1 Nodal Face Temperature ............................................................................. 5-191 5.4.8.2 ELEMENT FACE TEMPERATURE Data ................................................ 5-192 5.4.8.3 UNIFORM Element Face Temperature Data .............................................. 5-193 5.4.8.4 NON-UNIFORM Element Face Temperature Data .................................... 5-194

5.4.9 BODY FORCE Data ........................................................................................... 5-197 5.4.10 CENTRIFUGAL Loads Data ............................................................................ 5-198 5.4.11 ANGULAR ACCELERATION Loads Data .................................................... 5-199 5.4.12 NODAL FLUX Data ......................................................................................... 5-201 5.4.13 PRESCRIBED Field Variable Data .................................................................. 5-202 5.4.14 FLUX DENSITY Data ...................................................................................... 5-203

5.4.14.1.1 UNIFORM Flux Density Data........................................................... 5-204 5.4.14.1.2 NON-UNIFORM Flux Density Data................................................. 5-206

5.4.15 WAVE LOAD Data .......................................................................................... 5-212 5.4.16 TANK LOAD data ............................................................................................ 5-213 5.4.17 LOAD Functions ............................................................................................... 5-215

5.5 DIRECT Mass Input Data .......................................................................................... 5-217 5.5.1 UNITS command ................................................................................................ 5-217 5.5.2 LUMP ADDED MASS Data .............................................................................. 5-218

5.6 Initial Conditions Data ............................................................................................... 5-220 5.6.1 UNITS Command ............................................................................................... 5-220 5.6.2 RESIDUAL Initial Stresses ................................................................................. 5-221 5.6.3 RESIDUAL Initial Stresses for Stiffeners WST4 and SST4 .............................. 5-222 5.6.4 Initial Conditions ................................................................................................. 5-224

5.7 STOP Command ........................................................................................................ 5-226 6. Running Instructions ............................................................................................................... 6-1

6.1 DATA AREA Requirement ........................................................................................... 6-1 6.2 Data-Manager Parameters .............................................................................................. 6-1 6.3 File Status ....................................................................................................................... 6-3 6.4 Warnings and Errors ...................................................................................................... 6-4 6.5 Running Instructions ...................................................................................................... 6-5 6.6 ASAS Initialisation File ................................................................................................. 6-8 6.7 Extended Syntax in Data Files ....................................................................................... 6-9

6.7.1 IF/THEN/ELSE ....................................................................................................... 6-9 6.7.2 DATA REPLACEMENT ...................................................................................... 6-12 6.7.3 The DEFINE Command ........................................................................................ 6-12

6.8 Secondary Data Files within ASAS-NL Data .............................................................. 6-13 6.8.1 Use of @filename command ................................................................................. 6-13 6.8.2 Notes about the @ Command ............................................................................... 6-14

6.9 Soft Halt Facility .......................................................................................................... 6-15 Appendix - A Element Description Sheets ............................................................................... A-1

A.1 Facilities Available for each Element Type ............................................................. A-1 A.2 Element Axes Systems ............................................................................................. A-8

A.2.1 Local Axes on Beam Elements ............................................................................. A-8 A.3 Beam Offsets .......................................................................................................... A-11

A.3.1 OFFS Command .................................................................................................. A-11


vii Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

A.3.2 OFFG and OFSK Commands ............................................................................. A-12 A.3.3 OFCO Command ................................................................................................. A-13 A.3.4 Finite Element Description Sheets ...................................................................... A-14

A.4 References ............................................................................................................ A-136 Appendix - B Material Models ................................................................................................. B-1

B.1 Linear Elasticity ............................................................................................................ B-1 B.1.1 Isotropic Material .................................................................................................. B-1 B.1.2 Anisotropic Material .............................................................................................. B-1 B.1.3 Orthotropic Material .............................................................................................. B-1 B.1.4 Laminated Material for Shell Elements ................................................................. B-2 B.1.5 Woven Material ..................................................................................................... B-4

B.2 Non-Linear Elasticity .................................................................................................... B-5 B.2.1 Hyperelastic Material ............................................................................................ B-5

B.3 Plasticity ........................................................................................................................ B-6 B.3.1 Yield Criteria ......................................................................................................... B-6

B.3.1.1 Von Mises ...................................................................................................... B-6 B.3.1.2 Tresca ............................................................................................................. B-6 B.3.1.3 Ivanov ............................................................................................................ B-6 B.3.1.4 Mohr-Coulomb .............................................................................................. B-7 B.3.1.5 Drucker-Prager .............................................................................................. B-8 B.3.1.6 Stress Resultant Plasticity for Beams ............................................................ B-8 B.3.1.7 Coulomb Friction ........................................................................................... B-9 B.3.1.8 Tension Cut-off .............................................................................................. B-9 B.3.1.9 Inelastic Spring .............................................................................................. B-9

B.3.2 Hardening Rules .................................................................................................. B-10 B.3.2.1 Isotropic ....................................................................................................... B-10 B.3.2.2 Kinematic ..................................................................................................... B-11 B.3.2.3 Combined ..................................................................................................... B-11

B.3.3 Equivalent Strain ................................................................................................. B-12 B.4 CREEP ........................................................................................................................ B-12

B.4.1 In-Built Creep Laws ............................................................................................ B-13 B.4.2 User Supplied Creep Laws .................................................................................. B-14

B.5 Composite Failure ....................................................................................................... B-16 B.5.1 Lamina Failure Criteria ....................................................................................... B-16 B.5.2 Laminate Failure Criteria .................................................................................... B-20 B.5.3 Failure Laws ........................................................................................................ B-22

B.5.3.1 In-Built Failure Law .................................................................................... B-22 B.5.3.2 User-Defined Failure Laws .......................................................................... B-24

B.6 User Material ............................................................................................................... B-26 B.7 References ................................................................................................................... B-31

Appendix - C Solution Strategies in ASAS-NL ....................................................................... C-1 C.1 Introduction ................................................................................................................... C-1 C.2 Incremental - Iterative Procedures ................................................................................ C-3

C.2.1 Introduction ........................................................................................................... C-3 C.2.2 Basic Definitions ................................................................................................... C-7 C.2.3 Incrementation procedures .................................................................................... C-8


viii Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

C.2.4 Iteration procedures ............................................................................................... C-9 C.2.4.1 Type of constraint surface ............................................................................. C-9 C.2.4.2 Iteration techniques ...................................................................................... C-11

C.2.5 Solution methods ................................................................................................. C-14 C.2.5.1 Euler-Cauchy method .................................................................................. C-14 C.2.5.2 Self-correcting Euler-Cauchy ...................................................................... C-15 C.2.5.3 Full incremental - iterative method .............................................................. C-15

C.2.6 Conclusions ......................................................................................................... C-16 C.3 Computation of Stresses .............................................................................................. C-17

C.3.1 Forward Euler Integration Scheme ...................................................................... C-17 C.3.2 Backward Euler Integration Scheme ................................................................... C-19

C.4 Convergence and Auto-Recovery ............................................................................... C-20 C.4.1 Convergence Check ............................................................................................. C-20 C.4.2 Auto-Recovery .................................................................................................... C-20

C.5 Eigenvalue Analysis .................................................................................................... C-21 C.5.1 Linear Pre-buckling Case .................................................................................... C-21 C.5.2 Non-linear Pre-buckling Case ............................................................................. C-21 C.5.3 Spectral Analysis ................................................................................................. C-22 C.5.4 Natural Frequency Analysis ................................................................................ C-23

C.6 Contact Analysis ......................................................................................................... C-23 C.6.1 Penalty Method .................................................................................................... C-23 C.6.2 Augmented Lagrangian Method .......................................................................... C-24

C.7 References ................................................................................................................... C-24 Appendix - D Restarts .............................................................................................................. D-1

D.1 Introduction .............................................................................................................. D-1 D.2 Initial Analysis ......................................................................................................... D-1 D.3 Restarted Jobs ........................................................................................................... D-2 D.4 Examples .................................................................................................................. D-3

Appendix - E Example Data Files ............................................................................................ E-1 E.1 Example 1: BM3D Plasticity Model (T0574) ............................................................... E-1 E.2 Example 2: TCS9 Geometric non-linearity (T0533) .................................................... E-3 E.3 Example 3: QUX4 Incompressible behaviour (T0540) ................................................ E-4 E.4 Example 4: QUS4 Elasto-plastic stiffened shell (T0553) ............................................. E-6 E.5 Example 6: QUS4 transient dynamics (T0591) .......................................................... E-12

Appendix - F List of Freedom Names .......................................................................................F-1 Appendix - G Isoparametric Elements ..................................................................................... G-1

G.1 Curvilinear Axes ....................................................................................................... G-1 G.2 Integration Rules ...................................................................................................... G-1

Appendix - H ASAS/ASAS-NL Compatibility ........................................................................ H-1 Appendix - I POSTNL General Post-Processor Interface Program .......................................... I-1

I.1 Introduction ......................................................................................................................... I-1 I.2 Usage .................................................................................................................................. I-1 I.3 FEMVIEW Interface ........................................................................................................... I-2

I.3.1 Primary Nodal Variables ......................................................................................... I-4 I.3.2 Primary Element Based Variables ........................................................................... I-5

I.3.2.1 Rotation of Shell Element Based Variables ..................................................... I-5


ix Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

I.3.3 Secondary Element Based Variables ....................................................................... I-6 I.3.3.1 Laminated Composite Shells ........................................................................... I-6 I.3.3.2 Surface and Global Failure Indices .................................................................. I-7 I.3.3.3 Laminated Composite Bricks ........................................................................... I-7

I.4 PATRAN Interface ............................................................................................................. I-8 I.5 Printer Interface ................................................................................................................ I-10 I.6 Time Histories ................................................................................................................... I-15 I.7 Rotation of Element Based Variables for Shells .............................................................. I-23

I.7.1 Introduction ............................................................................................................ I-23 I.7.2 Restrictions ............................................................................................................ I-23 I.7.3 The Plane Stress Transformation ........................................................................... I-23 I.7.4 Determination of the Rotational Angle, θ .............................................................. I-24 I.7.5 User Definition of New Local Axes Direction ...................................................... I-24 I.7.6 User Definition of Element Top and Bottom Surfaces .......................................... I-26 I.7.7 References .............................................................................................................. I-27

I.8 Fracture Mechanics Processing ........................................................................................ I-28 I.8.1 Introduction ............................................................................................................ I-28 I.8.2 Restrictions ............................................................................................................ I-28 I.8.3 Notes on the use of Fracture Parameters ............................................................... I-29 I.8.4 Format of Contour Definition File ......................................................................... I-29 I.8.5 Example ................................................................................................................. I-29

Appendix - J Creep Analysis ..................................................................................................... J-1 J.1 Overview ............................................................................................................................. J-1 J.2 Creep Solution Methods ..................................................................................................... J-2 J.3 Convergence of Creep Solutions ........................................................................................ J-3 J.4 Automatic Timestepping ..................................................................................................... J-3 J.5 Example Preliminary Data .................................................................................................. J-5 J.6 Recommendations for Creep Analysis ............................................................................... J-5 J.7 References ........................................................................................................................... J-6

Appendix - K Transient Dynamics Analysis ............................................................................ K-1 K.1 Overview .................................................................................................................. K-1 K.2 Time Integration Algorithm ..................................................................................... K-2 K.3 Automatic Timestepping .......................................................................................... K-3 K.4 References ................................................................................................................ K-9

Appendix - L References .......................................................................................................... L-1 Appendix - M Wave Loading On Offshore Jacket Structures ................................................. M-1

M.1 Introduction ............................................................................................................. M-1 M.2 Water Axes .............................................................................................................. M-1 M.3 Wave Theories ......................................................................................................... M-2

M.3.1 Conventional wave theories ................................................................................. M-2 M.3.2 Shell New Wave .................................................................................................. M-2 M.3.3 Irregular Wave ..................................................................................................... M-3

M.4 Wave load data format ............................................................................................ M-5 M.5 WAVE LOAD Data ................................................................................................ M-6 M.6 Description of the Wave Load Data Block ............................................................. M-8

M.6.1 WAVE LOAD Data ............................................................................................. M-8


x Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

M.6.2 AMAS Command ................................................................................................ M-9 M.6.3 BEAM Element Command ................................................................................ M-10 M.6.4 Current BLOCKAGE Factor Command ........................................................... M-10 M.6.5 BUOYANCY Command ................................................................................... M-11 M.6.6 CURRENT Command ....................................................................................... M-12 M.6.7 DRAG Coefficients ........................................................................................... M-14 M.6.8 ELEVATION Command ................................................................................... M-15 M.6.9 END Command ................................................................................................. M-16 M.6.10 EXECUTE Command ..................................................................................... M-16 M.6.11 FREE Flooding Command .............................................................................. M-17 M.6.12 GRAVITY Command...................................................................................... M-18 M.6.13 GRID Wave Command ................................................................................... M-20 M.6.14 Marine GROWTH Command ......................................................................... M-27 M.6.15 HYDR Command ............................................................................................ M-28 M.6.16 Keulegan-Carpenter Number Tables ............................................................... M-32 M.6.17 Wave KINEMATICS Factor Command ......................................................... M-33 M.6.18 LFUN Data ...................................................................................................... M-34 M.6.19 MASS Inertia Coefficients .............................................................................. M-35 M.6.20 MOVE Command ............................................................................................ M-36 M.6.21 NANG Command ............................................................................................ M-37 M.6.22 NOBM Command............................................................................................ M-38 M.6.23 NOBO Command ............................................................................................ M-38 M.6.24 NOFR Command ............................................................................................. M-38 M.6.25 NOLO Command ............................................................................................ M-39 M.6.26 NOSW Command ............................................................................................ M-40 M.6.27 NOWI Command ............................................................................................. M-41 M.6.28 NOWL Command............................................................................................ M-42 M.6.29 OFFSET Command ......................................................................................... M-43 M.6.30 OUTPUT Control Command ........................................................................... M-44 M.6.31 PEXT Command.............................................................................................. M-44 M.6.32 POINT Current Command............................................................................... M-45 M.6.33 PHASE Command ........................................................................................... M-47 M.6.34 PRINT Command ............................................................................................ M-49 M.6.35 Reynolds Number Tables ................................................................................ M-49 M.6.36 SLWT Command ............................................................................................. M-51 M.6.37 SPECTRAL Command.................................................................................... M-52 M.6.38 Wave SPREADING Command ....................................................................... M-53 M.6.39 STOP Command .............................................................................................. M-54 M.6.40 TIDE Command .............................................................................................. M-54 M.6.41 TOLERANCE Command ................................................................................ M-56 M.6.42 UNITS Command ............................................................................................ M-56 M.6.43 VAXS Command ............................................................................................. M-57 M.6.44 VISCOSITY Command ................................................................................... M-58 M.6.45 VPOS Command ............................................................................................. M-58 M.6.46 WAVE Command............................................................................................ M-59 M.6.47 WIND Command ............................................................................................. M-60


xi Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

M.6.48 WPAR Command ............................................................................................ M-61 M.6.49 XMAS Data ..................................................................................................... M-63 M.6.50 ZONE Data ...................................................................................................... M-64

M.7 Valid Options Controlling Wave Load Calculation .............................................. M-65 Appendix - N Heat Analysis ..................................................................................................... N-1

N.1 Introduction .............................................................................................................. N-1 N.2 Heat Equations ......................................................................................................... N-1 N.3 Convection ................................................................................................................ N-2 N.4 Radiation .................................................................................................................. N-2 N.5 Controlling a Heat Analysis ..................................................................................... N-2 N.6 Saving Heat Analysis Results ................................................................................... N-3 N.7 Interfacing with Stress Analysis ............................................................................... N-4

Appendix - O Coupled Wind and Wave Load Analysis of Offshore Wind Turbine ............... O-1 O.1 Introduction .............................................................................................................. O-1 O.2 The Analysis ............................................................................................................. O-1 O.3 Data for FLXG job ................................................................................................... O-3

O.3.1 JOB Command ...................................................................................................... O-3 O.3.2 Generalized Mode Definition ................................................................................ O-3

O.4 Output from FLXG job ............................................................................................. O-5 O.4.1 Generalized Matrix Files ....................................................................................... O-5 O.4.2 Generalized External Force File ............................................................................ O-5

Introduction ASAS (Non-Linear) User Manual

Page 1-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

1. Introduction

1.1 General Capabilities

ASAS-NL is a computer program for the static and dynamic analysis of engineering structures and components which exhibit some form of non-linear response. It is designed for engineers to use, specifically for problems involving plasticity, creep and large displacement effects, including buckling and gapping. For linear elastic problems the parent program ASAS is usually more appropriate. The program is based on a finite element formulation of the structural behaviour and uses an incremental procedure to represent the loading process and response of the structure. A displacement formulation of the finite element method is used.

An extensive range of finite elements is provided for modelling both structures and continua. The material models available include most popular theories of elasto-plastic behaviour and some specialist models for failure. Large displacement effects may be taken into account where appropriate. Extensions to handle other nonlinear effects have been allowed for in the program’s modular design, and are being developed.

ASAS-NL can treat a wide range of loadings. Loads may be presented as any combination of point forces or moments, prescribed displacements, pressures, temperatures, body forces, centrifugal loads or angular accelerations and may be applied incrementally or specified as a function of time.

The program is a further development of the ASAS family and, although a separate program, it is fully compatible with other ASAS programs. Wherever appropriate the data input and output is ‘standard ASAS’.

The following ASAS programs interface with ASAS-NL through the interactive post-processing program, POSTNL:

FEMGEN/FEMVIEW Interactive graphical model building and results display.

In addition a number of proprietary general purpose graphics programs including PATRAN interface with ASAS-NL to provide capabilities for model generation and results viewing.

ASAS-NL is written in FORTRAN and is readily transportable to differing computer types. The present version is available on PC only.

ASAS-NL is thoroughly described in its documentation. This User Manual contains full instructions for using the system, including choice of facilities, data preparation and running instructions. Revisions of this User Manual are circulated to all registered holders.

1.2 Using this Manual

This document is intended to serve both as a reference manual for the experienced ASAS-NL user and also as an introduction to the program. In general the introductory and explanatory sections are contained in the first few sections and the reference sections are placed at the end or in Appendices. The level of presentation and background knowledge assumed of the user is adjusted to suit the complexity of the subject matter. No attempt is made to cover the theory of finite elements or structural mechanics, but useful references are provided in Appendix -L.



Section 2 is an introduction to the types of analysis available. It contains brief descriptions of the program’s

various capabilities and also introduces terminology used in later sections.

Section 3 describes the modelling facilities that are contained in ASAS-NL. It includes information and advice

on the element and material types available and information on key features such as node numbering, local axis

systems, supports, loading and control of the program.

The data required to run the program is described in outline, in Section 4 The function of each data block type

is explained and the procedures for controlling the operations of the program are presented. This section is

essential reading for both new and experienced users.

Section 5 is intended as a reference section. It describes the format of each block of ASAS-NL data and gives

examples of their use.

In Section 6 information relevant to specific machine installations is presented. Users should ensure that this

corresponds to their version. It contains running instructions and information for estimating size and cost

parameters together with any restrictions.

Various reference material is presented in Appendices.

Appendix -A is a key feature of the manual. It contains ‘element description sheets’, giving detailed

information about each element in the ASAS-NL library.

Appendix -B provides details of and reference to each material model available.

Appendix -C gives a description of the solution procedures used in ASAS-NL with an account of the control

options available to the user.

Appendix -D describes the Restart facility.

Appendix -E gives details of some example data files. A comprehensive series of test, verification and

educational input data files can be included with the computer programs.

Appendix -F gives a list of the names of the freedoms which may be present at a node.

Appendix -G explains the conventions for setting up local axes and the integration rules used for all

isoparametric elements.

Appendix -H lists necessary differences in data format between ASAS and ASAS-NL. These may impose

restrictions in modelling problems which are to run on both programs.

Appendix -I describes the interface program POSTNL required by various post-processors.



Appendix -J gives additional instructions for creep analyses.

Appendix -K describes transient dynamic analysis.

Appendix -L contains a list of general references.

Appendix -M describes the wave loading capability in ASAS-NL.

Appendix - N describes heat analysis

Appendix - O describes coupled wind and wave load analysis of offshore wind turbines

Types of Analysis Available ASAS (Non-Linear) User Manual


2. Types of Analysis Available

2.1 General

ASAS-NL is a general purpose computer program aimed at providing solutions to non-linear problems across the broad field of structural mechanics. Therefore the facilities included in the program are subject to continual enhancement as new problems arise and solution methods are improved. To accommodate this development to the ‘state of the art’, the program has a highly modular structure communicating with a ‘data manager’ which is tailored to the needs of non-linear analysis.

The analysis capabilities currently available include the following:

• Static linear elastic

• Static, non-linear incremental - STAT type

• Transient, non-linear incremental - TRAN type

• Eigenvalue extraction - buckling or natural frequency

• General field

• Piezo-resistivity - PIER type

• Steady state heat - HEAT type

• Transient heat - HTRA type

It should be noted that this categorisation influences the type of solution procedure which is employed by the program and not the actual structural behaviour (thus for example a solution could be obtained to a linear elastic problem using the non-linear incremental procedure - albeit inefficiently).

ASAS-NL solves the system of equations using the frontal solution technique. As well as an ordinary frontal solver, an optimised frontal solution is also available that can greatly reduce the solution time and storage requirements in medium to large problems.

2.1.1 Static Linear Elastic Solution

In general, a linear elastic problem is better tackled using the ASAS program. However, the linear elastic option is included for applications where the model can be classified as small and/or where a linear elastic analysis is the first tentative step in the design analysis before launching into a more expensive non-linear run. The facilities available in ASAS-NL are generally the same as those in ASAS. The main differences are a somewhat



reduced element library (see Section 3.1), treatment of a single loadcase at a time and the absence of the substructuring facility. An important addition in ASAS-NL is the ability to handle generalised plane strain.

2.1.2 Static Non-Linear Incremental Solution

This category includes problems in which the non-linearity is due to any combination of the following:

• large displacement effects

• non-linear elastic material behaviour

• plasticity

• laminated composite failure behaviour

• soil and rock-like material behaviour

• non-linear boundary conditions (gaps and rigid surface contact)

The loading may be applied in a proportional or quite general non-proportional manner. In the latter case a ‘pseudo’ time scale is defined by the user to specify the sequence of loading.

Any given type of non-linear behaviour can be restricted to certain areas of the structural model, by use of ‘groups’ of elements and by use of different material identifiers.

The analysis procedure for these problems requires that the load is applied incrementally and the program then provides several alternative methods for determining the structural response. These methods are a completely flexible combination of various incremental-iterative procedures such as load or displacement incrementation complemented by a selection of Newton-Raphson iteration techniques.

In the absence of other directives, the program automatically selects the Initial Stiffness iteration for all increments. However experienced users can control the type of method or combination of methods, to be used for each increment together with the order of non-linear theory required. A full explanation of the incremental and iterative methods available is contained in Appendix -C.

2.1.3 Transient Non-Linear Incremental Solution

This category includes all problems where the material or structural response is a function of real time.

(a) Creep Analysis

Creep is the generic term used in ASAS-NL to denote the time dependent material response associated with long timescales. See Appendix -J for further details. Allowance has been made within the modular design of ASAS-



NL for the more rapid time dependent material response associated with high velocity impact and metal forming processes. These capabilities are planned for future development.

(b) Non-Linear Transient Dynamic Analysis

Problems which require the inertia effects of the mass of the structure to be included come under the category of transient dynamic analysis. Such an analysis is required where loading varies rapidly such as during blast from an explosion or ground motion from an earthquake. In ASAS-NL the equations of motion are solved at discrete points in time with the solution advancing in a stepwise manner. All the non-linear effects associated with a static non-linear incremental solution (see Section 2.1.2) may be included in the analysis if required.

For transient dynamic analysis, the modelling of inertia (mass) is just as important as ensuring that the stiffness characteristics are adequately represented. Three basic forms of mass matrix are available in ASAS-NL:

(i) The program assembles the mass matrix from user specified lumped mass values at appropriate nodes to

produce a Direct Input Mass Matrix.

(ii) The program assembles the mass matrix from the mass of each element lumped at its nodes (the Element

Lumped Mass Matrix).

(iii) (The program assembles the mass matrix from the actual distribution of mass within each element (the

Element Consistent Mass Matrix).

These three forms can be mixed within a structure if required. The mass of selected elements can be omitted by flagging the appropriate element topology commands. If no mass type is selected specifically, the type of element mass matrix defaults to that given in Appendix -A.

2.1.4 Eigenvalue Extraction

In ASAS-NL, the two main applications of eigenvalue analysis are to provide solutions for stability and free vibration problems. The subspace iteration technique is employed to solve the eigenproblem which will compute the lowest few eigenvalues requested by the user.

(a) Stability Analysis

This type of analysis is used to determine the buckling loads and associated modes of the structures. The pre-buckling behaviour can either be linear or non-linear. Full details concerning stability analysis are given in Appendix C.5.1 and C.5.2.

(b) Natural Frequency Analysis

This type of analysis provides the natural frequencies and associated vibration mode shapes of unloaded or pre-loaded structures.



In ASAS-NL, natural frequency analysis can be performed on free-free structures provided that a suitable shift is specified.

Loading data need not be present for free vibration analysis but a warning message will be given. This facility allows the user to determine natural frequencies of an unloaded structure.

Full explanation of natural frequency analysis can be found in Appendix C.5.4.

2.1.5 Steady State Heat Solution

This category provides solution to steady state heat transfer problems. The procedure is principally applied to heat conductivity problems although secondary convective and radiative heat transfer effects may also be included.

For this type of solution, non-linearity arises from the temperature dependency of heat transfer coefficients. Their variations with temperature may be specified as temperature dependent material property data.

As in stress analysis, the heat input (cf loading) may be applied in a proportional or quite general non-proportional manner.

A selection of Newton-Raphson iteration techniques is available for non-linear solution as described in the static non-linear stress analysis solution.

2.1.6 General Field Analysis

There are a wide range of engineering problems, eg electrical conductivity, ideal fluid flow and seepage through a porous medium that are governed by Laplace’s equation. Field elements with a single degree of freedom at each node are available for the solution of such problems.

2.1.7 Piezo-resistivity Analysis

A piezo-resistive material is one which experiences a change in electrical conductivity when the applied stress field changes. ASAS-NL is capable of solving both the stress and the electrical field problem simultaneously. THIS CAPABILITY IS CURRENTLY RESTRICTED AND IS NOT GENERALLY AVAILABLE.

Program Features ASAS (Non-Linear) User Manual


3. Program Features

3.1 Types of Element

The ASAS-NL library contains elements which are capable of modelling both continuum and structural forms. The great majority are identical in their linear format to parent elements in ASAS, so that compatibility is maintained. Specialisations are, however, introduced as required for non-linear applications.

Each type of element has a distinctive four character name, which indicates its form and number of nodes.

e.g. TCS8 - Thick Curved Shell with 8 nodes

A full description of each element type is provided in the element description sheets of Appendix -A.

Most element types are ‘isoparametric’ and have considerable versatility to model geometric and material variations. However, excessive distortions from rectangular (or equilateral triangular) planform should be avoided. Most element matrices are evaluated using numerical integration. The number of integration points in the direction of the local curvilinear axes can be specified by the user, but the default values implemented in the program are normally recommended. The default integration rule generally corresponds to the ‘reduced integration technique’. Appendix -G gives details of the various integration rules available, and an explanation of local curvilinear axes.

In all elements, large displacement effects are taken into account by updating the geometry and using the geometric stiffness matrix and non-linear geometrical relations. These relations are defined employing an Updated Lagrangian formulation.

Elements may be placed together in ‘groups’. This is advantageous where it is required to vary, from group to group, the type of behaviour modelled or the output printed. Certain elements must belong to their own groups (see Appendix -A).

In the following sections elements are described according to their family.

3.1.1 Uniaxial Element

FLA2 - 2 node uniaxial constant stress element.

This element has some use as a tie/strut element, but its principal application is in association with other elements, to represent boundary conditions and stiffeners.

3.1.2 Plane Stress/Strain Elements

These elements are essentially 2-D and are intended for problems in which a state of plane stress or plane strain exists in the plane of the element.



TRM3 - 3 node isoparametric triangle

QUM4 - 4 node isoparametric quadrilateral

TRM6 - 6 node isoparametric triangle

QUM8 - 8 node isoparametric quadrilateral

Unless specifically requested, the elements are plane stress elements lying in 3-D space with three degrees of freedom per node. Special options convert them to plane strain, generalised (engineering) plane strain, or plane stress forms with two degrees of freedom per node. In generalised plane strain, the strain normal to the plane is everywhere uniform, but not zero. As a general rule, quadrilateral elements are to be preferred to triangles and the higher order elements with mid-side nodes to the lower order ones.

3.1.3 Axi-symmetric Solid Elements

These elements are intended for the idealisation of 3-D solids with a rotational axis of symmetry, under rotationally symmetric loading and support conditions

TRX3 - 3 node isoparametric triangular toroid

QUX4 - 4 node isoparametric quadrilateral toroid

TRX6 - 6 node isoparametric triangular toroid

QUX8 - 8 node isoparametric quadrilateral toroid

In general the higher order elements (QUX8 and TRX6) are better performers than the lower order ones and quadrilaterals are to be preferred to triangles.

3.1.4 Three-Dimensional Solids

The brick family are applicable to general 3-D solids under arbitrary loading.

BRK6 - 6 node isoparametric pentahedron (wedge)

BRK8 - 8 node isoparametric hexahedron

BR15 - 15 node isoparametric pentahedron (wedge)



BR20 - 20 node isoparametric hexahedron

LB15 - 15 node isoparametric laminated pentahedron (wedge)

LB20 - 20 node isoparametric laminated hexahedron

BR15 and BR20 are to be preferred in most situations to BRK6 and BRK8 due to their superior performance and versatile shape.

3.1.5 Gap/Interface Elements

A family of gap/contact and interface elements are available to model interface problems in two and three dimensions. Frictional forces can be included.

Gap elements are available to model node-to-node contact between two flexible structures.

GAP2 -can be used freely with the 2-D and 3-D elements but it is recommended that they interface with

the lower order elements.

GAPR-can be used to model tube-in-tube or external contact between two parallel tubes.

GAPX -is compatible with all the axisymmetric elements, but the lower order elements are to be

preferred.

Rigid surface interface elements are available to model contact between a structure and a rigid surface.

RGX3-rigid surface interface for use with lower order axisymmetric solid elements

RGX4-rigid surface interface for use with higher order axisymmetric solid elements

RG23-rigid surface interface for use with lower order 2-D plane elements

RG24-rigid surface interface for use with higher order 2-D plane elements

3.1.6 Plates, Shells and Beams

The plate and shell elements are isoparametric elements with six degrees of freedom per node. They are thick curved elements with transverse shear flexibility. The interpolation for the in-plane stretching behaviour is quite independent of the interpolation for bending. By using reduced integration they are in general satisfactory for both thick and thin shells (say diameter- thickness ratios of up to 1000).

QUS4 - 4 node quadrilateral facet shell.



TCS6 - 6 node generally curved triangular shell

TCS8 - 8 node generally curved quadrilateral shell

TCS9 - 9 node generally curved quadrilateral shell

Three elements are available to model stiffeners.

STF4 - 3 node isoparametric beam element with range of (closed) cross-sections

SST4 - 3 node isoparametric beam element with arbitrary open cross-section (no warping)

WST4 - 3 node isoparametric beam element with arbitrary open cross-section allowing warping

(7 degrees of freedom per node)



Two two-noded engineering beams are available. BEAM - 2 node 3-D beam element, transmitting both axial forces and bending moments and

suitable for most 3-D frames includes rigid offsets

BM2D - 2 node 2-D beam for plane frames subject to in-plane loading, allows for rigid offsets.

BM3D - 2 node 3-D beam element, transmitting both axial forces and bending moments, suitable for

most 3-D frames, which allows for the effect of shear deformation, arbitrary local axes, and

rigid offsets.

TUBE - 2 node 3-D beam element with hollow circular cross-section which allows for arbitrary

local axes and rigid offsets.

3.1.7 Spring/Dashpot Elements

These elements are linear or non-linear spring and/or dashpot elements with stiffness and/or damping in one specific direction. This line of action can be fixed or varied with deformation.

SPR1 - 2 node spring/dashpot element with translational freedoms

SPR2 - 2 node spring/dashpot element with rotational freedoms

3.1.8 Linespring Elements

These elements are used to model surface flaws on a shell structure. Plasticity can be included.

LSP3 - 3 node linespring element for use with higher order shell elements on a symmetric

boundary

LSP6 - 6 node linespring element for use with higher order shell elements

3.1.9 Uniaxial Field Elements

These elements are 1-D field elements used to represent uniaxial conduction, etc.

FAT2 - 2 node uniaxial field elements

FAT3 - 3 node uniaxial field elements



3.1.10 Two Dimensional Plane Field Elements

These elements are used to represent plane or 2-D regions in a field analysis. No through-thickness variations of the field variable is permitted.

TMT3 - 3 node triangular field element

QMT4 - 4 node quadrilateral field element

TMT6 - 6 node curved triangular field element

QMT8 - 8 node curved quadrilateral field element

3.1.11 Three Dimensional Solid Field Elements

These elements are used to represent 3-D continuum regions in a field analysis.

BRT6 - 6 node isoparametric wedge field element

BRT8 - 8 node isoparametric hexahedron field element

BT15 - 15 node isoparametric wedge field element

BT20 - 20 node isoparametric hexahedron field element

3.1.12 Axisymmetric Solid Field Elements

These elements are used to represent 3-D axisymmetric continuum regions in a field analysis.

TXT3 - 3 node isoparametric triangular field toroid

QXT4 - 4 node isoparametric quadrilateral field toroid

TXT6 - 6 node isoparametric triangular field toroid

QXT8 - 8 node isoparametric quadrilateral field toroid

3.2 Material Model Types

Several constitutive laws are available for material modelling. They are divided into groups of elasticity, plasticity, creep and failure. In general all material models require elastic material data and usually data for a plasticity, creep or composite failure model also. In addition, a user material interface is provided for users to define their own constitutive behaviour for a material. Details of all material models are given in Appendix -B.



Each material used in the analysis is identified by a number (the material integer) which is referenced by all elements comprised of that material. The same material integer is used for all the properties of a single material (i.e. for elastic, plastic and creep data).

All material properties may be temperature dependent. The relevant material values are specified at a set of reference temperatures and the program interpolates between them for the material properties at any required temperature.

3.2.1 Elasticity

Elasticity covers both linear elastic and non-linear elastic (temperature dependent or hyperelastic material) models. For linear elasticity, the material can be either isotropic, orthotropic, woven, anisotropic or laminate.

For isotropic linear elastic material, the modulus of elasticity, Poissons ratio, coefficient of linear expansion and density are generally required.

For orthotropic or woven material, the density, the three principal values of Young’s modulus, shear modulus, Poisson’s ratio and expansion coefficient are required.

Anisotropy is defined by giving either the coefficients of the general material elasticity matrix (i.e. the stress-strain relation) or the coefficients of the compliance matrix (i.e. strain-stress relation), together with the coefficients of linear expansion and density. The amount of information required for anisotropic material will vary with the type of element for which it is being used. The requirements of each element type are detailed in Appendix -A.

Laminate material is used to define composite shells and the density of the laminate may be provided. The layup configuration and the materials used in the laminate are defined as geometric properties.

The hyperelastic material model implemented in ASAS-NL is a modified form of the Mooney-Rivlin model which extends the original model to the compressible range. The Mooney-Rivlin model is associated with the analysis of rubber-like materials which are almost incompressible with the bulk modulus a few orders of magnitude larger than the shear modulus. The well known difficulties associated with this incompressibility for finite element solutions are overcome in ASAS-NL by modifying the volumetric part of the strain-displacement relationship. This involves a reduced order of pressure interpolation which is specified by the user as required. The Mooney-Rivlin hyperelastic material model requires two constants, C10 and C01 to be specified by the user.

3.2.2 Plasticity

Plasticity is the generic term used in ASAS-NL to describe all time-independent non-reversible material behaviour. It includes not only the classical plasticity theories applicable to most metals, but also some simple theories to account for the behaviour of soils, rocks and concrete.

There are two requirements of any definition of plastic behaviour:



(i) A yield criterion to define the stress level at which plastic deformation first occurs and which also

provides the constitutive relationship between plastic strains and stresses. ASAS-NL has been developed

to allow separate specification of yield criterion and flow rule and hence wide generality. However, all

material models of the current version have an associative flow rule implemented and the more general

capability is not yet utilised.

(ii) A hardening rule to define how the yield criterion is modified by subsequent plastic deformation.

3.2.2.1 Yield Criteria

The following yield criteria are available:

• Von Mises

• Tresca

• Ivanov

• Mohr-Coulomb

• Drucker-Prager

• Tension Cut

• Beam Stress Resultant

• Coulomb Friction

• Inelastic Spring

Both von Mises and Tresca criteria are widely applied to the behaviour of metals, but experimental evidence generally favours von Mises. The Tresca criterion is frequently used, on account of its simplicity, in analytical solutions and is useful for validation purposes.

The Ivanov yield criterion is applicable only to plate and shell behaviour and thus is restricted to certain elements. Yield is defined in terms of through thickness stress resultants (i.e. forces and moments per unit width).

Both Mohr-Coulomb and Drucker-Prager criteria are applicable to soils and rock-like materials. Implicit in these criteria is a dependence on the hydrostatic stress, which is a pre-requisite of any attempt to model soil behaviour.

The tension cutcriterion is applicable to model concrete cracking. Failure is defined in terms of principal stresses.

The beam stress resultant yield criterion is applicable only to the engineering beams. Yield is defined in terms of stress resultants and the whole section is assumed to plastify instantaneously.



The Coulomb friction criterion is only available for rigid surface elements (and implicitly to gap elements) to model the interface behaviour.

The inelastic spring model is only applicable to the spring elements. This can be used to model the hysteretic behaviour under cyclic loading.

3.2.2.2 Hardening Rules

Unless specifically requested, the program assumes that isotropic hardening (or softening) occurs. This corresponds to the yield surface expanding uniformly about the origin (for example a uniaxial model under cyclic loading yields at the same value in both tension and compression and no Bauschinger effect is reproduced). Isotropic hardening is usually satisfactory for problems where unloading does not occur and indeed for cyclic loading of work hardened metals.

Kinematic hardening is available on request. The yield surface translates as a rigid surface upon plastic deformation. With the Prager type the direction of travel is normal to the yield surface at the point concerned and is applicable only to solids and axisymmetric solid elements. Ziegler type hardening is an attempt to generalise Prager’s hypothesis to reduced stress spaces and results in the yield surface translating in the direction of the stress vector. A combination of either kinematic forms with isotropic hardening is available by giving the ratio of kinematic to isotropic hardening (see Appendix -B for further details).

The work hardening behaviour is defined by the material’s uniaxial stress-strain curve. This curve is specified by a tabular representation of point values for varying temperatures. Linear interpolation between these point values is used which effectively idealises the curve as a series of line segments and can be considered as equivalent to specifying a series of slopes. A special case of this type of description gives a bi-linear work hardening or perfectly plastic model if required.

In the absence of other directives then von Mises yield criteria and the associated Prandtl-Reuss flow equations with isotropic hardening are assumed. The user then need take no further action.

3.2.3 Creep

Creep is the generic term used in ASAS-NL to describe all time dependent material behaviour. Creep and plasticity models cannot be used concurrently in any one load step.

The creep material model requires the definition of a uniaxial creep strain rate and to extend this to multiple axes the Mises potential function and associative flow rule are used. Four general ‘In-Built’ equations (“Laws”) are available for the uniaxial creep strain rate and these optionally include strain or time hardening. The constants for the equations are supplied by the user to match the material being modelled. If the required behaviour cannot be defined by these then user-supplied subroutines may be added to the program to define the uniaxial rate as a function of stress, strain, time and temperature.



If supplying a creep subroutine users should note that many commonly used primary creep laws yield an infinite creep rate at zero time which can cause numerical problems in the program. This can be avoided by suitable adjustment of the creep law for times close to zero, or by providing a small offset to the time axis.

It is also important to ensure that any implied system of units in the creep law is consistent with the units being used in the analysis.

3.2.4 Failure

Failure material models are used in ASAS-NL to describe the material failure behaviour of composite laminates. Failure material properties may be specified to define the strength properties of a lamina, the strength properties of the whole laminate, or, the parameters required for in-built or user defined failure laws.

3.2.5 Field

Field material properties are used in ASAS-NL to describe the ‘material’ properties for the field elements. The actual type of properties will depend on the field problem being analysed. For example, if the electrical field problem is being analysed, the properties will relate to the electrical conductivities.

3.2.6 Piezo-Resistivity

Piezo-resistivity material properties are used in ASAS-NL to describe the properties of a piezo-resistive material for the coupled stress/electrical conduction problem.

3.2.7 Heat Convection

This type of material is used in ASAS-NL to model general non-linear convective heat transfer in a heat analysis.

3.2.8 Heat Radiation

This type of material is used in ASAS-NL to model radiant heat transfer in a heat analysis.

3.3 Loading

Within ASAS-NL the word ‘LOAD’ signifies any externally imposed influence and includes prescribed displacements and temperatures. Any number of different load types may be combined together and their



proportions may vary over the load history (i.e. the loading can be ‘non-proportional’). Only one loadcase can be analysed in a single analysis.

The individual load types are listed in the following sections.

3.3.1 Nodal Loads

A nodal load is a force or moment associated with a freedom at a node. Loads may be applied in skew directions by use of skew systems (see Section 3.6).

3.3.2 Prescribed Displacements

Prescribed displacements may be imposed on any nodal freedoms, in skew directions if required. The user first specifies which freedoms are to be prescribed and then quotes displacement values for them. The nodal reactions associated with each prescribed freedom are calculated automatically by the program.

3.3.3 Pressure Loads

A constant or spatially varying pressure distribution may be applied to any set of element faces. The distribution is defined by the pressure values at the nodes on the faces. The default direction in which the pressure acts depends on the element type and is described for each element in Appendix -A. Pressure can also be applied in a specific direction.

For large displacement problems the pressure load is of non-conservative (follower) character. If required, this however can be changed by the user to conservative load type (see Section 5.1 GROU/PROB/TITL command).

3.3.4 Distributed Loads

Distributed loads and intermediate point loads can be applied to some types of element as described in Apprendix A

3.3.5 Temperature Loads

The effect of thermal straining due to a given temperature distribution can be determined. The distribution can be defined at the nodes or on elements. Temperature loads are calculated from the difference between the supplied nodal temperatures and a pre-specified reference temperature. (The latter is taken as zero unless specified otherwise - see Section 4.3.4.) The required nodal temperatures can either be specified directly or



obtained from ASASHEAT using the HOTRAN program. (For details of the latter see the ASASHEAT User Manual).

On higher order elements, with mid-side nodes, only corner node temperatures are required. The program will over-ride, with interpolated values, any supplied temperatures for mid-side nodes.

Temperature fields which are discontinuous across element boundaries, can either be applied by using Groups with nodal temperatures or element temperatures.

For problems with temperature dependent material data, material properties are evaluated at the supplied nodal temperatures and the reference temperature is not used.

3.3.6 Face Temperature

The effect due to a difference of temperature through the thickness of a shell element can be determined. The program requires the temperatures of both faces at some or all of the nodes. Alternatively, the face temperature values on some or all of the elements can be specified.

On higher order elements, with mid-side nodes, only corner node temperatures are required. The program will over-ride, with interpolated values, any supplied temperatures for mid-side nodes.

Temperature fields which are discontinuous across element boundaries, can be applied by using Groups.

For problems with temperature dependent material data, material properties are evaluated at the mid- surface temperatures (i.e. average of top and bottom surfaces) and the reference temperature is not used.

3.3.7 Body Forces

Self weight, or the effect of uniform acceleration fields, are provided by this load type. The user specifies the components of acceleration along each of the three global axes, and the body forces are automatically determined for these acceleration components for all elements in the model. A density value must be specified for all materials. The units of density and acceleration must be consistent with the units used in the remainder of the data (see Section 3.11).

3.3.8 Centrifugal Loads

Centrifugal loading is available for most elements. It is applied by specifying the centre of rotation, together with the angular velocity about each of the three global axes. A density value is required for all materials. The units of density and angular velocity must be consistent with the units used in the remainder of the data (see Section 3.11).



3.3.9 Angular Accelerations

Angular acceleration loading is available for most elements. It is applied by specifying the centre of rotation together with the values of angular acceleration and/or velocity about each of the three global axes. A density value is required for all materials. The units of density, angular acceleration and velocity must be consistent with the units used in the remainder of the data (see Section 3.11).

3.3.10 Nodal Fluxes

A nodal flux is a flux associated with freedom T at a node. This load type applies to field analysis only.

3.3.11 Prescribed Field Variables

A prescribed field variable may be imposed on the nodal freedom in a field analysis. The user first specifies which freedoms are to be prescribed and then quotes values for them. The nodal reacted fluxes associated with each prescribed freedom are calculated automatically by the program.

3.3.12 Flux Densities

A constant or spatially varying flux density distribution may be applied to any set of element faces or volumes. The distribution is defined by the flux density values at the nodes on the faces or elements.

3.3.13 Wave Load

The loading due to wave, wind and current on fixed offshore structures may be included with this load type. The envionmental loads are only applied to BEAM, BM3D and TUBE elements.

3.3.14 Tank Loads

If a floating structure has internal tanks that are filled with fluid, the combination of gravity and any motion of the vessel will cause pressure loads on the walls of those tanks. By specifying the tank geometries together with the internal fluid levels and densities, ASAS(NL) can automatically calculate the pressure loads on the tank walls.



3.3.15 Load History

The load history (or load sequence in time independent problems) and the corresponding response of the model is defined by reference to a ‘pseudo-time’ axis. For other than creep or dynamic analyses pseudo-times have no physical meaning; their values are used only to sequence the application of load and identify the increments.

Unless directed otherwise the program assumes a load history corresponding to a single application of a proportionately increasing load.

More complex load histories may be specified in one of two ways. Firstly, the complete spatial load distribution can be defined explicitly at each required pseudo-time. Proportional loading is implied between each load state. This is usually the most convenient way when there are relatively few such load sets. Alternatively, a load history may be specified by supplying a set of ‘load functions’ to define a few reference load states. The functions define the proportion of each of the reference load’s components to be applied at any pseudo-time. This allows quite general application of non-proportional loading.

For problems with cyclic loading, there is provision to repeat automatically a given load history any number of times.

3.4 Node Numbers and Coordinates

Each node in the finite element idealisation must be given a unique positive integer number, so that an element can be identified unambiguously by the node numbers on its boundaries. The shape and orientation of an element is determined by the coordinates of these nodes.

If the structure has N nodes, the node number need not necessarily be within the range 1 to N; gaps in the numbering are allowed and are often helpful. The gaps should preferably be small (eg. less than N).

The geometry of the elements and of the structural model is defined by the coordinates of the nodes. In general, the coordinates must be supplied for all nodes on the structure. However, for elements with straight edges the coordinates of any mid-side nodes can be calculated by the program.

The coordinates of a node or group of nodes may be defined in any convenient rectangular cartesian, cylindrical polar or spherical polar coordinate system. An idealisation may use several of these coordinate systems. The only exception is an axisymmetric idealisation where the cylindrical polar coordinates which are implicit in the element must be input as a cartesian system.

The relationship of coordinate local axes or skew systems to the global system is given by the direction cosines of their axes relative to the global axes. Each direction cosine gives the projection of a unit vector along the skew axis on to the global axis. Skew systems must be right-handed and orthogonal.

It is only necessary to specify two of the axes; the third is computed automatically. If X’, Y’, Z’ represent the skew axes, and X, Y, Z the global axes, ASAS-NL requires the six direction cosines:

X’X, X’Y, X’Z, Y’X, Y’Y, Y’Z



where, for example X’X is the projection on to the global X axis of a unit vector along the skew X’ axis. For a 2-D system within the X-Y plane, both X’Z and Y’Z will be zero.

As an alternative to specifying the direction cosines of the local axis system with respect to the global axis system, a set of three node numbers may be used to identify the skew system, with ASAS-NL automatically calculating the direction cosines (see Section 5.2.7.2).

3.5 Element Numbering

The program numbers elements automatically in the order in which they are first defined (the “input element number”). Alternatively users can number each element explicitly (“user element number”). The user element number (which defaults to the input element number if it is not given) is used as an identifier to specify the group structure, integration rules and order of output.

Elements are defined by their constituent node numbers. The starting node and order of numbering (clockwise or counter-clockwise) determines the direction of the local curvilinear axes. (See Appendix -G).

The program reorders the elements internally (the “system element number”) in an attempt to keep the maximum frontwidth as small as possible. It allocates system element numbers on the basis of least node number order. Elements are then assembled into the front of this order. Special options may be used, however, to suppress this reordering and to use either the user or input element order within the solution process. (See MYEL and INEL options)

If no attention has been paid to the node number sequence, which will effect the order of system element numbering, the frontwidth optimiser can be invoked, using the PASS command, to reduce the incore frontwidth. Five different methods are available in the program, namely CUTHILL-MCKEE, KING, LEVY, PINA and SLOAN. CUTHILL-MCKEE is basically an algorithm for out-of-core bandwidth reduction but it may also be used to optimise the incore frontwidth effectively. The others, however, are all methods for incore frontwidth optimisation but, apart from SLOAN, they do take significantly more time to do the optimising (typically an order of magnitude or more per pass compared with CUTHILL-MCKEE). This increase can be offset by use of the user defined START node facility to reduce the number of passes attempted. The revised system element ordering is carried out internally without renumbering the nodes and therefore its operation is transparent to the user. Since the element ordering will be changed when using the frontwidth optimiser, the user or input element order options should not be specified.

3.6 Global and Local Axis Systems

Regardless of the system(s) used to define coordinates, the displacement freedoms within ASAS-NL are usually referred to the global axis system. This is a right-handed rectangular cartesian (X,Y,Z) system, except for the axisymmetric elements, which use a cylindrical polar system (R,Θ,Z). In some cases the global axis system is replaced for selected nodes or elements by a local axis system. There are three broad types of these: coordinate local axes, element local axes and nodal local axes. The latter are known as ‘skew systems’.



3.6.1 Coordinate Local Axes

Coordinate local axes are used to define the positions of nodes in space. Any required combination of cartesian, cylindrical polar or spherical polar systems may be used; all of them are transformed to the global system within the program. For each local system, the user provides the origin and the direction cosines relative to the global system. Coordinates may, of course, be entered directly in the global system if required.

3.6.2 Element Local Axes

Many types of element have their own local axes. These are used as the reference frame for stress and strain results and also, in certain elements, for the geometric properties. The direction of the element local axes is defined by the order and location of the nodes on the elements and in large displacement analyses will vary throughout the analysis. Full details are given in the relevant element description sheets in Appendix -A.

3.6.3 Skew Systems

Skew systems, otherwise known as nodal local axes, can be used for three purposes:

(i) To specify suppressions, prescribed displacements or constrained freedoms (see Section 3.7) in directions

other than those of the global axis system. All output of displacements and reactions is related to this new

axis system. Only one such skew system is permitted at a node.

(ii) To specify nodal loads in a direction other than the reference system, where the reference system is either

the global system or the global system as modified by a skew system defined in (i). For example, if a

node is skewed to allow a skew suppression, and a nodal load is required in the global direction, then a

further skew system is required to ‘re-skew’ the load back to the global system. Nodal loads applied with

a skew system are transformed to their components in the reference system described above. The axis

system at the node is not altered and hence any number of skew systems may be applied at a node to

accommodate various skewed nodal loads.

Each skew system is defined by a unique integer number - the skew integer. The same skew system may

be referred to in several places in the data.

The relationship of coordinate local axes or skew systems to the global system is given by the direction

cosines of their axes relative to the global axes. Each direction cosine gives the projection of a unit vector

along the skew axis onto the global axis. Skew systems must be right-handed and orthogonal. See

Section 5.2.7.1.



It is only necessary to specify two of the axes: the third is computed automatically. If X’, Y’, Z’

represent the skew axes and X,Y,Z the global axes, ASAS-NL requires the six direction cosines:

X’X, X’Y, X’Z, Y’X, Y’Y, Y’Z

where, for example, X’X is the projection onto the global X axis of a unit vector along the skew X’ axis.

For a two-dimensional system within the X-Y plane, both X’Z and Y’Z will be zero.

A skew system may also be defined in terms of 3 points whose coordinates are defined in the coordinate

data. See Section 5.2.7.2.

(iii) To specify the direction of the data supplied for anisotropic material properties. Anisotropic material

properties normally align with the element local axis system or the global axis system. By specifying a

skew integer on the material property data line it is possible to input material data in an alternative

direction. See Appendix B.1 for further details.

3.7 Structural Suppressions and Constraints

The movement of a node in any direction may be restrained by applying ‘suppressions’, or given a value by applying ‘prescribed displacements’. These may be applied to any freedom existing at the node and may be related to the global axis system or to a skew system defined for the purpose. (The freedoms at a node are determined by the elements meeting at the node.) ASAS-NL automatically calculates the reactions associated with such restraints. A freedom may also be made to depend linearly on any number of other freedoms by means of ‘constraint equations’.

For static analysis, it is essential to ensure that there are sufficient restraints on the idealised model to prevent any possibility of it behaving as a mechanism. In particular, the model or any part of it,should be prevented from moving or rotating as a rigid body.

3.8 Solution Procedures

3.8.1 Non-Linear Static Solution Procedures

The non-linear static solution procedures available in ASAS-NL are conventional incremental ones, with iterative correction within the increment. The user has wide ranging capabilities to control the nature and size of the increment, and to vary the frequency of updating of the stiffness matrix, the required number of iterations, convergence criteria and restart procedures to be invoked in the event of non-convergence.

The solution procedure commences by incrementing one of the following quantities (chosen by the user)

Generalised Load



Single Displacement Component

Displacement Vector Length (“arc-length” method)

External Work Measure

and then holding a value of the selected quantity constant throughout the iteration process.

The above procedures may be freely combined with any of the following iteration techniques

Standard Newton Raphson

Modified Newton Raphson

Initial Stiffness.

In all cases the iteration process can be accelerated by employing

Secant-Newton

or Line Search

techniques.

The Load Incrementation procedure is most suitable for cases of non-proportional loading. The other procedures are useful for problems involving multi-valued load-displacement relationships such as ‘snap-through’.

Solution procedures usually can be changed during the course of an analysis. In addition analyses may be re-started from previous load increments using a different solution strategy if required.

Appendix -C describes the inter-relationship of the different methods.

The size of increment, which may be either load or displacement, is normally determined by the user. However, in problems with proportional loading, the program can automatically determine initial plastic yield (or scale to a user defined level).

Convergence is, by default, assessed against residual forces. Displacements, element strains, stresses or total work may also be used.

Computation of stresses adopts the Forward Euler Integration Scheme by default and sub-incremental procedures for plastic stress redistribution may be used in conjunction with any solution procedure upon request. For von Mises yield criterion, Backward Euler integration scheme may also be used.



3.8.2 Non-Linear Transient Solution Procedures

Non-linear transient solution procedures are used in ASAS-NL to solve creep (time-dependent material response) problems, structural dynamics problems and transient thermal problems. These types of problems use a finite difference in time where the solution is advanced in a stepwise fashion using finite increments of time (time steps). Two distinct types of solution procedures are available; implicit and explicit schemes. The implicit scheme has the advantages of unconditional stability and allows larger timesteps compared to the alternative explicit scheme. The iterative nature of the implicit scheme ensures, in general, greater accuracy but at a much computational cost. In structural dynamics the two schemes may be combined in a single analysis to take of the benefits of both schemes. In addition to defining the list of solution times manually, automatic timestepping procedures are also available for both types of transient analyses. Further details concerning creep analysis may be found in Appendix -J. Further details concerning structural dynamics analysis may be found in Appendix -K. Further details concerning transient thermal analysis may be found in Appendix N.

3.8.3 Contact Analysis Solution Procedures

By default, the penalty method is adopted to solve problems involving gap and rigid surface elements. For rigid surface contact, the augmented Lagrangian method may be used upon request. Further details for these two methods are given in Appendix C.6.

3.8.4 Fracture Mechanics Solution Procedures

Depending on the nature of an analysis, fracture mechanics analysis may be performed in one of the following ways:

(i) Surface flaws on shell structures - use linespring elements and perform the analysis using any of the non-

linear static solution procedures

(ii) Cracks on 2-D planar or axisymmetric structures - perform the analysis as usual and save the appropriate

results on the post-processing file for POSTNL to evaluate the fracture mechanics parameters (e.g. J-

integral) (see Appendix I.8)

3.9 Program Organisation

ASAS-NL makes extensive use of files and it is helpful to classify these as either internal or external files. INTERNAL files are used for intermediate storage within a program and are deleted upon successful completion of the program. EXTERNAL files are permanent and are used for transporting information between the programs and between successive restarts. The user need not normally concern himself with internal files, but some understanding of the external file organisation is required.



When a restart is attempted information describing the current state of the analysis is required. Thus ASAS-NL allows the user to archive (or save) all relevant information at the end of any increment. This information is stored on two labelled external backing files. One file, called the STIFFNESS MATRIX ARCHIVE FILE (or stiffness file) contains all the element stiffness matrices for the model. The other file, the DATA-MANAGER ARCHIVE FILE (sometimes abbreviated to archive file) contains all other necessary information such as model description, control parameters, load history, stresses and displacements. When the information is written to the archive files, an integer number known as the CHECKPOINT number is used to identify the position of the archived information on the backing file for that load increment and is printed in the output file when the archiving has been accomplished. The two backing files are checkpointed separately.

When a restart is attempted, the internal file structure is re-created from the archived backing files using the checkpoint number supplied by the user in the restart data.

Distinction is made between ‘OLD’ and ‘NEW’ files in ASAS-NL to distinguish between the two pairs of files used in a restarted analysis. Backing files created by ASAS-NL (as output) are referred to as ‘NEW’ (Newarchive and Newstiffness) whilst backing files read by ASAS-NL (as input in restarts for instance) are referred to as ‘OLD’ (Oldarchive and Oldstiffness). For example, the data manager archive file named, say NLARCHIVE, by the user is understood to be the newarchive file when created but the oldarchive file when read by ASAS-NL when the restart is attempted.

ASAS-NL also makes full use of the ASAS file system. All the runs associated with a particular analysis, i.e. the initial run and any restarts and post-processing runs, must be under a common project name. This name is used to set up a project index file (the 10 file) which stores the details of every run carried out in this project.

The ASAS backing files created during a run are controlled by the structure name specified. A unique structure name must be assigned for each run within the same project.

3.10 Post-Processing

A post-processing program called POSTNL is available to provide an interface for transferring ASAS-NL results to a number of graphical display programs and to perform certain additional post-processing calculations. The information saved on the post-processing file is specified by the POST or RESU command in the preliminary data.

In addition, post-processing of ASAS-NL results may also be carried out using standard ASAS post-processors such as BEAMST, AXL and AMC. As before, the POST/RESU Command in the preliminary data is required to specify the information to be saved on the ASAS database. The increment number where results are saved will be recognised as the user load case number by the ASAS post-processors.

3.11 Data Units

The user is free to choose any system of units for his data, provided that the units employed form a consistent system so that all data are defined using the same units of force and length. It is also possible to define explicitly the units for the analysis. These can be locally overridden or changed within each data block if required.



The basic global units to be employed are defined in the Preliminary data using the UNITS command (see Section 5.1.42) where the units of force, length and, where appropriate, temperature are supplied. (Time is assumed to be in seconds). These basic units will be utilised as the default input and results units.

In order to facilitate the utilisation of different units for the various types of data, a units command can be used within the main body of the data to locally override the basic units defined in the Preliminary data. This facility enables each data block to have one or more different sets of data units which may or may not be the same as the global definitions.

The following example shows a simple structure where the basic global units are Newtons and Metres but the geometric properties have been supplied in both millimetres and inches.

Defined units Derived units SYSTEM DATA AREA 5000000 PROJECT ASAS STRUCTURE ASAS JOB STAT

TITLE *EXAMPLE

SOLV 1.0 OPTIONS GOON END UNITS N M Newtons Metres Kg END Centigrade (default) COOR CART 1 0.0 0.0 0.0 2 10.0 0.0 0.0 3 20.0 0.0 0.0 END ELEM MATP 1 BEAM 1 2 1 BEAM 2 3 2 END GEOM UNITS MM Newtons Millimetres Kgx10-3

1 BEAM 108.0 90.0 90.0 25.5 UNITS INCHES Newtons Inches. See note 3 below 2 BEAM 12.0 5.0 5.0 3.2 END MATE Newtons Metres Kg 1 2.0E11 0.3 0.0 0.0 END .. .



Notes

1. The units defined in the Preliminary data must be given for both force and length. The temperature unit is optional and defaults to centigrade. The mass unit is a derived quantity consistent with the units of length and force specified.

2. Locally defined units will be reset at the end of each data block or sub data block (see Section 5.1.42). Thus in the example above the units for the MATE data are reset to the global terms Newtons and metres automatically.

3. In the second units definition in the GEOM data, the force and length units do not form a consistent set and so a mass unit cannot be derived. This is acceptable to the program provided that the data being defined do not require a mass or density input. Thus units of Newtons and inches would be unacceptable in the MATE data where the density is specified. Table 3.1 provides a list of unit definitions which permit the calculation of a consistent mass unit.

4. Where mass data has to be supplied, the input can be simplified by locally choosing the appropriate units of force and length to provide a consistent unit of mass of either 1kg (using Newtons and metres) or 1lb (using Poundals and feet).

If units are employed, the cross checks and results will, by default, be printed in the basic global units defined in the Preliminary data and any data defined using local unit definitions will be factored appropriately.

Where the UNITS command is not used, the user must ensure that all data utilise a consistent system of units throughout. Three examples of consistent sets are shown below. 1. SI Units : Force in Newtons, length in metres, mass in kilograms, time in seconds, acceleration

in metres/sec2 2. Imperial Units : Force in pounds, length in feet, mass in slugs, time in seconds, acceleration in

feet/sec2 3. Imperial Units : Force in poundals, length in feet, mass in pounds, time in seconds, acceleration in

feet/sec2

For any other set of units, the unit of consistent mass will be a multiple of the basic unit of mass because it is a derived unit. The consistent unit of mass is obtained by dividing the unit of force by the acceleration due to gravity, which itself has units of length divided by time squared. A change in the unit of length, for example from feet to inches or metres to millimetres, requires a corresponding change to the unit of mass used for calculating the density.

A list of sets of consistent units is given in Table 3.1



Unit of force Unit of

length

Typical value

of E for steel G

Consistent

unit of mass

Density (mass/unit volume)

Steel Concrete

Newton

Newton

Newton

metre

cm

mm

2.1x1011

2.1x107

2.1x105

9.81

981

9810

1Kg

100Kg

1000Kg

7850

7.85x10-5

7.85x10-9

2400

2.40x10-5

2.40x10-9

Kilopond

Kilopond

Kilopond

metre

cm

mm

2.14x1010

2.14x106

2.14x104

9.81

981

9810

9.81Kg

981Kg

9810Kg

800

8.00x10-6

8.00x10-10

245

2.45x10-6

2.45x10-10

KNewton

KNewton

KNewton

metre

cm

mm

2.1x108

2.1x104

2.1x102

9.81

981

9810

103Kg

105Kg

106Kg

7.85

7.85x10-8

7.85x10-12

2.40

2.40x10-8

2.40x10-12

Tonne (f)

Tonne (f)

Tonne (f)

metre

cm

mm

2.14x107

2.14x103

2.14x101

9.81

981

9810

9.81x103Kg

9.81x105Kg

9.81x106Kg

0.800

8.00x10-9

8.00x10-13

0.245

2.45x10-9

2.45x10-13

Poundal

Poundal

foot

inch

1.39x1011

9.66x108

32.2

386

1lb

12lbs

491

2.37x10-2

150

7.23x10-3

Pound (f)

Pound (f)

foot

inch

4.32x1011

3.0x107

32.2

386

32.2lbs

(1 slug)

386lbs

15.2

7.35x10-4

4.66

2.25x10-4

Kip

Kip

foot

inch

4.32x106

3.0x104

32.2

386

3.22x104lbs

3.86x105lbs

1.52x10-2

7.35x10-7

4.66x10-3

2.25x10-7

Ton (f)

Ton (f)

foot

inch

1.93x106

1.34x104

32.2

386

7.21x104lbs

8.66x105lbs

6.81x10-3

3.28x10-7

2.08x10-3

1.0x10-7

Table 3.1 Examples of Consistent Sets of Units

1 Kip = 1000 pounds force 1 Kilopond = 1 Kilogram force

All times are in seconds Assumed specific gravity of steel = 7.85

Assumed specific gravity of concrete = 2.4

Data Preparation ASAS (Non-Linear) User Manual


4. Data Preparation

4.1 General

4.1.1 Data

Data for ASAS-NL is prepared as a series of ‘data blocks’, each specifying a particular feature of the problem. The data blocks are grouped into a number of sections such as structural description, boundary conditions, loading, etc. These data blocks are shown in Table 4.1.

The various sections must be entered in order, but within each section the order of the data blocks can be varied, although the user is advised to adopt the order shown. The sections for structural description, boundary conditions, loading, additional mass and initial conditions collectively define the finite element idealisation. The Preliminary data controls the solution of the problem including the type of material and structural behaviour that is sought.

The Preliminary data is compulsory and all the data blocks of the structural description section must be present except for the geometric properties and skew systems which are not always needed.

At least one data block from the boundary conditions section and one from the loading section must be present for static analysis. For natural frequency analysis loading is optional. Other sections are optional.

In a restarted analysis only the Preliminary data, suppressions, displaced freedoms, loading and additional mass can be changed. Initial conditions have no relevance.



Table 4.1 Data Blocks for ASAS-NL Data

Data Block Contents Section

Preliminary Data Control Parameters .......... ....................................................................... 5.1

Structural Description - Shape and Properties of the Model Coordinates ..................... .................................................................... 5.2.2 Element Topology ........... .................................................................... 5.2.3 Material Properties .......... .................................................................... 5.2.4 Geometric Properties ...... .................................................................... 5.2.5 Section Information ............................................................................. 5.2.6 Skew System ................... .................................................................... 5.2.7

Boundary Conditions - Restraints on the Model Suppressions ................... .................................................................... 5.3.3 Displaced Freedoms ........ .................................................................... 5.3.4 Constraint Equations ....... .................................................................... 5.3.5 Rigid Constraints ............ .................................................................... 5.3.6

Loading Applied to the Model Nodal Loads .................... .................................................................... 5.4.3 Prescribed Displacements .................................................................... 5.4.4 Pressure Loads ................ .................................................................... 5.4.5 Distributed Loads ............ .................................................................... 5.4.6 Temperature Loads ......... .................................................................... 5.4.7 Face Temperatures .......... .................................................................... 5.4.8 Body Forces .................... .................................................................... 5.4.9 Centrifugal Loads ............ .................................................................. 5.4.10 Angular Acceleration ...... .................................................................. 5.4.11 Nodal Flux ...................... .................................................................. 5.4.12 Prescribed Field Variable ................................................................... 5.4.13 Flux Density .................... .................................................................. 5.4.14 Wave Load ...................... .................................................................. 5.4.15 Tank Loads ..................... .................................................................. 5.4.16 Load Functions................ .................................................................. 5.4.17

Additional Mass Lumped Mass Values ...... ....................................................................... 5.5

Initial Conditions Residual Initial Stresses ................................................................... 5.6.2 Stiffener Residual Initial Stresses ........................................................ 5.6.3 Initial Conditions for Transient Dynamic Analysis ............................. 5.6.4

End of File STOP Command ............. ....................................................................... 5.7



4.1.2 Data Formats

4.1.2.1 General Principles

The input data for ASAS-NL are specified according to syntax diagrams similar to that shown below. The conventions adopted are described in the following pages. Detailed descriptions for each of the data blocks can be found in Section 5

Each data block commences with a compulsory header line and terminates with an END command which delimit the information from the other data. The sequence of the input data follows the vertical line down the left hand side of the page. If a data block can be omitted, this will be indicated as shown below.

Within each data block, each horizontal branch represents a possible input instruction. Input instructions are composed of keywords (shown in upper case), numerical values or alphanumerics (shown in lower case characters), and special symbols. Each item in the list is separated from each other by a comma or one or more blank spaces.

Numerical values have to be given in one of two forms:

(i) If an integer is specified a decimal point must not be supplied.

HEADER

KEYWORD

real

END

(alpha)

KEYWORD1

KEYWORD2

KEYWORD3

/integer/

//integer//

realinteger

HEADER

END



(ii) If a real is specified the decimal point may be omitted if the value is a whole number.

Exponential formats may be utilised where real numbers are required.

for example 0.004 4.0E-3 4.0D-3 are equivalent

similarly 410.0 410 4.10E2 are the same.

Alphanumerics are any non-numeric strings which may include the letters A-Z, numbers 0-9, and the characters : . , + - and /. The letters A-Z may be supplied in either upper or lower case but no distinction is made between the upper and lower case form. Hence “A” is assumed identical with “a”, “B” with “b” and so on.

For example CASE are all permissible alphanumeric strings

STR1

END

3mm

also COMB are all identical strings

Comb

comb

Alphanumeric strings must not include any special symbols (see below).

If certain lines are optional, these are shown by an arrow which bypasses the line(s)

In order to build up a data block, a line or series of lines may be repeated until the complete set has been defined. These are shown by an arrow which loops back.

Some data lines require an integer or real list to be input whose length is variable. This is shown by a horizontal arrow around the list variable.

real integer

HEADER

real

END

integer



real integer



Where one or more possible alternative items may appear in the list, these are shown by separate branches for each

An optional item in a line will be enclosed in brackets e.g.

The relevant data block description in Section 5 will detail the default value adopted if the item is omitted.

An input line must not be longer than 80 characters. Certain input instructions may extend onto continuation lines. Where this is allowable, the syntax diagram line is shown ending with an arrow (see Section 4.1.3).

4.1.3 Special Symbols

The following is a list of characters which have a special significance to the ASAS-NL input.

* An asterisk is used to define the beginning of a comment, whatever follows on the line will not be

interpreted. It may appear anywhere on the line, any preceding data will be processed as normal. For

example

(i) * THIS IS A COMMENT FOR THE WHOLE LINE

(ii) X Y RZ 1 16 24 27 *support conditions at ground level*

’ single quotes are used to enclose some text strings which could contain otherwise inadmissible characters.

The quotes are placed at each end of the string. They may also be used to provide in-line comments

between data items on a given line. For example

BM3D ’NODES’ 1 2 ’GEOM PROP’ 5

KEYWORD1

KEYWORD2

KEYWORD3

integer

real

integer

KEYWORD (alpha) integer

KEYWORD integer



, A comma or a blank will act as a delimiter between items in the line. For example

5, 10, 15 is the same as 5 10 15

Note that two commas together signify that an item has been omitted. This may be permissible for

certain data blocks. For example

5,, 15

Unless otherwise stated in the section describing the data block omitted numerical values are zero.

: A colon at the start of the line signifies that the line is a continuation from the previous line.

For example

5 is the same as 5 10 15

: 10

: 15

Note that this facility is only available in certain data blocks. See the appropriate detailed description of

each data block for details.

@ A command @filename may appear anywhere in a data file. When such a command is encountered, the

input of data switches to the file filename and data continues to be read from that file until either the end-

of-file is reached or an @ command is encountered in the secondary file.

When the end of the secondary file is reached, that file is closed and input switches back to the previous

data file. If, however, an @ command is found in the secondary file, input switches to yet another file.

This process can continue until a maximum of 5 secondary files are open simultaneously.

For example

@prelim.dat

@section1.dat

@section2.dat

@load.dat

section1.dat might then contain the lines

@coor.dat

@elem.dat

@mate.dat

@geom.dat



finally

coor.dat contains the coordinate data

elem.dat contains the element data

etc

4.2 Data Generation Facilities

4.2.1 Repeat Facilities

Lists of regular data can often be shortened by use of a repeat facility. A block of one or more lines of data may be identified by a delimiter character(/) and terminated by a repeat command (RP). The repeat command contains information on how many times the set of lines of data is to be generated and how the data is to be incremented for each generation. The general form is:

/ : delimiter character to identify the start of the data to be generated. It must be on a line of its own

KEYWORD : items not enclosed within two slashes will be repeated without any increment for generated real : data

/integer/ : indicates the data in the line which may be generated using the repeat facility. The slashes must not appear in the actual data

RP : command word to identify the end of the data to be generated

nrep : number of times the set of lines is to be generated, including the original data line(s)

incr : the increment to be added to the data items each time the block is generated

For example, suppose the data format is specified as

real

RP

/integer/

/

KEYWORD

nrep incr

/integer/ KEYWORD



It is required to generate integers 1,6,11,16,21,26,31,36,41,46. If the keyword is ALL the data could be

ALL 1 6 11 16 21 26 31 36 41 46

or

ALL 1

ALL 6

ALL 11

.

.

.

ALL 46

Using the repeat facility, the following examples all produce the same identical data

/

ALL

RP 10 5

or

/

ALL 1 6

RP 5 10

or

/

ALL 1

ALL 6

RP 5 10

4.2.2 Re-Repeat Facilities

The repeat facility can be extended to include a double repeat whereby data which has been expanded by use of the RP command may be repeated again with different increment values. The general form is



// : identifies the start of the data to be re-repeated. It must precede a / line

/ : identifies the start of the data to be repeated

KEYWORD : items not enclosed within two slashes will be repeated without any increment for generated real : data

//integer// : an item enclosed by // characters indicates data which can be modified using the re-repeat or repeat facility. The slashes must not appear in the actual data

RP : identifies the end of the data to be generated with the repeat facility

nrep : number of times the block of data is to be generated, including the original data line(s)

incr1 : the increment to be added to the data items for the second and subsequent generated blocks. (The first block corresponds to the original data)

RRP : identifies the end of the data to be generated with the re-repeat facility

nrrep : the number of times the expanded data from the repeat block is to be further generated, including the original repeat block

incr2 : the increment to be added to each of the expanded data items for the second and subsequent re-generated blocks. (The first block corresponds to the expanded data items)

For example, taking the previous example, if the data syntax was specified as

then the data could be

//

/

ALL 1

real

RP

//integer//

/

KEYWORD

nrep incr1

//

RRP nrrep incr2

KEYWORD integer



RP 5 10 generates 1,11,21,31,41 RRP 2 5 generates 6,16,26,36,46

Note, the order of the numbers generated by this example in Section 4.2.1 using RP and in Section 4.2.2 using RP and RRP is different. This may be important in a few cases where the order of the data supplied matters, for example, the generation of user element numbers.

4.2.3 List Generation in the Preliminary Data Section

Many of the commands in the Preliminary data require a list of integer data items following the keyword. This list can be created in a number of ways.

4.2.3.1 A Simple List

A simple list of integers can be written in free format with each number separated by a space or comma up to column 80.

Example: 1 6 11 16 17 18

1, 6, 11, 16, 17, 18

4.2.3.2 Generating a List with a Topological Variable

By use of ’topological variables’, a list of integers can be generated. This is very valuable for generating lists of regular numbers. It is not so useful for irregular lists.

GENERATING A LIST OF NUMBERS USING ONE MODIFIER

The most basic form of topological variable has the form (L)(N,M1). This is used to generate a list of L numbers at equal intervals. The first pair of brackets encloses the number L. The second pair of brackets encloses two integers, separated by a comma. The first of these integers, N, is the start value and the second integer, M1, is the increment for modifying the start value. Thus, the numbers N, N+M1, N+2M1, N+3M1 .......N+(L-1)M1 will be generated.

Example: (4) (3, 5)

This example will generate data for the four nodes 3, 8, 13, 18.

GENERATING A LIST OF NUMBERS USING TWO MODIFIERS

A more general form of the topological variables is as follows:

(L)(N,M1,M2)



This is used to generate a list of numbers at unequal intervals. Its application is similar to the topological variable with a single modifier. The second modifier M2 is used to change the value of M1 every time the latter is used. Modifiers may be positive or negative. The rules are as follows:

(a) The first number generated is the basic number N.

(b) The second number generated is N+M1.

(c) M1 is now modified by M2.

(d) The next number generated is the previous number modified by the new M1.

(e) Stages (c) and (d) are repeated until L numbers are generated.

Examples:

(i) The topological (5) (7,3,12) variable will create a list 7, 10, 25, 52, 91 by expanding in the following way:

First number generated: 7

Second number generated: 7 + 3 10

New M1 = 3 + 12 = 15

Third number generated: 10+15 25

New M1 = 15 + 12 = 27

Fourth number generated: 25+27 52

New M1 = 27 + 12 = 39

Fifth number generated: 52+39 91

(ii) (4) (25,2,-6) generates 25,27,23,13

(iii) (4) (2,0,3) generates 2,2,5,11

(iv) (4) (25,2,-6) (3) (2,3,3) generates 25,27,23,13,2,5,11



4.3 Description of Each Data Block

4.3.1 The Preliminary Data

4.3.1.1 General

The Preliminary data is the first block of ASAS-NL data and consists of all the information required to control the execution of the analysis. It can be divided into two sections, depending on whether the data applies to the problem as a whole (Problem section) or whether it is specific to a given group (Group section). Commands for the Problem section appear first and are then followed by Group section commands for each group in turn. Groups are defined by their constituent elements, if none are explicitly given then the program treats all elements as being in Group 1.

Collectively the Preliminary data fulfils the following functions

• System control (see Section 4.3.1.2)

This includes commands for naming and controlling backing files and setting the data area size. These

commands only appear in the Problem section.

• Solution algorithm definition (see Section 4.3.1.3)

These commands determine the solution method to be used and control its performance (e.g.

convergence) and again can only appear in the Problem section.

• Model behaviour (see Section 4.3.1.4)

Commands in this category control the type of structural and material behaviour that is to be modelled.

This can vary from group to group.

• Output control (see Section 4.3.1.5)

This includes not only the control of printed results and diagnostic monitoring, which can vary from

group to group, but also the saving of results on file for subsequent post-processing.

4.3.1.2 System Control

Commands in this category establish values of certain parameters controlling internal data storage and workspace, and also control the use of backing files.



The data area (freestore) required may be specified using the SYSTEM command. Its value is dependent on the size of problem; guidelines are given in Section 6

The data-manager parameters are automatically set by the program, but may be re-set using the SYSPAR command. Normally this will only be necessary for unusual jobs.

External files may be named and controlled by the data given with the PROJECT, STRUCTURE, NEWSTRUCTURE, FILE, SAVE and, (in restarted jobs) JOB commands. Although the program has defaults built in, it is recommended that, in all but the simplest of jobs, file names and status should be explicitly given.

Names of the files created by ASAS-NL are defined using FILE commands (except for the old data manager archive file required in restart jobs, which is given with the JOB command). In addition, depending on the file type, directives may also be required to define the file status (i.e. whether it is to be a ‘new’ file or whether an existing one, and in the latter case whether information is to be appended or overwritten). These directives are given using SAVE and FILE commands.

The ASAS backing file names are controlled by the PROJECT, STRUCTURE and NEWSTRUCTURE (restarted jobs only) commands. These provide identification of the model for use by ASAS postprocessing programs. As additional security, a label is attached to all external files. This label can be specified using the PROJECT command. Subsequent restart jobs making use of the files must then have the same PROJECT command.

4.3.1.3 Solution Algorithm

The solution procedure is controlled by information using the following commands.

1. Either STAT using the JOB command, specifying the request for a nonlinear static incremental solution

or TRAN using the JOB command, specifying the request for a transient solution procedure, i.e. including

creep or dynamic effects.

or HEAT using the JOB command, specifying the request for a steady state heat solution procedure.

2. Either SOLVE or RESTART commands specifying the times (Pseudo or real times) at which a solution is to be performed. The SOLVE command is used for initial analyses; the RESTART command whenever an analysis is restarted. SOLVE/RESTART are mandatory for JOB type TRAN involving creep

or SOLUTION or SRESTART commands specifying the number, size and nature of incremental steps at

which a solution is to be performed. SOLUTION is used for initial analysis, SRESTART for restarts.

Note that SOLUTION/SRESTART are not available with JOB type TRAN involving creep.

SOLUTION/SRESTART should be used for structural dynamics problems employing an automatic

timestepping procedure.

Full details about the above methods are given in Appendix -C and Appendix -K.



3. UPDATE command specifying the frequency of reformation of the global stiffness matrix (UPDA STIF), the global mass matrix (UPDA MASS) and updating loads and geometry (UPDA GEOM). Using these commands, a range of Newton-Raphson type iteration techniques are available.

The iteration can be accelerated with Secant Newton or Line Search techniques by using options SECN or

LINS respectively using the OPTION command.

Two methods of stress recovery are available. The default method is the Forward Euler integration

scheme. Sub-incremental procedures for plastic stress redistribution compatible with this scheme can be

requested by specifying the number of sub-increments using the PARAMETER command. The

alternative is the Backward Euler integration scheme, requested by option BAKE using the OPTIONS

command. Note that the Backward Euler integration scheme is only available with von Mises yield

criterion.

In case of diverging iteration an auto-recovery facility is available by specifying option AUTO using the

OPTION command.

In problems with proportional loading, an analysis may be scaled to first yield using the SCALE

command. The analysis must then be restarted.

4. CONVERGENCE command. The program will normally iterate until convergence is achieved. The required convergence criteria are defined using this command. If not given, appropriate default values are used.

5. ITERATION command. The maximum number of iterations attempted within a load step is set by default to 10. The ITERATION command provides a means of modifying this. If convergence is not achieved within this number then the analysis will terminate unless the option OVIT is given using the OPTIONS command. In this latter case out of balance residual forces are carried over to the next load increment and the program continues. Directive NRES with the GROUP or PROBLEM/TITLE command will set the out of balance forces to zero at the start of a new increment.

6. EIGN command specifies the times at which an eigenvalue analysis is to be performed. The type of eigenvalue analysis and the control parameters are defined using the SPIT command.

4.3.1.4 Model Behaviour

The material or structural behaviour is defined for each group as required. Each group is defined using a GROUP command containing four character directives which, together with the directive using the JOB command, determines the behaviour of the group. (If no group is explicitly given, then the PROBLEM/TITLE command serves the same purpose). Thus, for example, static large deflection elasto-plastic shell behaviour is specified by directives LARG and PLAS using the GROUP command, together with STAT using the JOB command. (Note that the actual solution is determined also by the commands discussed in Section 4.3.1.3 above.)



Each GROUP command is followed by an ELGROUP command defining the elements within the group. There is provision to vary the integration rule used in each element using the INTEGRATION command. There is also provision for elements to be ‘put-to-sleep’ and ‘woken-up’ using the SLEEP and WAKE commands.

4.3.1.5 Output Control

A range of commands are required to control output, depending on the type (e.g. results, data echoes, diagnostics) and whether it is to be printed or saved on file for subsequent post-processing.

In the absence of any explicit directives, the program will print ‘standard’ output consisting of an echo of the input data, expanded data lists, problem parameter summaries and the convergence details for each load increment followed by the tail sheet. NO DISPLACEMENT, VELOCITY, ACCELERATION, STRESS OR STRAIN RELATED QUANTITIES ARE PRINTED UNLESS ASKED FOR.

The printing of displacements, velocities, accelerations, stresses and strains and associated quantities is controlled by OUTPUT and BLOCK commands. The stress and strain related output depends on the element type (see Appendix A). The axis system (local or global) to which it refers can be controlled for some elements by directives specified using the GROUP command.

The printing of data lists and echoing of input data can be controlled by options using the OPTIONS command. The Preliminary data can also be interspersed with COMMENT and TEXT commands.

Diagnostic monitoring of the two constituent programs is controlled using PRENL and MONITOR commands.

Archiving of results to file for post-processing or viewing is controlled using the POST or RESU command. No results will be saved unless POST/RESU Command is specified and hence its usage is highly recommended.

Details of output are given in Section 4.4.

4.3.2 Structural Description Data - see Section 5.2

The Structural Description data defines the shape and physical properties of the idealisation. The following data blocks are involved:

(a) Coordinates Data (see Section 5.2.2)

This data defines the positions of the nodes. Coordinates may be given in rectangular cartesian,

cylindrical polar or spherical polar coordinate systems or in any combination of these. ASAS-NL

transforms all these local coordinates into a global rectangular cartesian system. If a list of coordinates is

requested, they are printed in the global system.

(b) Element Topology Data (see Section 5.2.3)



This data defines the location of each of the elements by reference to its node numbers. It also defines the

material properties associated with the element by reference to a material property integer. Most

elements must have their nodes listed in a given sequence. For details, see the element description sheets

in Appendix A.

Each element topology line contains an integer number which refers to the Geometric Property Data

(except for brick and axisymmetric solid elements). Each line also contains a flag which indicates

whether the element mass matrix is to be lumped, consistent or not used at all. If it is left blank in a

natural frequency analysis, the mass matrix for the element will default to the type indicated in Appendix

A.

The user may also assign a unique ‘element number’ to each element. This ‘user element number’

controls the order in which the results are printed and is also referred to by several commands in the

Preliminary data. The numbers are also used to reference elements for post-processing. If numbers are

not given by the user, the program numbers elements automatically in the order in which they first

appear.

(c) Material Properties Data (see Section 5.2.4)

This data defines the material properties which are referred to by the material property integers in the

Element Topology Data.

For each material sufficient data must be provided to fully define the behaviour and solution required.

All materials require elastic data. If PLAS or CREP appears with the PROBLEM, TITLE or appropriate

GROUP commands in the Preliminary data then data for a plastic (failure) or creep model respectively

are also required.

If the material is temperature dependent, the data for each type of behaviour (i.e. Elastic and Plastic) is

repeated in turn for a set of reference temperatures. The program interpolates linearly for data at

intermediate temperatures.

(d) Geometric Properties Data (see Section 5.2.5)

This data defines the geometric properties of the element, such as thickness and cross-sectional area.

Solid elements such as the brick family have no geometric properties.

For selected beam elements e.g. BEAM, BM2D, BM3D and TUBE, the properties may optionally be

input using section definitions which provide additional information with regard to shape and physical

dimensions (see Sections 5.2.6).

(e) Section Data (see Section 5.2.6)



This data is used as an alternative means to define properties for beam element types BM2D, BM3D, BEAM and TUBE. In order to generate the flexural properties for the structural analysis, the section shape and dimensions are supplied and the program automatically calculates the required geometric properties. If required, user defined flexural properties may also be supplied which will override those calculated from the section dimensions.

The section type and dimensions are stored so that the post-processor, BEAMST, can automatically calculate extreme fibre stresses without additional information.

(f) Skew Systems Data (see Section 5.2.7)

This data defines the relationship between the global axis system and any local axis system required at a

node. Each skew system can be defined either in terms of direction cosines or by 3 node points.

4.3.3 Boundary Condition Data - see Section 5.3

The Boundary Condition data defines how the idealisation is restrained or constrained.

(a) Suppression Data (see Section 5.3.3)

This data lists all the freedoms which are to be suppressed. If a freedom is suppressed in a direction other

than parallel to the global axis, then Skew Systems Data is also required (see Section 3.6.3).

(b) Prescribed Freedom Data (see Section 5.3.4)

All freedoms which are to be given a prescribed value of displacement, velocity or acceleration are listed

in this data. Freedoms may be prescribed in skew directions by reference to a skew system. The actual

values of displacements, velocities or accelerations to be applied are listed separately, in the Prescribed

Displacement, Velocities and Accelerations Data of Loading Data.

(c) Constraint Equations Data (see Section 5.3.5)

This data defines any required linear dependence between freedoms. The dependent freedom on the left

hand side of the constraint equation may be skewed by reference to a skew system. The linear

dependence must be meaningful; it is not valid for example, to have a suppressed freedom on the left side

of a constraint equation.

(d) Rigid Constraint Data (see Section 5.3.6)

This data block defines rigid connections between freedoms. A selection of rigid ‘elements’ is available

comprising rigid links, 2-D and 3-D rigid beams, rigid link systems and rigid beam systems. Systems are

also available to connect shell elements to brick elements.



The first node specified must be the independent node. The dependent freedoms may be skewed by

reference to a skew system.

(e) Freedom Release Data (see Section 5.3.2)

This data block defines freedoms which are to be disconnected on specified elements at specified nodes.

A released freedom may be skewed by reference to a skew system. The user element number and node

number is then given to describe each freedom to be released.

The facility is only available for beam elements with release provided in the beam local axis system. This

may be used to model pin joints and sliding connections.

If any of the freedoms specified in this data are referenced in any other Boundary Condition Data then the

Freedom Release Data block must be the first data block specified in the Boundary Condition Data.

4.3.4 Loading Data - see Section 5.4

The Loading data defines the loading history applied to the model.

Load histories may be defined in one of three ways (see Section 3.3.15):

• Proportional Loading - Section 4.3.4.1

• Load Functions - Section 4.3.4.2

• Specific Pseudo Times - Section 4.3.4.3

The three methods of defining load history cannot be mixed. The load history defined with Loading data may be cycled using the LOCYCLE command in the Preliminary data.

4.3.4.1 Proportional Loading

To specify proportional loading:

• Define a single load set containing as many load types (e.g. pressure, nodal temperatures) as necessary

• Leave the Pseudo Time blank on the SET data line

• A Load Function Data block is not required

• All nodal temperatures are taken as the reference temperature TREFLD (default 0.0) at zero pseudo

time.



The loads so defined are factored by a multiplier equal to the corresponding pseudo time to give the value at each load step.

4.3.4.2 Load Functions

To use load functions:

• For each load function, define a load set containing as many load types as necessary that describe the

load distribution. Each load set references a load function

• Leave the Pseudo Time blank on the SET data line

• Define load functions in the Load Function Data

Each load function is a tabulated table of pseudo times and factors giving the proportion of the load to be applied at that pseudo time. Proportional loading is assumed between tabulated values. Load set without a load function defined is assumed to have proportional loading.

4.3.4.3 Pseudo Times

To use pseudo times:

• For each time on the pseudo time axis that the total load distribution is known, define a load set of

(possibly many) load types describing the load state

• The Pseudo Time for the load set is given on the SET data line

• A Load Function Data block must not be present

• All loads not defined within a particular load set are taken as zero at that pseudo time

• All nodal temperatures are taken as the reference temperature TREFLD (default 0.0) at pseudo time

TIMBEG (default 0.0). All other loads are taken to be zero at pseudo time TIMBEG

• TREFLD and TIMBEG may be redefined using the PARAMETER command in the Preliminary data

• All temperatures explicitly defined within a load set at pseudo time TIMBEG are interpreted as a set

of user-supplied reference temperatures unless a solution is attempted at time TIMBEG in which case

the constant reference temperature TREFLD is assumed for all nodes. This facility allows the

reference temperature to be varied throughout the structure.

Proportional loading is assumed between load sets.



4.3.5 Additional Mass Data - see Section 5.5

The Additional Mass data defines the direct mass input values.

This data lists the freedoms and associated lumped mass (inertia) values which are to be added to the finite element model. With this ADDED MASS facility the mass matrix so described can augment the finite element mass. Each lumped mass must only be associated with the existing freedoms present on the elements generated by the element topology data.

Apart from natural frequency or transient dynamics analyses, only x, y, z masses are allowed; all others are ignored.

The added mass data specified are usually included in all relevant calculations (i.e. load when body loading applied and mass when inertia required). It is also possible to account for their effects selectively, enabling greater modelling flexibility.

4.3.6 Initial Conditions Data - see Section 5.6

The Initial Conditions Data defines an initial (residual) stress state. This should be self-equilibrating; if it is not, the ‘out of balance’ forces will be redistributed within the first load increment, but convergence may be poor.

The Initial Conditions Data also allows for the definition of initial displacements and/or velocities at the start of a transient dynamic analysis. Care should be taken that any initial conditions so specified are compatible with any prescribed displacements/velocities/accelerations.

4.4 Description of Output

The output file from ASAS-NL contains listings of checked and unchecked data and cross-reference tables describing the model as well as results of the non-linear analysis. In addition, two journal files may be produced from each run.

4.4.1 Data Input Echo and Checking

The following are produced during data input and checking stages:

PRELIMINARY DATA ECHO

A complete listing of the Preliminary data as supplied by the user is given.

PROGRAM CONTROL PARAMETERS

A complete listing of Program Control Parameters is given. These, in general, are controlled using the PARAMETER command in the Preliminary data, but default values are supplied automatically by the program.



Typical program parameters are the reference temperature for temperature loads and whether a sub-incremental analysis has been requested.

INPUT DATA ECHO

A complete echo of the rest of the input data as supplied by the user is given.

CHECKED DATA

A listing of all data describing the model after being checked is given. Error and Warning messages, as appropriate, are printed. This section contains expanded lists of coordinates, material properties, geometric properties, suppressions, constraints and load tables for each load set. This is followed by listings of checked residual stresses and results from further temperature checking if appropriate. Cross-reference tables giving group structure, integration rules and nodes are also given.

4.4.2 Analysis Results

The amount of output produced depends on the results requested by the user in the Preliminary data. The order of the load increments is dictated by the order of the solution times as given using the SOLVE command. Output for each increment will be as follows:

STIFFNESS REFORMATION

A message is given if the stiffness matrices of elements in any group are reformed in any iteration during any incremental step.

GEOMETRY REFORMATION

A message is given if the geometry is reformed in any iteration during any incremental step.

MASS REFORMATION

A message is given if the mass is reformed at any incremental step.

CONVERGENCE MONITORING

The incremental and total values of the convergence criterion are given for each iteration. This allows the rate of convergence to be monitored.

ARCHIVING

Checkpoint numbers on the data-manager archive file and element stiffness matrix file are given if the user specifically requests an archive at this load step using the SAVE command. The checkpoint number for the Data-Manager archive file is required in the Preliminary data when a restart is being attempted. An archive is always made following the final load increment if a SAVE command is present and the checkpoint number is then found on the Data-Manager Tail Sheet.



In addition, messages about information saved on the file for post-processing and plotting by ancillary program are also given.

OUTPUT

Displacements and Reactions, if requested, are given first. By default maximum values of displacements and summed reactions are printed for all increments for a linear or nonlinear static analysis. For a transient dynamics analysis, maximum values of velocities and accelerations are additionally output. If requested the program also prints values of displacements (velocities, accelerations) and reactions at all or selected nodes for all selected increments. Reactions include forces arising from application of prescribed displacements and constraint equations.

Other than displacements (velocities, accelerations) and reactions, the output depends on the type of analysis and the elements used. In the most general case, current stress, current total strain, elastic, inelastic and creep strain, current yield stress and yield strain, equivalent stress, equivalent strain, equivalent plastic strain and work may be requested for any element and any load increment. For shell and beam elements stress resultants at the centroidal surface sample points are available. If no directives are given then no stress and strains will be printed.

All stress and strain related quantities are computed and output at element integration points (see Appendix -G) referred to either global or element local axes. The choice of axis systems can be varied, if required, from group to group, but cannot be changed during the analysis.

In addition to stress and strain quantities, the material ‘status’ of an integration point is also printed under the column INDR/STATUS according to the following convention:

All relevant elements except gaps and rigid surfaces

E - 0 - elastic

U - 1 - elastic unloading (or reloading) following yield

P - 2 - yielded and loading

C - 3 - Cracking

F - 4 - fibre failure for composite analysis

M - 5 - matrix failure for composite analysis

L - 6 - lamina failure for composite analysis

S - 7 - transverse shear/normal stress failure for composite analysis

MS - 8 - M and S modes failure for composite analysis

Rigid surface or gap elements

1 - no contact

2 - stick

3 - slide in Y direction

4 - slide in Z direction

5 - slide in both Y and Z directions



Maximum values of displacements and largest equivalent stress, equivalent total strain, equivalent plastic strain and equivalent creep strain, where appropriate, are also given.

4.4.3 Analysis Summary

The following information is given at the end of a run:

DATA MANAGER TAIL SHEET

A complete listing of system control parameters is given. These, in general, are controlled using the SYSTEM and SYSPAR commands in the Preliminary data. The information may be used to monitor the efficiency of the analysis. This information is intended only for the experienced user. The checkpoint number of the data-manager file for a default archive on the last load increment is also given.

FILE STATUS

The status and disposition of all backing files accessed and created is given. The status is NEW for a virgin file or OLD for an existing one. The disposition is OPEN, CLSE (closed) or DEL (deleted). DEL files have been successfully deleted and CLSE files closed and saved.

MAIN RUN PARAMETERS

Listings of the main program parameters such as number of nodes and elements in the model are given. Solution characteristics such as number of accumulated iterations and maximum frontwidth are also given.

4.4.4 Journal Files

Two journal files are printed during an ASAS-NL run. The first file, called pnamJF (pnam is the project name),

contains a summary of the run information of all the runs in the project. The second file, called INCRJF,

contains condensed information about the main analysis, enabling the user to monitor interactively the

incremental iterative solution process. File INCRJF is normally deleted at the end of the analysis but it may be

saved using option SAVJ.

4.4.5 ASASNL Output Markers

Certain values which are helpful for either the assessment or control of the analysis are periodically output by ASASNL. To help find them using text editors, they are marked by a character string **nnnnnnnn, in columns 1 to 10, where nnnnnnnn is an indicative keyword.

Keyword Description



ACCL Summary information about acceleration technique used

ADJUST Adjusted value of next step size

AUCR Automatic creep timestepping. Summary information for automatically selected solution times

AUGMENT Augmentation of Lagrangian multipliers required

CHANGE Gives number of sampling points (INDR) to have changed state for increment

CONV Convergence performance parameters

CURRENT Current value of step size

DETK Stiffness determinant and number of negative stiffness and constraint pivots

DISP Start of displacement output

DMTAIL Data Manager tail sheet

DPCOM Constant Increment of Displacement Component - iteration performance parameters

DPVEC Constant Increment of Displacement Vector - iteration performance parameters

DPVECL Constant Increment of Displacement Vector, Linearised version - iteration performance parameters

DUMP Solution state saved for possible future restart or post-processing

EIGN Start of eigenvalue output

ELEM Start of element based output

ERROR Error flag

EXWRK Constant Increment of External Work Measure - iteration performance parameters

EXWRKL Constant Increment of External Work Measure, Linearised version - iteration performance parameters

FREQ No natural frequency analysis performed due to non +ve definite stiffness matrix

FILES Active files summary

FINISH Abnormal exit path following error

GEOM Geometry reformed

INCRnnnn Start of increment nnnn and pseudo time (Always 1.0 for SOLU)

LEVEL Load/displacement level exceeds preset value, job terminating

LINS Line Search performance information

MASS Mass reformed

MAXP Gives highest PLASTIC strain and position for increment

MAXS Gives highest STRESS and position for increment



MAXT Gives highest TOTAL strain and position for increment

PERT Perturbation introduced

POST Post-processing identifier saved to porthole file

SECN Secant-Newton performance information

STIFF Stiffness reformed

SUMM Summary information for this increment

TRACE Start of subroutine trace back

Data Formats ASAS (Non-Linear) User Manual


5. Data Formats

ASAS-NL data is organised into a series of data blocks, each containing a particular type of data. This chapter describes each data block individually. The layout of each block is explained, and some examples are given. The user need only refer to the sections describing the data blocks required for his current analysis.

Each block, except the Preliminary data, begins with a block header line. This header line defines the type of data which follows. The final line in each block must be an END, written on a line on its own. The final line in the data file must be a STOP, written on a line on its own.

The data blocks described in this chapter are:

Preliminary Data ..... ................ ................ ................ Section 5.1

Structural Data ........ ................ ................ ................ Section 5.2

Boundary Condition Data ......... ................ ................ Section 5.3

Loading Data .......... ................ ................ ................ Section 5.4

Additional Mass Data .............. ................ ................ Section 5.5

Initial Conditions Data ............. ................ ................ Section 5.6

STOP Data .............. ................ ................ ................ Section 5.7

Preliminary Data ASAS (Non-Linear) User Manual


5.1 The Preliminary Data

The preliminary data is the first block of ASAS-NL data. It defines the:

• memory size to be used for data handling

• job type (eg whether statics or dynamics)

• identity of the project

• structure or component to be processed within that project

• options which will affect the course of the run

• amount of printing produced

• files saved for further processing

All commands are identified by a unique command word at the start of the line. The first 4 characters of each command word are mandatory, others are optional. Free format is used, with ‘topological variables’ (see Section 4.2.3) used as an optional shorthand method for generating lists of required numbers.

The majority of commands are optional and can be placed in any order. However, the following are mandatory and must be supplied in the order given.

JOB

PROBLEM or TITLE

One of SOLVE or RESTART, SOLUTION, SRESTART or SCALE

END

Table 5.1 lists all possible commands in the preliminary data section. Mandatory commands are shown in bold. An asterisk against optional commands signifies that defaults are implied, details of which are given below:

SYSTEM Data area 1000000 PROJ Default project title is ‘ASAS-NL ARCHIVE FILE’ and project name is ASNL STRUCTURE Default name is ASNL NEWSTRUCTURE Default name is ASNN SYSP The various default values are given in Section 6, Table 6.1. CONV Residual convergence with Euclidean norm and tolerance 0.001. FILE The various default file names are given in Section 6, Table 6.1. INTE Use default integration rules. ITER Limit of 10 iterations for each load increment. PARA Various default values. See the PARAMETER command for details. PINO The default pressure interpolation order is that implied by the particular element

displacement variation. SAVE Archive data manager and global stiffness matrix for last increment only. SPIT Various default values. See the SPIT command for details. UPDA Reform stiffness matrix on first iteration of first increment only. WEIG The default values are unity for all freedom types.



The preliminary data commands fall into two sections, referred to as the problem and group sections. The problem section includes all the commands following the PROBLEM command up to the first occurrence of the GROUP command. All subsequent commands fall into the group section. The group section allows elements to be assigned to a particular group. The division of the finite element model into groups of elements is strongly recommended as many of the post-processing options in POSTNL are group related. Some elements, such as the bar element FLA2, have to be assigned to a separate group (or groups) if the model includes other element types. Table 5.1 indicates which section each command should appear in. The preliminary data commands invoke procedures (eg frontwidth optimisation) and sets parameters (eg the subspace iteration convergence tolerance) which are global in nature. Commands allowed within the group section control procedures and parameters that may be assigned to groups of elements, eg output of stresses and strains.



Section Category Comments

SYSTEM * Sets size of data area O PROJECT * Sets project name and title O Must be the STRUCTURE * Sets structure name O first section NEWSTRUCTURE * Sets new structure name O SYSPAR * Sets system parameters O

JOB M PROBLEM Titles output P M One only, TITLE P must follow JOB SOLVE Solution times P One only, RESTART Restart times P must follow SOLUTION Special solution control P M PROB or TITL SRESTART Special solution restart P SCALE Controls scaling of loads P O

COMMENT Comments in data PG O CONVERGENCE * Sets convergence criteria PG O EGEN Replaces ELGROUP for coupled G O analysis EIGN Eigenvalue solution P M for eigenvalues FILE * Backing file names P O recommended GROUP Group Titles G O ELGROUP Elements in group G O must follow GROUP SKIP Skip elements in group G O only use with ELGROUP HYDR Hydrodynamic database name P O mandatory for accessing hydrodynamic data INTEGRATION * Integration rules P O ITERATION * Iteration limits P O LOCYCLE Controls cyclic loading P O MONITOR Diagnostic monitoring in ASASNL P O OPTION Controlling options P O OUTPUT Controls output PG O BLOCK Controls output PG O must follow OUTput

PARAMETER * Sets problem parameters P O PASS Invokes frontwidth optimiser P O START Sets starting vectors P O must have PASS PINO * Defines pressure interpolation order P O POST Post-processing requirements P O recommended, RESU one only SAVE * Archive times P O SPIT * Set eigenvalue soln. parameters P O TEMPORAL Controls temporal integration for transient analysis P O TEXT Printed comments in output P O

UNITS Defines global analysis units P O recommended UPDATE * Controls solution procedure PG O WEIGHTS * Weighting factors for convergence P O WAKE Sets wake up time for elements P O SLEEP Sets sleep time for elements P O END Signifies end of Preliminary Data M last command

Name Description



Note P - Problem Section G - Group Section PG - Problem and Group Section M - Mandatory O - Optional * - Default available Table 5.1 Preliminary Data Commands

5.1.1 AQWA Command

This command defines the name of the AQWA hydrodynamic database files. The command (or HYDR) is mandatory if linkage to the hydrodynamic database is required, e.g. import of AQWA RAOs via the load function type RAOS.

Parameters

AQWA : Command keyword

aqwaid : name of the AQWA model to be processed. This is the name associated with the .RES file generated by AQWA-LINE. (Alphanumeric, up to 32 characters)

istr : identification number of the structure in the hydrodynamic model. If omitted defaults to 1. (Integer)

Notes 1. If the file name contains space, the specified name must be embedded in double quotes (“).

5.1.2 BLOCK Command

This command defines the type of output to be printed under control of the OUTPUT command(s). Optional

Parameters

AQWA aqwaid (istr)

blocno ident (ndelno)BLOCK



BLOCK : command keyword

blocno : identifying number of block

ident : output identifier, one or more of the following:

DISP displacements (problem section) STRS stresses STRN total strains INST inelastic strains ELAS elastic strains SRES stress resultants (beam and shell elements only) CRSN creep strains ESTR end segment smoothed stresses SSTR all segments smoothed stresses for WST4 and SST4 elements SSRE smoothed stress resultants ORIG origin of yield locus (for kinematic hardening)

ndelno : user defined list of nodes (for displacement only) or element numbers (for stresses or strains) given in topological format. If blank defaults to all nodes or elements (in group)

Notes

1. If GROUPS are used, then all commands controlling output (i.e. OUTPUT, BLOCK) must appear in the GROUP section other than commands controlling displacement output which always appear in the PROBLEM section.

2. BLOCK commands should immediately follow the parent OUTPUT command(s). 3. For a transient analysis including inertia effects, if DISP is specified, then velocities and

accelerations are also output.

5.1.3 COMMENT Command

Any number of these commands may be used anywhere in the Preliminary data. They are not included in the descriptive text block. Optional

Parameters

COMMENT : command keyword

alpha : any alphanumeric comment

COMMENT alpha



Note

COMMENT commands may only be used in the preliminary data. For comment lines in the main body of the data, use an asterisk at the start of the comment.

5.1.4 CONVERGENCE Command

This command defines the convergence criteria. Optional

Parameters

CONVERGE : command keyword

nmtype : type of norm, one of the following:

ABSN absolute norm EUCN euclidean norm (Default) MAXN maximum value SCAL scaled using diagonal stiffness terms

refvar : reference variable, one of the following:

DISP displacement Increments RESF residual forces (Default) STRN strain STRS stress

tol : tolerance value for convergence, default is 0.001. (Real)

Notes

1. For creep analysis, a reference variable may be chosen by the program according to the form of the solution. For details, see Appendix -J.

2. STRN and STRS Convergence Criteria are not available for shells using Ivanov yield criterion or engineering beams, ie BM2D, BM3D and TUBE.

Examples

The default convergence criterion

CONV EUCN RESF 0.001

Convergence criterion based on displacements

CONVERGE nmtype refvar tol



CONV EUCN DISP 1.0

5.1.5 EGEN Command

This command defines the elements to be generated in a group and must follow immediately its parent GROUP command. The command is only used in coupled analysis in place of ELGROUP command for the automatic generation of field elements.

Parameters

EGEN : compulsory keyword

grpno : group number from which the elements are generated

elincr : user element number increment with respect to corresponding element in group grpno

Notes

1. The topology of elements specified in EGEN will be generated automatically by the program, and should not be given explicitly in the ELEM data.

2. Automatically generated field elements will have material property integer (1000+IMAT) and geometric property integer (1000+IGEOM) assigned. IMAT and IGEOM are the material property integer and geometric property integer respectively of the parent displacement element.

5.1.6 EIGN Command

This command invokes an eigenvalue analysis. Compulsory for eigenvalue analysis.

Parameters

EGEN grpno elincr

EIGN

ptinc1

SELP (ptinc2)

ALL



EIGN : command keyword

ptinc1 : list of pseudo times (Real) or increments (Integer) at which an eigen solution is to be attempted. These must occur with the preceding SOLVE, SOLUTION, RESTART, SRESTART or SCALE commands

SELP : keyword (optional but required for perturbation analysis)

ptinc2 : selected pseudo time (Real) or increment (Integer) for inclusion of perturbation load vector (default is the first pseudo time or increment on the list)

Notes

1. The type of eigenvalue analysis is determined by the matrix specified with the SPIT command, together with other control information.

2. The pseudo times must be in ascending order. 3. Pseudo times are required for SOLVE problems: increment numbers are required for special solution

problems, e.g. ARCL. 4. To achieve results similar to a frequency analysis with ASAS (Linear), use EIGN 0.0 in a static job

solving at time 0.0 (assuming that at time 0.0 the loading is zero). Note that if a frequency analysis is performed with loading, then natural frequencies may change due to load stiffening and other non-linear effects.

5.1.7 ELGROUP Command - (Group Section Only)

This command defines the elements in a group and must follow immediately its parent GROUP command. It is valid only in conjunction with a GROUP command. If no group is defined, then all elements are assumed to be in group 1. Conversely, if groups are used, then every element must be explicitly assigned to one or other group. Optional

Parameters

ELGROUP : command keyword

elno : list of element numbers given in topological format. (Integer)

Note

1. Gaps and FLA2 elements must always belong to their own group and must not be mixed with other element types.

2. The SKIP command can be used to switch off some elements defined in the ELGROUP command. The order of ELGROUP and SKIP commands within a group is not important.

ELGROUP elno



Examples

Assign elements 1 to 10 to group 3

GROU 3 * BEAM ELEMENTS

ELGR 1 2 3 4 5 6 7 8 9 10

Alternative method using topological format

ELGR (10) (1,1)

5.1.8 END Command

This must be the last command in the preliminary data. Compulsory

Parameter

END : command keyword

5.1.9 FILE Command

Defines names and attributes of files. Recommended

Parameters

FILE : command keyword

ftype : keyword to identify file type, one of the following:

ARCH new archive file NSTF new stiffness file OSTF old stiffness file POST post-processor file MODL ‘PATRAN’ or ‘FEMVIEW’ formatted model file

END

FILE ftype fname

NEW

OLD

(APPEND)

OVER

NEW should be given on SAVE command



fname : filename of up to 12 characters (including extension)

NEW : keyword to denote file is new

OLD : keyword to denote file already exists

APPEND : keyword required to append new information to end of file (default)

OVER : keyword required if new information is to overwrite existing information

Notes

1. The old archive file, if required, is defined with the JOB command. 2. The default values for existing files is given in Section 6 3. Keywords APPEND and OVER are applicable to file types POST and MODL only. Leave blank for

ARCH, NSTF and OSTF. 4. If the old stiffness file is omitted in a restart, the required filename will be retrieved from information

stored in the old archive file.

Example

Naming the porthole file for post-processing with POSTNL

FILE POST CRANEPST

5.1.10 GROUP Command - (Group Section Only)

A Group is a subset of elements in the structural model, all of which have the same non-linear behaviour. This behaviour can vary between Groups. The Group command defines the behaviour by means of directives. In some cases it is possible to define the same directives at Group and Problem level, in which case the lower level Group definition applies. Optional

The Group command must be followed immediately by the ELGR command.

Parameters

GROUP : command keyword

grpno : identifying number of the group. (Integer, 1-9999)

direct : 4 character directives defining structural and material model. May be one or more of the following:

GROUP grpno (direct) title)(*



PLAS take plasticity effects into account LARG include large displacement effects in the calculation of strains and geometric

stiffness matrices. This directive should be accompanied by the command UPDATE GEOM (see UPDATE command)

CONL use conservative pressure loading - i.e. calculate pressure loads using original geometry throughout. Only applicable with UPDATE GEOM (see UPDATE command)

NRES do not carry forward residuals into next increment FLNS form natural stiffness (i.e. Young’s modulus*Area) for FLA2 and FAT2 elements CREP creep analysis NREC (only use with the GROUP command). The stresses will not be recovered nor

element stiffnesses be reformed for elements in the group EXPL user explicit temporal integration scheme for transient analysis

* : character to indicate the following text (up to and including column 80) forms a title for this group

title : any alphanumeric group title. It must be preceded by an asterisk (*). The title is used in the output from ASASNL to describe the group

Notes

1. If no directives are given, linear elastic behaviour is assumed with the default implicit temporal integration scheme for transient analysis.

2. Gaps and FLA2/FAT2 elements must always belong to their own group and must not be mixed with other element types. In general, it is strongly recommended that each group defined comprises only one element type to facilitate post-processing of the analysis results.

5.1.11 HYDR Command

This command defines the name and details of the file containing the hydrodynamic information. The command is mandatory if linkage to the hydrodynamic data is required, e.g. import of RAOs via the load function type RAOS.

HYDR AQWA aqwaid (istr)

NRAO filename (wfform) (wdform) (raoform) (rotform)

Parameters



HYDR command keyword AQWA keyword to signify that hydrodynamic data is obtained from AQWA aqwaid name of the AQWA model to be processed. This is the name associated with the .RES file

generated by AQWA-LINE. (Alphanumeric, up to 32 characters) istr identification number of the structure in the hydrodynamic model. If omitted defaults to 1.

(Integer) NRAO keyword to signify that hydrodynamic data is obtained from a neutral RAO data file filename name of the neutral RAO file. (Alphanumeric, up to 32 characters) wfform format of wave frequency data, one of the following: FREQ frequency in rad/s (Default) PERD period in s HRTZ frequency in Hz wdform format of wave direction data, one of the following: XPOS positive X direction is 0° (Default) XNEG negative X direction is 0° raoform format of RAO data, one of the following: AP amplitude and phase angles (Default) RI real and imaginary parts rotform format of rotational units in RAO data, one of the following: DEG degrees (Default) RAD radians Notes 1. The format of the neutral file is described as follows:

Frequency/Period value Direction value X (surge) X (surge) Y (sway) Y (sway) Z (heave) Z (heave) RX (roll) RX (roll) RY (pitch) RY (pitch) RZ (yaw) RZ (yaw)

The 6 numbers representing the RAO are in pairs of Amplitude and Phase or Real and Imaginary. The data lines are repeated for each wave frequency and direction.

2. Maximum number of wave frequencies allowed is 50. Maximum number of wave directions allowed is 40. 3. Wave directions are assumed to be in degrees and in the range -100 to +180. 4. The rotational units specified apply to all phase and rotational RAO values. 5. If the file name contains space, the specified name must be embedded in double quotes (“).

6. A positive phase angle is considered as lagging. Example Example of a neutral RAO data file with data supplied at 2 frequencies 0.34907 rad/s and 0.36960 rad/s and 5 directions 0°, 45°, 90°, 135°, and 180°. 0.34907 0.00 0.6997 88.98 0.0000 -104.31 2.0823 13.11 0.0000 0.31 0.1507 88.35 0.0000 46.90



0.34907 45.00 0.5048 89.01 0.5046 89.02 2.0826 13.09 0.0874 -91.84 0.0954 88.15 0.0000 -134.89 0.34907 90.00 0.0000 123.22 0.6994 88.98 2.0823 13.11 0.1382 -91.64 0.0000 23.57 0.0000 -94.99 0.34907 135.00 0.5048 -90.99 0.5046 89.02 2.0826 13.09 0.0874 -91.84 0.0954 -91.85 0.0000 -47.76 0.34907 180.00 0.6997 -91.02 0.0000 87.73 2.0823 13.11 0.0000 162.66 0.1507 -91.65 0.0000 146.91 0.36960 0.00 0.6585 88.53 0.0000 -177.96 3.0661 36.08 0.0000 -159.88 0.1134 87.68 0.0000 -152.22 0.36960 45.00 0.4780 88.59 0.4779 88.60 3.0668 36.06 0.0630 -92.74 0.0682 87.26 0.0000 -62.60 0.36960 90.00 0.0000 104.89 0.6583 88.53 3.0661 36.08 0.1047 -92.32 0.0000 19.68 0.0000 -42.51 0.36960 135.00 0.4780 -91.41 0.4779 88.60 3.0668 36.06 0.0630 -92.74 0.0682 -92.74 0.0000 -120.04 0.36960 180.00 0.6585 -91.47 0.0000 91.21 3.0661 36.08 0.0000 -35.18 0.1134 -92.32 0.0000 -24.82

5.1.12 INTEGRATION Rule Command

This command defines the integration rules to be used by specified elements. If not present the default rule is used. Optional

Parameters

INTEGRATION : command keyword

intx : integration order or rule number in element local directions. All three numbers must be

INTEGRATION intx inty intz (elno)



inty given. (Integer) intz

elno : list of element numbers in topological format. (Integer) If blank, defaults to all elements (in group)

Notes

1. See Appendix -G for default integration rules for each element type. 2. intz should be 1 for 2-D elements. 3. If zero is specified for any rule number then that rule number is set at the default value. 4. If an invalid integration rule is specified for an element then that element’s default values will be used. 5. If more than one set of integration rules is specified for any given element then the final set will be used.

Examples

Allow for five layers through the thickness for QUS4 shell element numbers 1 to 25 in a plasticity analysis.

INTE 1 1 5 (25) (1,1)

Similar example but for TCS8 shell elements

INTE 2 2 5 (25) (1,1)

5.1.13 ITERATION Command

This command specifies the maximum number of iterations to be performed within a load increment. Optional

Parameters

ITERATION : command keyword

n : maximum number of iterations in every increment up to and including the solution time/ increment ptminc, if specified. (Integer)

TO : keyword

ptminc : solution pseudo-time/time (Real) or increment (Integer) up to which this specification of n is to apply

END : keyword indicating that n applies for all solutions times/increments to the end of the analysis

ITERATION n TO

END

ptminc



Notes

1. If no ITERATION command is present a maximum of 10 iterations are assumed for each increment. 2. The run will terminate if convergence is not achieved within the specified number of iterations, unless

option OVIT (OVerride ITeration limit) is specified in the OPTION command. 3. If a solution is performed at a pseudo-time/time/increment greater than the last pseudo-

time/time/increment specified with an ITERATION command, then the maximum number of iterations performed will be that specified on the last ITERATION command. To revert to the default, specify ITERATION 10 TO END as the last ITERATION command.

Example

Allow up to 20 iterations to time 5.0, 15 iterations from time 5.0 to 7.0 and revert to default for all remaining times

ITER 20 TO 5.0

ITER 15 TO 7.0

ITER 10 TO END

5.1.14 JOB Command

Defines analysis type and for restart jobs the old archive file name and required checkpoint number on the old archive file. Compulsory

Parameters

JOB : command keyword

NEW : optional keyword indicating that this run will create a new project data base

OLD : optional keyword indicating that this run will add to an existing project data base

REPL : optional keyword indicating that this run will replace a previous run of the same structure on the project database

STAT : keyword indicating static analysis

TRAN : keyword indicating a transient analysis, ie including creep or inertia effects

JOB

oldarch (nchkpt)STAT

PIER

TRAN

HEAT

(NEW)(OLD)

HTRA

(REPL)



PIER : keyword indicating a piezo-restivity analysis

HEAT : keyword indicating a steady state heat analysis

HTRA : keyword indicating a transient heat analysis

oldarch : old archive file name up to 8 characters. This is only required for restarts

(nchkpt) : number of the required restart checkpoint on the old archive file (brackets must appear). If omitted the highest checkpoint on the old archive file is taken. This is only required for restarts. (Integer)

Notes

1. The default project status is OLD for a restart job and NEW otherwise

5.1.15 LOCYCLE Load Cycle Command

This command defines cyclic loading. Optional

Parameters

LOCYCLE : command keyword

ptime1 : pseudo time for start of cycle - T1. (Real)

ptime2 : pseudo time at finish of cycle - T2. (Real)

Notes

1. The starting and finishing times, T1 and T2 respectively, refer to the first cycle. Cyclic loading, period T2 minus T1, follows.

2. T1 need not necessarily be the first time specified with the SOLVE command but T1 minus T0 must be less than T2 minus T1.

3. The load cycle times and the parameters TREFLD and TIMBEG cannot be redefined in a restart. This means that if the loads are redefined on restart they must lie within the load cycle range of the initial run.

5.1.16 MONITOR Command

This command controls diagnostic monitoring in ASASNL. Optional and not normally required.

ptime1 ptime2 LOCYCLE



(i) For the main analysis stage.

Parameters

MONITOR : command keyword

stage : stage identifier, one of the following:

INIT initialisation stage LOAD load generation STIF stiffness REDU reduction SOLV solve UPDT update STRE stress recovery UPD1 update 1 UPD2 update 2 SCAL scaling to first yield MASS mass generation EIGN eigenvalue extraction SPIT eigenvalue extraction OUTP output PORT post-processing output file AUTM automatic timestepping AUGM augmented Lagrangian ALL monitoring on all stages

subkey : names of subroutines and/or keywords to be monitored. Keywords (set throughout the stage) may be one or more of the following:

ALL monitor all subroutines in stage STOPnn abort program run at start of this stage in increment nn, where nn is zero filled

and right justified CLAIM monitor dynamic storage allocator TOTAL print contents of freestore area on CLEAR COMMON print common block contents at start of stage EXTEND set extended logging mode for subroutine tracing package BRIEF set compact logging mode for subroutine tracing package DTAILS print length and type of each record in Data Manager tail section DTAILL print length, type and contents of each record in Data Manager tail section VPUTS print length and type of each VPUTI or VPUTR

stage subkeyMONITOR



VPUTL print length, type and contents of each VPUTI or VPUTR VGETS print length and type of each VGETI or VGETLR VGETL print length, type and contents of each VGETI or VGETR MODMAN monitor data manager page file in Data Manager tail section PCHAIN call subroutine PCHAIN in stage header PUSAGE monitor page usage in the stage PUFULL as for PUSAGE but with more information OVROFF switch off overflow check DISKFL monitor status of disc files ROTAWS includes rotations in the initial configuration in the stress recovery stage when an

element wakes up so that they will not cause straining (rotations not included by default) usage MONI STRE ROTAWS

TEMPWS assumes that there is no sudden change of temperature when an element wakes up in the load generation stage (by default newly activated elements are set to the reference temperature)

usage MONI LOAD TEMPWS

Note

Several MONITOR commands can be used to monitor different stages with different subkey values if required.

(ii) For all other stages:

Parameters

MONITOR : keyword

FULL : print the contents of the file transfers on reading and writing

READ : print the contents of the file transfers on reading only. Print the header only (not contents)

on writing

MONITOR WRITE

ALLFULLREAD

FREESTORE

BRIEF

optionSYOP

FLAG

SENTRY

v alue

file

INDEX



WRITE : print the contents of the file transfers on writing only. Print the header only (not contents)

on reading

BRIEF : print the headers for the file transfers but not the contents on reading and writing

ALL : monitor all ASAS logical files

file : list of ASAS logical file numbers to be monitors

INDEX : monitor the ASAS Project Index file

FREESTORE : monitor the allocation of space in the Data Area

SYOP : the ASAS program has a number of system monitoring options which can be switched on

FLAG using this command

option : the number of the system option

value : the value assigned to the system option

SENTRY : monitor the entry into each Fortran subroutine

Notes

1. Specific information relating to these monitoring features can be found in the ASAS Programmer’s Manual.

2. Many of these features produce large amount of formatted output. 3. Several MONITOR commands can be used in the same run.

Example

MONITOR BRIEF 13 15 3

MONITOR FREESTORE

5.1.17 NEWSTRUCTURE Command

To define the new structure name to be associated with the results created by a restarted run. Required by restarted jobs only but highly recommended.

Parameters

NEWSTRUCTURE nsname



NEWSTRUCTURE : keyword

nsname : structure name to be associated with the results being created by the current restarted run in order to identify these results from others in the project. nsname must be unique for this project (alphanumeric, 4 characters).

Notes

1. If the NEWSTRUCTURE command is omitted then nsname defaults to the name ASNN. However, since the structure name must be unique within a project, the default must not be assumed more than once if the project contains a series of restarts.

2. A STRUCTURE command is normally required in conjunction with NEWSTRUCTURE to define the name of the existing structure

5.1.18 OPTION Command

This command defines options applicable to the problem. Optional

Parameters

OPTION : command keyword

option : 4-character keyword to identify option. May be one or more of the following: APIW complete wave load to the requirements of API RP2A (See Appendix M.7) APIC vary current profile using non-linear stretching as recommended in the API RP2A

Code of Practice. Default when APIW is selected (See Appendix M.7) AUCR automatic timestepping for creep (see Appendix -J) AUTO automatic restart of increment with reduced size (see MXAUTO and STEPRF

with PARAMETER command) when solution is not available, divergence or slow convergence. Used only with SOLUTION command. Not applicable for creep

BAKE backward Euler method for plasticity (see Appendix C.3) BODY check for sensible density values BRIG rigorous buoyancy load calculation (See Appendix M.7) CCOG calculate centre of gravity of the model CCON print the constraint equations input data CCOO print the coordinate input data CDIR print the direct mass input data CDIS print the displaced freedoms input data

optionOPTION



CELE print the element topology input data CGEO print the geometric property input data CLOA print the load input data CLST solve constraint equations last. Note that this method cannot remove local

singularities. High speed frontal solver only CMAT print the material property input data CONV Include convective acceleration terms when APIW is operative. Default for non

APIW analyses (See Appendix M.7) COOR print coordinate data CORE write element stiffnesses etc. to data manager instead of backing files CSKE print the skew systems input data CSUP print the suppressions input data DDEC delete the decomposed stiffness disc file before an eigenvalue analysis DATA perform a data check run only DIRE print the direct mass input data DTRS initial conditions supplied in a transient dynamic restart to the previous solution ELAX print offset and local axes information for each beam and tube element in the

structure ELEM print the element topology data EPSN engineering plane strain model for membranes FCRO print full summary for automatically selected creep solution times (summary is

short by default) FDMS print a list of freedoms at each node FEMV produce ‘FEMVIEW’ analysis model file (see note) FIXD read data input in fixed format FNUM print a list of freedom numbers (I.e position of freedom in solution vector) FSOL instruct the program to use the ordinary frontal solver GAUS print out stress sampling points for elements with stress output GEOM print the geometric property data GLST global stress output (see Appendix -A for valid element types) GOON continue with solution even when warnings present in data HYDR print detailed elemental hydrodynamic information (see Appendix M.7) IEST use initial elastic stiffness for first iteration when there is residual stress input INEL use input element order for solution order LINS use line search procedure (cannot be used with CONSIT with the SOLUTION

command) LOWE convert all higher order element types to lower order ones in steady state heat

analysis. When used, the geometric properties data must refer to the lower order element types only

MATE print the material properties data MCON vary current profile to maintain mass conservation. This is not recommended for

use with API analyses (See Appendix M.7) MYEL use user element order for solution order



NODL print only selected expanded data (“No Data List”) NOKC no centrifugal stiffness to be included in tangent stiffness matrix NOKP no pressure load stiffness to be included in tangent stiffness matrix NOPF no porthole file created for post-processing using POSTNL NOPG suppress page throws in output NORE no resultants calculated for applied loads during data checking OVIT override iteration limit (i.e. continue to next load increment when iteration limit

exceeded) PATN produce ‘PATRAN’ neutral file for analysis model (see note) PLSN plane strain model for membrane elements PRNO print only selected input data RELC vary current profile such that the velocities are not at absolute depths, but relative

depths (See Appendix M.7) RVOF switch off relative velocity formulation in Morison’s equation for wave load

calculation (See Appendix M.7) SAVJ save journal file INCRJF SECN use Secant-Newton acceleration (SOLVE solution procedure only) SKEW print the skew systems data SURF use temperature at node 1 to determine material properties. Only apply to FAT2

elements with FLNS option (see GROUP or PROBLEM commands) TRAP trapezoidal rule used for through thickness integration for shells TWOD convert plane stress membranes and FLA2 to 2-D forms VEXT no modification to current profile in the presence of wave, simple extrapolation is

used above still water level. Default for non-APIW analyses. (See Appendix M.7)

VISC use viscoplastic creep solution method (See Appendix -J). Not available for creep law LAW4.

Note

FEMV and PATN are mutually exclusive options.

5.1.19 OUTPUT Command

This command defines the points in time at which results are to be output.



Parameters

OUTPUT : command keyword

blocno : number of the block controlled by this command. A BLOC command is then required. (Integer)

TGEN : keyword indicating that a list of times is to be generated

stime : start time for list of generated times. (Real)

timei : time increment to be added to start time for list of generated times. (Real, ≥ 0.0)

ntime : total number of generated times, including start time. (Integer, > 0)

IGEN : keyword indicating that a list of increments is to be generated

incst : start increment for list of generated increments. (Integer)

iinc : increment to be added to start increment for list of generated increments. (Integer, > 0)

nincs : total number of generated increments, including start increment. (Integer, > 0)

ALL : keyword indicating that output is required at all times/ increments

INCR : keyword indicating that a list of increment numbers are supplied

incno : increment number for which results are to be output. (Integer)

TIME : keyword indicating that a list of pseudo-times are supplied

ptime : pseudo-time for which results are to be output. (Real)

Notes

1. If GROUPS are used, then all commands controlling output (i.e. OUTPUT, BLOCK) must appear in the GROUP section other than commands controlling DISPlacement output which always appear in the PROBLEM section.

2. INCR or IGEN may only be used with SOLUTION solution method.

ALL

INCR incno

TIME ptime

IGEN

TGEN

incst

stime timei ntime

iinc nincs

OUTPUT blocno



3. TIME or TGEN may only be used with SOLVE solution method. 4. If the list of pseudo times/increments at which output is required is too long for one line, specify further

OUTPUT commands with the same block number. 5. If a time or increment is re-specified with a subsequent OUTPUT command the output identifiers with

the associated BLOCK command(s) are overwritten.

5.1.20 PARAMETER Command

This command enables the values of certain problem parameters to be set. Optional

Parameters

PARAMETER : command keyword

ident : alphanumeric identifier. See table below.

pval : value of parameter ident. See table below. (Real or Integer)

Identifier Definition and value

SUBINC Number of plasticity subincrements (default 1) (see Appendix C.3). (Integer)

SUBTOL Plasticity strain tolerance used to calculate a number of plasticity sub-increments (see Appendix C.3). (Real)

MXSUBI Limit for number of plasticity subincrements (default 20). (Integer)

TREFLD Reference temperature for temperature loads. (Real)

TAZERO Absolute zero temperature for radiation calculations. (Real)

GAPSTF Gap stiffness factor (default 1.0E3). (Real)

GAPSMA Gap residual stiffness factor (default 1.0E-8) See GAP element description sheets (Appendix -A). (Real)

TIMBEG Pseudo time corresponding to zero load state (default 0.0). (Real)

DRILF Stiffness multiplier for fictitious local RZ stiffness for shells (default 1.0E-08). (Real)

PENFUN Penalty function multiplier for fictitious local RZ stiffness for shells (used in conjunction with FLATOL) (default 1.0). (Real)

PARAMETER ident pv al



FLATOL Shell flatness threshold to activate penalty function control of local RZ stiffness (largest angle between opposite diagonal normals in degrees) (default 90.0). (Real)

SHEARL Shear locking reduction factor for TCS and TSD elements (default 19.2). (Real)

LNMULT Line search multiplier for control parameter adjustment. (Real)

EIGCNV Subspace iteration convergence tolerance (default 1.0E-05). (Real)

MXAUTO Limit for number of repeated AUTO restarts for special solution methods (default 3). (Integer)

FINCMX Maximum step increasing actor for special solution methods. (default 1.5 for LOAD, 10.0 for ARCL, TARCL and CONSIT). (Real)

TINCMX Maximum timestep for special solution method LOAD. (Real)

TINCMN Minimum timestep for special solution methods LOAD. (Real)

KSIGNL Number of consecutive step increasing signal before actual increase is made for special solution method LOAD (default 2). (Integer)

STEPRF Step reduction factor in auto-restart for special solution methods (default 0.5). (Real)

SCONLO Solution diagonal decay ratio - warning threshold (default 1.0E5). (Real)

SCONHI Solution diagonal decay ratio - abort threshold (default 1.0E12). (Real)

SERCH1 Line search tolerance for interpolation (default 1.0). (Real)

SERCH2 Line search tolerance for extrapolation (default 0.7). (Real)

SERCL1 Lower limit for line search factor (default 0.01). (Real)

SERCL2 Upper limit for line search factor (default 10.0). (Real)

FACLSP Line spring factor (default 0.4). (Real)

MXAUGM Maximum number of Lagrangian augmentations (default 0). (Integer)

GAPCVG Penetration tolerance for Lagrangian augmentations (default 0.001). (Real)

TANCVG Tangential relative displacement tolerance at stick positions for Lagrangian augmentation (default 0.001). (Real)

Notes

1. SUBINC and SUBTOL are mutually exclusive. 2. TREFLD and TIMBEG cannot be redefined on a restart. 3. Some identifiers may be specified in both the PARAMETER and TEMPORAL command. If an

identifier is defined more than once, the last definition will be assumed.



5.1.21 PASS Command

This command invokes the frontwidth optimisation facility. Optional

Parameters

PASS : command keyword

method : optional word; KING, LEVY, PINA, or SLOAN, to indicate method of optimising. If blank, CUTHILL-MCKEE is assumed. However, when the optimised frontal solver is adopted, the default method is SLOAN.

npass : number of attempts to reduce the frontwidth. If blank, defaults to 2 for SLOAN and 10 for other methods. (Integer)

Note

1. The frontwidth optimiser assumes that all elements with the same node number are connected together according to data given in element topology data. In the situation where elements contain an auxiliary node (SST4, STF4, and WST4), it is advisable to assign a unique node number to each auxiliary node so that the final outcome of the optimisation process will not be affected.

2. Two passes are always performed with SLOAN unless npass is explicitly set to 1.

3. The SLOAN method is only available with the optimised frontal solver.

5.1.22 PINO Pressure Interpolation Order Command

The PINO command defines the pressure interpolation order to be used by specified elements. To avoid numerical problems with incompressible or nearly incompressible materials, this command may be used to specify a different (lower) interpolation order for the volumetric strain. If the PINO command is not present the normal displacement formulation is used. Optional

Parameters

PINO : command keyword

PASS (method) (npass)

PINO inpr (elno)



inpr : pressure interpolation order. (Integer)

elno : list of element numbers in topological format. (Integer)

If blank, defaults to all elements (in group)

Notes

1. This command is recommended for use with the hyperelastic material model 2. The recommended pressure interpolation orders and the associated element types are given below:

Interpolation Elements order

1 BRK6 BRK8 BR15 BR20 QUM4 QUM8 TRM3 TRM6 QUX4 QUX8 TRX3 TRX6

3 QUM8 TRM6 QUX8 TRX6

4 BR15 BR20

Example

A rubber membrane with a mesh of 100 high order membrane elements (QUM8’s and TRM6’s)

PINO 3 (100) (1,1)

5.1.23 PROBLEM and TITLE Command

This command is mandatory and must immediately follow the JOB command.

Parameters

PROBLEM : command keyword

TITLE : command keyword

direct : 4 character directives defining structural and material model to be used. May be one or more of the following:

PROBLEM

(direct)

TITLE

title)(*



GLST compute stresses/strains in global axis system LOST compute stresses/strains in local axis system PLAS take plasticity effects into account LARG include large displacement effects in the calculation of strains and geometric

stiffness matrices. This directive should be accompanied by the command UPDATE GEOM (see UPDATE command)

CONL use conservative pressure loading - i.e. calculate pressure loads using original geometry throughout. Only applicable with UPDATE GEOM (see UPDATE command)

NRES do not carry forward residuals into next increment. FLNS form natural stiffness (i.e. Young’s modulus*Area) for FLA2 and FAT2 elements CREP creep analysis EXPL use explicit temporal integration scheme for transient analysis

* : character to indicate the following text forms the title

title : any alphanumeric title of up to 60 characters including blanks. It must be preceded by an asterisk (*). This title will be printed at the top of each page of ASASNL output

Notes

1. If no directives are given linear elastic behaviour is assumed with the default implicit temporal integration scheme for transient analysis and stresses are computed in the element default axis system.

2. This is a global switch and will set these directives for all groups regardless of what is put on the GROUP commands. You can, however, add other directives with the GROUP commands.

3. The first six characters of the title are used for the problem name. 4. The PROBLEM command and TITLE command are identical and interchangeable.

5.1.24 PROJECT Command

To define a name and title for the project. Optional but project name is recommended.

Parameters

PROJECT : command keyword

pname : project name for current run (Alphanumeric, 4 characters, first character must be alphabetic). If pname is omitted, then pname defaults to the name ASNL

* : character to indicate following text forms the project title.

PROJECT (* title) (pname)



title : any alphanumeric title of up to 60 characters including blanks. It must be preceded by an asterisk (*). The default project title is ‘ASAS-NL ARCHIVE FILE’

Notes

1. All runs with the same project name access the same ASAS data base and hence this must be the same in all restarts. A project data base consists of one project file (with a file name consisting of the 4 characters of pname with the number 10 appended) which acts as an index to other files created under this project, together with those other files.

2. The title is used by the program as an identifier for the archive files saved. Subsequent jobs requiring to use those files must have the same identifying title (in addition to the correct file names with the FILE command).

5.1.25 RESTART Command

This command is used in restarted runs in place of the SOLVE command. It defines times at which a solution is to be attempted. It must follow the PROBLEM or TITLE command. Compulsory

Parameters

RESTART : command keyword




ntime : total number of generated times, including start time. (Integer, >0)

time : time for solution. (Real)

Notes

1. All times must be non-negative. 2. The first time, time1, must correspond with the time on the restart file for the chosen checkpoint and

agree within 3 decimal places. The checkpoint number is defined using the JOB command. 3. No solution is attempted at time, time1. 4. Solution times may be continued using subsequent RESTART commands.

TGEN stime timei ntime

time

RESTART



5. All solution times specified must be greater than or equal to zero. (In general they must be greater than or equal to TIMBEG, the zero load start time.) The list must also be in ascending order i.e. time (i+1) ≥ time(i).

6. If load functions are used, then all solution times specified must be greater than, or equal to the first pseudo time specified with each load function.

7. On a restart, only the preliminary data, suppressions, displaced freedoms, loading and additional mass can be changed. Material property data may also be changed but only if the analysis type has been changed from the initial run.

8. If temperature data is redefined on restart, the number of load sets must be the same as on the initial run.

5.1.26 RESU (or POST) Commands

This command defines the points and the information to be saved for post-processing with POSTNL, on the file specified on a corresponding FILE command. It also defines the points where information is to be saved on the ASAS database. Recommended

Parameters

RESU : command keyword

POST : command keyword (same meaning as RESU)

outid : output identifier, one or more of the following:

DISP displacements (temperatures for heat) VELO velocities (temperature rates for heat) ACCN accelerations REAC reactions (reactive nodal heat for heat) STRS stresses (fluxes for heat) STRN total strain (field for heat) INST inelastic strains ELAS elastic strains SRES stress resultants WORK element mechanical work (NOT saved to ASAS database)



TEMP temperatures (NOT saved to ASAS database) EIGN mode shapes CRSN creep strains SUMR output summary of maximum displacements, velocities, accelerations, summed

reactions and solution control information (only summed reactions saved to ASAS database)





IGEN : keyword indicating that a list of increments is to be generated

incst : start increment for list of generated increments. (Integer)

iinc : increment to be added to start increment for list of generated increments. (Integer, > 0)

nincs : total number of generated increments, including start increment. (Integer, > 0)

ALL : keyword indicating that information is to be stored for all increments

INCR : keyword indicating that a list of increment numbers is supplied

incno : increment number for which results are to be stored. (Integer)

TIME : keyword indicating that a list of times is supplied

time : time for which results are to be stored. (Real)

Notes

1. SRES must be saved if layer stresses/strains or failure indices are required to be recovered in POSTNL for an elastic laminated shell analysis.

2. DISP, STRS, STRN, ELAS and INST (if plasticity) must be saved if fracture mechanics processing is required in POSTNL. For creep fracture, CRSN must also be saved in addition and results from at least two increments must be available.

3. INCR or IGEN may only be used with SOLUTION solution method. 4. TIME or TGEN may only be used with SOLVE solution method. 5. Information written to the ASAS database consists of two parts. The first part is equivalent to the

specification of SAVE LOCO FILES in ASAS. Data which will only be generated for ASAS compatible element types, are written to the “35 file”. The second part concerns with saving of results. This information is written to the “45 file”.

6. If post-processing using POSTNL is not required, option NOPF can be used to supress the generation of porthole file. Data will always be written to the ASAS database



7. POST/RESU command alone will cause saving of DISP, STRS and SUMR in all increments/times. In addition, the SURFACE FAILURE results will be saved to the ASAS database in a job involving plasticity or failure.

8. If the results database is to be used in any post-processing run then a RESU command must be included in the initial ASAS run to initialise the database.

9. The last POST/RESU command at a time overrides all the previous specifications.

5.1.27 SAVE Command

This command defines points at which run information is stored on the stiffness and data manager archive files. File names are defined on appropriate FILE commands. Optional

Parameters

SAVE : command keyword

NEW : keyword to indicate that new files are to be created

OLD : keyword to indicate that existing files are to be used - information is appended to the old files (except that a restarted run from an intermediate checkpoint will override previously dumped information for higher checkpoints)

STEP : keyword to indicate that information is to be stored every ‘ninc’ increments

ninc : see above. (Integer)

ROLL : keyword to indicate that a rotating set of ‘nsol’ solutions will be stored on the archive file

nsol : see above. (Integer)

ALL : keyword to indicate that information is to be stored after all load increments

ptminc : pseudo time (Real) or increment (Integer) for which restart information is to be stored

SAVENEW

OLD ALL

ptminc

STEP ninc

(ROLL nsol)



Notes

1. If OLD then there should not be any FILE commands referring to new stiffness and archive files. 2. Information is saved on the stiffness archive file only if stiffnesses have been updated since the previous

checkpoint. 3. Information is always saved on both files on the last increment of a successful analysis. 4. ROLL should not be used to hold less than 3 increments.

5.1.28 SCALING Command

Controls scaling of applied loads for proportional loading to a factor times yield stress on first load increment. See Note.

Parameters

SCALE : command keyword

ident : an alphanumeric identifier. If no identifier is specified, then applied loads are scaled until first yield is reached. Allowable identifiers are as follows:

RPROP Reference proportion for scaling. The reference value for scaling is this proportion multiplied by the yield stress. The default value is one.

SCALIM This specifies a ceiling value to the load factor. If omitted no limiting value is enforced.

val : value for selected identifier. (Real)

Note

This command is an alternative to the SOLVE command. The job terminates after scaling to the value given and can be restarted as requested. No SAVE command is required.

5.1.29 SKIP Command - (Group Section Only)

This command defines the elements to be skipped from a group. It is valid only in conjunction with an ELGROUP command.

Optional

SCALE ident v al



Parameters

SKIP : command keyword

elno : list of element numbers given in topological format. (Integer)

Notes

The order of ELGROUP and SKIP Commands within a group is not important.

Example

Assign elements 1, 2, 4, 6, 9, 10 to group 3

GROU 3 * BEAM ELEMENTS ELGR (10) (1,1) SKIP 3 5 SKIP (2) (7,1)

5.1.30 SLEEP Command

This command defines the elements which will become inactive (sleep) during part of the analysis. Optional

Parameters

SLEEP : command keyword

ptime : pseudo time at which element sleeps (SOLVE). (Real)

incno : increment number at which element sleeps (SOLUTION). (Integer)


SKIP elno

ptime

incno

SLEEP elno



Notes

1. The same element number cannot be specified more than once in the entire list of SLEEP commands. This means that an element cannot sleep more than once during a run.

2. The element is put to sleep before the solution for the specified time/increment number is obtained. Thus the element is inactive for the time/increment number specified and for all times/increment numbers thereafter. It is important to note that global mass, damping and stiffness matrices are not updated unless specifically requested. Appropriate UPDATE commands should be specified at the time/increment number specified with the SLEEP command.

3. If the pseudo time specified is within the lower and upper limits of solution times given on the SOLVE (or RESTART) commands, then it must coincide with one of the solution times.

4. If both WAKE and SLEEP times/increment numbers are present for an element, the wake time/increment has to be before the sleep time/increment number.

5. The list of element numbers specified with the WAKE/SLEEP commands cannot be changed during any subsequent restart analysis.

6. Care should be taken using the WAKE/SLEEP commands when load type NODAL LO has been specified. Internally, ASAS-NL attaches all nodal loads to the element with the highest system element number which references the freedom to which the nodal load is applied. When an element which has nodal loads attached in this manner is woken up or put to sleep, the nodal load is also woken up or put to sleep, as are all element loads.

5.1.31 SOLUTION Command

Defines automatic load (or time) stepping procedure for static and transient dynamics analysis in a virgin run (used instead of SOLVE command). If used this command must immediately follow the PROBLEM or TITLE commands. For restarted runs, the SOLUTION command is replaced by the SRESTART command. Note that SOLUTION (and SRESTART) cannot be used for creep analysis. Instead, the creep automatic timestepping procedure is activated by specifying AUCR in the OPTION command together with SOLVE (or RESTART)

Parameters

SOLUTION: command keyword

method : special solution method name (Alphanumeric). Valid methods are:

LOAD Constant load control. This method is applicable to static analysis with any load

history types. It is not suitable for predicting limit point or snap behaviour.

ARCL Cylindrical arc-length control (i.e. constant displacement vector increment

(DPVEC)). Constraint on the step size has quadratic form, thus no distinction

SOLUTION direct v almethod ninc



between the positive and negative path direction is available. This method is

applicable to static analysis with proportional loading only. It can deal with limit

point or snap behaviour.

TARCL Linearised cylindrical arc-length control. This method is applicable to static

analysis with proportional loading only. It can deal with limit point or snap

behaviour.

CONSIT Constant displacement component increment (DPCOM) control. Constraint on the

step size has linear form, thus positive and negative value of an increment is

recognised. This method is applicable to static analysis with proportional loading

only. It can deal with limit point or snap behaviour.

DOMFRQ Dominant frequency control. This method is applied to transient dynamics analysis

using implicit time integration only.

MAXFRQ Maximum frequency control. This method is applied to transient dynamics analysis

using explicit time integration only

ninc: maximum number of increments to be attempted.

direct: alphanumeric directive. See table below

val: value(s) associated with the directive. (Integer, Real or Character, see table below)

Below are the directives for use with the SOLUTION and SRESTART commands.

(A) For method LOAD


FIRTIM The first solution pseudo-time. (Real, ≥last solution time) FIRTIN The initial pseudo-time increment. (Real, >0.0) MAXTIM The maximum solution time. (Real, ≥last solution time) ITERD Desired number of iterations per increment. If set to zero step size adjustment is independent of number of iterations (default 4). (Integer, ≥0)

Notes

1 FIRTIM and/or FIRTIN must be specified. If FIRTIM is omitted, the first solution time is assumed to be the last solution time in the previous run (or 0.0 for a new run). Conversely, if FIRTIN is omitted, the initial time step size is taken as the difference between FIRTIM and the last solution time (or 0.0 for a new run). If both are specified, the first solution time will be FIRTIM while the next step (i.e. the second step) will have a step size of FIRTIN.

2 Additonal control parameters are available in the PARA commands. These include FINCMX, TINCMN, TINCMX, KSIGNL, STEPRF and MXAUTO.



3 The automatic load procedure may not be effective when there is a sudden change of loading from the previous increments. If difficulty arises, a restart should be carried out with the load stepping control parameters re-defined.

4 The run terminates when either the maximum number of increments or the maximum solution time is reached. In the latter case, the last solution will always be attempted at time MAXTIM.

5 Further details are given in Appendix C.

(B) For methods ARCL, TARCL and CONSIT


WORKC Adopts constant external work increment control in conjunction with ARCL or CONSIT. May not be used on first restart following standard solution procedure.

Switch tolerance. If set to zero this procedure is used in all increments. (Real) AUTO Automatic selection of displacement component to be controlled. Used with CONSIT

only. Size of incremental displacement. (Real)

INITPR Defines initial step size. Used with ARCL and TARCL only. Initial proportion of reference load. (Real)

INCDIS Defines initial step size. Mandatory with CONSIT and optional for ARCL and TARCL. Three parameters to follow:

Nominated node. (Integer) Nominated freedom name. (Alphanumeric) Initial incremental displacement of nominated freedom. (Real)

ITERD Desired number of iterations per increment. If set to zero step size adjustment is independent of number of iterations (default 4). (Integer, ≥0)

MAXIPR Maximum incremental proportion of reference load. used with CONSIT only. (Real) MAXLOD Terminates the run when this proportion of reference load is exceeded. (Real) MAXDIS Terminates the run when total displacement of the specified freedom is exceeded. Three

parameters to follow: Nominated node. (Integer) Nominated freedom name. (Alphanumeric) Maximum displacement of nominated freedom. (Real)

CONDIR Controls loading direction. Used on restarts with ARCL and TARCL only.. Controlling parameter taking value +1.0 or -1.0. (Real)

Notes

1 INITPR or INCDIS must be specified when ARCL or TARCL is used. 2 Additional control parameters are available in the PARA commands. 3 These procedures can only be applied to static analysis with proportional loading. 4 For analysis containing a dead load set (i.e. non-proportional part) and a live load set (i.e. proportional

part), the dead loads may be applied in a SOLVE run followed by restart using the special solution procedure for the live loads. In this case, only the proportional load data is required in the SRESTART run.



(C) For methods DOMFRQ and MAXFRQ


FIRTIM The first solution time. (Real, ≥last solution time) FIRTIN The initial timestep size. (Real, >0.0) MAXTIM The maximum solution time. (Real, ≥last solution time) ITERD Desired number of iterations per increment. if set to zero step size adjustment is

independent of number of iterations (default 4). (Integer, ≥0)

Notes

1 FIRTIM and/or FIRTIN must be specified. If FIRTIM is omitted, the first solution time is assumed to be the last solution time in the previous run (or 0.0 for a new run). This setting is useful for determining the consistent initial accelerations from given initial conditions and/or initial loading. Conversely, if FIRTIN is omitted, the initial time step size is taken as the difference between FIRTIM and the last solution time (or 0.0 for a new run). If both are specified, the first solution time will be FIRTIM while the next step (i.e. the second step) will have a step size of FIRTIN.

2 Additional control parameters are available in the PARA and TEMP commands. 3 Further details are given in Appendix K.

5.1.32 SOLVE Command

This command invokes the classical solution method (incremental Newton-Raphson) and defines points at which a solution is to be attempted for a virgin run. It must follow either the PROBLEM/TITLE command. In restarted runs it is replaced by the RESTART command.

Parameters

SOLVE : command keyword




SOLVE

TGEN stime timei ntime

time




time : time at which a solution is to be attempted. Times must be non-negative. (Real)

Notes

1. List of times may be continued using subsequent SOLVE commands. 2. The solution method activated by the SOLVE command can be used for static problems of proportional

or non-proportional loading. The latter is defined by explicitly specifying load history. Otherwise proportional loading is assumed with the load multiplier equal to the time at each solution point.

3. This solution method is compulsory for creep analysis. 4. All solution times specified must be greater than or equal to zero. (In general they must be greater than or

equal to TIMBEG, the zero load start time.) The list must also be in ascending order i.e. time(i+1) ≥ time(i).

5. If load functions are used for solution times specified outside the pseudo times specified with each load function, extrapolation will be used.

5.1.33 SPIT Command

This command sets the parameters for the Subspace Iteration Eigen Solution. If present it must be accompanied by an EIGN command. Optional and only for Eigen Solution.

Parameters

SPIT : command keyword

KGEOM : keyword to indicate that the current small displacement stiffness Ko and the geometric stiffness KG matrices are to be used for a buckling analysis

UNITM : keyword to indicate that the current small displacement stiffness Ko and the unit I matrices are to be used for a spectral analysis

MASS : keyword to indicate that the current tangential stiffness KT and the mass M matrices are to be used for a natural frequency analysis

ident : alphanumeric identifier. See table below

val : value associated with the specified identifier. (Integer and Real)


SPIT UNITM

KGEOM

MASS

ident v al



NORME Eigenvector normalisation. (Integer) 0 Maximum component is 1.0 (default) 1 Euclidean norm is 1.0

SCOPE Scope of solution. (Integer) 0 Eigenvalues and modes (default) 1 Eigenvalues only

NHIGHF Number of eigenvalues required. (Integer) 1≤NHIGHF≤NSUBSP (default to 1)

NSUBSP Number of eigenvalues to iterate over (size of subspace). If omitted then default value is calculated automatically by the program. (Integer) 0≤NSUBSP≤NFREE, where NFREE is the number of free freedoms.

LMSPIT Maximum number of iterations in eigenvalue solution (default 45) (Integer)

EIGCNV Convergence tolerance in eigenvalue solution (default 0.00001). (Real)

SELMOD Number of mode selected for perturbation. 1<SELMOD<NHIGHF (default 1). (Integer)

PERTMG Relative magnitude of perturbation (default 0.005). (Real)

STURM Sturm sequence check flag. (Integer) 0 = no check (default) 1 = check required

SHIFT Eigenvalue shift (default 0.0). (Real) The shift should be specified in eigenvalue units for buckling problems. The shift should be specified in frequency units (Hz) for natural frequency problems

STARTV Method for forming the Starting Vectors 0 = Vectors generated based on the stiffness to mass ratio (default) 1 = Use last calculated eigenvectors as starting vectors

Notes

1. To obtain the KG matrix for SST4/WST4 elements the LARG directive must be specified with the GROUP or PROBLEM/TITLE commands.

2. See Appendix C.5 for further details concerning eigenvalue analysis. 3. Load stiffness will only be ignored if CONL is specified with the GROUP or PROBLEM/TITLE

commands. 4. A shift must be applied if there are not enough suppressions in the model to remove all the rigid body

motions. Eigenvalue analysis of a free structure is allowed for UNITM and MASS provided no loading is applied. The structure must have adequate suppressions for KGEOM.

5. NHIGHF and NSUBSP will be reset if their specified values are outside the allowable bounds.



6. The eigenvalues of a shifted problem are arranged in ascending order of their distance from the shift origin. The eigenvalues of the original problem, which are reported in the output file, will be given in the same order.

7. The sturm sequence check implemented assumes that the lowest modes have been computed and the eigenvalues are monotonially increasing. It should not be applied to problems where these conditions are not satisfied. One such example is when a shift is applied to determine the higher modes directly.

8. The use of last calculated eigenvectors as starting vectors is only allowed in a restart analysis if the subspace size NSUBSP remains unchanged between runs.

5.1.34 SRESTART Special Solution Restart Command

Defines special solution options for restart run. (Used instead of RESTART command and must follow the PROBLEM or TITLE command.)

Parameters

SRESTART : command keyword

FROM : keyword

incno : increment number of increment immediately before start. (Integer)

method : special solution method name. See SOLUTION command for valid names.

ninc : maximum number of increments to be attempted.

direct : alphanumeric directive The directives used vary according to the special solution option selected. See the table detailed with the SOLUTION command, and below.

val : value(s) associated with the directive. (Integer, Real or Character)

The directive below is for use with SRESTART command only.


STEP Defines directly step size. Used with ARCL only. Length of incremental displacement vector. Is used as an alternative to INITPR or INCDIS. (Real)

SRESTART FROM incno direct v almethod ninc



Notes

1. The loading information will not be correctly transferred to the ASAS database if the restart adopts a variable load solution procedure (e.g. ARCL) while the initial run adopts a fixed load procedure (SOLV or SOLU LOAD). This may affect the results of code checking using BEAMST.

5.1.35 START Command

This command defines the list of starting node numbers for any renumbering attempt specified with the PASS command. This command must only be used in conjunction with the PASS command and need not be present. If absent the renumbering will commence from a point chosen by the program. (A maximum of 3 START commands can be provided and each one can consist of up to 10 nodes). Optional

Parameters

START : command keyword

nodeno : node number with which to start any renumbering attempt. A maximum of 10 node numbers may be specified. (Integer)

Notes

1 Up to 3 starting vectors may be specified.

2 Number of passes will be equal to number of starting vectors if START is used.

3 START will have no effect on the Sloan method and, thus, is not required when adopting this method.

5.1.36 STRUCTURE Command

To define the structure name for a new run or an existing model name for a restarted run. Optional but recommended.

Parameters

STRUCTURE : keyword

START nodeno

STRUCTURE sname



sname : structure name. The name must be unique from all other structure names in this project. (Alphanumeric, 4 characters, the first character must be alphabetic)

Notes

1. sname is used as a prefix for all ASAS backing files created during a new run. The four characters are appended with two digits to create each individual file. In a restarted job, this defines an existing structure from which the current run is based upon.

2. If the STRUCTURE command is omitted then the project name pname is used in place of sname

Example

STRUCTURE SHIP

5.1.37 SYSPAR Command

This command, if present, must precede the JOB command. It allows the values of certain system parameters to be reset. Optional

Parameters

SYSPAR : command keyword

ident : alphanumeric identifier. See table below

val : value associated with the specified identifier. (Integer or Logical)


LPGSIZ Data manager page size. (Integer, must not exceed 16383)

MINPAG Minimum number of incore pages reserved for data manager. (Integer)

LTPAGE Maximum length of page directory. (Integer, must not exceed 65535)

LMJIA Length of archive file major index. (Integer, must not exceed 16383)

MANREC Default length of subindex. (Integer)

IPERM 1 = use permanent files; 0 = use temporary files. (Integer)

NOPAG Block multiplier for LENTRK (length solution backing files). (Integer)

SINDEC .TRUE. if reduced stiffness to be archived (if .FALSE., this file will be reformed by decomposing the stiffness file on restarts) (Logical)

SYSPAR ident v al



LEVSYS System abort level. (Integer)

MXCONS The maximum of MXCONS and NCONEQ constraint equations will be allowed for restarts. (Integer.) NCONEQ is the number of constraint equations in the initial run.

OPENFL Default number of keys with which an internal ASAS file is opened (integer)

Notes

1. See Table 6.1 for default values and Section 6.2 for the significance of some of the system parameter. 2. In a restart, new constraint equations can be added but cannot contain a constant term. 3. LPGSIZ and LMJIA must be the same and the program will ensure this if either is specified.

5.1.38 SYSTEM Command

To define the amount of data space to be allocated during the run. Optional.

Parameters

SYSTEM : command keyword

SMALL : keyword indicating data manager page size

MEDIUM : keyword indicating data manager page size (default size)

LARGE : keyword indicating data manager page size

DATA : keyword

AREA : compulsory keyword

memory : amount of memory (in 4 byte words) to be used by this run. A minimum of 1000000 is assumed. (Integer)

initm : initial memory reserved. Not normally used. (Integer)

Note

See Table 6.1 for optional page sizes.

(MEDIUM)

SMALL

LARGE

SYSTEM DATA AREA memory (initm)



5.1.39 TEMPORAL Command

This command allows the user to vary the temporal integration scheme used for transient analysis and the parameters associated with automatic timestepping.

Parameters

TEMPORAL : command keyword

ident : alphanumeric identifier. See table below.

val : value of identifier. See table below.


TALPHA Temporal integration scheme coefficient (default 0.0). (Real)

TBETA Temporal integration scheme coefficient (default 0.5). (Real)

TGAMMA Temporal integration scheme coefficient (default 0.25). (Real)

VALPHA Creep integration weighting factor. Any value between 0.0 and 1.0 may be used. (Default 0.0). (Real)

DCSTMX Autocreep control parameter (use with OPTION AUCR only). Maximum incremental creep strain. (Real)

DCESMX Autocreep control parameter (use with OPTION AUCR only). Maximum ratio of incremental creep strain to total strain. (Real)

DSIGMX Autocreep control parameter (use with OPTION AUCR only). Maximum ratio of incremental stress to total stress. (Real)

TINCMX Automatic timestepping control parameter for creep and transient dynamics. Maximum timestep. (Real)

TINCMN Automatic timestepping control parameter for creep and transient dynamics. Minimum timestep. (Real)

FINCMX Automatic timestepping control parameter for creep and transient dynamics. Maximum ratio of new timestep to previous timestep. (Real)

FIRSTP Autocreep control parameter (use with OPTION AUCR only). First timestep for this solution or restart. (Real)

MXINCS Autocreep control parameter (use with OPTION AUCR only). Maximum number of timesteps for this solution or restart. (Integer)

TEMPORAL ident v al



TFACLO Automatic timestepping control parameter for transient dynamics. Lower limit on ξ for no change in timestep. (Real)

TFACHI Automatic timestepping control parameter for transient dynamics. Upper limit on ξ for no change in timestep. (Real)

TFACRJ Automatic timestepping control parameter for transient dynamics. Limit on ξ below which the current solution will be rejected. (Real)

FRAPRD Automatic timestepping control parameter for transient dynamics. Desired fraction of the characteristic period for determining the timestep. (Real)

KSIGNL Automatic timestepping control parameter for transient dynamics. Number of consecutive timestep increasing signal before an actual increase is made. (Integer)

IPDICT Predictor type for transient dynamics. (Integer) 1. Predictor acceleration equals to 0.0. (Default) 2. Predictor displacement equals to displacement at end of last step. Note that this must not be used in explicit analysis or when TBETA=0.0.

HGAMMA Temporal integration scheme parameter for transient heat (default 1.0). (Real)

Notes

1. See Appendix -J for full details concerning the individual parameters for creep analysis. 2. See Appendix -K for full details concerning the individual parameters for transient dynamic analysis. 3. See Appendix N for full details concerning the individual parameters for transient heat analysis 4. Some identifiers may be specified in both the PARAMETER and TEMPORAL commands. If an

identifier is defined more than once, the last definition will be assumed.

5.1.40 TEXT Command

To define a line of text to be printed once only at the beginning of the output. Several TEXT lines may be defined to give a fuller description of the current analysis on the printed output.

Optional

Parameters

TEXT : command keyword

TEXT text



text : this line of text will be printed once, at the beginning of the output. (Alphanumeric, up to 75 characters)

Example

TEXT THIS EXAMPLE OF THE TEXT

TEXT COMMAND IS SPREAD

TEXT OVER THREE LINES

5.1.41 TITLE Command

See PROBLEM Command for full details of this command.

5.1.42 UNITS Command

Recommended.

This command allows the user to define the units to be employed in the analysis and the default units for the input data. The defined unit set will appear on each page of the printout as part of the page header. If this command is omitted then no units information will be reported and the units of all data supplied must be consistent (see Section 3.11).

If the UNITS command is employed, facilities exist to locally modify the input data units within each main data block. See Sections 5.2.1, 5.3.1, 5.4.1, 5.5.1 and 5.6.1 for further details.

5.1.42.1 Global UNITS Definition

This specifies the units to be employed for the analysis and provides the default units for input and printed output.

Parameters

UNITS : keyword

unitnm : name of unit to be utilised (see below)

UNITS unitnm



The units of force and length must be supplied. Temperature is optional and defaults to centigrade. A time unit of seconds is assumed. A default angular unit of radians is used for results reporting. The default input angular unit varies according to the data block and must not be specified on the basic UNITS command.

Restriction

The program calculates a consistent unit of MASS based upon the length and force units supplied. The permitted combinations of force and length are given in Table 3.1.

Valid unit names

Length unit METRE(S), M CENTIMETRE(S), CM MILLIMETRE(S), MM MICROMETRE(S) MICM NANOMETRE(S) NANM FOOT, FEET, FT INCH, INCHES, IN

Force unit NEWTON(S) N KILONEWTON(S) KN MEGANEWTON(S) MN TONNEFORCE(S) TNEF POUNDAL(S) PDL POUNDFORCE, LBF KIP(S) KIP TONFORCE(S) TONF KGFORCE(S) KGF

Temperature unit CENTIGRADE, C FAHRENHEIT, F

Example 1. Input data units and results units to be in units of Kips and feet

UNITS KIPS FEET

The derived consistent unit of mass will be 3.22x104 lbs.

Please also refer to Example 1 of Section 5.1.19.1 of the ASAS user manual.



5.1.43 UPDATE Command

These commands determine the type of solution procedure, by controlling the frequency with which the stiffness and mass matrices are reformed and the structure geometry updated. If no update commands are specified, the program defaults to the initial (elastic) stiffness procedure.

Parameters

UPDATE : command keyword

GEOM : keyword to update the structure coordinates each iteration

MASS : keyword to reform the mass matrix to account for changes in geometry

STIF : keyword to reform the stiffness matrix to account for changes in stress/strain level and/or

geometry

ELAS : keyword to reform stiffness using elastic material properties

INCR : keyword to reform matrix on first iteration only

ITER : keyword to reform matrix on every iteration

KTO : keyword to reform stiffness matrix on first iteration of first increment only (default)

KT1 : keyword to reform stiffness matrix on first iteration

KT2 : keyword to reform stiffness matrix on second iteration

ALL : keyword to perform update specified for all increments

ptminc : pseudo time/time (Real) or increment number (Integer) at which update is to be performed

UPDATE ALL

ptminc

GEOM

MASS

STIF (ELAS)

INCR

ITER

KT1

KT2

KT0



Notes

1. Except for cases when the nonlinearity is low, updating of the geometry and the stiffness matrix should be combined with the directive LARG with the PROBLEM/GROUP command.

2. For the case of pressure loading, the current geometry is always used to calculate the equivalent nodal loads. Therefore, using UPDATE GEOM will result in non-conservative pressure loading.

3. If OPTION VISC is set (for viscoplastic creep solution) the stiffness matrix is automatically updated at each iteration.

5.1.44 WAKE Command

This command defines the elements which will become active (wake up) during part of the analysis. Optional

Parameters

WAKE : command keyword

ptime : pseudo time at which element wakes up (SOLVE). (Real)

incno : increment number at which element wakes up (SOLUTION). (Integer)


Notes

1. The same element number cannot be specified more than once in the entire list of WAKE commands. This means that an element cannot wake up more than once during a run.

2. The element is woken up after the solution for the specified time/increment number has been obtained, including any eigensolution requested. Thus, the element is effectively active from the time/increment number following the time/increment number specified with the WAKE command. It is important to note that global mass, damping and stiffness matrices are not updated unless specifically requested. Appropriate UPDATE commands should be specified for the time/increment number when the element becomes active, i.e. at the time/increment number following the time/increment number specified with the WAKE command.

3. If the pseudo time specified is within the lower and upper limits of solution times given on the SOLVE (or RESTART) commands, then it must coincide with one of the solution times.

4. If both WAKE and SLEEP times/increment numbers are present for an element, the wake time increment number has to be before the sleep time/increment number.

WAKE

ptime

elno

incno



5. The list of element numbers specified with the WAKE/SLEEP commands cannot be changed during any subsequent restart analysis.

6. Care should be taken using the WAKE/SLEEP commands when load type NODAL LO has been specified. Internally, ASAS-NL attaches all nodal loads to the element with the highest system element number which references the freedom to which the nodal load is applied. When an element which has nodal loads attached in this manner is woken up or put to sleep, the nodal load is also woken up or put to sleep, as are all element loads.

5.1.45 WEIGHTS Command

This command is used in conjunction with the DISP or RESF options of the CONVERGE command to enable the user to weight each term when calculating the convergence criteria.

Parameters

WEIGHTS : command keyword

freedom : freedom name. (Alphanumeric)

rval : weight associated with the specified freedom. (Real)

Notes

1. See Appendix -F for list of valid freedom names. 2. Freedom names omitted will have a weight of unity.

freedom rv alWEIGHTS

Structural Data ASAS (Non-Linear) User Manual


5.2 Structural Description Data

These data blocks define the physical properties and shape of the structure.

The following data blocks are defined

Coordinates ............. ................ ................ see Section 5.2.2

Element Topology ... ................ ................ see Section 5.2.3

Material Properties .. ................ ................ see Section 5.2.4

Geometric Properties ................ ................ see Section 5.2.5

Section Information .................. ................ see Section 5.2.6

Skew Systems .......... ................ ................ see Section 5.2.7

5.2.1 UNITS Command

If global units have been defined using the UNITS command in the Preliminary data (Section 5.1.42), it is possible to override the input units locally to each data block by the inclusion of a UNITS command. The local units are only operational for the data block concerned and will return to the default global units when the next data block is encountered.

In general, one or more UNITS commands may appear in a data block (but see notes below) thus permitting the greatest flexibility in data input. The form of the command is similar to that used in the Preliminary data.

Parameters

UNITS : keyword


Notes

1. Force, length, temperature and angular unit may be specified. Only those terms which are required to be modified need to be specified, undefined terms will default to those supplied on the global units definition unless previously overwritten in the current data block. In the case of the angular unit, the default depends on the data block concerned, see below.

2. Valid unit names are as defined in Section 5.1.42.1.

UNITS unitm



3. The mass unit is derived from the force and length unit currently defined. In order to determine the consistent mass unit the force and length terms must both be either metric or imperial. Valid combinations are shown in Table 3.1. This requirement is only necessary where mass or density data is being specified, in other cases inconsistencies are permitted. See Note 4 below and Section 3.11.

4. Applications for each data type

COOR - Coordinate data - only one UNITS command is permitted for each co-ordinate system defined and must appear immediately after the header command. If different units are required, a new co-ordinate system must be defined. The default angular unit is DEGREES.

ELEM - Element data - UNITS not applicable.

MATE - Material data - UNITS command may appear anywhere. Force and length units must be within a consistent set.

GEOM - Geometric data - UNITS command may appear anywhere. Refer to data definitions for individual element type for the default angular unit assumed.

SKEW and NSKW - Skew systems - UNITS not applicable.



Example

Data Operational Units Notes

SYSTEM DATA AREA 5000000

PROJECT ASAS

JOB STAT TITLE *

EXAMPLESOLV 1.0

OPTIONS GOON

UNITS KIPS FEET Kips, feet, centigrade Global definition END

*

COOR

CART

UNITS MM Kips, mm, centigrade, Default angular 1 0.0 100.0 0.0 degs unit is degrees 2 0.0 200.0 0.0 for co-ordinates FIN

CART FRED

UNITS M Kips, m, centigrade, Requires M as unit 101 0.1 0.1 0.0 degs Therefore define 102 0.1 0.2 0.0 new coor system END

*

ELEM Units not used in * elem topology MATP 1

BEAM 1 2 1

BEAM 101 102 1

BEAM 2 102 2

END

MATE Kips, feet, centigrade Units revert to 1 4.32E06 0.3 0.0 1.52E-02 global input END Mass unit is * 3.22 x 104 lbs GEOM Kips, feet, centigrade 1 BEAM 0.3 0.18 0.18 0.03

UNITS IN Kips, inch, centigrade 2 BEAM 8.4 24.7 29.8 1.13

END



5.2.2 COORDINATE Data

The coordinate data may comprise one or more local coordinate systems. Each of these systems must be headed by a Coordinate System Header Line and all except the last terminated by a FIN keyword. The last system of coordinate data is terminated by an END keyword.

Parameters

COOR : compulsory header keyword to denote the start of the coordinate data

CART : keywords to denote the start of each local coordinate system CYLI SPHE

IMPE : keyword to denote imperfection data

FIN : keyword to denote the end of each local coordinate system, except the last

END : compulsory keyword to denote the end of the entire coordinate data

CART

(units)

COOR

CYLI

SPHE name

(name)

DCOS

ORIG

node

RP

RRP

FIN

x'x x`y x'z y'x y'y y'z

x y z

nrep inode

nrrep iinode

IMPE amplxyz

SIN

COS

hleng1

harno1

SIN

COS

hleng2

harno2

END

x-origin y-origin z-origin

x-inc y-inc z-inc

x-inc y-inc z-inc



Notes

1. The coordinate values are in the current local coordinate system or in the global system if no local system has been defined.

2. For cylindrical systems (CYLI) x,y,z are replaced by r, θ, z.

3. For spherical systems (SPHE) x,y,z are replaced by r, θ, φ.

4. For a detailed description of each parameter see Sections 5.2.2.1 to 5.2.2.4.

5.2.2.1 Local Coordinate System Header

To define the type of local coordinate system. Optional, if omitted CART is assumed.

Parameters

CART : cartesian system, global or local

CYLI : cylindrical polar system

SHPE : spherical polar system

name : name of the coordinate system. Optional for CART and if blank, the global cartesian system is

assumed. Compulsory for CYLI and SPHE. (4 character alphanumeric, 1st character must be

alphabetic.)

DEG : keyword used when the angular unit is degrees for θ and φ. If both DEG and RAD are omitted,

degrees are assumed.

RAD : keyword used when the angular unit is radians.

Note

For an axisymmetric model the global axis system is the unnamed cartesian system with x and z equivalent to r and z.

5.2.2.2 Local Coordinate System Orientation

One DCOS command and one ORIG command must be included for each cylindrical or spherical system, and for each named cartesian system. Neither is needed for the global cartesian system with the name omitted. These lines define the origin and direction of the local axis system.

CART

RAD

CYLI

SPHE name

(name)

DEG



Parameters

DCOS : keyword

x’x, x’y, x’z : 6 directional cosines. See Section 5.2.7.1 for a full description. (Real) y’x, y’y, y’z

ORIG : keyword

x-origin : 3 global coordinates of the origin of the local system. (Real) y-origin z-origin

DCOS

ORIG x-origin y-origin z-origin

x’x x’y x’z y’x y’y y’z



Coordinates for Cartesian Systems

x Distance from the local origin in the local x’ direction

y Distance from the local origin in the local y’ direction

z Distance from the local origin in the local z’ direction

Coordinates for Cylindrical Polar Systems

R Distance from the local origin in the local x’y’ plane.

θ Angle from the +ve side of the local x’ axis in the local x’y’ plane (+ve for right-hand screw rule applied to +ve local z’). z Distance from the local origin in the local z’ direction.

Coordinates for Spherical Polar Systems

R Distance from the local origin in 3-D.

θ Angle from the +ve side of the local x’ axis in the local x’y’ plane (+ve for right-hand screw rule applied to +ve local z’).

φ Angle from the +ve side of the local z’ axis to the radius, measured in 3-D.



5.2.2.3 Node Coordinates

Parameters

node : node number. (Integer, 1-999999)

x, y, z : 3 coordinates for the node in a cartesian system. (Real)

r, θ, z : 3 coordinates for the node in a cylindrical polar system

r, θ, φ : 3 coordinates for the node in a spherical polar system

RP : keyword to indicate data generation from the previous / symbol

nrep : the number of times the data is to be generated. (Integer)

inode : node number increment to be added each time the data is generated. (Integer)

x-inc : cartesian coordinate increments to be added each time the data is generated. (Real)

y-inc

z-inc

r-inc : cylindrical coordinate increment to be added each time the data is generated. (Real)

θ-inc

z-inc

r-inc : spherical coordinate increment to be added each time the data is generated. (Real)



θ-inc

φ-inc

RRP : keyword to indicate data generation from the previous // symbol.

nrrep : the number of times the data is to be generated. (Integer)

iinode : node number increment to be added each time the data is generated. (Integer)

Examples

Example of single coordinate data block using the global cartesian axis system.

COOR CART 1 0.0 0.0 0.0 2 10.0 0.0 0.0 / 3 0.0 10.0 0.0 RP 4 1 10.0 0.0 0.0 / 7 5.0 20.0 0.0 RP 2 1 0.0 0.0 4.0 END

Example of a coordinate data block which uses several local axis systems beginning with the global cartesian axis system.

COOR **** THE GLOBAL CARTESIAN SYSTEM, 8 NODES DEFINED CART // / 66 20.1 0.0 -1.0 RP 3,1 0.0 4.0 0.0 RRP 2,4 -10.0 0.0 0.0 69 20.0 0.0 -1.0 73 11.0 0.0 0.0 FIN **** A CYLINDRICAL SYSTEM, NAMED BWL2, 20 NODES DEFINED CYLI BWL2 DEG DCOS 1.0 0.0 0.0 0.0 1.0 0.0 ORIG 0.0 0.0 0.0 / 1 5.0 0.0 0.0 9 5.0 22.5 0.0 7 6.0 0.0 0.0 12 6.0 22.5 0.0 11 6.0 22.5 8.0 RP 4,12 0.0 45.0 0.0 FIN **** 2ND CYLINDRICAL SYSTEM, NAMED HNDL, 7 NODES DEFINED CYLI HNDL DEG DCOS 1.0 0.0 0.0 0.0 -1.0 0.0 ORIG 26.0 0.0 0.0 /



85 10.0 0.0 -1.0 RP 3,1 0.0 30.0 0.0 / 92 10.0 0.0 -5.0 RP 2,-4 0.0 60.0 0.0 / 93 9.5 0.0 -0.5 RP 2,1 0.0 60.0 0.0 END

5.2.2.4 Coordinate Imperfection Data

Defines variations from the nodal coordinate values in the current local coordinate system.

Notes

1. Up to 10 IMPE lines are allowed in each local coordinate system.

2. All variation data is calculated for a node from the original local system coordinates and is then applied to these coordinate values before any conversion to the global cartesian system.

3. To input a variation depending on one direction only, use the COS parameter and hleng or harno value of zero for the term corresponding to the direction of constant variation.

Cartesian Systems

Parameters


ampl : amplitude of imperfection

X,Y,Z : keywords to denote which coordinate direction is effected

SIN, COS : keywords to denote a sine or cosine variation

hlengx : half-wavelength value for variation in corresponding coordinate direction hlengy hlengz

Variation data will be generated of the form:



Cylindrical Systems

Parameters



SIN,COS : keywords to denote a sine or cosine variation

harno : harmonic number of angular variation

hleng : half wavelength value for variation in location z direction

Radial variation data will be generated of the form:

Spherical Systems

Parameters

IMPE amplSIN

COS

SIN

COSharno hleng

IMPE amplSIN

COS

SIN

COSharno1 harno2





SIN,COS : keywords to describe a sine or cosine variation

harno1 : harmonic number of angular variation in θ direction

harno2 : harmonic number of angular variation in φ direction

Radial variation data will be generated of the form:



Example

Example of a coordinate data block which uses several local axis systems and imperfection data.

COOR **** THE GLOBAL CARTESIAN SYSTEM, 8 NODES DEFINED CART // / 66 20.1 0.0 -1.0 RP 3,1 0.0 4.0 0.0 RRP 2,4 -10.0 0.0 0.0 69 20.0 0.0 -1.0 73 11.0 0.0 0.0 IMPE 0.01 X COS 4.0 COS 0.0 FIN **** A CYLINDRICAL SYSTEM, NAMED BWL2, 20 NODES DEFINED CYLI BWL2 DEG DCOS 1.0 0.0 0.0 0.0 1.0 0.0 ORIG 0.0 0.0 0.0 / 1 5.0 0.0 0.0 9 5.0 22.5 0.0 7 6.0 0.0 0.0 12 6.0 22.5 0.0 11 6.0 22.5 8.0 RP 4,12 0.0 45.0 0.0 IMPE 0.01 COS 4 COS 4.0 FIN **** 2ND CYLINDRICAL SYSTEM, NAMED HNDL, 7 NODES DEFINED CYLI HNDL DEG DCOS 1.0 0.0 0.0 0.0 -1.0 0.0 ORIG 26.0 0.0 0.0 / 85 10.0 0.0 -1.0 RP 3,1 0.0 30.0 0.0 / 92 10.0 0.0 -5.0 RP 2,-4 0.0 60.0 0.0 / 93 9.5 0.0 -0.5 RP 2,1 0.0 60.0 0.0 IMPE 0.01 COS 6 COS 0.0 END

5.2.3 Element Topology Data

To define each element which makes up the structure.



Parameters

ELEM : compulsory header keyword to denote the start of the element data.

MATP : keyword to define the material to be assigned to all following elements until another MATP line is used.

material : material property integer. The material properties are defined in Section 5.2.4. (Integer,1-9999)

eltype : element type. (Alphanumeric, 4 characters.) See Appendix -A for a full list of elements available.

mtype : type of mass matrix for this element (natural frequency analysis). For defaults, see Appendix -A. Permitted Values: C - consistent mass L - lumped mass N - no mass

nodes : list of node numbers to define the element. (Integer, 1-99999)

geom : geometric property integer. (Integer, 1-9999.) Not required for certain element types, see Appendix -A.

elno : user number for the element. Every user element number, whether user defined or program generated, must be unique. Generated elements are numbered successively in increments of 1. If omitted the element numbers are assigned by the program, numbered according to the input order of the elements, see Section 4.3.2. (Integer, 1-99999)

RP : keyword to indicate the generation of data from the previous / symbol.


inode : node number increment. (Integer)

RRP : keyword to indicate the generation of data from the previous // symbol.

eltype (mtype) //nodes// geom (elno)

ELEM

MATP material

RP nrep inode

RRP nrrep iinode

END




iinode : node number increment. (Integer)

END : compulsory key word to denote the end of the element topology data.

Notes

1. Continuation lines may be used if needed to define nodes, geom and elno.

2. Where mid-side nodes are at the midpoint and their coordinates have not been defined in the COOR data, the node number must be included in the nodes list.

Examples

An example of a simple element topology data block.

ELEM

MATP 1

FLA2 8 9 1

FLA2 9 10 2

FLA2 8 10 1

FLA2 10 11 1

END

An example of element topology data using data generation.

ELEM

MATP 1

/

FLA2 1 21 3

FLA2 1 41 2

FLA2 41 21 2

RP 10,1

END

An example of the use of element numbers and continuation lines.

BR15 1 2 3 4 5 6

: 21 23 25

: 41 42 43 44 45 46 130

5.2.4 Material Property Data

This data block defines the material models which will be used in the analysis. For each material required the user should associate an integer number (the ‘material property integer’) which applies to all the properties of a material and is used to cross-reference the material from other data blocks such as element topology. The types of behaviour which may be associated with each material are:



• Elastic, either isotropic, orthotropic, woven, anisotropic, hyperelastic or laminated (for shells) (see Section 5.2.4.1).

• Plastic, or more generally, time independent irreversible behaviour according to various theories (see Section 5.2.4.2).

• Creep or time dependent material behaviour (see Section 5.2.4.3).

• Failure properties associated with limiting values for stresses and/or strains for laminated composites (seeSection 5.2.4.4).

• User defined material (see Section 5.2.4.1).

• Material properties for general field analysis problems, eg electric conduction. (see Section 5.2.4.1)

• Piezo-resistive material properties (see Section 5.2.4.1)

• Convection and radiation models for heat analysis. (see Section 5.2.4.1)

A material may be defined by a combination of the above properties with the same integer identifier.

In general, all properties may be a function of temperature. This is specified by repeating material data at a number of temperatures. The program interpolates linearly between these temperatures. The same temperatures should be used for all material data types.

The material integer is unique to the problem and the same number cannot be used to reference different materials in different groups.

Elasticity data must precede any plasticity data, which in turn must precede any creep data.



Parameters

MATE : compulsory header keyword to denote the start of the material properties data

mat : material property integer used to label different materials. (Integer, 1-9999)

ISO : keyword to define an isotropic material

ORTH : keyword to define an orthotropic material

WOVE : keyword to define a woven material

AISO : keyword to define an anisotropic material

AISI : keyword to define an anisotropic material by specifying the inverse of the stress-strain relations i.e. strain-stress relations

HYPE : keyword to define a hyperelastic material. (Continuum elements only)

LAMI : keyword to define a laminated material. (Shell and laminated brick elements only)

UMAT : keyword to define a user supplied material



FIEL : keyword to define general field properties

PIER : keyword to define piezo-resistive material properties

CVEC : keyword to define heat convection properties

RADI : keyword to define heat radiation properties

PLAS : keyword to define plastic material properties

CREP : keyword to define creep material properties

FAIL : keyword to define failure data for orthotropic and laminated materials only

END : compulsory keyword to denote the end of the material properties data block

Notes

1. For full details for each type of material see Sections 5.2.4.1, 5.2.4.2, 5.2.4.3, 5.2.4.4 and Appendix -B.

2. Every material referenced in the element topology data must be fully defined in this data block.

3. PLAS not available with AISO, AISI, ORTH, WOVE or HYPE materials.

4. FAIL only available with ISO, AISO, ORTH, WOVE and LAMI materials.

5.2.4.1 Elastic Material Properties

To define the properties for isotropic and anisotropic elastic material.

5.2.4.1.1 Isotropic material properties

Parameters

mat : material property integer. (Integer, 1-9999)

ISO : keyword to define the material as isotropic

elas : modulus of elasticity. (Real)

poisson : Poisson’s ratio. (Real, 0.0 <poisson< 0.5)

mat ISO elas pois (expan) (dens) (dampm) (dampk) (temp)

: (ISO) elas pois expan dens dampm dampk temp

kn



expan : linear coefficient of thermal expansion. (Real)

dens : density, mass per unit volume. (Real)

dampm : damping factor for mass. (Real)

dampk : damping factor for elastic stiffness. (Real)

temp : temperature at which these properties apply. (Real)

kn : effective contact stiffness for gap elements and normal contact stiffness parameter for rigid surface elements. (Real)

Notes

1. The expansion coefficient is optional and is only required if temperatures are to be included in any of the loading applied to the structure.

2. The density is optional and is only required if acceleration or centrifugal loads are to be included in any loading applied to the structure, or if a natural frequency or transient dynamics analysis is to be performed.

3. The damping factors, dampm and dampk, are optional and are only required for a transient dynamics analysis.

4. The temperature is optional and is only required if the material properties vary with temperature and temperature loading is applied to the structure.

5. If an optional value is specified, all preceding optional values must also be specified.



Examples

A simple example with one material and no temperature or inertia type loading.

MATE

1 ISO 21.0E4 0.3

END

An example with several materials including the expansion coefficient and the density.

MATE

10 ISO 0.298E8 0.3 0.1182E-4 0.283

20 ISO 0.312E8 0.31 0.1212E-4 0.298

30 ISO 0.151E8 0.3 0.1566E-4 0.206

END

An example with one material which is temperature dependent but with no inertia type loading

MATE

1 ISO 7.200E10 0.3 16.32E-6 0.0 0.0 0.0 0.0

: 7.200E10 0.3 16.32E-6 0.0 0.0 0.0 70.0

: 7.098E10 0.3 18.26E-6 0.0 0.0 0.0 100.0

: 7.047E10 0.3 18.16E-6 0.0 0.0 0.0 200.0

: 6.895E10 0.3 18.92E-6 0.0 0.0 0.0 300.0

: 6.767E10 0.3 19.60E-6 0.0 0.0 0.0 400.0

: 6.640E10 0.3 20.20E-6 0.0 0.0 0.0 500.0

: 6.462E10 0.3 20.76E-6 0.0 0.0 0.0 600.0

END

5.2.4.1.2 Orthotropic material properties

Parameters


skew : optional skew system identifier, see Section 5.2.7. (Integer)

ORTH : keyword to define the material as orthotropic

density : density, mass per unit volume. (Real)






E11-E33 : Young’s moduli in local 1, 2 and 3 directions respectively. (Real) (The program will set E33=E22 if E33 is specified as zero.)

G12-G31 : shear moduli in local 12, 23 and 31 planes respectively. (Real)

ν12-ν13 : Poisson’s ratios in local 12, 23 and 13 planes respectively. (Real)

(The program will set ν23= ν12 and/or ν13= ν12 if any of these is specified as zero.)

α11-α33 : coefficients of thermal expansion in the local 1, 2 and 3 directions respectively. (Real)

fl : loss factor, i.e. volume fraction of material with no stiffness. If not specified, fl = 0.0. (Real)

Notes

1. The density is optional and is only required if acceleration or centrifugal loads are to be included in any loading applied to the structure, or if a natural frequency or transient dynamics analysis is being performed.


3. The orthotropic properties must start on the first continuation line and may then spread onto further continuation lines as required.



6. Up to 13 properties are expected but if less than 13 are specified, then the remaining properties default to zero.

7. The Poisson’s ratios ν21, ν32 and ν31 are determined inside the program from

Examples

An example of an orthotropic material for a QUM8 element.

MATE

1 ORTH

: 7.8E6 2.6E6 0.0

11E22E12=21 νν

22E33E23=32 νν

11E33E13=31 νν



: 1.3E6 0.0 0.0

: 0.25 0.0 0.0

END

An example of an orthotropic material with temperature dependency for a QUX8 element.

MATE

1 ORTH 0.0 0.0 0.0 20.0

: 4.3E6 2.1E6 3.4E5 8.8E5 0.0 0.0 0.25 0.13 0.0

: 0.13E-5 0.23E-5 -0.12E-6

1 ORTH 0.0 0.0 0.0 80.0

: 4.3E6 1.8E6 3.2E5 4.4E5 0.0 0.0 0.21 0.17 0.0

: 0.17E-5 0.25E-5 -0.12E-6

END

5.2.4.1.3 Woven material properties

Parameters



WOVE : keyword to define the material as woven





E11-E33 : Young’s moduli in local 1, 2 and 3 directions respectively of the orthotropic sub-lamina. (Real) (The program will set E33=E22 if E33 is specified as zero.)

G12-G31 : shear moduli in local 12, 23 and 31 planes respectively of the orthotropic sub-lamina. (Real)

ν12-ν13 : Poisson’s ratios in local 12, 23 and 13 planes respectively of the orthotropic sub-lamina. (Real)

(The program will set ν23= ν12 and/or ν13= ν12 if any of these is specified as zero.)



α11-α33 : coefficients of thermal expansion in the local 1, 2 and 3 directions respectively. (Real)

fl : loss factor, i.e. volume fraction of material with no stiffness. If not specified, fl = 0.0. (Real)

Notes



3. The woven properties must start on the first continuation line and may then spread onto further continuation lines as required.



6. Up to 13 properties are expected but if less than 13 are specified, then the remaining properties default to zero.

7. The Poisson’s ratios ν21, ν32 and ν31 are determined inside the program from

Examples

An example of an orthotropic material for a TCS8 element with loss factor 0.2.

MATE

1 WOVE

: 150E9 10E9 0.0

: 5.7E9 3.4E9 5.7E9

: 0.25 0.0 0.0

: 0.17E-5 0.25E-5 0.0 0.2

END

5.2.4.1.4 Anisotropic material properties

There are two options available to anisotropic behaviour. The first specifies the matrix C in relation σ=Cε (in which σ is stress and ε strain). The second specifies the inverse of C to give strains as a function of stress.

11E22E12=21 νν

22E33E23=32 νν

11E33E13=31 νν



Parameters



AISO : keyword to define the material as anisotropic with properties defining the stress-strain relations

AISI : keyword to define the material as anisotropic with properties defining the strain-stress relations



dampk : damping factor for mass. (Real)

temp : temperature at which these properties apply

properties : coefficients of the anisotropic stress-strain matrix (AISO) or the strain-stress matrix (AISI) and linear coefficients of expansion. See Appendix -A for a full definition of which terms are required for each type of element. (Real)

Notes



3. The anisotropic properties must start on the first continuation line and may then spread onto further continuation lines as required.

4. A total of 30 properties is always needed, composed of up to 24 material constants and 6 coefficients of thermal expansion. The coefficients of thermal expansion must start at position 25.


matAISO

AISI

: properties

(density) (dampm) (dampk) (temp)(skew)



Examples

An example of an anisotropic material for a BR20 element.

MATE 1 AISI : 0.536044 -0.16081 0.536044 -0.16081 -016081 0.536044 : 0.0 0.0 0.0 0.139372 0.0 0.0 : 0.0 0.0 0.139372 0.0 0.0 0.0 : 0.0 0.0 0.139372 0.00172 0.00172 0.00172 : 0.0 0.0 0.0 0.0 0.0 0.0 END

An example of an anisotropic material for a QUM8 element

MATE 1 AISO : 23600.0 5720.0 20575.0 0.0 0.0 16750.0 : 0.0 0.0 0.0 12650.0 0.0 0.0 : 0.0 0.0 0.0 0.0 0.0 0.0 : 0.0 0.0 0.0 0.16E-4 0.14E-4 0.01E-4 : 0.0 0.0 0.0 0.0 0.0 0.0 END

5.2.4.1.5 Hyper-elastic material properties

Parameters


HYPE : keyword to define the material as hyper-elastic

bulk : bulk modulus. (Real)

con1 : Mooney-Rivlin constant, C10. (Real)

con2 : Mooney-Rivlin constant, C01. (Real)

expan : linear coefficient of thermal expansion. (Real)

dens : density, mass per unit volume. (Real)


mat HYPE

: (HYPE)

bulk con1 con2 (expan) (dens) (dampm) (dampk) (temp)

bulk con1 con2 expan dens dampm dampk temp



dampk : damping factor for stiffness. (Real)


Notes

1. The damping factor for stiffness is currently restricted to be zero.

2. The expansion coefficient is optional and is only required if temperatures are to be included in any of the loading applied to the structure.

3. The density is optional and is only required if acceleration or centrifugal loads are to be included in any loading applied to the structure, or if a natural frequency analysis is to be performed.




Example

A simple example with one material and no temperature or inertia type loading.

MATE

1 HYPE 1.0E4 80.0 20.0

END

5.2.4.1.6 Laminated Material Properties

Parameters



LAMI : keyword to define the material as a laminated shell




mat (skew) LAMI (density) (dampm) (dampk) (temp)




Notes

1. The skew system identifier is optional and is only required if the laminate material reference axis system does not coincide with the global axis system.

2. The density is optional and is only required if acceleration or centrifugal loads are to be included in any loading applied to the structure, or if a natural frequency or transient dynamics analysis is being performed. If the density is specified both here and with the materials forming the laminate, the density specified here will be used. If the density is omitted (or given a value of 0.0) the density for the laminate will be calculated from the laminae densities in the manner described in Appendix -B.

3. The damping factors, dampm and dampk, are optional and are only required for a transient dynamics analysis. If damping factors are specified both here and with the materials forming the laminate, the factors specified here will be used. If the damping factors are omitted (or given a value of 0.0) the damping factors for the laminate will be calculated from the laminae damping factors in the manner described in Appendix -B.

4. The temperature is optional and is only required if the material properties vary with temperature and temperature loading is applied to the structure. If the properties specified here are temperature dependent then the materials forming the laminate must be specified with the same range of temperatures.

5. If an optional value is specified, all preceding optional values must be specified.



Example

A simple example of a laminated material where the material axes coincide with the global axis system (no skew required), where the density is to be calculated from the laminae densities but where the damping factors for the laminate are specified.

MATE

1 LAMI 0.0 0.039 0.0102

END

5.2.4.1.7 User Material Properties

Parameters


UMAT : keyword





Notes

1. If thermal coefficients are supplied they must start at the 25th position as for AISO material properties.

2. See Appendix B.6 for details concerning the user material interface.

3. The density is optional and is only required if acceleration or centrifugal loads are to be included in any loading applied to the structure, or if a natural frequency analysis is to be performed.




mat UMAT

: up to 24 user material properties

(density) (dampm) (dampk) (temp)

up to 6 thermal coefficients



5.2.4.1.8 Field Material Properties

Parameters


skew : skew system integer

FIEL : keyword to define the material as field

kxx,kyy,kyy : conductivities in xx direction, yy direction, etc. (Real)

kxy,kyz,kzx

dens : generalised density. (Real)


Notes

1. If only kxx is specified, it is assumed that the material is isotropic (ie kxx = kyy = kzz and kxy = kyz = kzx = 0)


3. For heat analysis, the generalised density is defined as the product of the specific heat capacity and the density.

5.2.4.1.9 Piezo-resistivity Material Properties

Parameters


mat (skew) FIEL kxx (dens) (temp)

:

(kyy) (kzz) (kxy) (kyz) (kzx)

(FIEL) kxx dens tempkyy kzz kxy kyz kzx

mat (skew) PIER (dum) (temp)

: q n µn p π11

(dum) (dum)

µp π12 π44



skew : skew system integer. (Integer, 1-9999)

PIER : keyword to define material as piezo-resistivity

dum : dummy


q : unit charge

n : carrier concentration (n)

µn : carrier mobility (n)

p : carrier concentration (p)

µp : carrier mobility (p)

π11 : Piezo-resistance coefficient, 11



Notes

1. A total of 8 properties are always needed.


3. The piezo-resistivity properties must start on the first continuation line and may then spread onto further continuation lines as required.

5.2.4.1.10 Convective Heat Material Properties

Parameters

mat : material property integer. (integer, 1 - 9999)

CVEC : keyword to define the material as convective heat

h : film coefficient in the heat transfer equation. (Real)

mat CVEC h r

:

(temp)

(CVEC) h r temp



r : power index in the heat transfer equation. (Real)

temp : temperature at which the properties apply. (Real)

Notes

1. This material type is used to model convective heat transfer of the form: q=h.(T1-T2)r

2. CVEC material can only be used with FAT2 element in a heat analysis

5.2.4.1.11 Radiant Heat Material Properties

Parameters

mat : material property integer. (integer, 1 - 9999)

RADI : keyword to define the material as radiant heat

σ : Stefan-Boltzmann constant (Real)

ε : effective surface emissivity. (Real)

temp : temperature at which the properties apply. (Real)

Notes

1. This material type is used to model radiant heat transfer of the form: q=σ.ε.(Τ1

4-Τ24)

2. The temperatures required in the radiation equation are relative to absolute zero temperature. The default temperature units assumed by ASAS(NL) are degrees Centigrade. If other temperature units are used for an analysis, the correct absolute zero temperature in the appropriate units must be specified using the PARA TAZERO command.

3. RADI material can only be used with FAT2 element in a heat analysis.



5.2.4.2 Plastic Material Properties

To define the properties for a plastic material. Plastic material properties must be preceded by the elastic isotropic material properties for any individual material integer.

A number of different plasticity models are available which are activated by 4-character directives defined on the first line together with other basic data. Depending on the directives, so additional types of commands may also be necessary. The directives fall into three categories:

(1) Yield Criteria

MISE - Mises yield criterion to be used

TRES - Tresca yield criterion to be used

MOHR - Mohr-Coulomb yield criterion to be used

DRUC - Drucker-Prager yield criterion to be used

TCUT - Tension cutcriterion to be used

COUL - Coulomb friction yield criterion to be used (rigid surface elements only)

IVAN - Ivanov (gross section) yield criterion to be used (shell elements only)

BEM2 - Beam stress resultant (gross section) yield criterion to be used (BM2D element only)

BEM3 - Beam stress resultant (gross section) yield criterion to be used

(BEAM/BM3D/TUBE elements only)

BEAM - Generalised beam stress resultant (gross section) yield criterion to be used

(BEAM/BM3D/TUBE elements only)

SPRG - Inelastic model for spring elements

If no directive is given, then MISE’s criterion is assumed.

(2) Post-Yield Behaviour

TABL - Tabular definition of uniaxial post-yield behaviour to be used.

If this directive is not given bi-linear behaviour is assumed.

(3) Hardening Rule

PPRA - Prager type of kinematic hardening (see Note 2)

PZIG - Ziegler type of kinematic hardening

If no directive is given isotropic hardening is assumed.

Notes

1. Associative flow rules are used in all cases.

2. Prager type kinematic hardening is inapplicable to elements using a reduced stress space - i.e. plane stress membranes, beams and shells.

3. Temperature loads cannot be used in conjunction with IVANOV yield criterion.



4. Kinematic hardening is only available for MISE and TRES criteria

(mat) PLAS

(MISE)

TRES

sigy ep hard (temp)

(mat) PLAS BEAM Po Mpz Mpy (temp)

(MISE)

TRES

: properties

sigy (ep) (temp)

PPRA

PZIG

: sigy ep (hard) temp

(mat) PLAS IVAN sigy

(mat) PLAS BEM2 Po Mpz (temp)

BEM3 Po Mpz (temp)Mpy

: C1 (C2) (C3) (C4) (C5) (C6)

(mat) PLAS TABL sigy (temp)

PPRA

PZIGsigy hard (temp)

(mat) PLAS COUL kt mu shrlmt

(mat) PLAS c phi (temp)MOHR

DRUC

TCUT

TCUT

(mat) PLAS SPRG K1 K2



Parameters

mat : property integer. (Integer, 1-9999)

PLAS : keyword to define the material as plastic

MISE : yield criterion keyword

TRES : yield criterion keyword

TCUT : yield criterion keyword

sigy : uni-axial yield stress. (Real)

ep : slope of post yield stress/strain relation. (Real)


PPRA : kinematic hardening keyword

PZIG : kinematic hardening keyword

hard : for keywords PPRA and PZIG, the ratio of isotropic to kinematic hardening. 1.0 for isotropic hardening, 0.0 for pure kinematic hardening. (Real)

MOHR : yield criterion keyword

DRUC : yield criterion keyword

c : cohesion

phi : angle of friction

COUL : yield criterion keyword

kt : tangential contact stiffness parameter (unit: stress per unit length). (Real)

mu : coefficient of friction. (Real)

shrlmt : limiting shear stress. (Real)

IVAN : yield criterion keyword

BEM2 : yield criterion keyword

Po : yield force. (Real)

Mpz : yield moment about beam local z axis. (Real)

BEM3 : yield criterion keyword

Mpy : yield moment about beam local y axis. (Real)

BEAM : yield criterion keyword



C1 - C6 : yield function constants in the equation: C1(P/Po)C2 + C3(Mz/Mpz)C4 + C5(My/Mpy)C6 = 1 (Real)

SPRG : inelastic spring model keyword

K1 : unloading stiffness factor (Real) (set to 1.0 if zero specified)

K2 : kinematic hardening factor (Real)

TABL : keyword required if a tabular definition of the uni-axial post yield behaviour is to be specified

properties : if TABL is specified, properties will consist of pairs of stress/strain values defining the uniaxial post yield behaviour. The strains required are total strains. (Real)

Notes

1. All elastic material property data must appear before the plastic material property data for any individual material integer.

2. For details of the various models, see Appendix B.3.

3. The slope of the post yield stress/strain curve must be less than the elastic modulus. Apart from tension cutmaterial, the slope must be non negative (i.e. ≥0.0). For tension cutmaterial, the slope must not be less than -E/ν

4. If the material properties vary with temperature, each set of data should be repeated for a different temperature.

5. The following notes apply to tabulated definition only:

(a) The stress-strain table may be continued on as many lines as necessary.

(b) For linear elastic/plastic material the first point in the table (σ,ε) will correspond to a point after yield.

The coordinates of the yield point are computed from the elastic modulus and yield stress.

(c) The program interpolates linearly for intermediate points.

(d) There are a maximum of 40 different strain values allowed.

(e) A slope defined in the table should not be equal to the elastic modulus. Apart from tension cutmaterial

the slope must be non negative (i.e. ≥ 0.0) For tension cutmaterial, the slope must not be less than -E/ν.

(f) If curves are specified for different temperatures (see third example) then the order the plasticity data is

presented should correspond to the order in which the elastic data is presented.



Examples

Simple elastic-perfectly plastic model with isotropic hardening.

MATE

1 ISO 21000.0 0.3

PLAS MISE 250.0

END

Simple elastic-plastic model with isotropic hardening.

MATE

1 ISO 21000.0 0.3

PLAS MISE 250.0 30.0

END

Metal satisfying MISE’s yield criterion and associated flow rule with isotropic hardening. Uniaxial behaviour is as in figure below.

MATE

10 ISO 21900.0 0.3 0.276E-6 0.0 T1 20900.0 0.3 0.276E-6 0.0 T2 20500.0 0.3 0.276E-6 0.0 T3 PLAS MISE TABL σy1 T1 : σ11 ε11 σ12 ε12 σ13 ε13 : σ14 ε14 σ15 ε15 PLAS MISE TABL σy2 T2 : σ21 ε21 σ22 22 σ23 ε23 PLAS MISE TABL σy3 T3 : σ31 ε31 σ32 ε32 σ33 ε33 END



5.2.4.3 Creep Material Properties

To define the properties for a material with creep. Creep material properties must be preceded by elastic isotropic material properties and plastic material properties if present.

This data defines the creep law to be used for each material type. The user may choose from 4 in-built laws. Alternatively up to 5 user supplied laws (in subroutine form) can be used. Appendix B.4 gives full details. In-built laws require creep constants which are given in the data. Creep constants for use with the user supplied laws may be defined if required.

Parameters


CREP : keyword to define the material properties for creep

NORT LAW2 : keyword to define ASAS-NL creep law LAW3 LAW4 USE1 USE2 : keyword to define user supplied creep law USE3 USE4


constants : creep law constants. (Real)

Note

Refer to creep law expressions in Appendix B.4 for definition of creep constants.

CREP (temp)(mat)

: constants

NORT LAW2 LAW3 LAW4 USE1 USE2 USE3 USE4 USE5



Examples

Norton (power) law for a Cr-Mo-V ferritic stainless steel. No temperature or time dependence. Units: N, mm.

σε 10.42-28c 10x2.05=

MATE

1 ISO 1.41E5 0.3

CREP NORT

: 2.05E-28 10.42 0.0

END

Norton (power) law with temperature dependence but no time dependence. Units: N, mm, °C.

σε 10.42-28c 10x2.05= T=525°C

σε 10.42-28c 10x6.72= T=550°C

σε 10.42-27c 10x2.05= T=575°C

MATE

1 ISO 1.41E5 0.3 16.0E-6 7.93E-9 0.0 0.0 525.0

: 1.36E5 0.3 16.0E-6 7.93E-9 0.0 0.0 550.0

: 1.31E5 0.3 16.0E-6 7.93E-9 0.0 0.0 575.0

CREP NORT 525.0

: 2.05E-28 10.42 0.0

CREP NORT 550.0

: 6.72E-28 10.42 0.0

CREP NORT 575.0

: 2.05E-27 10.42 0.0

END

Creep law 2 which represents primary/secondary creep or secondary/tertiary creep. Note that the creep law is implicitly temperature dependent. Further versatility is available by allowing the coefficients to vary with temperature as illustrated in the example above. This example is for a Cr-Mo-V ferritic stainless steel for a temperature range of approximately 565° ± 50°, Units: N, mm, seconds and °C.

et10x9.69+e10x7.46= /T10x-3.1161.3645.4-16/T10x-3.1165.4-5c

44

σσε

MATE

1 ISO 1.31E5 0.3 16.0E-6 7.9E-9

CREP LAW2

: 7.46E-5 5.4 0.0 3.11E4

: 9.69E-16 5.4 1.364 3.116E4

END



Blackburn law for 316 stainless steel. Note that no numerical creep data is required and that the units assumed by ASAS-NL are N, mm, seconds and °C.

MATE

1 ISO 1.53E5 0.3 14.0E-6 7.93E-9 0.0 0.0 450.0

: 1.48E5 0.3 14.0E-6 7.93E-9 0.0 0.0 537.0

: 1.43E5 0.3 14.0E-6 7.93E-9 0.0 0.0 580.0

: 1.38E5 0.3 14.0E-6 7.93E-9 0.0 0.0 593.0

: 1.33E5 0.3 14.0E-6 7.93E-9 0.0 0.0 648.0

: 1.28E5 0.3 14.0E-6 7.93E-9 0.0 0.0 700.0

CREP LAW4

END

5.2.4.4 Failure Material Properties

To define the failure (limiting) values for lamina stresses and strains and laminate stress/strain resultants.

Parameters


FAIL : keyword to define the properties as failure values FLW1 FLW2 FLW3 : keyword to define failure law type FLW4 FLW5 temp : temperature at which these properties apply. (Real)

Notes

1. FLW1 and FLW2 are in-built lamina failure laws. FLW3 to FLW5 are user-defined laws. See Appendix B.5.3 for further details.

2. The actual failure values required depend upon whether lamina or laminate values are being defined (see following sections).

FAIL (temp)(mat)

: up to 14 failure v alues

FLW1 FLW2 FLW3 FLW4 FLW5



5.2.4.4.1 Lamina Failure Values

The following data input is required for an elastic laminated composite.

Parameters


FAIL : keyword to define the properties as failure values


xt, xc : limiting direct tensile and compressive stresses respectively in fibre direction. (Real)

yt, yc : limiting direct tensile and compressive stresses respectively normal to fibre in direction 2. (Real)

zt, zc : limiting direct tensile and compressive stresses respectively normal to fibre in direction 3. (Real)

s12 : limiting shear stress of lamina in 1-2 plane. (Real)



zl : limiting interlaminar tensile stress. (Real)

sl : limiting interlaminar shear stress. (Real)

ε1t, ε1c : limiting direct tensile and compressive strains respectively in fibre direction. (Real)

ε2t, ε2c : limiting direct tensile and compressive strains respectively normal to fibre in direction 2. (Real)

ε3t, ε3c : limiting direct tensile and compressive strains respectively normal to fibre in direction 3. (Real)

γ12 : limiting shear strain of lamina in 1-2 plane. (Real)





Notes

1. Up to 20 failure values are expected but if less are specified then the remaining values default to zero.

2. If a failure value is set (or defaults) to zero, the relevant term in the failure criterion is ignored.

3. Isotropic, orthotropic or anisotropic failure material properties must be preceded by material properties.

4. Using the above data, a number of lamina failure criteria are evaluated in POSTNL when options FEMV-LAMI are selected. See Appendix B.5.1 for further details.

5.2.4.4.2 Plastic Lamina Failure FLW1 Values

The following data input is required for a ‘plastic’ laminated composite i.e. when an element referencing this material belongs to a group of elements with directive PLAS.

Parameters



FLW1 : keyword to denote that the in-built failure law type 1 is to be used. See Appendix B.5.3.1 for

details

ftype : failure criterion for matrix failure. Valid keywords are:

TSWU - Tsai-Wu (default)

TSAI - Azzi-Tsai

HOFF - Hoffman

NORR - Norris

MISE - von Mises

MXCS - maximum stress












β E : dimensionless material parameter β E defining the reduction in fibre stiffness after matrix failure.

0 ≤ β E ≤ 1.0. A value of β E=0.0 means no reduction in fibre stiffness, a value of 1.0 means a

complete loss of fibre stiffness. (Real)

β 2 : dimensionless material parameter β2 defining the reduction in fibre stiffness after fibre failure. (0

≤ β 2 ≤ 1.0). By default, β 2=0.0 and this means that the matrix stiffness is assumed after fibre

failure. For β 2 •0.0, the fibre stiffness after failure is (1- β 2) times its value before failure.

Notes


2. If the failure law type is left blank, the failure data will have the same meaning as for an elastic laminated composite. When analysis beyond first ply failure is required, FLW1 will be assumed with β E= β 2=0.0.


5.2.4.4.3 Plastic Lamina Failure FLW2 Values

The following data input is required for a ‘plastic’ laminated composite, i.e. when an element referencing this material belongs to a group of elements with directive PLAS.

Parameters



FLW2 : keyword to denote that the in-built failure law type 2 is to be used. See Appendix B.5.3.1 for details



ftype : failure criterion for matrix failure. Valid keywords are:

TSWU - Tsai-Wu (default)

TSAI - Azzi-Tsai

HOFF - Hoffman

NORR - Norris

MISE - von Mises

MXCS - maximum stress










β 1- β 8 : dimensionless material parameters defining the reduction in lamina stiffness after different modes of

failure. (0 ≤ β i ≤ 1.0). The default of all the β s are β =0.0. See Appendix B.5.3.1 for details

Notes


2. If a failure strength is set (or defaults) to zero, the relevant term in the failure criterion is ignored.

5.2.4.4.4 Laminate Failure Values

The following data input is required for an elastic laminated composite when it is required that failure criteria in terms of the shell stress/strain resultants are to be calculated.

(mat) FAIL

:

(temp)

xyψ xψ yψ xε yε xyε xzε yzε



Parameters




xε : allowable direct strain in element local x direction. (Real)

yε : allowable direct strain in element local y direction. (Real)

xyε : allowable shear strain in element local xy plane. (Real)

xψ : allowable bending curvature in element local x direction. (Real)

yψ : allowable bending curvature in element local y direction. (Real)

xyψ : allowable torsional curvature in element local xy plane. (Real)

xzε : allowable shear strain in element local xz plane. (Real)

yzε : allowable shear strain in element local yz plane. (Real)

Notes

1. Using the above data, the laminate failure criterion as described in Appendix B.5.2 is evaluated in POSTNL when options FEMV-GFAI are selected. Note that up to four further user defined criteria may be evaluated and that up to 14 failure values may be specified. To be consistent with the calculation of the first failure criterion, the first 8 failure values should be those defined above.

2. The laminate failure data must be specified immediately after the LAMI material property data.




Examples

A simple example of an orthotropic lamina for a laminated shell with failure values specified for the direct stresses in the fibre directions only.

MATE

1 LAMI

10 ORTH 1350.0

: 84.0E6 6.0E6 0.0 2.1E6 2.1E6 2.1E6 0.34 0.0 0.0

: -3.0E-6 35.OE-6 0.0

10 FAIL

: 1280.0E3 290.0E3

END

An example showing the data for 3 different orthotropic laminae for a laminated shell with failure values for all stress components.

MATE

1 LAMI

10 ORTH 1350.0

: 84.0E6 6.0E6 0.0 2.1E6 2.1E6 2.1E6 0.34 0.0 0.0

: -3.0E-6 35.OE-6 0.0

10 FAIL

: 1280.0E3 290.0E3 39.0E3 150.0E3 52.0E3

20 ORTH 1610.0

: 130.0E6 9.0E6 0.0 4.8E6 4.8E6 4.8E6 0.28 0.0 0.0

: -0.1E-6 28.0E-6 0.0

20 FAIL

: 1370.0E3 1000.0E3 42.0E3 200.0E3 60.OE3

30 ORTH 1800.0

: 40.0E6 8.0E6 0.0 4.0E6 4.0E6 4.0E6 0.25 0.0 0.0

: 6.3E-6 36.0E-6 0.0

30 FAIL

: 800.0E3 600.0E3 36.0E3 150.0E3 60.0E3

END

An example showing the data for a non-linear composite material composed of layers of orthotropic material obeying failure law 1 (FLW1)

MATE

11 ORTH

: 5.72E4 3.9E3 3.9E3 2.3E3 2.3E3 2.3E3 0.35 0.35 0.35

11 FAIL FLW1

: 1.3E3 1.3E3 12.0 53.0 34.0 0.8

1 LAMI

END



An example showing the data for a linear elastic composite material composed of two different orthotropic materials with a laminate failure criterion based on limiting curvatures only.

MATE

1 LAMI

1 FAIL

: 0.0 0.0 0.0 0.015 0.015 0.015

2 ORTH

: 5.72E4 3.9E3 3.9E3 2.3E3 2.3E3 2.3E3 0.35 0.35 0.35

3 ORTH

: 3.81E4 4.75E3 4.7E3 2.3E3 2.3E3 2.3E3 0.32 0.32 0.32

END

5.2.5 Geometric Properties Data

To define the geometric properties, such as thickness, area, or bending inertia, for every element used in the structure.

Parameters

GEOM : compulsory header keyword to denote the start of the geometric property data

geom : identifying number of the geometric properties integer. This number must be unique, and independent of the type of element. (Integer, 1-999999)

eltype : element type. This must correspond with the element type defined in the element topology data for this geometric property integer

sect : keyword to denote cross-section type for element STF4

properties : list of geometric properties. See Appendix -A for the details of which properties are required for each element type. Continuation lines may be used if necessary. (Real)

CABL : keyword to denote the cable option for element FLA2. See Appendix -A for further details

END : keyword to denote the end of the geometric properties data block

GEOM

geom eltype (sect) properties

END

CABL properties:



Notes

1. Geometric property data for elements SST4 and WST4 must be input in a different format. Details are given in Section 5.2.5.1.

2. Geometric property data for elements SPR1 and SPR2 must have stiffness and/or damping properties. Details are given in Section 5.2.5.2.

3. Geometric property data for laminated shells requires additional information concerning the layup sequence. Details are given in Section 5.2.5.3.

4. Geometric property data for rigid surface elements requires additional information concerning the definition of rigid surface geometry. Details are given in Section 5.2.5.4.

5. Geometric property data for beam elements where local axes orientation and/or offsets may be defined is given in section 5.2.5.5

Example

A simple example of geometric property data for a model composed of beams and shells.

GEOM 1 STF4 RECT 0.05 0.05 0.0 0.0 0.0 : 0.05 0.05 0.0 0.0 0.0 : 0.05 0.05 0.0 0.0 0.0 2 TCS8 0.010 3 TCS8 0.008 END

5.2.5.1 Geometric Properties - (WST4 and SST4)

To define geometric properties for stiffeners (WST4 and SST4) the following format is used in the geometric properties data.

Parameters

geom eltype (isec) rmul

MCOR

SCON

FIN

segno nstart nfinish nstat nlay thick

mn scoor tcoor




eltype : element type. This must correspond with the element type defined in the element topology data for this geometric property integer. (One of WST4 or SST4)

isec : median point corresponding to warping origin (WST4 only). (Integer)

rmul : rigidity multiplier (1.0 for full cross-section, 0.5 for half symmetric section). (Real)

MCOR : compulsory header keyword to denote start of median point coordinate definition

mn : median point number (consecutive). (Integer)

scoor : s coordinate of median point. (Real)

tcoor : t coordinate of median point. (Real)

SCON : compulsory header keyword to denote start of segment connectivity data

segno : segment number (consecutive)

nstart : start median point of segment. (Integer)

nfinish : finish median point of segment. (Integer)

nstat : number of stations along segment. (Integer)

nlay : number of layers through the thickness of segment. (Integer)

thick : segment thickness. (Real)

FIN : indicates end of the property set

Notes

1. See element description sheet (Appendix -A) for details of stiffener elements.

2. Median point numbers can be assigned in any convenient manner. Segment numbering however is not arbitrary but must adhere to the following rules:

(a) The first segment starts at a free edge.

(b) Each subsequent segment starts from the end of a previously defined segment.



3. The full cross-section geometry must always be defined irrespective of the value specified for rmul

Example

An example of a tee-section stiffener with the origin at the junction of web and flange

GEOM

1 SST4 1.0

MCOR

1 -0.2 0.0

2 0.0 0.0

3 0.2 0.0

4 0.0 0.256

SCON

1 1 2 3 3 0.012

2 2 3 3 3 0.012

3 2 4 5 3 0.015

FIN

END

5.2.5.2 Geometric Properties - (SPR1 and SPR2)

Stiffness and/or damping characteristics are required for springs SPR1 and SPR2 in the following format.



Parameters

geom : identifying number of the geometric properties. This number must be unique and independent of the element type. (Integer, 1-999999)

eltype : element type (one of SPR1 or SPR2)

Px,Py,Pz : global coordinates of a point which defines the line of action of the spring. (Real)

STIF : keyword to denote that stiffness characteristics are to be defined for springs

stifprops : linear stiffness, K, or tabulated values of displacement (or rotation) and force (or moment) (δ1, F1, δ2, F2....... δn, Fn). (Real)

DAMP : keyword to denote that damping characteristics are to be defined for springs

dampprops : linear damping factor, C, or tabulated values of velocity (or angular velocity ) and force (or moment) (v1, F1, v2, F2....... vn, Fn). (Real)

Notes

1. STIF and DAMP must be the first item on a line after the continuation marker (:).

2. If px, py and pz are zero, the line of action of the spring coincides with the local X axis (see element description in Appendix -A).

3. The stiffness and damping properties are extrapolated beyond the user defined points.

4. A maximum of 20 pairs of (δ,F) and (v,F) are allowed.

5. The angular unit must be radians and this cannot be changed

6. S and V must be specified in ascending order.

7. The spring curve must pass through the origin when applied to an inelastic material model.

geom eltype px py pz

: DAMP dampprops

: STIF stifprops



Examples

An example of a rotational spring with constant stiffness, no damping and aligned with the element local axis system.

GEOM

1 SPR2

: STIF 200.0

END

An example of a translational spring/dashpot with piecewise linear definition of stiffness and damping with a fixed line of action.

GEOM

2 SPR1 1.0 1.0 0.0

: STIF -0.5 -300.0 -0.2 -200.0

: 0.1 400.0 0.4 600.0 0.7 650.0

: DAMP -60.0 -3000.0 -30.0 -2500.0

: 0.0 0.0 20.0 4000.0 50.0 5000.0

END

5.2.5.3 Geometric Properties - (Laminated Construction)

To define the geometric properties and layup data for laminated elements.

δ�

F F

v.

geom eltype

: mat thick

: LAMI nlam

properties

(sym)

theta (layno)

RP nrep



Parameters

geom : identifying number of the geometric properties integer. This number must be unique and independent of the type of element. (Integer, 1-999999)

eltype : element type. This must correspond with the element type defined in the element topology data for this geometric property integer. (One of QUS4, TCS6, TCS8, TCS9, LB15 or LB20)

properties : list of geometric properties. These must be specified for shells and omitted for bricks. See Appendix -A for details of which properties are required for each element type. Continuation lines may be used if necessary. (Real)

LAMI : compulsory keyword to denote that the data for a laminate is to be defined

nlam : number of laminae of which the laminate is composed or half the number of laminae if sym is set to 1. See below. (Integer)

sym : optional flag to be set to 1 if a symmetrical laminate. By default sym will be set to zero which implies that data for all laminae is to be supplied. (Integer)

mat : material property integer defining the material for this lamina. (Integer)

thick : the thickness of this lamina. (Real)

theta : the angle between the principal material axis direction for this lamina and the laminate principal material axis direction. Default unit is degrees. (Real) Note: -90° ≤ theta ≤ + 90°

layno : layer number to be assigned to layer. If omitted, layers are numbered sequentially commencing at one. The layer number is only used for post-processing purposes at present. (Integer)

RP : keyword to indicate the generation of lamina data from the previous / command.

nrep : number of times the data is to be repeated. (Integer)

Notes

1. The shell nodal thicknesses must be specified and be non-zero. The laminae data specified here are used to calculate the equivalent anisotropic material matrix coefficients C1 to C24 in the manner described in Appendix -B. The thickness terms appearing in the C matrix as described in Appendix -A are interpolated from the nodal thicknesses supplied here. For laminated brick elements, the laminated thickness is directly obtained from the element geometry and the nodal thickness data are not required.

2. The properties mat, thick, theta and layno are repeated nlam times. There is no limit to the number of laminae that may be used to define a laminate.

3. The material for a lamina may be defined as isotropic, orthotropic or anisotropic.

4. Layer number 1 lies on the bottom surface of an element as defined by the element local axis system. See Appendix -A.



5. A number of layers, delimited by a / command and an RP command, may be repeated nrep times to create a regular region of the laminate. See example 3.

Examples

A simple example of the geometric property data for a laminated QUS4 shell element of constant thickness equal to the sum of the thicknesses for all laminae. The laminate is composed of 5 laminae using 2 different material types. The layup sequence is [-90/-45/0/45/90].

GEOM 1 QUS4 7.0 : LAMI 5 : 10 1.0 -90.0 : 10 1.0 -45.0 : 20 3.0 0.0 : 10 1.0 45.0 : 10 1.0 90.0 END

An example showing the geometric property data for a laminated and tapered TCS8 shell element where the sum of the thicknesses of all the laminae equals the average thickness for the element as defined by the nodal thicknesses. Note that the laminate is formed of 4 laminae but as the layup is symmetrical sym is set to 1. The layup sequence is [90/0/0/90] or in abbreviated form [90/0]s.

GEOM 1 TCS8 5.0 5.0 5.0 4.0 : 3.0 3.0 3.0 4.0 : LAMI 2 1 : 98 1.0 90.0 : 99 1.0 0.0 END

An example showing the use of both the symmetry option and the repeat facility for a laminate brick composed of a total of 60 layers. Two materials are used, one is orthotropic and the other is isotropic. The corresponding material data is also shown.

GEOM 1 LB20 : LAMI 30 1 / : 11 0.045 0.0 : 12 0.06 0.0 : 11 0.045 90.0 RP 10 END * MATE 1 LAMI 11 ORTHO : 25.0E6 1.0E6 1.0E6 0.5E6 0.2E6 0.5E6 0.25 0.25 0.25 12 ISO 3.7E6 0.3 END



5.2.5.4 Geometric Properties - (Rigid Surface Elements)

To define the geometric properties, if present, and rigid surface geometry for rigid surface elements.

Parameters


eltype : element type. This must correspond with the element type defined in the element topology data for this geometric property integer, (one of RG23, RG24, RGX3 or RGX4)

thick : nodal thickness, only required for element types RG23 and RG24 when attached to plane stress membrane elements. See Appendix -A for details of which properties are required for each element type. Continuation lines may be used if necessary. (Real)

RIGS : keyword to denote that geometry of the rigid surface is to be defined

nseg : number of segments defining the rigid surface. (Integer)

LINE : keyword to denote that the current segment type is linear

CIRC : keyword to denote that the current segment type is circular

node1 : node number at start of segment. (Integer)

node2 : node number at end of segment. (Integer)

node 3 : node number defining centre of the segment if circular. (Integer)

Notes

1. The coordinates of the node numbers must be defined in the Coordinate data.

2. The order of input of the nodes defines the direction of positive progression along the rigid surface (indicated by s in the example below). A right handed rotation of 90° from the positive tangent direction then defines the outward normal to the surface (i.e. n in example below).

3. The user should ensure that the rigid surface definition extends far enough to cover all expected motions of the deforming and rigid parts of the model.

:

geom eltype (thick)

: RIGS nseg

LINE

CIRC

node1 node2

node1 node2 node3



Example

An example of an axisymmetric rigid punch

GEOM

1 RGX3

: RIGS 3

: LINE 1 2

: CIRC 2 3 5

: LINE 3 4

END

1

n

s 2 n

s35

n

s

4

CL



5.2.5.5 Definition of geometric properties for beam elements having local axes definition

and/or rigid offsets

There are four engineer’s theory of bending, two-node beam types in ASAS for which the user can define the local axes and/or specify rigid offsets. In order to prevent confusion, the data requirements for each of these have been presented explicitly. These definitions may be used in any combination together with the general definition described in Section 5.2.5 to build a complete geometric data block (headed by the keyword GEOM and terminated by the keyword END) for a structure consisting of a mixture of any of the ASAS elements.

a) BEAM

b) BM2D

Notes

1. Only 4 offset values are specified relating only to offsets in the global XY and local X’Y’ planes.

2. Only skewed systems that are a rotation about the global Z may be used.

:

geom BEAM

OFFG

OFFS

OFSKOFCO

glboff

locoff

skew skwoff

coords

a iz iy j

sectid

:

geom BM2D

OFFG

OFFS

OFSKOFCO

glboff

locoff

skew skwoff

coords

sectid

a iz ay



c) BM3D

d) TUBE

nodeno

:

geomsectid

OFFG

OFFS

OFSK

OFCO

glboff

locoff

skew skwoff

coords

BM3D

NODE

GPOS

GNEG

SPOS

BETA angle

(COOR)

SNEG

VECT vcoor

axisskew

(XY)

XZay(SHAR)*

pcoor

a iz iy jaz

* Shear areas must not be defined here if section data has been referenced. The shear areas should be given as part of the section data.

nodeno

:

geomdia thick

OFFG

OFFS

OFSK

OFCO

glboff

locoff

skew skwoff

coords

TUBE

NODE

GPOS

GNEG

SPOS

BETA angle

(COOR)

SNEG

VECT vcoor

axisskew

(XY)

XZ

pcoorsectid



Parameters

a) General

geom : identifying number for the geometric property. This number must be unique, a separate

number being required for every different element type as well as for each differing

geometric definition. (Integer)

BEAM, BM2D, : element type. This must correspond to the element type defined in the element topology

BM3D, TUBE referencing this geometric property.

sectid : section identifier. (Alphanumeric up to 12 characters). This refers to a section input as

SECTION data. See Section 5.2.6.

b) Axes Definition

BETA : keyword to denote that local axis defined by beta angle (rotation of default local axes about

member X axis). See Appendix A.2.

angle : beta angle. (Real, degrees)

NODE : keyword to denote that local axis defined by third node point. See Appendix A.2.

nodeno : third node number. (Integer)

COOR : keyword to denote that local axis defined by third point coordinates. See Appendix A.2.

pcoor : global coordinates (x, y, z) of third point. (Real)

GPOS : keyword to denote that local axis defined by positive axis direction in global reference

plane. See Appendix A.2.

GNEG : keyword to denote that local axis defined by negative axis direction in global reference


SPOS : keyword to denote that local axis defined by positive axis direction in a skewed reference


SNEG : keyword to denote that local axis defined by negative axis direction in a skewed reference


axis : axis defining global/skewed reference plane (X,Y or Z).

skew : skew integer for defining skewed reference plane. (Integer)

VECT : keyword to denote that local axis defined by vector. See Appendix A.2.



vcoor : global coordinates (x,y and z) which define a vector direction from the origin.

XY,XZ : keywords to denote that axis being defined is in local XY or local XZ plane. See Appendix

A.2.



c) Offset Definition

OFFG : keyword to denote that offsets are to be defined using global coordinate axes. See

Appendix A.3.

glboff : global offset values for both ends of the beam element. (Real)

OFFS : keyword to denote that offsets are to be defined using the elemental local axes. See

Appendix A.3.

locoff : local offset values for both ends of the beam element. (Real)

OFSK : keyword to denote that offsets are to be defined using a skewed coordinate axis system.

See Appendix A.3.

skew : integer for the skew system in which offsets are to be defined.

skwoff : skewed offset values for both ends of the beam element. (Real)

OFCO : keyword to denote that offsets are to be defined by explicit definition of the global end

coordinates of the physical member.

coords : coordinates of both ends of the physical member. (Real)

d) Basic properties (see Appendix A for full element specification)

a : cross-sectional area, constant for section. (Real)

iz : 2nd moment of area about local ZZ axis, constant for section. (Real)

iy : 2nd moment of area about local YY axis, constant for section. (Real)

j : torsion constant, constant for section. (Real)

SHAR : keyword indicating that shear areas follow.

ay : shear area in local Y, constant for section. (Real)

az : shear area in local Z, constant for sectio. (Real)



Notes

1. Nonsections must not be assigned to TUBE elements.

2. Only relevant flexural properties will be utilised for a given element type, for example

BEAM BM2D BM3D TUBE

Area A

Moment of Inertia IZ

Moment of Inertia IY

Torsion constant J

Shear Area AY

Shear Area AZ

♦

♦

♦

♦

♦

♦

♦

♦

♦

♦

♦

♦

♦

Diameter D

Thickness T

♦

♦

3. When the properties for some beams are to be given by section data and for others explicitly, the two types of definition may be mixed.



5.2.6 Section Data

To define section type, dimensions and properties for sections to be used with element types BEAM, BM2D, BM3D and TUBE elements.

Parameters

SECT : compulsory header to denote the start of the section data.

sectid : section identifier. (Alphanumeric, up to 12 characters). This identifier must be unique and is independent of the section type.

type : type, or shape, of section being defined. (Alphanumeric, up to 4 characters).

Valid types are: WF wide flange FBI Fabricated I beam TUB tubular RHS rolled hollow section BOX fabricated box CHAN channel ANGL angle TEE tee PRI general prismatic section

: FLEXflexprops

proptype property

SECT

sectid type XSEC dimensions

END

sectid FAB ftype dimensions

: ftype dimensions

: ORIG

TOP (zoff)

BOTT (zoff)

(CENT)

LEFT (yoff)

RIGH (yoff)

(CENT)



see Section 5.2.6.1

XSEC : keyword to denote that cross-section dimensions are to be defined on this line. See Note 1

dimensions : list of section dimensions. See Section 5.2.6.1 for the details of which dimensions are required for each section type. (Real)

FAB : keyword to denote that a FABricated plate section is to be defined on this and subsequent lines.

ftype : type of dimensional property being defined for Fabricated plate section (Alphanumeric, up to 4 characters).

Valid types are: BLOC flat plate section CURB curved plate section CUT cut line POIN stress point

see Section 5.2.6.2

FLEX : keyword to denote that geometric properties are to be defined on this line. See Note 1

flexprops : list of geometric properties. For all section types this is AX,IZ,IY,J,AY,AZ

where AX cross sectional area IZ principal moment of inertia about element local Z axis IY principal moment of inertia about element local Y axis J torsion constant AY effective shear area for forces in element local Y direction AZ effective shear area for forces in element local Z direction

Shear strain is neglected for a given direction if AY and/or AZ is zero.

proptype : name of geometric property to be defined. Valid names are AX,IZ,IY,J,AY,AZ with the meaning as above.

property : value to be assigned to the named geometric property.

Notes

1. For any given section identifier XSEC and/or FLEX commands may be supplied with the following interpretations.

If only XSEC is defined, the geometric properties will be automatically calculated by the program for use

in the structural analysis.

If only FLEX is defined, all property values must be supplied.

If both XSEC and FLEX commands are utilised, any geometric properties explicitly defined will

overwrite those calculated from the section dimensions. This feature permits modification to the stiffness

of the section to model ring or web stiffeners, built up sections, etc.



2. The FLEX and XSEC sub-commands and associated data are interchangeable, i.e. FLEX appears on the sectid line with the (optional) XSEC command on a continuation line.

e.g W24x100 WF XSEC 24.0 12.0 0.775 0.468

: FLEX 29.11 2950.0 223.4 4.405

is the same as

W24x100 WF FLEX 29.11 2950.0 223.4 4.405

: XSEC 24.0 12.0 0.775 0.468

3. For FABbricated plate sections, notes 1 and 2 also apply but XSEC replaced by BLOC, CURB, CUT or POIN. The order of these data lines are interchangeable, but a logical sequence is recommended.

4. Only 4 POIN definitions may be used for each FABricated section.

5.2.6.1 Section Types and Dimensions

ASAS only requires areas and inertias to be specified for beam elements to determine the elemental forces. In order to simplify data input the section dimensions may be supplied in lieu of, or in addition to, the flexural properties. The following describes the dimensions required for each section type currently valid in ASAS.

Note

The axes shown correspond to the local axes of the member for element types BEAM, BM3D, TUBE and BM2D.

Example

SECT

W24x100 WF XSEC 24.0 12.0 0.775 0.468

P3.5STD TUB XSEC 4.0 0.226

: FLEX 2.68 4.79 4.79 1.34

W18x105 WF FLEX 30.621 1836.4 249.07 6.7164

R10x6x3/8 RHS XSEC 10.0 6.0 0.375

: FLEX IZ 184.0

END

Tube - Type TUB

Two dimensions must be defined

Values are D T

where D is the outer diameter T is the wall thickness



Wide flange - Type WF

A maximum of five dimensions can be provided : the first four are obligatory.

Values are D B TF TW (F)

where D is the beam depth B is the flange width TF is the flange thickness TW is the web thickness F is the fillet radius (optional, assumed zero)

Fabricated I beam - Type FBI

A maximum of six dimensions can be provided : the first four are obligatory.

Values are D BT TT TW BB TB

where D is the beam depth BT is the top flange width TT is the top flange thickness TW is the web thickness BB is the bottom flange width (optional, assumed same as BT) TB is the bottom flange thickness (optional, assumed same as TT)



Rolled Hollow Section - Type RHS

A maximum of four dimensions can be provided: the first three are obligatory.

Values are D B T (F)

where D is the beam depth B is the beam width T is the thickness F is the fillet radius (optional, assumed zero)

Fabricated Box - Type BOX

A maximum of five dimensions can be provided: the first four are obligatory.

Values are D B TT TS TB

where D is the beam depth B is the beam width TT is the thickness of the ‘top’ plate TS is the thickness of the ‘side’ plates TB is the thickness of the ‘bottom’ plate (optional, assumed same as TT)



Channel - Type CHAN




Angle - Type ANGL

A maximum of four dimensions can be provided: the first three are obligatory.

Values are D B T (F)

where D is the beam depth B is the flange width T is the thickness F is the fillet radius (optional, assumed zero)



Tee - Type TEE




Prismatic section - Type PRI

Two dimensions must be defined. For this section type, the flexural properties must also be defined.

Values are D B

where D is the maximum depth crossing the Z axis B is the maximum breadth crossing the Y axis

5.2.6.2 Fabricated Plate Sections

The Fabricated plate section is defined by a series of plate segments arranged to form the required cross-section. These plate segments may either be straight (BLOC) or curved (CURB), and are defined by their dimensions and location, with respect to an arbitrary origin on the cross-section. In addition, cut lines may be introduced, to prevent adjacent segments being physically joined. Finally, up to four stress points may be defined on the section for the purpose of stress evaluation in post-processing.



BLOC - Straight Plate Segment

A maximum of seven values can be provided: the first four are obligatory.

Values are L T YL ZL (AL C1 C2)

where L is the length of the plate segment T is the thickness of the plate segment YL is the Y location of plate centroid ZL is the Z location of plate centroid AL is the angular orientation of the plate (optional, assumed zero) C1 is the integer for the first associated cell C2 is the integer for the second associated cell (C1 and C2 are optional, assumed zero)

Note

AL must be in range -90° to +90°

CURB - Curved Plate Segment

A maximum of eight values can be provided: the first five are obligatory

Values are R T A YL ZL (AL C1 C2)

where R is the mean radius of plate segment T is the thickness of the plate segment A is the angle subtended by the plate YL is the Y location of the plate centroid ZL is the Z location of the plate centroid AL is the angular orientation of the plate (optional, assumed zero) C1 is the integer for the first associated cell C2 is the integer for the second associated cell (C1 and C2 are optional, assumed zero)

Note

A and AL are measured anti-clockwise (AL from Z axis) in degrees.



CUT - Cut Line

A maximum of four values can be provided: the first two are obligatory

Values are Y1 Z1 (Y2 Z2)

where Y1, Z1 give the position of start of cut line Y2, Z2 give the position of end of cut line (optional, assumed same as Y1, Z1)

Note

Cut line must occur at a segment boundary. If only two values specified, the nearest boundary will be cut.

POIN - Stress Point

Two values must be defined.

Values are Y1 Z1

where Y1, Z1 give the position of the stress point

Example

SECT

FABSEC001 FAB BLOC 50 10 45 25 0 1 *segment 1

: CURB 15 10 90 30 50 0 1 *segment 2

: BLOC 20 10 20 65 90 1 *segment 3

: BLOC 70 10 5 35 0 1 *segment 4

: BLOC 30 10 25 25 90 1 *segment 5

: BLOC 30 10 25 5 90 *segment 6

: CUT 40 5 *segment 6&1

: POIN 0 0 *stress point 1




END

Notes

1. The location of the segments may be defined in relation to any origin. The centroidal axes will be calculated automatically.



2. The axes used to define cut lines and stress points must be the same as that used to locate the segments.

3. The positioning of stress points is not restricted in any way. Thus a stress point could be off the section.

5.2.7 Skew System Data

There are two methods of defining skew systems. These are by the ‘skew system’ data using direction cosines and by the ‘nodal skew’ data using 3 node points. The two facilities are complementary, the user may use either or both types of data as is convenient.

5.2.7.1 Skew Systems - Direction Cosines

To define skew systems in terms of six direction cosines.

Parameters

SKEW : compulsory header keyword to denote the start of the skew system data


x’x,x’y,x’z : 6 directional cosines. (Real)

y’x,y’y,y’z

END : compulsory keyword to denote the end of the skew system data block

Notes

1. The skew integers must be unique between the SKEW and NSKW data.

2. The direction cosines supplied are checked for unity and orthogonality as follows:

3.

SKEW

skew x'x x'y x'z y'x y'y y'z

END

zx+yx+xx 222 ′′′ = 1.0 ± 0.001

= 1.0 ± 0.001

= 0.0 ± 0.001

zy+yy+xy 222 ′′′

zyz*xy+yy*xx+yx*x ′′′′′′



Example 1

Example of Skew Systems data

SKEW 1 0.8660 0.5000 0.0 -0.5000 0.8860 0.0 2 0.6830 0.2588 -0.6830 0.1830 -0.9659 -0.1830 END

The first line gives the direction cosines for a local axis system which has local Z’ coincident with global Z, and local X’ and local Y’ rotated by 30° in the global XY plane.

Angle between local X’ and global X = 30° Direction cosine X’X = 0.8660 Angle between local X’ and global Y = 60° Direction cosine X’Y = 0.5000 Angle between local X’ and global Z = 90° Direction cosine X’Z = 0.0 Angle between local Y’ and global X = 120° Direction cosine Y’X = -0.5000 Angle between local Y’ and global Y = 30° Direction cosine Y’Y = 0.8660 Angle between local Y’ and global Z = 90° Direction cosine Y’Z = 0.0

Example 2

The second line gives the direction cosines for a local axis system which is inclined to all the global axes.

The local X’ axis is defined by the coordinates (36,24,37) and (46,27.789,27). The distance between these points is:

14.641=37)-(27+24)-(27.789+36)-(46 222

Hence, the direction cosines for local X’ are given by:

Similarly, the local Y’ axis is defined by two points 10.353 apart and the direction cosines for local Y’ are given by:

Y'

Y

X'

X30°�

Y'

X'Z'

(37.895,14,35.105)

(46,27.789,27)

(36,24,37)

0.6830=64114.36-46=XX′ 0.2588=

64114.24-27.789=YX′ -0.6830=

64114.37-27=ZX′

0.1830=35310.

36895.37=XY −′ -0.9659=35310.

2414=Y Y − -0.1830=35310.

37150.35=ZY −′



5.2.7.2 Skew Systems - Nodal Definition

To define skew systems in terms of three node points

Parameters

NSKW : compulsory header keyword to denote the start of the nodal skew data


node1 : 3 node numbers. Used to define a local axis set in the following manner. The line from the first node2 node to the second node defines the local x’ direction. The plane defined by the three nodes node3 contains the local y’ direction which lies from the first node towards the third. The local z’ axis

forms a right handed set with local x’ and y’

END : compulsory keyword to denote the end of the nodal skew system data block

Notes

1. The skew integers must be unique between SKEW and NSKW data.

2. The nodes used to define a skew system must appear in the COOR data. It is not necessary for these nodes to be physically present on the structure i.e. they need not appear in the ELEM data.

Example

The first line in the example below describes a 2-D rotation in the x-y plane. Note, the global z axis points towards the reader but the local z’ axis, forming a right handed set with x’ and y’, points away from the reader.

NSKW

100 16 25 37

101 109 216 54

END

NSKW

skew node1 node2 node3

END

y'

x'

z

y

xz'

25

37

16

Boundary Conditions Data ASAS (Non-Linear) User Manual


5.3 BOUNDARY Conditions Data

These data blocks define the various ways in which the structure is supported and constrained.

The following data blocks are defined

Freedom Releases .... ................ ................ see Section 5.3.2

Suppressions ............ ................ ................ see Section 5.3.3

Displaced Freedoms ................. ................ see Section 5.3.4

Constraint Equations ................ ................ see Section 5.3.5

Rigid Constraints ..... ................ ................ see Section 5.3.6

Note

Freedom Release Data, if it exists, must be the first data block in the Boundary Conditions Data.

5.3.1 UNITS Command

The units command is not valid in the Boundary Conditions Data and will be ignored. Therefore any constants and factors utilised in constraint equations must be consistent with any global units (analysis units) defined in the Preliminary Data (see Section 5.1.42).

5.3.2 FREEDOM Release Data

To define elements which are to have particular freedoms released from being rigidly connected to the surrounding elements. Release can only apply to beam elements and the freedoms released are in their local axis system. See Notes below for more details. If used, freedom release data must be the first data block in the Boundary Conditions Data.



Parameters

RELE : compulsory header to define the start of the freedom release data.

skew : skew system integer. (Integer) Optional.

dof : name of freedom to be released. See notes.

elno : user element number of element to be released. (Integer)

node : node number on the element at which the freedom is to be released. (Integer)

RP : keyword to indicate data generation from the previous / symbol.

nrep : the number of times the data is to be generated.

ielem : user element number increment. (Integer)



nrrep : the number of times the data is to be generated.

iielem : user element number increment. (Integer)


END : compulsory keyword to denote the end of the freedom release data

RELE

(skew)

nrep inode

END

RP

RRP nrrep iinode

//elno//dof //node//

ielem

iielem



Notes

1. Only one skew system is allowed at a node. A node may not be given a different skew system in the suppression data from that defined in the freedom release data, etc.

2. When beam offsets are used at an element and node which is to be released, the release is applied to the element at the offset position in the offset local axes.

3. Care should be taken when using local releases on a beam which has its local axes defined by the coordinates of a 3rd point in the geometric property data. If the basic COOR data has been rotated by use of a DCOS command, the 3rd point is not similarly rotated.

Local Releases

Local releases are only available on the following element types: BEAM, BM2D, BM3D and TUBE. Valid released freedom names are X, Y, Z, RX, RY and RZ. (only X, Y and RZ for BM2D)

Rotational releases may be used to put hinged or pinned connections into the member. Translational releases will produce a sliding joint.

The user should not specify an excessive number of releases for an element. For example one release of a local RX freedom will be adequate to prevent that member carrying torque, but if both RX local freedoms of an element are released then that element can turn on its own axis as a local mechanism.

Displacements corresponding to the local releases are not calculated or printed.

If a skew is defined, all skewable degrees of freedom at the node are rotated to the new axis system, not only those defined by dof.



Example

1. In this example, three beam elements with User elements number 5, 7 and 10 meet at node 20. Elements 7 and 10 have local RZ released to create a pinned joint. RZ on element 5 is not released. If a release had been applied to element 5, the original RZ freedom would be left with zero stiffness and would need to be suppressed to prevent a local singularity in the structure. (Note that the rotations on elements 7 and 10 cannot be obtained).

RELE

RZ 7 20

RZ 10 20

END

5.3.3 SUPPRESSED Freedoms Data

This data defines the nodes and freedoms which are to be suppressed. Any degree of freedom defined here will have a value of zero for displacement for all load cases in the results.

Parameters

SUPP : compulsory header to define the start of the suppressed freedom data


dof : names of the freedoms to be suppressed. Up to 5 freedoms may be defined. See Appendix -F

10

75

Y

X

20

SUPP

(skew)

nrep inode

END

RP

RRP nrrep iinode

dof //nodes//



nodes : list of nodes at which the degrees of freedom are to be suppressed. Continuation lines may be

used if required. (Integer)

RP : keyword to indicate the generation of data from the previous / symbol


inode : node number increment to be added each time the data is generated by the RP command. (Integer)

RRP : keyword to indicate the generation of data from the previous // symbol


iinode : node increment to be added each time the data is generated by the RRP command. (Integer)

END : compulsory keyword to define the end of the suppressed freedom data



Notes

1. The word ALL may be used to indicate that all freedoms at the given node or nodes are to be suppressed.

2. If a skew is defined, all skewable degrees of freedom at the node are rotated to the new axis system, not only those defined by dof.

3. Reference to a node number or degrees of freedom which does not exist on the structure will produce a warning message. Reference to a node number outside the range of node numbers used on the structure will produce an error message.

Examples

A simple example of the use of several freedoms at a node, a skew system and the use of ALL.

SUPP

X Y RZ 15 25 35 39 40

1 Z 19

ALL 1 20

END

An example to suppress the Z degree of freedom for all nodes in a 2-D membrane structure, say 500 nodes.

SUPP

/

Z 1

RP 500 1

END

5.3.4 Prescribed Freedom Data

This data defines the nodes and freedoms which can be given a prescribed non-zero value of displacement, velocity or acceleration in the load data. See also Section 5.4.3.



Parameters

DISP : compulsory header to define the start of the prescribed displacement data

VELO : compulsory header to define the start of the prescribed velocity data

ACCN : compulsory header to define the start of the prescribed acceleration data

skew : optional skew system identifier (see Section 5.2.7)

dof : names of the freedoms to be displaced. Up to 5 freedom may be defined. See Appendix -F

nodes : list of nodes at which the degrees of freedom are to be given a fixed displacement, velocity or

acceleration. Continuation lines may be used if required. (Integer)






iinode : node number increment to be added each time the data is generated by the RRP command.

(Integer)

END : compulsory keyword to define the end of the prescribed displaced freedom data

DISP

(skew)

nrep inode

END

RP

RRP nrrep iinode

dof //nodes//

VELOACCN



Notes

1. Only one of the three compulsory headers is allowed in an analysis.

2. The word ALL may be used to indicate that all freedoms at the given node or nodes are to have prescribed displacements, velocities or accelerations.

3. If a skew is defined, all skewable degrees of freedom at a node are rotated to the new axis system, not only those defined by dof.

4. If a skew is used at a node, the same skew integer must be defined when the prescribed displacement, velocity or acceleration is defined in the loading data. See Section 5.4.3.

5. Prescribed velocities and accelerations may only be used in transient dynamic analyses.

6. Reference to a node number or degrees of freedom which does not exist on the structure will produce a warning message. Reference to a node number outside the range of node numbers used on the structure will produce an error message.

7. For transient analysis, non-zero prescribed displacements or velocities should not be applied at time t = 0.0. Any such values specified will be ignored by the program. The initial conditions (INIT) data block should be used to specify initial conditions instead.

Example

An example to define nodes 126 and 128 as having displaced freedoms in the Y direction.

DISP

Y 126 128

END

5.3.5 CONSTRAINT Equation Data

This data defines degrees of freedom on the structure whose displacements are to be linearly dependent on one or more other degrees of freedom in the structure. Currently, constraint equation data is not allowed in explicit transient dynamics analysis.



Parameters

CONS : compulsory header to define the start of the constraint equation data

skew : optional skew system identifier. Only the dependent node is skewed. (Integer)

Data for the dependent freedom on the left hand side of the constraint equation:

ddof : dependent freedom name. See Appendix -F

dnode : dependent node number. (Integer)

Data for the independent freedoms on the right hand side of the constraints equation:

factor : multiplying factor for the following independent freedom. (Real)

dof : independent freedom name. See Appendix -F

node : independent node number. (Integer)



inode : node number increment to be added each time the data is generated by the RP command.

(Integer)


nrrep : the number of times the data is to be generated


(Integer)

END : compulsory keyword to define the end of the constraint equation data

CONS

(skew)

nrep inode

END

RP

RRP nrrep iinode

dof //node//ddof //dnode// factor



Notes

1. Continuation lines may be used where necessary.

2. The word ALL cannot be used in the constraint equation data. Each equation must be separately and explicitly defined or generated with RP and RRP commands.

3. If a skew is defined for a dependent node, all skewable degrees of freedom at the dependent node are rotated to the new axis system, not only the ddof freedom. Freedoms at the independent nodes are unaffected by this skew.

4. The equations must be organised in such a way that a dependent freedom is never used in another constraint equation as an independent freedom.

for example Y18 = 0.5Y20 + 0.5Y21

Y16 = Y18

is not admissable since Y at node 18 is the dependent freedom in the first equation and an independent

freedom in the second. These equations should be rearranged as

Y18 = 0.5Y20 + 0.5Y21

Y16 = 0.5Y20 + 0.5Y21

5. Dependent freedoms must be truly free and not suppressed, displaced or otherwise restrained.

6. A constant term may be introduced into the right hand side of the equation. In this case the node number and freedom of the first independent term should be omitted and the factor becomes the constant displacement. This is equivalent to constraining to a displaced freedom with the same displacement. (See example 3 below).

7. Constraints may be used to remove local singularities in a structure. For example, an out-of-plane membrane freedom which has zero stiffness may be constrained to a suitable neighbouring point which has stiffness.

However, constraints cannot be used to remove a rigid body motion from a whole structure which is due

to a lack of overall support. This can only be done with suppressed or displaced nodes.

8. The forces associated with the constraint systems are printed out as reactions.

9. Note that constraint equations may sometimes be used to remove local singularity but this must be treated with caution. Consider the example where a model is created by joining together two detached components, one properly supported and one unrestrained, through the use of constraints, singularity can be removed if each dependent freedom of a constraint lies in the supported side of the model and the element that it is being attached to has a lower system number than the other side where the constraint is connecting to.



Examples

In this example, the displacements of node 19 in the global X and Y directions are to be tied to the global X, Y and RZ displacements of nodes 30 and 33. Because the displacements are all related to the global axes, there is no need for skew systems. The displacements are related by the following equations:

X19 = 0.5 X30 + 0.5 X33

Y19 = 0.3 X30 - 0.3 Y30 + 0.5 RZ30 - 0.3 X33 + 0.3 Y33

CONS

X 19 0.5 X 30 0.5 X 33

Y 19 0.3 X 30 -0.3 Y 30 0.5 RZ 30

: -0.3 X 33 0.3 Y 33

END

A Pin-ended Beam

The beam 88-89 is to be attached by a pin joint to the continuous column 23-24-25. The nodes 24 and 89 have the same coordinates. In this example the joint is taken to a ball joint, with complete freedom of rotation. The details of some joints require the constraining of one or two of the rotational freedoms.

CONS

X 89 1.0 X 24

Y 89 1.0 Y 24

Z 89 1.0 Z 24

END

A Rigid Edge

The edge 1-2-3 of the structure is to be kept rigid whilst node 2 is to be displaced by 0.2 units in the X-direction. The displacements are related by the equation:

X2 = 0.2 = (X1 + X3) /2

giving:

X2 = 0.2 (a prescribed displacement)

X3 = 0.4 - X1

CONS

X 3 0.4 -1.0 X 1

END

25

88 8924

23

4

5

6

1

2

3

0.2



5.3.6 RIGID Constraints Data

To define rigid regions of the structure. Rigid constraints (rigid elements) are a more convenient method of specifying constraint equations for particular modelling situations. They can be considered as equivalent to a string of one or more rigid elements linking the list of nodes. Currently, rigid constraint data is not allowed in explicit transient dynamics analysis.

Parameters

RCON : compulsory header to denote the start of the rigid constraint data

skew : optional skew system identifier. Only the dependent freedom is skewed. (Integer)

eltype : rigid element type. See notes. Allowable element types are RLNK, RBM2, RBM3, RLSY,

RBSY, SBRK, SBSY

indep : independent node number. (Integer)

nodelist : list of dependent nodes. (Integer) Continuation lines may be used if required



inode : the increment for the independent node and the dependent nodes. (Integer)

RRP : keyword to indicate data generation from the previous // symbol


iinode : the increment for the independent node and the dependent nodes. (Integer)

END : compulsory keyword to denote the end of the rigid constraint data

RCON

(skew)

nrep inode

END

RP

RRP nrrep iinode

//nodelist//eltype //indep//



Notes

1. The following Rigid Element types are available:

RLNK - 3-D rigid pin-ended link

RBM2 - 2-D rigid beam

RBM3 - 3-D rigid beam

RLSY - 3-D rigid pin-ended link system

RBSY - 3-D rigid beam system

SBRK - shell-brick interface link

SBSY - shell-brick interface system

2. Currently, there is a restriction that the dependent node must not be skewed in large displacement analysis.

The characteristics of each element are as follows:

Name RLNK RBM2 RBM3 RLSY RBSY SBRK SBSY

No of Nodes

Nodal

coordinates

Degrees of

Freedom linked

by the element

(Minimum)

2

X,Y,Z

X,Y,Z

2

X,Y

X,Y,RZ

2

X,Y,Z

X,Y,Z

RX,RY,RZ

arbitrary

X,Y,Z

X,Y,Z

arbitrary

X,Y,Z

X,Y,Z

RX,RY,RZ

2

X,Y,Z

X,Y,Z

for

dependent

X,Y,Z

RX,RY,RZ

for

independent

arbitrary

X,Y,Z

X,Y,Z

for

dependent

X,Y,Z

RX,RY,RZ

for

independent



Rigid Systems

RLSY This is a 3-D pin-jointed rigid link system whereby one node can be rigidly connected to an

arbitrary number of other nodes on a structure. The single independent node must have at least

X,Y,Z degrees of freedoms. The dependent nodes will have X,Y,Z as dependent freedoms.

Since the system reduces to a triangulated series of rigid links, it may not be entirely rigid in all

three dimensions. For example, a RLSY with all nodes in a plane will not be rigid normal to the

plane. If full rigidity is required, use RBSY.

RBSY This is a 3-D rigid-jointed rigid beam system whereby one node can be rigidly connected to an

arbitrary number of other nodes on a structure. The independent node and all dependent nodes

must have X, Y, Z, RX, RY, RZ degrees of freedom.

SBSY This is a shell-brick interface system whereby one node on a shell element is connected to an

arbitrary number of nodes on brick elements that lie in the shell normal (thickness) direction. The

independent node must be a shell node and have X,Y,Z,RX,RY,RZ degrees of freedom. The

dependent nodes are brick nodes and will have X,Y,Z degrees of freedom.

Use of Rigid Elements

The following rules apply:

1. All nodes used to define a rigid element must be connected to the structure. In the situation where a rigid element is connected between a node in space and a node on the structure a dummy element must first be used to connect the two nodes. Elements with compatible degrees of freedom must be used.

2. Skew integers refer to the dependent node for rigid elements RLNK, RBM2, RBM3 and SBRK. Skew integers are not valid for RLSY, RBSY and SBSY and if specified will be ignored.

3. An independent freedom can be suppressed, displaced, or constrained; dependent freedoms cannot.

4. The addition of rigid elements may overcome local singularity in a structure but this must be treated with caution. See notes in Section 5.3.5.

5. There are no limitations on the number of rigid elements joining at a node or the number of occurrences

of a dependent node.

Loading Data ASAS (Non-Linear) User Manual


5.4 Loading Data

These data blocks define the various types of loading which can be applied to the structure.

The following load types are available

Nodal loads .............. ................ ................ ................ ................ see Section 5.4.3

Prescribed displacements, velocities and accelerations ............... see Section 5.4.4

Pressure loads .......... ................ ................ ................ ................ see Section 5.4.5

Distributed loads ..... ................ ................ ................ ................ see Section 5.4.6

Temperature loads ... ................ ................ ................ ................ see Section 5.4.7

Face temperature loads ............. ................ ................ ................ see Section 5.4.8

Body force loads...... ................ ................ ................ ................ see Section 5.4.9

Centrifugal loads ..... ................ ................ ................ ................ see Section 5.4.10

Angular acceleration loads ....... ................ ................ ................ see Section 5.4.11

Nodal flux ............... ................ ................ ................ ................ see Section 5.4.12

Prescribed Field Variable ......... ................ ................ ................ see Section 5.4.13

Flux density ............. ................ ................ ................ ................ see Section 5.4.14

Wave load................ ................ ................ ................ ................ see Section 5.4.15

Tank loads ............... ................ ................ ................ ................ see Section 5.4.16

Load functions ......... ................ ................ ................ ................ see Section 5.4.17

5.4.1 UNITS Command

If global units have been defined using the UNITS command in the Preliminary data (Section 5.1.42), it is possible to override the input units locally to load type by the inclusion of a UNITS command. The local units are only operational for the current load type concerned and will return to the default global units when the next load type, or loadcase, is encountered.

In general, one or more UNITS commands may appear in a data block thus permitting the greatest flexibility in data input. The form of the command is similar to that used in the Preliminary data.



Parameters

UNITS : keyword


Notes

1. Force, length, temperature and angular unit may be specified. Only those terms which are required to be modified need to be specified, undefined terms will default to those supplied on the global units definition unless previously overwritten in the current data block.

2. The default angular unit for all load types is radians


Example

Data Operational Units Notes


PROJECT ASAS

STRUCTURE ASAS

JOB STATTITLE * EXAMPLESOLV 1.0

UNITS NEWTON METRE Newtons, metres, Global definition END centigrade .

..LOAD 2

SET 1 ‘NODAL AND DISTRIBUTED LOADS’

NODAL LO

UNITS KN Kilonewtons, metres, Note default X 10.0 5 6 7 radians angular unit Y 15.0 1 2

UNITS MM Kilonewtons, Note default RY 250.0 8 millimetres, radians angular unit RZ 300.0 5 6 7

END

DISTRIBU Newtons, metres, Units revert to Y BL1 1000.0 1200.0 5 6 radians global units Z BL1 900.0 1050.0 5 6

UNITS KN Kilonewtons, metres Change force

UNITS unitnm



Y BL1 1.5 1.6 5 6 unit to KN END

*

SET 2 ’DISTRIBUTED LOAD ONLY’

DISTRIBU Newtons, metres, New loadcase reverts Z BL5 1200.0 5 6 radians units to global END

STOP

5.4.2 LOADING Data

The loading data consists of a header keyword followed by one or more sets of load data.

Parameters

LOAD : compulsory header keyword to denote the start of the loading data

nset : total number of load sets to be specified. Optional. (Integer 1-9999). If supplied, nset must equal

the number of load sets supplied.

SET : compulsory keyword denoting the start of a load set

setno : set number. Every set number must be unique. (Integer, 1-9999)

ptime : pseudo time for load set, required only if loading is defined using pseudo-times. (Real)

title : load case title. (Alphanumeric string, 40 characters)

LOAD (nset)

SET setno (ptime) title

loadtype

data

END



loadtype : keyword to denote the start of each type of load data

END : compulsory keyword to denote the end of the data for each load type

Notes

1. If the load history is defined using load functions, then the load function data must be after all other loading data have been specified.

2. Proportional loading is assumed if there is only one load set and both pseudo-time and load function data are absent.

3. Title must be specified in quotes if the first word is a number.

5.4.3 NODAL LOADS Data

To define the application of nodal loads to the structure. These may be forces or moments.

Parameters

NODAL LO : compulsory header keyword to denote the start of nodal load data

skew : skew system integer. (Integer)

dof : freedom name. See Appendix -F

load : value of nodal load. (Real)

nodelist : list of the node numbers which are being loaded. (Integer)



NODAL LO

(skew)

nrep inode

END

RP

RRP nrrep iinode

//nodelist//dof load






iinode : node number increment to be added each time the data is generated by the RRP command. (Integer)

END : compulsory keyword to denote the end of the nodal load data for this load case

Notes

1. Any of the degrees of freedom which exists at a node by virtue of the element types attached to it can be loaded with nodal loads.

2. The nodal loads are applied in the global axis system or, if a skew system has been applied in the Boundary Condition data, in the node local axis system, as defined by that skew system.

3. If a skew system integer is used in the nodal load data, the direction of the applied loads is the combination of this skew system and any skew system applied in the Boundary Condition data.

4. Use of a skew system in the nodal load data does not cause the degrees of freedom at the node to be rotated by that amount. The nodal loads are resolved into separate components.

5. If the same node and freedom are loaded more than once in the nodal loads for a load case, the loads are additive.

Example

An example of a single load set consisting only of nodal loads. A point load of 25.0 is applied in the X direction at all nodes from 1 to 150.

LOAD 1

SET 100 ’TO GENERATE 150 NODAL LOADS’

NODAL L0

//

/

X 25.0 1

RP 10 1

RRP 15 10

END



5.4.4 PRESCRIBED Displacements, Velocities and Accelerations Data

To define the values of displacements, velocities or accelerations to be applied in this load case to those freedoms declared as prescribed freedoms in the Boundary Condition data (see Section 5.3.4).

Parameters

PRESCRIB : compulsory header keyword to denote the start of prescribed freedoms data

skew : skew system integer. Optional. (Integer)

dof : freedom name. See Appendix -F

prval : value of prescribed displacement, velocity or acceleration. (Real)

nodelist : list of the node numbers to which the prescribed displacement, velocity or acceleration is to be applied. (Integer)







END : compulsory keyword to denote the end of prescribed freedoms data

PRESCRIB

(skew)

nrep inode

END

RP

RRP nrrep iinode

//nodelist//dof prval



Notes

1. All freedoms used in the prescribed displacements, velocities or accelerations data must have been defined in the prescribed freedoms data (see Section 5.3.4).

2. In any load case, a prescribed displacement, velocity or acceleration is set to zero if it is not assigned a value and in this case a suppression is assumed for this freedom.

3. If a skew system has been defined in the Boundary Conditions data for a prescribed freedom node, the same skew integer must appear in prescribed displacement, velocity or acceleration load data for that node.

Examples

An example of prescribed displacements for two load sets. In case 1, both nodes are given equal displacement. In case 2, node 15 is given zero displacement and has become, in effect, a suppression.

LOAD 2

SET 1 1.0 ’EQUAL DISPLACEMENT OF 5mm’

PRESCRIB

Z 5.0 10

Z 5.0 15

END

SET 2 2.0 ’NODE 10 DISPLACED, NODE 15 FIXED’

PRESCRIB

Z 5.0 10

Z 0.0 15

END

STOP

5.4.5 PRESSURE Load Data

To define uniform pressure or varying pressure loading applied to the faces of panel or solid elements.



Parameters

PRESSURE : compulsory header to denote the start of pressure load data.

LDIR : keyword to define direction of pressure load.

dir : load direction. Optional. Valid names are:

GX global X direction GY global Y direction GZ global Z direction X local X direction Y local Y direction Z local Z direction Default direction is assumed if dir is omitted.

U : keyword to define data as uniform pressure.

F : keyword to define data as face definition.

P : keyword to define data as nodal pressure values.

FIN : keyword to denote the end of a block of U data, F data or P data.

END : compulsory keyword to denote the end of the pressure load data for this loadcase.



Note

1. The sign convention for pressure in the default direction on each element type is defined in the element description sheets in Appendix -A.

2. Local pressure load direction is only permitted for shell elements.

5.4.5.1 UNIFORM Pressure Load Data

To define values of the uniform pressure and the element faces to which they are applied.

Parameters

U : keyword to define uniform pressure data

lfunno : load function number; required if, and only if, LFUN specified. (Integer)

press : value of the uniform pressure. (Real)

nodes : the element faces to which the uniform pressure is applied. A face of an element is defined by up

to 3 corner nodes. (Integer)




(Integer)




(Integer)

U

nrep inode

FIN

RP

RRP nrrep iinode

//nodes//press(lfunno)



FIN : keyword to denote the end of the uniform pressure data block

Notes

1. A face of a panel or a face of a brick is defined by any 3 corner nodes on the face. For TRX6 and QUX8 a face is defined by the 3 nodes forming the loaded edge. For TRX3 and QUX4 a face is defined by the two nodes forming the loaded edge and any other node on the element.

2. For panel elements, if 2 corner nodes are supplied, pressure is applied to the edge of the element, positive towards the centre of the element. If 3 corner nodes are supplied, pressure is applied normal to the face of the elementin the local element axes.

3. For coincidental faces, for example where a panel overlays the face of a brick, the program will apply the pressure to the element with the lowest user number. The direction of the pressure load will be determined by this element’s local axis system.

4. See Table 6.1 for default values and Section 6.2 for the significance of some of the system parameter.

5.4.5.2 NON-UNIFORM Pressure Load Data

To define non-uniform pressure on element faces. A face can have a different value of pressure at each node. The data required is a set of face (F) definitions followed by a set of nodal pressure values (P). Unspecified mid-side node pressures are interpolated between adjacent corner nodes.

FACE Data

To define the element faces to which non-uniform pressure is to be applied. This data must be followed by a list of nodal pressure values.

Parameters

F : keyword to define face data

nodes : the element faces to which the non-uniform pressure is applied. A face is defined by up to 3

corner nodes. (Integer)

F

nrep inode

FIN

RP

RRP nrrep iinode

//nodes//






(Integer)




(Integer)

FIN : keyword to denote the end of set of face definitions



PRESSURE Data

To define the nodal pressure values which are to be applied to the previously defined set of element faces.

Parameters

P : keyword to denote nodal pressure data


press : value of the pressure at the nodes. (Real)

nodes : the nodes to which the pressure is applied. These nodes must exist on the faces defined by the

preceding set of face definitions. (Integer)







FIN : keyword to denote the end of a nodal pressure block

Notes

1. To define a region of non-uniform pressure, a set of one or more element faces is defined. The set of face data is terminated by a FIN keyword. This is immediately followed by a set of nodal pressure values which must be sufficient to completely define the pressure field over the selected faces. The nodal pressure data is also terminated by a FIN keyword, unless it is the final set in which case it is terminated by an END keyword.

P

nrep inode

FIN

RP

RRP nrrep iinode

//nodes//press(lfunno)



2. Regions of uniform pressure and non-uniform pressure may be mixed in any order.

3. A face of a panel or a face of a brick is defined by any 3 corner nodes on the face. For TRX6 and QUX8 elements, a face is defined by the 3 nodes forming the loaded edge. For TRX3, and QUX4 elements, a face is defined by the 2 nodes forming the loaded edge and any other node on the element.

Examples

Two Uniform Pressures are to be applied, a pressure of 10 over area 1-2-3-8-7-6, and a pressure of 20 over area 3-4-5-10-9-8. The following lines will generate the data.

PRESSURE

U 10.0 1 2 7

U 10.0 2 3 8

* EXAMPLE OF GENERATING PRESSURE ON SEVERAL FACES

/

U 20.0 3 4 9

RP 2 1

END

Non-uniform Pressure on one face. The program will assign a pressure of 7.5 to node 2 and 11.0 to node 4 by interpolation between the adjacent corner nodes.

67

8 9 10

1 2 3 4 5

p = 10 p = 10 p = 20 p = 20

7 6

5

4

3 2 1

8

p = 5 p = 10 p = 12

p = 10

p = 5

p = 5



PRESSURE

F 1 5 7

FIN

P 5.0 1 7 8

P 10.0 3 6

P 12.0 5

END

Example of a complete block of Pressure data for Uniform and Non-uniform Pressures

PRESSURE

U 20.0 1 2 8

U 20.0 7 8 14

FIN

//

/

F 2 3 9

RP 2 6

RRP 3 1

FIN

P 20.0 2 8 14

P 10.0 3 9 15 4 10 16

P 15.0 5 11 17

FIN

/

U 5.0 5 6 12

p = 2020

10 10

15

5

13 14 15 16 17 18

7 8 9 10 11 12

1 2 3 4 5 6



RP 2 6

END

5.4.6 DISTRIBUTED Load Data

This type of loading consists of patterns of load applied to the element as opposed to being applied to the nodes. Distributed Loads data can contain several load patterns, and an element can be loaded with several load patterns of the same or different types within one load set.

The following load patterns are available:

BL1 - Linearly varying normal load or bending moment on beams

BL2 - Linearly varying axial load or torque on beams

BL3 - Stepped uniform load on beams

BL4 - Partial uniform axial or normal load, torque or bending moment on beams

BL5 - Intermediate axial or normal point load, torque or bending moment on beams

BL6 - Partial linearly varying normal or axial load, torque or bending moment on beams

BL7 - Partial quadratically varying normal or axial load, torque or bending moment on beams

BL8 Equal and opposite axial or normal point load, torques or bending moments on beam elements applied at both ends

GL1 - Linearly varying global load, torque or bending moment on beams

GP1 - Linearly varying global load, torque or bending moment on projected length of beams

GL4 - Partial uniform global load, torque or bending moment on beams

GP4 - Partial uniform global load, torque or bending moment on projected length of beams

GL5 - Intermediate global point load, torque or bending moment on beams

GL6 - Partial linear varying global load, torque or bending moment on beams

GP6 - Partial linear varying global load, torque or bending moment on projected length of beams

GL7 - Partial quadratically varying global load, torque or bending moment on beams

GP7 - Partial quadratically varying global load, torque or bending moment on projected length of beams

ML1 - Varying shear load along the edge of membrane and shell elements

ML2 - Varying normal load on the edge of membrane and shell elements



ML3 - Varying transverse shear load on the edge of membrane and shell elements

CB1 - Varying distributed load on STF4

The general form of the distributed loads data block is shown below. A detailed description of each type of distributed load and its parameters are given in the following sections. See Appendix A, element descriptions.

Parameters

DISTRIBU : compulsory header keyword to denote the start of distributed load data.

dof : freedom code for the direction of loading.

type : type of distributed loading to be applied.

values : values of force and distance to describe the loading. (Real)

nodes : node numbers to define the loaded elements. (Integer)

ELEM : keyword to indicate following data are element numbers.

elno : element numbers to define the loaded elements. (Integer)

EDGE : keyword to indicate following data is an edge number.

edgeno : edge number of the element to be loaded. (Integer)

RP : keyword to indicate the generation of data from the previous / symbol.


inc : node or element number increment to be added each time the data is generated by the RP

command. (Integer)

dof

nrep inc

END

RP

RRP nrrep iinc

//elno//type

DISTRIBU

v alues

//nodes//

//elno//

ELEM

ELEM//edgeno//EDGE



RRP : keyword to indicate the generation of data from the previous // symbol.


iinc : node or element number increment to be added each time the data is generated by the RRP

command. (Integer)



Example

To apply a uniformly distributed load (BL1) of 8/unit length in the local Y direction to a BM3D defined by nodes 15 and 18.

Y BL1 8.0 8.0 15 18

Notes

1. For BL, GL and GP type loading, the elements to which the loads relate are defined by the two end nodes. If two or more beam elements are defined between the same two nodes (and in the same order), the loaded element cannot be uniquely identified and the program will apply the load to the element with the lowest user number. If this is not appropriate, the user may overcome this problem in a number of ways.

(i) Use element number input.

(ii) Alter the user element numbers.

(iii) Reverse the order of the element topology and associated loading for the second beam.

(iv) Subdivide second and subsequent elements into two or more beams.

(v) Use different node numbering for the two beams and apply constraint equations to join them together.

2. There is a restriction in the repeat facility where nodal type input and element type input may not be in the same repeat block.

3. The continuation facility is available in both nodal and element type input. However, the first line must contain at least two nodes or one element. The continuation line must contain the keywords ELEM/EDGE if element type input is being used.

4. The edge number follows the topology of the element, eg edge 2 is between nodes 2 and 3 of a 4-nodal quadrilateral element and edge 3 is between nodes 5 and 1 of a 6-noded triangular element.

Examples

DISTRIBU

ML2 10.0 10.0 10.0 EDGE 1 ELEM 2 3 4

: EDGE 2 ELEM 5 6 7

DI STRIBU

Y BL6 10.0 10.0 0.0 8.5 ELEM 100 101

: ELEM 102 103 104

DISTRIBU

Y BL1 5.0 5.0 2 3

: 3 4

: 4 5



5.4.6.1 Local Beam Distributed Loads

The local distributed loads on beams (BL types) are applied in terms of the local axis system, with X’ along the length of the element. A load is +ve when applied to the beam in the +ve direction of the local axis as defined by the element topology data and geometric property data. For normal loads which are not in a local axis plane, the appropriate components must be derived.

The Load Patterns BL1, BL2, BL6 and BL7 can be used to apply uniform load as well as linearly varying load. The Load Pattern BL7 can be used to apply linearly varying load as well as quadratically varying load.

Load pattern BL8 is useful particularly to impose initial strain conditions such as those arising from thermal loading when nodal temperatures are not appropriate.



Y”X”21

Y”X”

21

Y”X”21

Y”X”21

Y”X”21

Y”X”21

Y”X”21

Y”X”21

Y”X”21

Y”X”21

Y”X”21

Y”X”21

Y”X”21

Y”X”21

Y”X”21

Y”X”21

Y”X”

21

Y”X”21

Y”X”21

Y”X”21

Y”X”21

Y”

X”21

Y”X”21

Y”X”21

Y”X”

21

Normal

Bending

Axial

Normal

Normal

Axial

Bending

Torsion

Normal

Axial

Bending

Torsion

BL2

BL3 BL4

BL5 BL6

BL7 BL8

Normal

Axial

Bending

Torsion

Normal

Axial

Bending

Torsion

Normal

Axial

Bending

Torsion

Torsion

DISTRIBUTED LOAD PATTERNS BL1, BL2, BL3, BL4, BL5, BL6, BL7, BL8 on BEAM, BM2D, BM3D, TUBE

BL1



Example of Distributed Load Data for BL Patterns

Data

DISTRIBU

Y BL1 -10.0 -15.0 1 3

Y BL1 -15.0 -20.0 3 5

/

Y BL1 -10.0 -10.0 2 4

RP 2 2

Y BL4 -14.0 8.0 34.0 5 6

Y BL4 -16.00 0.0 26.0 3 4

Y BL5 -2000 9.0 3 4

Y BL5 -2000 38.00 3 4

END

34

8

p = 14

p = 20 p = 10

26

p = 16

p = 15 p = 10

3

9

38

2000 2000

p = 10 p = 101

56

4

2



5.4.6.1.1 BL1 and BL2 Load Patterns

Distributed Load Pattern BL1 - Linearly varying normal load or moment

Element Valid freedom directions

BEAM Y” Z” RY” RZ”

BM2D Y” RZ”

BM3D Y” Z” RY” RZ”

TUBE Y” Z” RY” RZ”

Distributed Load Pattern BL2 - Linearly varying axial load or torque


BEAM X” RX”

BM2D X”

BM3D X” RX”

TUBE X” RX”

Data Line

Parameters

dof : local freedom code for direction of loading. See list above.

BL1 : load pattern type BL2

force1 : force/unit length at end 1. (Real)


node1 : pairs of node numbers to define the elements to which this loading applies. (Integer) node2


elno : list of element numbers to which this loading applies. (Integer)

21

21

Y”

X”

Normal

Bending

X”

Y”

Y”

X”21

Y”

X”21

Axial

Torsion

dof//node1//

force2force1BL1

BL2

//node2//

//elno//ELEM



Note

The nodes must be listed in the same order as the element topology data.

Example

See Section 5.4.6.1

5.4.6.1.2 BL3 Load Pattern

Distributed Load Pattern BL3 - Stepped uniform normal load


BEAM Y” Z”

BM2D Y”

BM3D Y” Z”

TUBE Y” Z”

Data Line

Parameters


BL3 : load pattern type.



dist : distance to load step from end 1. (Real)




Y”

X”21

Normal

dof force2force1BL3 dist//node1// //node2//

//elno//ELEM



Notes

(i) The nodes must be listed in the same order as the element topology data.

(ii) This loading must not be applied to stepped beams. Apply in two parts using BL4 or BL6 loading.

Example

See Section 5.4.6.1


Distributed Load Pattern BL4 - Uniform normal or axial load, moment or torque over a part of the element


BEAM X” Y” Z” RX” RY” RZ”

BM2D X” Y” RZ”

BM3D X” Y” Z” RX” RY” RZ”

TUBE X” Y” Z” RX” RY” RZ”

Data Line

Parameters



force : force/unit length. (Real)

dist1 : distance to start of loaded part from end 1. (Real)

21

21

21

Y”

X”

Y”

X”21

Y”

X”

Y”

X”

Normal

Axial

Bending

Torsion

dof dist1forceBL4 dist2//node1// //node2//

//elno//ELEM



dist2 : distance to finish of loaded part from end 1. (Real)




Note


Example

See Section 5.4.6.1


Distributed Load Pattern BL5 - Intermediate point load or moment






Data Line

Parameters


21

Y”

X”

21

Y”

X”

21

Y”

X”

21

Y”

X”

Normal

Axial

Bending

Torsion

dof distforceBL5//node1// //node2//

//elno//ELEM




force : value of the point load or moment. (Real)

dist : distance to load point from end 1. (Real)




Note


Example

See Section 5.4.6.1


Distributed Load Pattern BL6 - Linearly varying normal or axial load, torque or moment over part of the element






Data Line

Y”

X”21

Y”

X”21

Y”

X”21

Y”

X”21

Normal

Axial

Bending

Torsion

dof dist1force1BL6 dist2force2//node1// //node2//

//elno//ELEM



Parameters

dof : local freedom code for direction of loading. See above list


force1 : force/unit length at the start of the loaded part. (Real)

force2 : force/unit length at the end of the loaded part. (Real)

dist1 : distance to the start of the loaded part from end 1. (Real)

dist2 : distance to the finish of the loaded part from end 1. (Real)




Note


Example

See Section 5.4.6.1


Distributed Load Pattern BL7 - Quadratically varying normal or axial load, torque or moment over part of the element






21

21

Y”

X”21

Y”

X”21

Y”

X”

Y”

X”

Normal

Axial

Bending

Torsion



Data Line

Parameters




force2 : force/unit length at the centre of the loaded part. (Real)



dist2 : distance to the end of the loaded part from end 1. (Real)




Note


Example

See Section 5.4.6.1


Distributed Load Pattern BL8 - Equal and opposite point loads or moments at either end of beam

dof dist1force1BL7 dist2force2 force3//node1// //node2//

//elno//ELEM








Data Line

Parameters



force : value of the load or moment. This value of load is applied to the beam (not the node) in an equal

and opposite sense at each end of the beam. (Real)




Note


Example

See Section 5.4.6.1

5.4.6.2 Global Beam Distributed Loads

The global beam distributed loads (GL and GP types) are similar to the BL load types except that the loading is applied in terms of the global axis system.

dof forceBL8//node1// //node2//

//elno//ELEM

21

21

21

21

Y”

X”

Y”

X”

Y”

X”

Y”

X”

Normal

Axial

Bending

Torsion



The load for GL type loading is applied to the beam in one of the global directions with the value of loading defined in terms of load per unit length of the beam element.

For GP type, loading is also applied in global direction but the value of loading is defined in terms of load per unit length measure in the plane normal to the direction of the load.

GL5

Y”X”

2

1

Global X

Y”X”

2

1

Global RY

Y”

X”

X

Z

Global X

1

2

Y”

X”

Global Z

1

2

GL1

Y”X”

2

1

Y”

X”

2

1

Global X

Global RZ

GL4

X

Z

X

Z

Y”

X”

Global X

1

2

Y”

X”

Global Z

1

2

GP1

Y”X”

2

1

Global X

Y”

X”

2

1

Global RZ

GP4

X

Z

X

Z

DISTRIBUTED LOAD PATTERNS GL1, GP1, GL4, GP4, GL5, GL6, GP6, GL7, and GP7 on BEAM, BM2D, BM3D, TUBE



GL6 GP6

GL7 GP7

Y”X”

2

1

Y”

X”

2

1

Global X

Global RY

Y”X”

2

1

Global X

Y”

X”

2

1

Global RY

Y”X”

2

1

Y”

X”

2

1

Global X

Global RY

Y”X”

2

1

Global X

Y”

X”

2

1

Global RY

X

Z

X

Z

X

Z

X

Z

DISTRIBUTED LOAD PATTERNS GL1, GP1, GL4, GP4, GL5, GL6, GP6, GL7, and GP7 on BEAM, BM2D, BM3D, TUBE



Example

Example of Distributed Global Loads

Data

DISTRIBU

X GP1 80.0 20.0 1 2

/

Z GL1 10.0 10.0 2 3

RP 2 1

X GL5 17.2 5.0 4 5

END

5.4.6.2.1 GL1 and GP1 Load Patterns

p = 10.0

p = 10.0 p = 10.0

p = 20.0

p = 80.0

1

2

3

4

Z

Y

X

Global Axis Sy stem

5

5.0

p = 17.2



Distributed Load Pattern GL1 - Linearly varying Global load or moment

Distributed Load Pattern GP1 - Linearly varying Global Projected load or moment


BM2D X Y RZ

BM3D X Y Z RX RY RZ

TUBE X Y Z RX RY RZ

Data Line

Parameters

dof : global freedom code for direction of loading. See list above

GL1 : load pattern types GP1



Y”

X”

GL1 - Global X

1

2

Y”

X”

1

2

Y”

X”

GP1 - Global X

1

2

Y”

X”

1

2

GP1 - Global Z

X

Z

GL1 - Global Z

dof //node1//force2force1GL1

GP1

//node2//(lfunno)




Note


Example

See Section 5.4.6.2.


Distributed Load Pattern GL4 - Uniform Global load or moment over a part of the element

Distributed Load Pattern GP4 - Uniform Global Projected load or moment over a part of the element


BM2D X Y RZ

BM3D X Y Z RX RY RZ

TUBE X Y Z RX RY RZ

Data Line

Parameters

dof : local freedom code for direction of loading. See list above

Y”X”

2

1

Y”

X”

2

1

GL4 - Global X

GL4 - Global RZ

Y”X”

2

1

GP4 - Global X

Y”

X”

2

1

GP4 - Global RZ

X

Z

//node1//dist1force dist2 //node2//GL4

GP4

dof (lfunno)



GL4 : load pattern type

GP4


force : force/unit length. (Real)

dist1 : distance to start of loaded part from end 1. (Real)

dist2 : distance to finish of loaded part from end 1. (Real)

node1 : element node numbers. (Integer)

node2 Note


Example

See Section 5.4.6.2

5.4.6.2.3 GL5 Load Pattern

Distributed Load Pattern GL5 - Intermediate Global point load or moment


BM2D X Y RZ

BM3D X Y Z RX RY RZ

TUBE X Y Z RX RY RZ

Data Line

Y”X”

2

1

Y”

X”

2

1

Global X

Global Z

Y”X”

2

1

Global RY

Y”

X”

2

1

Global RZ

X

Z

dof //node1// dist force GL5 //node2// (lfunno)



Parameters




force : value of the point load or moment. (Real)

dist : distance to load point from end 1. (Real)


node2 Note


Example

See Section 5.4.6.2


Distributed Load Pattern GL6 - Linearly varying Global load or moment over part of the element

Distributed Load Pattern GP6 - Linearly varying Global Projected load or moment over part of the element


BM2D X Y RZ

BM3D X Y Z RX RY RZ

TUBE X Y Z RX RY RZ

Data Line

Y”X”

2

1

Y”

X”

2

1

GL6 - Global X

GL6 - Global RY

Y”X”

2

1

GP6 - Global X

Y”

X”

2

1

GP6 - Global RY

X

Z



Parameters

dof : local freedom code for direction of loading. See above list


GP6





dist2 : distance to the finish of the loaded part from end 1. (Real)


node2 Note


Example

See Section 5.4.6.2


Distributed Load Pattern GL7 - Quadratically varying Global load or moment over part of the element

//node1//dist1(lfunno) dist2force2 //node2//GL6

GP6

dof force1



Distributed Load Pattern GP7 - Quadratically varying Global Projected load or moment over part of the element


BM2D X Y RZ

BM3D X Y Z RX RY RZ

TUBE X Y Z RX RY RZ

Data Line

Parameters



GP7



force2 : force/unit length at the centre of the loaded part. (Real)



dist2 : distance to the end of the loaded part from end 1. (Real)


node2 Note


Y”X”

2

1

Y”

X”

2

1

GL7 - Global X

GL7 - Global RY

Y”X”

2

1

GP7 - Global X

Y”

X”

2

1

GP7 - Global RY

X

Z

dof //node1//dist1(lfunno) dist2force2 force3 //node2//GL7

GP7

force1



Example

See Section 5.4.6.2

5.4.6.3 Panel Edge Distributed Loads

Distributed Load Patterns ML1, ML2 and ML3 can be applied on element types QUM4, QUM8, QUS4, TCS6, TCS8, TCS9, TRM3, TRM6.

Load Pattern ML1 - Varying axial load along an edge

The load is positive if it acts in the direction of the order of nodes in the element topology data. For QUM8, TCS6, TCS8, TCS9, TRM6 a quadratic variation of the load is allowed, so linear variation and uniform loading are also acceptable. For QUS4, QUM4, TRM3 a linear variation of load is allowed, so uniform loading is also acceptable. For a curved edge, the loading is tangential at any point.

Load Pattern ML2 - Varying normal load along an edge

The load is positive if it acts away from the centre of the element. For QUM8, TCS6, TCS8, TCS9, TRM6 a quadratic variation of load is allowed, so linear variation and uniform loading are also acceptable. For QUM4, TRM3, QUS4, a linear variation of load is allowed, so uniform loading is also acceptable. For a curved edge, the loading is normal to the edge at any point.



Load Pattern ML3 - Varying Transverse Edge Shear Load

The load is positive if it acts in the positive local Z direction for the element.

For QUM8, TCS6, TCS8, TCS9 and TRM6 a quadratic variation of load is allowed, so linear variation and uniform loading are also acceptable. For QUM4, QUS4 and TRM3 a linear variation of load is allowed, so uniform loading is also acceptable. For a curved element the load is always normal to the surface of the element.

Data Line

Parameters

ML1 : load pattern types

ML2

ML3


force1 : value of the load/unit length at the first corner node on the edge. (Real)

force2 : value of the load/unit length at the second corner node on the edge. (Real)

force2force1

ML1

ML2 force3

ML3//elno//ELEM//edgeno//EDGE

//nodes//



force3 : value of the load/unit length at the mid-side node for QUM8, TCS6, TCS8, TCS9, TRM6. This

mid-side value must be calculated and given. Any value for low order elements. (Real)

nodes : element node list of the edge of the element to be loaded. (Integer)

EDGE : keyword to indicate following data are edge numbers.

edgeno : edge number of the element to be loaded. (Integer)


elno : element numbers to define the loaded elements. (Integer)

Notes

Order of the nodes in element node list

1. node number of first corner on the edge

2. node number of second corner on the edge

3. node number of any other corner on the element

Example

Example of Distributed Load Data for ML Patterns



Data

DISTRIBU

ML2 -10.0 -10.0 -10.0 1 3 8

ML2 -10.0 -10.0 -10.0 6 1 3

ML2 -15.0 -10.0 -11.0 11 6 8

ML2 -21.0 -15.0 -18.0 16 11 13

ML1 -7.0 -7.0 -7.0 13 18 16

ML1 8.0 8.0 8.0 18 16 11

END

5.4.6.4 Curved Beam Distributed Loads

Distributed Load Pattern CB1 on element STF4

Normal (freedom Y’s or Z’s), axial (freedom X’s), torsional (freedom RX’s) and bending (freedom RY or RZ) loads are allowed. The load is applied in terms of the local axis system, with X’ along the length of the element and Y’ and Z’ as defined in Appendix -A.

Data Line

Parameters

dof : local freedom code for direction of loading

CB1 : load pattern type

dof force2force1CB1 force3//nodes//

//elno//ELEM




force1 : value of load/unit length at end 1. (Real)

force2 : value of load/unit length at mid-side node. (Real)

force3 : value of load/unit length at end 2. (Real)

nodes : element node list. (Integer)


elno : list of element numbers to define the loaded elements. (Integer)

Note




Example

Example of Distributed Load Data for Pattern CB1

Data

DISTRIBU

X CB1 -34.4 -34.4 -34.4 42 43 48

Y CB1 -6.6 -3.3 -9.9 42 43 48

END

5.4.7 TEMPERATURE Load Data

5.4.7.1 NODAL Temperature Data

To define the temperature values at node points throughout the structure.

Y'

X'42

43 48

q=34.4 (uniform)

p=6.6

p=3.3

p=9.9



Parameters

TEMPERAT : compulsory header keyword to denote the start of the nodal temperature data

GROU : keyword to indicate that the following temperature data applies to a single group

grpno : group number to which temperature data applies. (Integer)

temp : temperature value at the nodes. (Real)

nodes : list of nodes at which the given value of temperature applies. (Integer)


nrep : number of times the data is to be generated. (Integer)

inode : node increment to be added each time the data is generated by the RP command. (Integer)


nrrep : number of times the data is to be generated. (Integer)


GRES : keyword to indicate reading temperatures from the database of a previous thermal analysis

sname : 4 character structure name where temperature results are to be retrieved from.

Ic : user load case number in the thermal analysis. By default, Ic has the same user load case number as that specified in the stress analysis. (Integer)

isub : the load sub-case number. Default is 0. (Integer)

TEMPERAT

GROU

temp

nrep inodeRP

RRP nrrep iinode

//nodes//

END

grpno

GRES sname (lc) isub (node1) (node2)



node1 : the lower limit of a node range where results will be transferred. The default value 0 means from the lowest node on structure. (Integer)

node2 : the upper limit of a node range where results will be transferred. The default value 0 means to the highest node on structure. (Integer)

END : compulsory keyword to denote the end of the temperature data block

Notes

1. Temperature values are actual temperatures. The thermal loads are calculated due to the difference between these and the reference temperatures.

2. Any missing corner node temperature is taken as the reference temperature.

3. Mid-side node temperatures, whether specified or not, are always linearly interpolated between adjacent corner nodes. For elements without mid-side nodes, the average temperature on element is taken to calculate the thermal strain.

4. Loading due to temperatures and face temperatures is additive at common nodes

5. Nodal and element temperature data must not be present in the same load set.

6. If the material properties are temperature dependent, temperature load, if specified, must be present in all of the runs (i.e. initial and restarts). If any run does not have temperature load, then the reference temperature should be specified in the data

7. The following points are concerned with the usage of the GRES command.

• Temperature results must have been saved in a previous thermal analysis under the same project.

• It is assumed that all the structural corner nodes have the same node numbers as the thermal model.

• The node range data node1 and node2 enable certain nodes to be excluded from the stress analysis.

This facility is useful if non-structural nodes have been used in the thermal model, for example, to

model ambient temperature in convection or radiation boundaries.

• It is acceptable to have more than one GRES command in a local case.

• GRES can be specified together with ordinary nodal temperature data in the same load case.

5.4.7.2 ELEMENT Temperature Data

To define uniform or varying temperatures on elements. See Section 5.4.7.3 for details of uniform element temperature data and Section 5.4.7.4 for non-uniform element temperatures data.



Parameters

EL TEMPE : compulsory header to denote the start of element temperature data.

U : keyword to define data as uniform element temperature.

E : keyword to define data as element definition.

T : keyword to define data as nodal temperature values.

FIN : keyword to denote the end of a block of U data, E data, or T data.

END : compulsory keyword to denote the end of the element temperature data block.

5.4.7.3 UNIFORM Element Temperature Data

To define values of the uniform temperature and the elements to which they apply.

EL TEMPE

U

FIN

elnotemp

E

FIN

elno

T

FIN

nodestemp

END



Parameters

U : keyword to define uniform temperature data.

temp : value of the uniform temperature. (Real)

elno : list of user element numbers to which the uniform temperature is applied. (Integer)



ielno : user element number increment to be added each time the data is generated by the RP command.

(Integer)



iielno : user element number increment to be added each time the data is generated by the RRP command.

(Integer)

FIN : keyword to denote the end of the uniform temperature data block.

5.4.7.4 NON-UNIFORM Element Temperature Data

To define non-uniform temperature on elements. An element can have a different value of temperature at each node. The data required is a set of element (E) definitions followed by a set of nodal temperature values (T). Mid-side temperatures are always linearly interpolated between the adjacent corner nodes.

U

nrep ielno

FIN

RP

RRP nrrep iielno

//elno//temp



ELEMENT Data

To define the elements to which non-uniform temperature is to be applied. This data must be followed by a list of nodal temperature values.

Parameters

E : keyword to define element data.

elno : list of user element numbers to which the non-uniform temperature is applied. (Integer)




(Integer)




(Integer)

FIN : keyword to denote the end of set of element definitions.

E

nrep ielno

FIN

RP

RRP nrrep iielno

//elno//



TEMPERATURE Data

To define the nodal temperature values which are to be applied to the previously defined set of elements.

Parameters

T : keyword to denote nodal temperature data

temp : value of the temperature at the nodes. (Real)

nodes : the nodes to which the temperature is applied. These nodes must exist on the elements defined by

the preceding set of element definitions. (Integer)







FIN : keyword to denote the end of a nodal temperature block.

Notes

1. To define a region of non-uniform element temperature, a set of one or more elements is defined. The set of element data is terminated by a FIN keyword. This is immediately followed by a set of nodal temperature values which must be sufficient to completely define the temperature field over the selected elements. The nodal temperature data is also terminated by a FIN keyword, unless it is the final set in which case it is terminated by an END keyword.

2. Regions of uniform element temperature and non-uniform element temperature may be mixed in any order.

T

nrep inode

FIN

RP

RRP nrrep iinode

//nodes//temp



3. Unspecified corner node temperatures are taken as the reference temperature.

4. Mid-side node temperatures, whether specified or not, are always linearly interpolated between adjacent corner nodes. For elements without mid-side nodes, the average element temperature is taken to calculate the thermal strain.

5. Loading due to element temperature and element face temperature are additive.

6. If temperature is defined more than once on an element the loadings will be additive.

7. Nodal and element temperature data must not be present in the same load set.

8. If the material properties are temperature dependent, temperature load, if specified, must be present in all of the runs (i.e. initial and restarts). If any run does not have temperature load, then the reference temperature should be specified in the data.

Example

In this example 5 BM3D elements are given element temperature values. Elements 11 and 12 have a constant temperature of 50°, element 13 varies from 50° to 75°, element 14 varies from 75° to 100° and element 15 varies from 50° to 25°.

EL TEMPE

/

U 50.0 1

RP 2 1

FIN

/

E 13

RP 2 1

FIN

T 50.0 3

T 75.0 4

T 100.0 5

FIN

E 15

FIN

T=50 50 50

75100

1 2 3 4 5

11 12 13 14

6

25

50



T 50.0 5

T 25.0 6

END

5.4.8 FACE TEMPERATURE Data

5.4.8.1 Nodal Face Temperature

To define temperature gradients through plate and shell elements in terms of face temperatures at node points throughout the structure.

Parameters

FACE TEM : compulsory header to denote the start of nodal face temperature data

GROU : keyword to indicate that the following face temperature data applies to a single group

grpno : group number to which face temperature data applies. (Integer)

temp1 : temperature value on face 1. (Real)


nodes : list of nodes at which the face temperatures apply. (Integer)



nrep inode

END

RP

RRP nrrep iinode

FACE TEM

temp1 temp2 //nodes//

GROU grpno




RRP : keyword to indicate data generation from the previous // symbol



END : compulsory keyword to denote the end of the face temperature data block

Notes

1. The position of Face 1 and Face 2 for each element is defined in the element description sheets in Appendix -A.

2. Since face temperatures are applied to all elements attached to the given nodes within the specified group, care must be taken to ensure the consistent use of local axes on adjacent elements.

3. Loading due to temperature and face temperature are additive.

4. Nodal and element face temperature data must not be present in the same load set

5. Notes for temperature data also apply here.

6. If the material properties are temperature dependent, temperature load, if specified, must be present in all of the runs (i.e. initial and restarts). If any run does not have face temperature load, then the reference temperature should be specified as the top and bottom surface temperatures in the data.

5.4.8.2 ELEMENT FACE TEMPERATURE Data

To define uniform or varying face temperatures on elements. See Section 5.4.8.3 for details of uniform element face temperature data and Section 5.4.8.4 for non-uniform element face temperature data.



Parameters

EL FACET : compulsory header to denote the start of element face temperature data.

U : keyword to define data as uniform face temperature.

E : keyword to define data as element definition.

T : keyword to define data as nodal face temperature values.

FIN : keyword to denote the end of a block of U data, E data, or T data.

END : compulsory keyword to denote the end of the element face temperature data block.

5.4.8.3 UNIFORM Element Face Temperature Data

To define values of the uniform face temperatures and the element faces to which they are applied.

EL FACET

U

FIN

elnotemp1

E

FIN

elno

T

FIN

nodestemp1

END

temp2

temp2



Parameters

U : keyword to define uniform face temperature data.



elno : list of user element numbers to which the uniform face temperature is applied. (Integer)




(Integer)




(Integer).

FIN : keyword to denote the end of the uniform face temperature data block.

5.4.8.4 NON-UNIFORM Element Face Temperature Data

To define non-uniform face temperature on elements. An element can have a different value of face temperature at each node. The data required is a set of element (E) definitions followed by a set of nodal temperature values (T) on element faces. Mid-side face temperatures are always linearly interpolated between adjacent corner nodes.

U

nrep ielno

FIN

RP

RRP nrrep iielno

//elno//temp1 temp2



ELEMENT Data

To define the element faces to which non-uniform face temperature is to be applied. This data must be followed by a list of nodal face temperature values.

Parameters

E : keyword to define element data.

elno : list of user element numbers to which the non-uniform face temperature is applied. (Integer)




(Integer)




(Integer)

FIN : keyword to denote the end of set of element definitions.

E

nrep ielno

FIN

RP

RRP nrrep iielno

//elno//



FACE TEMPERATURE Data

To define the nodal face temperature values which are to be applied to the previously defined set of elements.

Parameters

T : keyword to denote nodal face temperature data.



nodes : the nodes to which the face temperature is applied. These nodes must exist on the elements

defined by the preceding set of element definitions. (Integer)







FIN : keyword to denote the end of a nodal face temperature block.

Notes

1. To define a region of non-uniform face temperature, a set of one or more elements is defined. The set of element data is terminated by a FIN keyword. This is immediately followed by a set of nodal face temperature values which must be sufficient to completely define the temperature field over the selected elements. The nodal face temperature data is also terminated by a FIN keyword, unless it is the final set in which case it is terminated by an END keyword.

T

nrep inode

FIN

RP

RRP nrrep iinode

//nodes//temp1 temp2



2. Regions of uniform and non-uniform face temperature may be mixed in any order.

3. The position of Face 1 and Face 2 for each element is defined in the element description sheets in Appendix A.

4. Care must be taken to ensure the consistent use of local axes on adjacent elements because the definitions of Face 1 and Face 2 are local axes dependent.

5. Unspecified values for element corner nodes are taken as the reference temperature. Mid-side node temperatures, whether specified or not, are always linearly interpolated between adjacent corner nodes. For elements without mid-side nodes, the average temperature on each face is taken to calculate the thermal strain.

6. Loading due to temperatures and face temperatures are additive.

7. If face temperature is defined more than once on an element, the loading will be additive.

8. Nodal face temperature and element face temperature data must not be present in the same load set.

9. If the material properties are temperature dependent, temperature load, if specified, must be present in all of the runs (i.e. initial and restarts). If any run does not have temperature load, then the reference temperature should be specified as the top and bottom surface temperatures in the data.

Example

Uniform Element Face Temperature on 4 elements

EL FACET

/

U 100.0 50.0 1

RP 4 1

END

5.4.9 BODY FORCE Data

To define forces due to linear acceleration of the structure, arising from the mass of the elements and added masses. Only one body force loading may be defined per load set.

1 2 3 4 temperature on face 1 = 100.0 temperature on face 2 = 50.0



Parameters

BODY FOR : compulsory header keyword to denote the start of body force data

x-acc : values of acceleration in the direction of the three global axes. (Real) y-acc z-acc

END : compulsory keyword to denote the end of the body force data block

Notes

1. A +ve acceleration produces +ve forces along the corresponding axis. Thus if the vertical global axis is positive upwards, a negative value of ‘g’ is required to generate self weight.

2. Non-zero values of density must be included for any materials used for elements whose mass is to be included in the calculation of the body forces.

3. Accelerations must be input in units (Length/Time2) consistent with those used for length and density.

Example

An example of a body force load set.

BODY FOR

0.0 10.5 32.2

END

5.4.10 CENTRIFUGAL Loads Data

To define forces due to uniform rotation about a given point, arising from the mass of the elements and added mass. Only one centrifugal loading may be defined per load set.

END

BODY FOR

x-acc y-acc z-acc



Parameters

CENTRIFU : compulsory header keyword to denote the start of the centrifugal load data

xc : global coordinates of the centre of rotation of the structure. (Real) yc zc

x-vel : values of angular velocity in radians/sec about the the three global axes. (Real) y-vel z-vel

END : compulsory keyword to denote the end of the centrifugal load data block

Note

Non-zero values of density must be included for any materials used for elements whose mass is to be included in the calculation of the centrifugal forces.

Example

An example of a centrifugal load case.

CENTRIFU

17.3 103.0 96.5 0.134 0.53 0.05

END

5.4.11 ANGULAR ACCELERATION Loads Data

To define forces due to angular velocity and angular acceleration about a given point, arising from the mass of the elements and added masses. Only one angular acceleration loading may be defined per load set.

END

CENTRIFU

xc yc zc x-vel y-vel z-vel



Parameters

ANG ACCE : compulsory header keyword to denote the start of the angular acceleration data

xc,yc,zc : global coordinates of the centre of rotation of the structure. (Real)

x-acc : values of angular acceleration in radians/sec2 about the three global axes. (Real) y-acc z-acc

x-vel : values of angular velocity in radians/sec about the three global axes. If omitted zero is y-vel assumed. (Real) z-vel

END : compulsory keyword to denote the end of the angular acceleration data block

Notes

1. Non-zero values of density must be included for any materials used for elements whose mass is to be included in the calculation of angular acceleration forces.

2. Element forces due to angular accelerations are based on the total mass of an element subject to the velocities and accelerations pertaining at the centroid of that element. Therefore large elements positioned close to the centre of rotation can produce significant discretisation errors.

3. The sign convention for angular accelerations is such that input of a positive clockwise acceleration will produce element forces acting in a counter-clockwise direction. Note, this convention is different to the body force convention where a positive input value produces element forces in the positive direction.

Example

An example of an angular acceleration load case.

ANG ACCE

15.9 0.0 -17.6 0.16 0.02 0.0 0.23 -0.07 0.0

END

END

ANG ACCE

xc yc zc (x-vel y-vel z-vel) x-acc y-acc z-acc



5.4.12 NODAL FLUX Data

To define the application of nodal fluxes to the structure. This load type may only be specified in a HEAT analysis.

Parameters

NODAL FL : compulsory header keyword to denote the start of nodal flux data

dof : freedom name. Must be T

load : value of nodal load. (Real)

nodelist : list of the node numbers which are being loaded. (Integer)







END : compulsory keyword to denote the end of the nodal load data for this load case

Note

If the same node and freedom are loaded more than once in the nodal flux data for a load case, the fluxes are additive.

NODAL FL

nrep inode

END

RP

RRP nrrep iinode

//nodelist//dof load



Example

An example of a single load set consisting only of nodal fluxes. A point flux of 25.0 is applied at all nodes from 1 to 150.

LOAD 1

SET 100 1.0 ’TO GENERATE 150 NODAL FLUXES’

NODAL FL

//

/

T 25.0 1

RP 10 1

RRP 15 10

END

5.4.13 PRESCRIBED Field Variable Data

To define the field variable values to be applied in this load case to those freedoms declared as prescribed freedoms in the Boundary Condition data (see Section 5.3.4).

Parameters

PRESCRIB : compulsory header keyword to denote the start of prescribed freedoms data

dof : freedom name. Must be T

prval : value of prescribed field variable. (Real)

nodelist : list of the node numbers to which the prescribed field variable is to be applied. (Integer)



PRESCRIB

nrep inode

END

RP

RRP nrrep iinode

//nodelist//dof prval







END : compulsory keyword to denote the end of prescribed freedoms data

Notes

1. All freedoms used in the prescribed field variables data must have been defined in the prescribed freedoms data (see Section 5.3.4).

2. In any load case, a prescribed field variables is set to zero if it is not assigned a value and in this case a suppression is assumed for this freedom.

Examples

An example of prescribed field variable data for two loadcases. In case 1, both nodes are given equal values. In case 2, node 15 is given a value of zero.

LOAD 2

SET 1 1.0 ’EQUAL TEMPERATURE OF 5’

PRESCRIB

T 5.0 10

T 5.0 15

END

SET 2 2.0 ’NODE 10 = 5 DEG, NODE 15 = ZERO’

PRESCRIB

T 5.0 10

T 0.0 15

END

STOP

5.4.14 FLUX DENSITY Data

To define uniform or varying flux density applied to the faces of panel or solid elements, or generated within an element. This load type may only be specified in a HEAT analysis.



Parameters

FLUX DEN : compulsory header keyword to denote the start of pressure load data

V : keyword to define data as uniform flux density

E : keyword to define data as face or element definition

D : keyword to define data as nodal flux density values

FIN : keyword to denote the end of a block of V data, E data or D data

END : compulsory keyword to denote the end of the pressure load data block

5.4.14.1.1 UNIFORM Flux Density Data

To define values of the uniform flux density and the elements or element faces to which they are applied.

FLUX DEN

V

FIN

//nodes//fden

E

FIN

//nodes//

D

FIN

//nodes//fden

END



Parameters

V : keyword to define uniform flux density data

fden : value of the uniform flux density. (Real)

nodes : the elements or element faces to which the uniform flux density is applied. An element is defined

by up to 4 corner nodes. A face of an element is defined by up to 3 corner nodes. (Integer)




(Integer)




(Integer)

FIN : keyword to denote the end of the uniform flux density data block

Notes

1. For surface flux, a face of a brick is defined by any 3 corner nodes on the face. For TMT6, QMT8, TXT6 and QXT8, a face is an edge defined by the 3 nodes forming the loaded edge. For TMT3, QMT4, TXT3 and QXT4, a face is an edge defined by the two nodes forming the loaded edge. Here flux density is defined as flux per unit area.

2. For internal flux, a brick element is defined by any 4 corner nodes on the element. The nodes must not all lie on one face. For membrane or axisymmetric solid field elements, an element is defined by any 3

V

nrep inode

FIN

RP

RRP nrrep iinode

//nodes//fden



corner nodes on it. The nodes must not all lie on one edge, however. Here flux density is defined as flux per unit volume.

3. If both surface and internal fluxes are present, they must be defined in separate data blocks.

5.4.14.1.2 NON-UNIFORM Flux Density Data

To define non-uniform flux density on elements or element faces. An element or a face can have a different value of flux density at each node. The data required is a set of element or face (E) definitions followed by a set of flux density values (D). Unspecified mid-side node flux densities are interpolated between adjacent corner nodes.

ELEMENT/FACE Data

To define the elements or element faces to which non-uniform flux density is to be applied. This data must be followed by a list of nodal flux density values.

Parameters

E : keyword to define element/face data

nodes : the elements or element faces to which the non-uniform pressure is applied. An element is defined

by up to 4 corner nodes. A face is defined by up to 3 corner nodes (see Notes 3 and 4 in Flux

Density Data). (Integer)




(Integer)



E

nrep inode

FIN

RP

RRP nrrep iinode

//nodes//




(Integer)

FIN : keyword to denote the end of set of element/face definitions



FLUX DENSITY Data

To define the nodal flux density values which are to be applied to the previously defined set of elements or element faces.

Parameters

D : keyword to denote nodal flux density data

fden : value of the flux density at the nodes. (Real)

nodes : the nodes to which the flux density is applied. These nodes must exist on the elements/faces

defined by the preceding set of element/face definitions. (Integer)







FIN : keyword to denote the end of a nodal flux density block

Notes

1. To define a region of non-uniform pressure, a set of one or more elements or element faces is defined. The set of element/face data is terminated by a FIN keyword. This is immediately followed by a set of nodal flux density values which must be sufficient to completely define the flux density field over the selected elements/faces. The nodal flux density data is also terminated by a FIN keyword, unless it is the final set in which case it is terminated by an END keyword.

2. Regions of uniform flux density and non-uniform flux density may be mixed in any order.

D

nrep inode

FIN

RP

RRP nrrep iinode

//nodes//fden



3. For surface flux, a face of a panel or a face of a brick is defined by any 3 corner nodes on the face. For TXT6 and QXT8 a face is defined by the 3 nodes forming the loaded edge. For TXT3 and QXT4 a face is defined by the two nodes forming the loaded edge and any other node on the element. Here, the flux density has unit flux per unit area.



4. For internal flux, a brick element is defined by any 4 corner nodes on the element. The nodes must not all lie on one face. For membrane or axisymmetric solid field elements, an element is defined by any 3 corner nodes on it. The nodes must not all lie on one edge, however. Here the flux density has unit flux per unit volume.

5. If both surface and internal fluxes are present, they must be defined in separate data blocks.

Examples

Two Uniform Flux Densities are to be applied, a surface flux density of 10 over edge 1-2-3, and an internal flux density of 20 over volume covered by 3-4-5-10-9-8. The following lines will generate the data.

FLUX DEN

* SURFACE FLUXES

V 10.0 1 2

V 10.0 2 3

* FIN TO SEPARATE SURFACE AND VOLUME FLUX DATA

FIN

* EXAMPLE OF GENERATING FLUXES ON SEVERAL FACES

* INTERNAL GENERATED FLUXES

/

V 20.0 3 4 9

RP 2 1

END

67

8 9 10

1 2 3 4 5

dv = 20 dv = 20

ds = 10



Example of a non-uniform flux density on an element. The program will assign a flux density of 7.5 to node 2 and 11.0 to node 4 by interpolation between the adjacent corner nodes.

FLUX DEN

E 1 5 7

FIN

D 5.0 1 7 8

D 10.0 3 6

D 12.0 5

END

Example of a complete block of flux density data for uniform and non-uniform volume flux densities

7 6 5

4

3 2 1

8

d = 5 d = 10 d = 12

d = 10

d = 5

d = 5

dd = 20 20

10 1015

5

13 14 15 16 17 18

7 8 9 10 11 12

1 2 3 4 5 6



FLUX DEN

V 20.0 1 2 8

V 20.0 7 8 14

FIN

//

/

E 2 3 9

RP 2 6

RRP 3 1

FIN

D 20.0 2 8 14

D 10.0 3 9 15 4 10 16

D 15.0 5 11 17

FIN

/

V 5.0 5 6 12

RP 2 6

END

5.4.15 WAVE LOAD Data

Parameters

WAVE LOA : compulsory keyword to denote start of the wave data

data : wave load data (see Appendix -M for detailed descriptions)

END : compulsory keyword to denote end of the wave data

Notes

1. Wave load data should not be defined more than once in the entire load deck. The loading specified will be applied to all load sets.

WAVE LOA

data

END



2. The wave loading generated cannot be scaled using any of the load history types. The LFUN command in the wave load data should be used instead to associate the loading with a load function.

3. SOLU procedure cannot be used when wave load is present.

4. If modification of wave environment is required during an analysis, this can be achieved by restart with modified wave data supplied.

5.4.16 TANK LOAD data

To define pressure loading on the tank walls due to action of the fluid inside a tank. The specified tank load data will be converted to pressure loads by the programe internally.

Parameters

TANK LOAD : compulsory header to denote the start of tank load data

ACCN : command keyword to denote the start of tank acceleratio data. The accelerations will apply to all following sets until antoher ACCN command is encountered.

xtrans : Translational acceleration in global X direction (Real)

ytrans : Translational acceleration in global Y direction (Real)

ztrans : Translational acceleration in global Z direction (Real)

xrot : Rotational acceleration about the global X axis (Real)

yrot : Rotational acceleration about the global Y axis (Real)

zrot : Rotational acceleration about the global Z axis (Real)

setname : ASAS set name containing elements forming the tank (up to 8 characters)

elno : User element number of an element in tank with known internal surface (Integer)

TANK LOAD

ACCN

setname

ztransxtrans

END

ytrans xrot zrotyrot

elno inface elev denfl



inface : Internal fact indicator for element elno (Integer) 1 +ve local z side is internal -1 -ve local z side is internal

elev : Z elevation of fluid surface in tank (Real)

denfl : fluid density (Real)

END : compulsory keyword to denote the end of the tank load data block

Notes

1. Both pressure and tank load data can appear in the same load case.

2. Accelerations of the tank structure are required in the ACCN data and these are equal and opposite to those experienced by the fluid. It is assumed that the accelerations for the whole tank are uniform and given by the accelerations at the centre of gravity position of the fluid in the tank.

3. The accelerations specified in an ACCN data will apply to all sets that follow the command until another ACCN command is encountered.

4. A positive gravitational acceleration must be added to the Z acceleration data (ztrans) in order to include the effect of gravity. It is assumed that gravity always acts in the global Z direction.

5. Fluid surface is assumed to remain still, i.e. sloshing effect is ignored.

6. Tank load can only be applied to shell and membrane elements as stated in Appendix A. All other element types in the set will be ignored.

7. Tank pressure loads will only be calculated for the wetted nodes (i.e. nodes that are on or below the fluid surface elevation elev).

8. A warning will be given if the element set does not form a proper tank shape. Pressure loads will still be calculated for the elements and this will enable the application of tank loading to other modelling situations, e.g. applying hydostatic pressure to a wall.

9. Each tank should only contain elements that form the surface of the tank (i.e. those that will be subjected to internal pressure). Any stiffeners modelled by shell elements must be excluded from the tank set or else pressure will be incorrectly applied to them. An error will be reported if a branched surface is encountered.

10. The tank surface must be continuous. A warning will be given if a discontinuity is encountered and only the part containing the first element will have pressure loading applied.

Example

Tank load on set ABCD, hydrostatic pressure only.



TANK LOAD

ACCN 0.0 0.0 9.81 0.0 0.0 0.0

ABCD 100 1 20.0 1025.0

END

5.4.17 LOAD Functions

The load functions must follow all other other loading data.

Load functions provide a method for applying non-proportional loads. Two basic types are available; piecewise linear and continuous. The piecewise linear type is defined as a series of ‘time-factor’ pairs. The value of the load at time ‘time’ is the reference load multiplied by the value of ‘factor’. The continuous load function types are defined in terms of mathematical functions. The value of the load at time ‘time’ is the reference load multiplied by the value of the function. Load functions must not be used if pseudo-times have been used in specifying the loading.

Parameters

LOAD-FUN : compulsory header keyword to denote the start of the load function data

lfunno : load function number. This corresponds to the load set number specified in the loading data. (Integer)

time : time. (Real)

factor : multiplying factor for load at time time. (Real)

SINU : keyword to denote continuous sinusoidal load function

A,w,p : constants in the expression Asin(wt + p) where t is time. (Real). Note: (wt + p) is in radians

lfunno time factor

END

lfunno

SINU A w p

EXPO a b

POLY c d e f

(t1) (t2)

(t1) (t2)

(t1) (t2)

RAOS (t1) (t2)

LOAD-FUN



t1 : time to start ramping up the load function (Real)

t2 : time to finish ramping up the load function (Real)

EXPO : keyword to denote continuous exponential load function

a,b : constants in the expression ae-bt where e is the base of the natural logarithm and t is time. (Real)

POLY : keyword to denote continuous polynomial load function

c,d,e,f : constants in the expression ct2 + dt3 + et4 + ft5 where t is time. (Real)

RAOS : keyword to denote a RAO load function

END : compulsory keyword to denote the end of the load function data

Notes

1. Times must be in ascending order within each load function definition.

2. Any number of lines may be used to identify a load function defined by time-factor pairs.

3. The times in the list time do not have to be identical to the list of times specified with the SOLV command. In such cases linear interpolation is used to calculate load multipliers corresponding to each time specified with the SOLV command.

4. Non-proportional loading cannot be used in conjunction with special solution techniques as defined by the SOLU command.

5. All constants (except the optional parameters t1 and t2) must be specified when using the continuous load function types SINU, EXPO and POLY.

6. For the special load function types, the load factor applied will be scaled by a ramping factor R. This factor takes the following value:

R = 0.0 if t < t1

R = (t-t1) / (t2-t1) if t1 ≤ t ≤ t2

R = 1.0 if t > t2

R = 1.0 if both t1 and t2 are not specified

Additional Mass Data ASAS (Non-Linear) User Manual


5.5 DIRECT Mass Input Data

To define mass on the structure in addition to that implied by the elements. The direct mass data consists of one Direct Mass input header, followed by the mass data. The data consists of an input type header followed by the appropriate data.

Parameters

DIRE : compulsory header keyword to denote the start of the Direct Mass data

LUMP : keyword for lumped added mass input

END : compulsory keyword to denote the end of each block of Direct Mass data

5.5.1 UNITS command

If global units have been defined using the UNITS command in the Preliminary Data (see Section 5.1.42), it is possible to override the input units locally by the inclusion of UNITS command. The local units are only operational for the data block concerned and will return to the default global units when the next END command is encountered.

One or more UNITS commands may appear in a data block thus permitting the greatest flexibility in data input. The form of the command is similar to that used in the Preliminary Data.

Parameters

UNITS : keyword


DIRE

mass

END

dof nodes

LUMP ADDED MA

(mtype)

UNITS unitnm



Notes

1. The mass unit is not defined explicitly, but is derived from the force and length unit currently defined. In order to determine the consistent mass unit the force and length terms must both be either metric or imperial. Valid combinations are shown in Table 3.1.

2. Force, length, and angular unit may be specified. Only those terms which are required to be modified need to be specified, undefined terms will default to those supplied on the global units definition unless previously overwritten in the current data block.

3. For a list of valid unit names see Section 5.1.42.1.

5.5.2 LUMP ADDED MASS Data

To define the lumped mass input.

Parameters

LUMP : compulsory header keyword to denote the start of lumped mass data

ADDED MA : keyword to define that the following mass terms are to be added to any element mass

mtype : optional keyword defining the mass usage L - mass for load calculation only M - mass for mass calculation only If omitted (default), the mass will be included in all calculations.

mass : value of the lumped mass. (Real)

dof : freedom name to define the direction in which the mass is active. See Appendix -F

nodes : list of node numbers to which the mass is applied. (Integer)

mass

nrep inode

END

RP

RRP nrrep iinode

dof //nodes//

LUMP ADDED MA

(mtype)









END : compulsory keyword to denote the end of the lumped mass data block

Notes

1. Whether or not the mass of any particular element is included depends on the setting of the mass flag in the element topology data.

2. Freedom name TRA may be used to assign the mass to the X, Y, Z freedoms at the nodes. Freedom name ROT may be used to assign the mass to the RX, RY, RZ freedoms.

3. If a node is skewed in Boundary Condition data, any added lumped mass terms input for that node are

assumed to be in the skewed directions.

Initial Conditions Data ASAS (Non-Linear) User Manual


5.6 Initial Conditions Data

These data blocks allow the user to define the initial residual stress state of the elements and the initial nodal displacements and velocities for a transient dynamic analysis. This data is optional.

The following data blocks are available

Residual initial stresses ............ ................ ................ see Section 5.6.2

Residual initial stresses for stiffeners ........ ................ see Section 5.6.3

Initial conditions ...... ................ ................ ................ see Section 5.6.4

5.6.1 UNITS Command

If global units have been defined using the UNITS command in the Preliminary data (Section 5.1.42), it is possible to override the input units locally by the inclusion of a UNITS command. The local units are only operational for the data block concerned and will return to the default global units when the next END command is encountered.

In general, one or more UNITS commands may appear in a data block thus permitting the greatest flexibility in data input. The form of the command is similar to that used in the Preliminary data.

Parameters

UNITS : keyword


Notes

1. Force, length and angular unit may be specified. Only those terms which are required to be modified need to be specified, undefined terms will default to those supplied on the global units definition unless previously overwritten in the current data block.

2. The default angular unit for all load types is radians


UNITS unitnm



5.6.2 RESIDUAL Initial Stresses

This data defines a residual stress state from which the analysis is initiated. Optional.

Parameters

RESI : compulsory header keyword to denote the start of the residual initial stress data

ALL : keyword to indicate that all integration points for element elno have the same residual initial

stress values

inptno : integration point number to which the following residual initial stresses apply. (Integer)

rstval : residual initial stress values, the number of which depend upon the element type. See table below.

(Real)

elno : element number to which the residual initial stress values apply. (Integer)



ielem : element number increment to be added each time the data is generated by the RP command.

(Integer)



iielem : element number increment to be added each time the data is generated by the RRP command.

(Integer)

RESI

ALL

inptno

RP nrep ielem

END

rstval //elno//

RRP nrrep iielem



END : compulsory keyword to denote the end of the residual initial stress data

Notes

1. The number of stress components (NST) for different element types and their orders are given in the following table:

Element type NST Location in vector 1 2 3 4 5 6

Uniaxial 1 XX - - - - -

Plane Stress 3 XX YY XY - - -

Plane Strain 4 XX YY XY ZZ - -

Axisymmetric 4 RR ZZ HH RZ - -

3-D solids 6 XX YY ZZ XY YZ ZX

Thick beams, STF4 3 XX XY(XT)* XZ(-)* - - -

Shells 5 XX YY XY XZ YZ

* for tube or box sections, XT is the tangential shear stress component

2. The stresses are defined in the stress output axis system as specified in Appendix -A.

5.6.3 RESIDUAL Initial Stresses for Stiffeners WST4 and SST4

This data defines the residual axial stress for stiffener elements. Optional.

The residual stress is read in for two end nodes of the element and all median points of the cross-section. For details of median points see Geometric Property Data, see Section 5.2.5.1.

Stresses are interpolated from element end nodes to Gauss points and from median points to segment integration points. A linear interpolation is used in both cases.



Parameters

RESD : compulsory header keyword to denote the start of the residual initial stress data for stiffeners

WST4 and SST4

ND1 : keyword to indicate that the following residual stress values refer to node one

ND2 : keyword to indicate that the following residual stress values refer to node two

ALL : keyword to indicate that the following residual stress values refer to both node one and node two

rstval : list of residual initial axial stress values for each median point. (Real)

elno : element number to which the residual initial axial stress values apply. (Integer)



ielem : element number increment to be added each time the data is generated by the RP command.

(Integer)



iielem : element number increment to be added each time the data is generated by the RRP command.

(Integer)

END : compulsory keyword to denote the end of the residual initial stress data for stiffeners WST4 and

SST4

RESD

ND1

ALL

RP nrep ielem

END

rstval //elno//

RRP nrrep iielem

ND2



Notes

1. The RESD data block must follow the RESI data block if both are present.

2. If the same elements appear in both the RESD and the RESI data then the residual stress is the sum of stress from both sets of data.

3. Values of residual axial stress are assigned to cross-sectional median points in increasing number order. The number of values should not exceed the number of median points for the element cross section. Median points which are not assigned a stress value are assumed to have zero residual axial stress.

4. Free format continuations (:) may be used but, if they are used, the keywords ND1, ND2 and ALL should appear at the start of each new line.

5. For any particular element, the residual axial stress values required for both ends and for all median points must be defined at one point.

5.6.4 Initial Conditions

This data defines the initial conditions of the structure at the start of a transient dynamic or heat analysis. Optional.

Parameters

INIT : compulsory header keyword to define the start of the initial condition data for a transient dynamics

analysis

dof : a freedom code. See Appendix -F

disp : an initial displacement. (Real)

velo : an initial velocity. (Real)

INIT

disp v elo

END

dof //node//

RP nrep inode

RRP nrrep iinode

tempT //node//



T : freedom code for temperature (heat analysis only)

temp : initial temperature

node : list of node numbers at which the initial condition is applied. (Integer, 1-99999)




(Integer)




(Integer)

END : compulsory word to define the end of the initial conditions

Notes

1. If a node is skewed in the Boundary Condition data, any initial conditions specified will be assumed to be in the skewed direction.

2. If non-zero initial conditions are given, the first solution time must be time 0.0 for a new analysis and the last static solution time if it is restarted from a static job.

3. In a restart, the initial conditions specified may be total values or in addition to the previous solution. By default, total values are assumed and Option DTRS should be set if incremental values are specified.

Example

This example gives the X freedom of nodes 1,2,3,4 an initial displacement of 0.0 and an initial velocity of 1.0.

INIT

/

X 0.0 1.0 1 2

RP 2 2

END

STOP Data ASAS (Non-Linear) User Manual


5.7 STOP Command

To define the termination of the input data for this run.

Parameter

STOP : compulsory keyword

STOP

STOP Data ASAS (Non-Linear) User Manual


Running Instructions ASAS (Non-Linear) User Manual


6. Running Instructions

6.1 DATA AREA Requirement

The amount of workspace or DATA AREA specified with the SYSTEM command depends mainly on the number of elements and nodes in the model. An analysis will abort if insufficient workspace is allocated. Some of the data area (dependent on system parameters) is always reserved for the data-manager, (see next section). The default value for DATA AREA is 1000000 but a higher value may be required for very large problems. The size of the data area is defined in terms of Integer words (ie 1 word = 4 bytes). Note, the word freestore is often used in place of data area, but both terms have the same meaning.

6.2 Data-Manager Parameters

Parameters that control the operation and efficiency of the data-manager are set by default. They are normally adequate for most analyses, but may be insufficient for large analyses. In this case a re-analysis must be performed and default system parameters re-set using the Preliminary Data SYSPAR command. Default values for the system parameters are given in Table 6.1.

A certain amount of the workspace (LPGSIZ*MINPAG) is always reserved for the data-manager from the data area allocation defined with the SYSTEM command. Both parameters MINPAG and LPGSIZ may be increased to reduce the amount of ‘paging’ by the data-manager. This, however, will increase the demand of data area required.



System Parameter Description

Default Size

SMALL MEDIUM LARGE

LPGSIZ Data-manager pagesize 256 512 1024

MINPAG Minimum page reserve for data-manager

10 10 10

MANREC Default length of sub-index 335 335 335

LTPAGE Maximum length of page directory 65535 65535 65535

NOPAG Solution Blocking Factor 10 1 10 1 10 1

1. NOPAG will be automatically reduced if there is insufficient freestore available.

Table 6.1 System Parameters



Default Name Type Description Can Name be Overwritten?

ZZZOARCH External Old Archive file Yes ZZZNARCH External New Archive file Yes ZZZOSTIF External Old Stiffness file Yes ZZZNSTIF External New Stiffness file Yes ZZZPORTF External Porthole file Yes ZZZMODEL External PATRAN/FEMVIEW Neutral

file Yes

pnamJF** External Project journal file No INCRJF External Analysis journal file No

Default Name Default Status Default Attribute Deleted on

Successful Completion?

May be Overwritten?

ZZZOARCH Unset Append No Yes* ZZZNARCH New Append No No ZZZOSTIF Old Append No Yes* ZZZNSTIF New Append No No ZZZPORTF New Append No No ZZZMODEL New Append No No pnamJF** Old Append No No INCRJF Old Append No* No

* Upon request by user

** pnam is the project name

Note

First three letters of each file name may vary from installation to installation.

Table 6.2 External Files

6.3 File Status

The names, types and contents and default attributes of all internal and external files are given in Table 6.2.

The user is cautioned that conflicts can arise if default names are used, due to files with the same name remaining from previous runs. It is recommended that files are explicitly named.

The types, names and dispositions of all files used in an analysis are listed in the output files under the heading FILE STATUS. Table 6.3 contains a list of possible dispositions.



Mnemonic Action

DEL Deleted

OPEN Open

CLSE Closed, but not deleted

Table 6.3 Dispositions of Internal and External Files

6.4 Warnings and Errors

Errors resulting in unsuccessful analyses may result for a variety of reasons:

Data Errors

Insufficient Data Area Allocated to the Program

Backing Files Not Open Correctly

System Parameters Insufficient for Analysis

Most errors result in a controlled exit, a system abort message, a sub-routine traceback indicating the subroutine in which the program halted and a message describing the error.

Data problems with the user may result in either error or warning messages. An error message indicates a problem that prevents satisfactory execution of the analysis. In this case, the job will terminate after the stage where errors are reported. Warnings indicate problems or inconsistencies with the data, but which can still allow successful analysis. In this case the analysis will terminate before the main analysis unless the option GOON is given with the preliminary data OPTION command.

Messages such as:

ERROR FOR UNIT 8 NAME ZZZOARCH, MODE 3, DISPOSITON 1, STATUS 0

indicate an error in opening a file (ZZZOARCH for example). Table 6.4 indicates the various possible values for Mode, Disposition and Status.

Occasionally large analyses may fail because the default system parameters are insufficient for the analysis (see Section 6.2).

Parameter Value Description

MODE 1 3

Existing File New File

DISPOSITION 1 2 3

STATUS various Machine dependent error code. See specific machine documentation



Table 6.4 Mode, Disposition and Status of Files

If a premature exit is made from ASAS-NL, then there will be an internal file called pnamJF (pnam is the project name), created which indicates the stage the program had reached when the exit was made. The different stages are given in Table 6.5.

Stage Number Description

1 Read and echo data. Preliminary checking

2 Check and print data

3 Determine the parameters for solution process

4 Main analysis

Table 6.5 Stage Numbers for ASAS-NL

If a premature exit is made within the main analysis (i.e. stage 4), a journal file called INCRJF will also be saved indicating the current increment and iteration being analysed when the exit was made.

6.5 Running Instructions

The program ASAS-NL is required to run an ASAS-NL analysis. In addition, if a restart is attempted, the data-manager oldarchive file and stiffness matrix oldarchive file must be present in the default directory (these files are named with the FILE commands).

The instructions to run ASAS-NL have been kept to a minimum with all file assignments being initiated from within the program as the run proceeds.

The PC version of ASAS-NL is run as a Windows process. The program is issued with an accompanying icon which may be displayed on the main Windows desktop. There are three ways in which a program may be run

1. Click on the Program Icon

By clicking on the program icon, the following form will be displayed:



The data file name may be identified by clicking on the Browse button. A file structure will be displayed from which the data file may be identified. Double clicking on the file will place it in the Data File Name display box. Alternatively, the data file name and its path may be typed in the display box. By default, the analysis will be run in the directory defined by the path to the data file.

Command line parameters can be defined in this display box. The following parameters may be used to define the location of files:

/DATA= will define the name of the data file and, optionally, its location. By default .dat will be appended if no file extension is given.

/OUT= will define the name of the results file and, optionally, its location. By default this will be set to the data file prefix appended with .out, e.g. for an input file of hull.dat the results file will be hull.out.

/PATH= will define the path to the data and results file. This will be used if there is no path defined on /DATA= or /OUT=

/BACK= will define the directory in which the analysis is to be run. This may be different from the location of the data and results files.

/CLEAR will clear the dialog window. The default is for it to remain in position at the end of the run.

/LOCK will write a lock file. This may be interrogated with the WAITLOCK process to determine when the process has completed. See note below.

/EXPAND will expand all @ files, resolves all IF/THEN/ELSE references, and carries out all data replacements (see below). This generates a new data file with a .exp extension. Note that the use of /EXPAND does not run the program itself, rather it is a pre-processor for generating expanded data.

Parameters must be separated by a space on the command line.

To start the analysis, click on the OK button. This will display a dialog window similar to that shown below:



At the end of the run a message is displayed that the analysis has completed and requests an Exit confirmation. Clicking on ”Yes” or pressing the enter key on the keyboard will close the dialog window. Clicking on ”No” will allow the window to be processed according to the command buttons. Note that the use of /CLEAR automatically closes the dialog window when the analysis has completed.

2. Drag and Drop

Using Windows Explorer, a data file may be dragged and dropped on the program icon. This will automatically initiate the analysis in the directory of the data file. To run ASASNL, drop the data file onto the ASASNL icon.

3. Using a Windows Command Prompt

The program can be run in a Windows Command Prompt using a command of the form: asanl DataFileName or asasnl /DATA=DataFileName /OUT=ResultsFileName [/parameter] assuming the directory where the program is installed (e.g. c:\asash) in on the path correctly. The optional /parameter equates to any of the valid command line parameters given above e.g. /CLEAR, /PATH=c:\asash\test.



Typing the program name on its own is equivalent to clicking on the program icon as described above.

It is not now possible on the PC to use the redirect symbols < and > to define data and results files.

Running ASAS-NL from batch files on PCs

As ASAS-NL now runs as a process, it may not be possible for a number of jobs to be run consecutively. This is because when a command is issued to start an ASAS-NL run, the process begins and control may return immediately to the DOS shell or the .BAT file. So, if a .BAT file is being used, as each process begins, control is returned to the file and the next command is executed.

This has been overcome in the ASAS suite of programs with the use of a LOCK file. If the /LOCK parameter (see above) is used, a file called $_$_LOCK is created. A program WAITLOCK has been written that can then be run following an ASAS program. This program will wait until the LOCK file has been deleted, which occurs when the preceding ASAS run completes. When the LOCK file has been deleted, WAITLOCK itself completes and allows the next command to be executed.

Example Batch File

ASASNL hull /LOCK

WAITLOCK

6.6 ASAS Initialisation File

The ASAS initialisation file allows the user to define the default file extensions to be used. The file is called asas.ini. There are three locations in which the file may be stored. These are searched in the following order:

1. In the current directory

2. In a directory pointed to with the environmental variable ASAS_INI.

3. In a directory pointed to with the environmental variable ASAS_SEC.

Currently, the following data items may be defined in the asas.ini file.

The first line must be [General] starting in column 1.

The next lines may be one or more of the following, all starting in column 1:

Default_input_extension=ext where ext is the user’s preferred extension for the input file. Default is .dat

Default_output_extension=ext where ext is the user’s preferred extension for the output file. Default is .out



Noclobber=on (or ON or On) prevents the output file from being overwritten if it already exists in the current directory.

The two default extensions will only be used if no extension is given for either input or output files on the command line, eg

asasnl.exe hull

The output default extension will also be used if the input file name is specified with an extension and no output file is specified on the command line, eg

asasnl.exe hull.dat

6.7 Extended Syntax in Data Files

6.7.1 IF/THEN/ELSE

ASASNL data is often very similar for several runs. Differences can occur when data is used for linear and dynamic analysis, when two similar components are being created or different loading is required in a series of runs. These similarities will vary for each different user.

The IF/THEN/ELSE feature allows the user to create a path through a data file conditional upon one or more pieces of key data on the command line or embedded within the data.

This feature is best described with an example of a linear and a natural frequency run.

The three columns below describe the two separate sets of data, and then how they can be merged together.

Static Data Transient Data Merged Data job stat job tran if static then

job stat else job tran endif

project test project test project test options nobl options nobl options nobl save new 1. 2. 3. 4. if static then

else save new 1. 2. 3. 4. endif

coor, elem, mate, geom supp, disp, load

coor, elem, mate, geom supp, disp, load

coor, elem, mate, geom supp, disp

resi if static then



else resi endif

stop stop stop

Note: In this example, coor, elem, load, etc represent complete sets of data.

The command line to run this data would be either:

asasnl.exe hull /static for a static run

or

asasnl.exe hull /#static for a transient run

Thus any parameter after a /, except the reserved parameters listed in section 6.5, is treated as a logical parameter. This takes the value true if on its own, or false if preceded by #.

This has been extended to allow for testing against a value, as in the following example:

Static Data Transient Data Merged Data job stat job tran if save#tran then

job stat else job tran endif

project test project test project test options nobl options nobl options nobl save new 1. 2. 3. 4. if save=tran then

save new 1. 2. 3. 4. else endif

etc etc etc

The command line to run this data would be either:

asasnl.exe hull /save=tran for a transient run

or

asasnl.exe hull for a static run

Thus the parameter following / may be of the form:



/param param is true when encountered in the data

/#param param is false when encountered in the data

/param=value param is true in the data if it equals value

/param#value param is false in the data if it does not equal value

Any parameters not defined on the command line are assumed to be false.

Then in the data, the test following IF and ELSEIF is

IF param THEN the lines of data following are used if param is true

IF #param THEN the lines of data following are used if param is false

IF param=value THEN the lines of data following are used if param equals value

IF param#value THEN the lines of data following are used if param does not equal value

The full sequence of possible IF/THEN/ELSE statements is:

IF logical1 THEN

these lines are used if logical1 is true

ELSEIF logical2 THEN


ELSEIF logical3 THEN


ELSE

these lines are used if none of the above is true

ENDIF

The ELSE command is not mandatory, but if it is omitted, then there could be situations when none of the lines is used between the IF and ENDIF.

There is no limit to the number of ELSEIF statements. Nesting up to five levels may be used.

Note that it is important that there must be no embedded spaces in the parameter test.



6.7.2 DATA REPLACEMENT

Specified character strings in the data may be replaced with values defined on the command line.

Consider the following data file:

job stat project %proj options nobl end coor, elem, mate, geom, supp, disp decks load 1 case 1 Point load of %load nodal lo z %load 200 end stop

Then the command line would be, for example:

asasnl.exe hull %proj=a001 %load=5000

When interpreting the data, each time %proj was encountered, it would be replaced by the characters a001, and %load replaced by the characters 5000.

To maintain compatibility between UNIX and the PC, the $ may be used instead of %. The two characters are completely interchangeable and the existence of one implies also the existence of the other. Thus the command line could be: asasnl.exe hull $proj=a001 $load=5000

It should be noted that if any of the replacement strings is not satisfied in a data file a warning will occur for each one. Processing will continue, but there will probably be errors in the data where the unsatisfied replacement strings are being interpreted.

6.7.3 The DEFINE Command

The command line data may be embedded within the data file itself by using a DEFINE command. This has the same effect as setting logical values on the command, but they can change during the processing of the file. For example:

define %proj=a001

define %load=5000

job stat

project %proj

options nobl



end

etc

When the data is interpreted, the replacement strings would take the values as on the define lines. However, they may be overridden by a different value on the command line. The command line value takes precedence if a string replacement is used on a command line and also on a DEFINE command. Thus, if the command line had been:

asasnl.exe hull %proj=a002

then the project would have been interpreted as project a002 instead.

The DEFINE commands do not have to be placed at the start of the data file. They may occur anywhere prior to the first use of the parameter.

6.8 Secondary Data Files within ASAS-NL Data

The command @filename may appear anywhere in a data file. When such a command is encountered, the input of data switches to the file filename and data continues to be read from that file until either the end-of-file is reached or an @ command is encountered in the secondary file.

When the end of the secondary file is reached, that file is closed and input switches back to the previous data file. If, however, an @ command is found in the secondary file, input switches to yet another file. This process can continue until a maximum of 5 secondary files are open simultaneously.

6.8.1 Use of @filename command

There are many ways in which such a facility can be used, some examples of which are listed below.

(a) The user may prepare each data block in a separate file and these files may then be referenced by a simple

main datafile which consists of @ commands only.

For example, hull.dat may contain the lines

@prelim.dat

@phase1.dat

@phase2.dat

@load.dat

phase1.dat may then contain

@coor.dat

@elem.dat

@mate.dat

@geom.dat



Finally, coor.dat contains the coordinate data

elem.dat contains the element data

etc.

(b) The user may prepare his data as in example (a) above but may have a number of variants of some of the

data blocks, for example, geometry data, support data and load data.

A number of small data files containing @ commands can be prepared to pull together the various data

blocks in whatever combinations may be required.

(c) The user may have a block of data, such as some loading data which he needs to repeat in a number of

different loadcases. If these data are stored in a file, for example pressure.dat, they may be read at

any point by including a command @pressure.dat.

(d) On some computers, the file editors may not handle very long files conveniently. In such cases the data

file may be split into convenient sections for editing without the need to recombine into one file before

the analysis run.

6.8.2 Notes about the @ Command

1. The filename on the @ command line may be up to 79 characters long . This name may include the path name to the directory as well as the filename.

Examples of the @ command

(a) @coor.dat - switch to file coor.dat

(b) @ coor.dat - spaces are allowed between @ and filename

(c) @/asasdata/coor.dat - an absolute path (/asasdata) is included

(d) @bridge/coor - reference to a subdirectory (bridge) is included

(e) @h:\data\coor - reference to a different drive and directory on a PC

(f) @..\data\coor - reference to a directory relative to the current directory

2. @ may be nested to a depth of 5 secondary files open at any one time in addition to the main data file.

3. A secondary file is closed when the end-of-file is reached whereupon control returns to the line following the @ command in the higher level data file.



4. Any one file may be opened several times in one run using @ commands, provided that it has been closed before being accessed for a second time. Conversely, no file may be opened more than once within a given nesting of @ commands. (Recursion is

not allowed).

5. A secondary file which contains all or part of the preliminary data must not also contain any other data, such as coordinates or elements. Such a secondary file must terminate at or before the END command for the preliminary data.

6.9 Soft Halt Facility

There may be occasions when it is desirable to halt an analysis before all increments have been completed. This may be achieved by creating a file named ZZZSHALT in the directory in which the program is running. At the completion of each increment, ASASNL checks for the existence of this file and terminates accordingly.

Appendix A ASAS (Non-Linear) User Manual

Page A-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - A Element Description Sheets

A.1 Facilities Available for each Element Type

This Appendix contains a detailed description of each of the finite element types within ASAS-NL, arranged in alphabetical order. They can be grouped as follows:

Stress/structural elements

Uniaxial FLA2

Plane Strain/Plane Stress TRM3, QUM4, TRM6, QUM8

Axisymmetric Solid TRX3, QUX4, TRX6, QUX8

3-D Solid BRK6, BRK8, BR15, BR20

3-D Laminated Solid LB15, LB20

Shell/Plate QUS4, TCS6, TCS8, TCS9

Beam/Stiffener STF4, BEAM, BM2D, BM3D, TUBE

Beam/Stiffener of arbitrary SST4, WST4

(open) cross-section

Gap GAP2, GAPX, GAPR

Spring/Dashpot SPR1, SPR2

Rigid surface interface RGX3, RGX4, RG23, RG24

Linespring LSP3, LSP6

Field elements

Uniaxial FAT2, FAT3

2-D Plane TMT3, QMT4, TMT6, QMT8

Axisymmetric Solid TXT3, QXT4, TXT6, QXT8

3-D Solid BRT6, BRT8, BT15, BT20



The following chart summarises the facilities available to each element.

Following the chart is a description of rigid offsets for beams.

Appendix A

Page A-4

ASA

S (N

on-Linear) User M

anual

Elem. Type

Material Models

Large Disp.

Tangent Stiffness

Mass Matrix

Skew Sys.

Default Int. Rule

Elastic Plastic Fail Creep Iso. Hype

. Aniso/ Orth/ Wove

n

Lami. Field von Mises

Tresca Mohr/Dru

c

Tension

Cut-off

Ivanov Spring Coul. Frict.

Kine. Hard.

von Mises

Geom. Stiff

Cent. Stiff

Press. Stiff

BEAM ♦ ♦ ♦ ♦ ♦ ♦

BM2D ♦ ♦ ♦ ♦ ♦ ♦

BM3D ♦ ♦ ♦ ♦ ♦ ♦

BRK6 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 1x1x2

BRK8 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 2x2x2

BRT6 ♦ 1x1x2

BRT8 ♦ 2x2x2

BR15 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 1x3x2

BR20 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 2x2x2

BT15 ♦ 1x3x2

BT20 ♦ 2x2x2

FAT2 ♦ 1x1x1

FAT3 ♦ 2x1x1

FLA2 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦

GAP2 ♦ ♦

GAPR ♦ ♦

GAPX ♦ ♦

LB15 ♦ ♦ ♦ ♦ ♦ ♦ ♦ 1x3x1 per layer

LB20 ♦ ♦ ♦ ♦ ♦ ♦ ♦ 2x2x1 per layer

LSP3 ♦ ♦ 3x1x1

LSP6 ♦ ♦ 3x1x1

QMT4 ♦ 2x2

QMT8 ♦ 2x2

QUM4 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 2x2

QUM8 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 2x2

QUS4 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 1x1x3

QUX4 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 2x2

QUX8 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 2x2

Table A.1 Facilities available to each element type

Appendix A

Page A-5

ASA

S (N

on-Linear) User M

anual

Elem. Type

Load Types

Nodal Loads

Presc. D,V,A

Press. Loads

Dist. Loads

Temp.

Loads

Face Temp

.

Cent. Loads

Body Force

s

Ang. Acce.

Tank Loads

Nodal Flux

Presc. Field

Flux Dens.

BEAM ♦ ♦ ♦ ♦ ♦ ♦ ♦

BM2D ♦ ♦ ♦ ♦ ♦ ♦ ♦

BM3D ♦ ♦ ♦ ♦ ♦ ♦ ♦

BRK6 ♦ ♦ ♦ ♦ ♦ ♦ ♦

BRK8 ♦ ♦ ♦ ♦ ♦ ♦ ♦

BRT6 ♦ ♦ ♦

BRT8 ♦ ♦ ♦

BR15 ♦ ♦ ♦ ♦ ♦ ♦ ♦

BR20 ♦ ♦ ♦ ♦ ♦ ♦ ♦

BT15 ♦ ♦ ♦

BT20 ♦ ♦ ♦

FAT2 ♦ ♦

FAT3 ♦ ♦

FLA2 ♦ ♦ ♦ ♦ ♦ ♦

GAP2 ♦ ♦

GAPR ♦ ♦

GAPX ♦ ♦

LB15 ♦ ♦ ♦ ♦ ♦ ♦ ♦

LB20 ♦ ♦ ♦ ♦ ♦ ♦ ♦

LSP3 ♦ ♦

LSP6 ♦ ♦

QMT4 ♦ ♦ ♦

QMT8 ♦ ♦ ♦

QUM4 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦

QUM8 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦

QUS4 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦

QUX4 ♦ ♦ ♦ ♦ ♦ ♦ ♦

QUX8 ♦ ♦ ♦ ♦ ♦ ♦ ♦

Table A.1 Facilities available to each element type (cont.)

Appendix A

Page A-6

ASA

S (N

on-Linear) User M

anual

Elem. Type

Material Models

Large Disp.

Tangent Stiffness

Mass Matrix

Skew Sys.

Default Int. Rule

Elastic Plastic Fail Creep Iso. Hype

. Aniso/ Orth/ Wove

n

Lami. Field von Mises

Tresca Mohr/Dru

c

Ivanov

Spring Coul. Frict.

Kine. Hard.

von Mises

Geom. Stiff

Cent. Stiff

Press Stiff

QXT4 ♦ 2x2

QXT8 ♦ 2x2

RGX3 ♦ ♦ ♦ ♦ 2x1x1

RGX4 ♦ ♦ ♦ ♦ 3x1x1

RG23 ♦ ♦ ♦ ♦ 2x1x1

RG24 ♦ ♦ ♦ ♦ 3x1x1

SPR1 ♦ ♦ ♦

SPR2 ♦ ♦ ♦

SST4 ♦ ♦ ♦ ♦ ♦ ♦ ♦

STF4 ♦ ♦ ♦

♦ ♦ ♦ ♦ ♦ ♦ ♦

2x3x3 Rect 2x8x1 Tube

2x12x1 Box

TCS6 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 1x3x3

TCS8 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 2x3x3

TCS9 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 2x3x3

TMT3 ♦ 1x1

TMT6 ♦ 1x3

TRM3 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 1x1

TRM6 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 1x3

TRX3 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 1x1

TRX6 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 1x3

TUBE ♦ ♦ ♦ ♦ ♦

TXT3 ♦ 1x1

TXT6 ♦ 1x3

WST4 ♦ ♦ ♦ ♦ ♦ ♦ ♦


Appendix A

Page A-7

ASA

S (N

on-Linear) User M

anual

Elem. Type

Load Types

Nodal Loads

Presc. D,V,A

Press. Loads

Dist. Loads

Temp. Loads

Face Temp.

Cent. Loads

Body Forces

Ang. Acce.

Tank Loads

Nodal Flux

Presc. Field

Flux Dens.

QXT4 ♦ ♦ ♦

QXT8 ♦ ♦ ♦

RGX3 ♦ ♦

RGX4 ♦ ♦

RG23 ♦ ♦

RG24 ♦ ♦

SPR1 ♦ ♦

SPR2 ♦ ♦

SST4 ♦ ♦ ♦ ♦ ♦

STF4 ♦ ♦ ♦ ♦ ♦ ♦ ♦

TCS6 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦

TCS8 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦

TCS9 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦

TMT3 ♦ ♦ ♦

TMT6 ♦ ♦ ♦

TRM3 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦

TRM6 ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦

TRX3 ♦ ♦ ♦ ♦ ♦ ♦ ♦

TRX6 ♦ ♦ ♦ ♦ ♦ ♦ ♦

TUBE ♦ ♦ ♦ ♦ ♦ ♦ ♦

TXT3 ♦ ♦ ♦

TXT6 ♦ ♦ ♦

WST4 ♦ ♦ ♦ ♦ ♦

Notes

1. Elastic material data must be supplied.

2. The geometric stiffness is invoked by directive LARGe with the Problem or Group Title commands. The centrifugal stiffness is included by default if the structure is spinning. Symmetrized load stiffness is included by default if the structure is subject to pressure loading.




A.2 Element Axes Systems

All elements have some form of local element axes system associated with them. These are used for the purpose of defining material axes and element related loading and also for the calculation and display of stress results. For some elements the global axes system is used as the element local axis system. All other elements have a local system (as defined in the element description sheets which follow) normally based on the order in which the element nodes are specified in the element topology data. The general rules used for defining the local axes for elements of certain types are outlined in the following sections.

It must be noted that adjacent elements not using the global axes system can have a completely different orientation of local axes system. For this reason the nodal stress/force results on adjacent elements may not be averaged directly but must be re-orientated into a consistent axes system first. This type of re-orientation may be conducted for the shell elements by the post processor POSTNL.

A.2.1 Local Axes on Beam Elements

The beam elements have the local X direction along the axis of the beam from the first node towards the last node. The local Y and Z axes are normal to the beam axis and defined according to element specific rules (as described in the individual element description sheets). For beam element types BM3D and TUBE the local Y and Z directions may be explicitly defined in the geometric property data for the element by specifying the plane containing the local Y or Z direction. For a TUBE element, the local axis definition may be omitted, in which case a default local axis system is used. See TUBE element description sheets.

The planes of the local Y and Z axes may be defined by one of the following methods:

COOR command (Default) This gives the coordinates of a point in the local XY plane with the local Y axis positive towards this point

from end 1 of the element. If command XZ is also present, the point defines the local XZ plane with local

Z positive towards the point.

NODE command This works in the same way as for COOR except that the node number of a point with the required

coordinates is given.

BETA command This gives an angle through which the default local Y and Z axes are to be rotated about the element local

X axis. The default axes for BM3D assume the coordinate point in the local XY plane (XZ plane if

command XZ is present) to be the origin, and for the TUBE are as given when the coordinate point is

omitted.

GPOS, GNEG commands This gives an axis X,Y or Z which will be taken as a vector lying in the required local XY plane. The

GPOS or GNEG keyword gives the positive or negative global direction as defining the positive direction

for the local Y axis so defined. If command XZ is also present, then the vector lies in the required local XZ

plane and the GPOS or GNEG defines the direction for the positive local Z axis.



SPOS, SNEG commands This gives a skewed X,Y or Z axis, which will be taken as a vector lying in the required local XY plane.

The SPOS or SNEG keyword and the skew system integer gives the positive or negative skewed global

direction as defining the positive direction for the local Y axis so defined. If command XZ is also present,

then the vector lies in the required local XZ plane and the SPOS or SNEG defines the direction for the

positive local Z axis.

VECT command This gives the coordinates of a point defining a vector from the origin, lying in the required local XY plane

with the local Y axis positive in the direction of the vector. If command XZ is also present, then the vector

defines the required local XZ plane with the local Z axis positive in the direction of the vector.

These are shown diagrammatically in the following table.

For a further description of data formats see Section 5.2.5.5.



node1

node2X'

Z'(10,20,0)

COOR 10 20 0 [XY]

node1

node2X'

Z'(10,20,0)

COOR 10 20 0 XZ

Y'

Y'

node1

node2X'

Z'NODE 501 [XY]

Y'

node1

node2X'

Z'

NODE 501 XZ

Y'

501 501

node1

node2X'

Z' BETA 35 [XY]

Y'

β�=35°�

default Y'default Z'

β�

node1

node2X'

Z'

BETA 35 XZ

Y'

β�=35°�

default Z'

node1

node2X'

Z'

GPOS Y [XY]

Y'

Y

Z

X

node1

node2X'

Y'

GNEG Y XZ

Y'Y

Z

X

Z'

node1

node2X'

Z'

SNEG 1 Z [SY]

Y'

Y

Z

XYs Xs

Zs

node1

node2X'

Z'

SPOS 1 X XZ

Y'

Y

Z

XYs Xs

Zs

node1

node2X'

Z' VECT 5 4 3 [XY]

Y' |5,4,3|

node1

node2X'

Z'

VECT 5 4 3 XZ

Y'|5,4,3|

default Y'



A.3 Beam Offsets

The element types BEAM, BM2D, BM3D, and TUBE can have rigid offsets defined at each node.

It is normally assumed that a beam member has its centroidal axes lying along the line joining the two end nodes and that it is flexible throughout its length. Often, however, this is not the case. Sometimes the centroidal axis is offset from this line. It may also be appropriate when modelling the intersection of two beams at a node to consider the end portion of one of the beams to be rigid.

Rigid offsets may be defined by the OFFG, OFFS, OFSK or OFCO command in the Geometric Properties Data (Section 5.2.5). The offset command for an element occurs after the Geometric Properties commands for that element.

One command is required for each set of geometric property data which describes a member with offsets

An offset beam element has two local axis systems. Local X’,Y’,Z’ refer to the node points used to define the element and X”,Y”,Z” refer to the physical ends of the element centroidal axis after the offsets have been taken into account. If the member has no offsets then X’,Y’,Z’ and X”,Y”,Z” are coincident.

Figure A.1 Local Axes for a Beam with Offsets

A.3.1 OFFS Command

For the OFFS command, the local offsets are defined as the distances from the physical ends of the member centroidal axes to the nodes, measured in the local X’,Y’,Z’ axes system.

Positive values of the local offsets ex, ey, ez, are as shown:

Y'

Y”

X'

X”

Z”

Z'

Node1Node2

End1End 2

Y'Y”

Node 2Node1 Node 1X'

X”

eyexey

ex

ey

ez

Y'

Z'



Figure A.2 Beam Offsets Defined using OFFS

Notes

1. ex at node 2 is measured in the negative x’ direction such that a shortening at either end of the beam is given by a positive ex value.

2. The command has the keyword OFFS and the six offset values ex, ey, ez values for node 1 followed by ex, ey, ez values for node 2.

3. For BM2D element, 4 values of offset are required, ex, ey values for node 1 followed by ex ey for node 2

Example

Example of an Offset BM3D

175 BM3D 17.5 145.0 97.3 5.7

: 0.0 225.0 1107.0 0.0 0.0

: OFFS 12.7 4.3 0.0 0.0 4.3 0.0

A.3.2 OFFG and OFSK Commands

For the OFFG and OFSK commands, the offsets are defined as the distances from the nodes to the physical ends of the member centroidal axis, measured in the global or skewed global axes system.

Figure A.3 Beam Offsets Defined using OFFG or OFSK

Notes

(i) The OFFG command has the keyword OFFG and the six offset values ex, ey, ez values for node 1 followed by ex, ey, ez values for node 2.

(ii) The OFSK command has the keyword OFSK followed by a skew system integer to identify the skewed global axes system. This is then followed by 6 offset values as above.

(iii) For BM2D element, 4 values of offset are required, ex, ey, values for node 1 followed by ex, ey for node 2.

Y

Node 2

Node1Node 1

Y

X

ey

ex

ey

ey

ez

Z

ex(-ve)



Example

Example of offset beam elements.

175 BM3D 17.5 145.0 97.3 5.7

: 0.0 225.0 1107.0 0.0 0.0

: OFFG -5.0 0.0 2.0 0.0 -8.0 6.0

1 BEAM 64.2 1208.0 497.0 23.0

: OFSK 6 1.0 0.0 0.0 -1.0 0.0 5.0

A.3.3 OFCO Command

For the OFCO command, the global coordinates of the physical ends of member centroidal axes are required.

Figure A.4 Beam Offsets Defined using OFCO

Notes

1. The command has the keyword OFCO and the 6 coordinate values x,y,z for end 1 followed by x,y,z for end2.

2. For BM2D element, 4 values of coordinates are required, x,y for end 1 followed by x,y for end 2.

Example of offset BM3D

175 BM3D 17.5 145.0 97.3 5.7

: 0.0 225.0 1107.0 0.0 0.0

: OFCO 10.0 5.0 8.0 12.0 3.0 20.0

Y

Node 2

Node1

X

(x1,y1z1)

(x2,y2,z2)



A.3.4 Finite Element Description Sheets

Beams/Bars

BEAM 2 node beam with constant cross section and rigid offset and special orientations for three dimensional structures

BM3D 2 node beam with constant cross section and rigid offsets for three dimensional structures. BM2D 2 node beam with constant cross section and rigid offsets for two dimensional structures. FLA2 2 node axial element with varying cross section. TUBE 2 node circular tube element with constant cross section and rigid offsets.

Solid Elements

BRK6 6 node straight edged wedge. BRK8 8 node straight edged brick. BR15 15 node wedge. BR20 20 node brick. LB15 15 node laminate wedge. LB20 20 node laminate brick.

Axisymmetric Elements

QUX4 Axisymmetric quadrilateral solid with straight or curved edges. QUX8

TRX3 Axisymmetric triangular solid with straight or curved edges.

TRX6

Membrane Elements

QUM4 4 node quadrilateral membrane with varying thickness and plane strain options. QUM8 8 node isoparametric quadrilateral membrane with varying thickness and plane strain options. TRM3 3 node triangular membrane with varying thickness and plane strain options. TRM6 6 node isoparametric triangular membrane with varying thickness and plane strain options.



A.3.4 Finite Element Description Sheets Gap Elements

GAP2 2D/3D node-to-node interface/gap element. GAPX axisymmetric node-to-node interface/gap element. GAPR node-to-node radial interface/gap element

Beam/Stiffener Elements

SST4 curved beam/stiffener element with thin-walled open section. STF4 curved beam/stiffener with solid rectangular, tube and box section. WST4 curved beam/stiffener element with thin-walled open section including warping.

Rigid Surface Interface Elements

RGX3 rigid surface interface for use with axisymmetric elements TRX3 and QUX4. RGX4 rigid surface interface for use with axisymmetric elements TRX6 and QUX8. RG23 rigid surface interface for use with plane elements TRM3 and QUM4. RG24 rigid surface interface for use with plane elements TRM6 and QUM8.

Shell Elements

TCS6 6 node triangular element for modelling thick and thin shell applications. TCS8 8 node quadrilateral element for modelling thick and thin shell applications. TCS9 9 node quadrilateral element for modelling thick and thin shell applications. QUS4 4 node quadrilateral shell element for modelling thick and thin shell applications.

Note all elements can have laminated composite material properties

Special Elements

SPR1 Translational spring element between 2 nodes with damper. SPR2 Rotational spring element between 2 nodes with damper.



A.3.4 Finite Element Description Sheets Linespring Elements

LSP3 elasto-plastic line-spring element for use with high order shell elements for modelling surface flaws, symmetric boundary.

LSP6 elasto-plastic line-spring element for use with high order shell elements for modelling surface flaws.

Uniaxial Field Elements

FAT2 2 node uniaxial field element with varying cross-section. FAT3 3 node curved uniaxial field element with varying cross-section.

3-D Solid Field Elements

BRT6 6 node straight edged wedge. BRT8 8 node straight edged brick. BT15 15 node wedge. BT20 20 node brick.

Axisymmetric Field Elements

QXT4 Axisymmetric quadrilateral solid with straight or curved edges. QXT8 TXT3 Axisymmetric triangular solid with straight or curved edges. TXT6

2-D Plane Field Elements

QMT4 4 node quadrilateral membrane with varying thickness. QMT8 8 node isoparametric quadrilateral membrane with varying thickness. TMT3 3 node triangular membrane with varying thickness. TMT6 6 node isoparametric triangular membrane with varying thickness.



BEAM

Three-dimensional Beam Bending Element with Uniform Cross-section and Special Orientation of the Local Axes

NUMBER OF NODES 2

NODAL COORDINATES x, y, z

DEGREES OF FREEDOM X, Y, Z, RX, RY, RZ at each node

GEOMETRIC PROPERTIES A Cross-sectional area (≥ 0.0) (uniform) Iz”z” Principal moment of inertia about the local Z” axis (≥ 0.0)

Iy”y” Principal moment of inertia about the local Y” axis (≥ 0.0) J Torsion constant (≥ 0.0)

OFFSETS The OFFG, OFFS, OFSK, OFCO commands can be used to define rigid offsets at each end. For further details see Section 5.2.5.5 and Appendix A.3.

MATERIAL MODEL ELASTIC - Isotropic

PLASTIC - Stress resultant model based on generalised plastic hinge theory. Note that hinges can only form at nodes. See Appendix -B for details.

Material properties may be temperature dependent if required.

LOAD TYPES Nodal loads Prescribed displacements Temperature loads Distributed load patterns BL1, BL2, BL3, BL4, BL5, BL6, BL7, BL8 GL1, GL4, GL5, GL6, GL7 GP1, GP4, GP6, GP7 Body Forces Centrifugal Loads Angular Acceleration Wave load

MASS MODELLING Consistent Mass

Lumped Mass (used by default)

FORCE OUTPUT The forces are exerted by the nodes on the element and related to the centroidal local axes.

Axial Force X”X” at each end Transverse shears QY” and QZ” at each end Torque X”X” at each end Bending Moments Y”Y” and Z”Z” at each end

BEAM

1

2



INTEGRATION RULES There are no integration points for the element, all the necessary element matrices being formed explicitly.

BEAM



LOCAL AXES A beam element has two local axes systems. The X’Y’Z’ local axes are associated with end nodes of the element. The X”Y”Z” local axes are associated with the end points of the centroidal axis of the element, taking account of any non-zero rigid offsets.

If all offsets are zero, X’Y’Z’ and X”Y”Z” are coincident.

Geometric properties, distributed loads and output forces are all referred to the X”Y”Z” local axes.

Local X” lies along the centroidal axis from end 1 towards end 2. Local Z”

must lie in the global XY plane with +ve local Y” on the +ve side of the global

XY plane. In the special case where local Y” is also in the global XY plane,

local Y” must lie in the global Y direction. BM3D should be used for a beam

with general orientation of local Z”.

See also Section 5.2.5.5 and Appendix A.2.1.

SIGN CONVENTIONS Axial force positive for tension Shear force positive for end 2 sagging relative to end 1 Torque positive for clockwise rotation of end 2 relative to end 1, looking from end 1 towards end 2 Bending moment Positive for sagging Shear QY” +ve Shear QZ” +ve

Moment Z”Z” +ve Moment Y”Y” +ve

LIMITATIONS Length must be >0.0

REFERENCE A.1

DATA EXAMPLES ELEM

MATP 1

BEAM 9 10 3

BEAM 10 11 2

END

GEOM

2 BEAM 27.1 1469.7 1614.1 2766.9

3 BEAM 39.2 2006.3 1987.0 3124.8

END

BEAM

Y''

X''1 2

Z''

X''1 2



Two-dimensional Beam Bending Element with Uniform Cross-section, Lying in the Global XY Plane

NUMBER OF NODES 2

NODAL COORDINATES x, y Option TWOD must be specified

DEGREES OF FREEDOM X, Y, RZ at each node

GEOMETRIC PROPERTIES A Cross-sectional area (> 0.0) (uniform) Iz”z” Principal moment of inertia about the local Z” axis (> 0.0) Asy”Effective shear area (shear strain is neglected if Asy” is blank)

OFFSETS The OFFG, OFFS, OFSK, OFCO commands may be used to define rigid offsets at each end. For further details see Appendix A.3 and Section 5.2.5.




LOAD TYPES Nodal loads Prescribed displacements Temperature loads Distributed load patterns BL1, BL2, BL3, BL4, BL5, BL6, BL7, BL8 GL1, GL4, GL5, GL6, GL7 GP1, GP4, GP6, GP7 Body Forces Centrifugal Loads Angular Acceleration

MASS MODELLING Consistent Mass Lumped Mass (used by default)

FORCE OUTPUT The forces are exerted by the nodes on the element, and related to the local axes. Note that for an offset beam the forces output are related to the member centroidal axes.


BM2D

Y

X

1

2



LOCAL AXES The X’Y’ local axes are associated with the end nodes of the member. The X”Y” local axes are associated with the physical ends of the centroid of the member after taking account of any non-zero rigid offsets. If the offsets are all zero then X’Y’ and X”Y” are coincident.

Local X’ (X”) lies along the element from node 1 (end1) towards node 2 (end2). Local Z’ (Z”) must lie in the global Z direction. Local Y” forms a right handed set with local X” and local Z”

The geometric properties Iz”z” and Asy” are related to X”Y” system. Distributed loads are also in the X”Y” system.

See also section 5.2.5 and Appendix A.2.1

SIGN CONVENTIONS Axial force +ve for tension Shear force +ve for node 2 sagging relative to node 1 Bending moment +ve for sagging

Shear QY” +ve

Moment Z”Z” +ve


REFERENCE A. 1

DATA EXAMPLE ELEM

MATP 1

BM2D 9 10 3

/

BM2D 10 11 2

RP 6 1

END

GEOM

2 BM2D 27.1 1469.7

3 BM2D 39.2 2006.3 32.8

END

BM2D

Y'

X'1 2



Three-dimensional Beam Bending Element with Uniform Cross-section and any Orientation of the Local Axes

NUMBER OF NODES 2



GEOMETRIC PROPERTIES A Cross-sectional area (> 0.0) (uniform)

Iz”z” Principal moment of inertia about the local Z” axis (> 0.0) Iy”y” Principal amount of inertia about the local Y” axis (> 0.0) J Torsion constant (> 0.0)

Local Axis Definition - see Section 5.2.5.5 and Appendix A.2.1. Asy” Effective shear area for forces in Y” direction (Y” shear strain is neglected if Asy” is blank) Asz” Effective shear area for forces in Z” direction (Z” shear strain is neglected if Asz” is blank)







FORCE OUTPUT The forces are exerted by the nodes on the element, and related to the local axes. Note that for an offset beam the forces output are related to the element centroidal axes.

BM3D

1

2




BM3D



LOCAL AXES The X’Y’Z’ local axes are associated with the end nodes of the member. The X”Y”Z” local axes are associated with the physical ends of the centroid of the member after taking account of any non-zero rigid offsets. If the offsets are all zero then X’Y’Z’ and X”Y”Z” are coincident.

Local X’ (X”) lies from node 1 (end1) towards node 2 (end2). Local Y’ (Y”) lies in the plane defined by the two nodes (ends) and a third point defined in the Geometric Properties list. This third point must not lie on the X’ or X” axes. Local Y’ (Y”) lies from node 1 (end1) and is +ve towards the third point. Local Z’ (Z”) forms a right-handed set with local X’ (X”) and local Y’ (Y”).

The geometric properties A, Iy”y”, Iz”z”, Asy”, Asz” and J all refer to the X”Y”Z” system. Distributed loads are also in the X”Y”Z” system.

If a local axis definition is not supplied, a 3rd point with coordinates of 0.0, 0.0, 0.0 is assumed.

See also Section 5.2.5.5 and Appendix A.2.1

SIGN CONVENTIONS Axial force +ve for tension Shear force +ve for node 2 sagging relative to node 1 Torque +ve for anti-clockwise rotation at node 1 and clockwise rotation at node 2 looking from node 1 towards node 2 Bending moment +ve for sagging

Shear QY” +ve Shear QZ” +ve Moment Z”Z” +ve Moment Y”Y” +ve


REFERENCE A. 1

DATA EXAMPLE ELEM

MATP 1

BM3D 9 10 3

/

BM3D 10 11 2

RP 6 1

END

GEOM

3 BM3D 39.2 2006.3 1987.0 3124.8 -1.4 2.3

: -18.1 32.8 13.7

END

BM3D

Y''

X''

1 2

Z''

X''1 2



Isoparametric Brick Element with Quasi-linear Strain Variation

NUMBER OF NODES 6


DEGREES OF FREEDOM X, Y, Z at each node

GEOMETRIC PROPERTIES None

MATERIAL MODELS ELASTIC - Isotropic - Orthotropic - Woven - Anisotropic

Anisotropic matrix (C or C-1) - referred to axis system selected for output (global by default)

6 coefficients of thermal expansion αxx, αyy, αzz, αxy, αyz, αzx, referred to axis system selected for output.

- Hyperelastic

PLASTIC - von Mises, Tresca, Mohr-Coulomb, Drucker-Prager, Tension cut, yield criteria. Isotropic, Kinematic (Prager or Ziegler) or Combined Hardening.

CREEP - von Mises.

Material Properties may be temperature dependent if required.

BRK6

12

3

4 5

6

=

σxx

σyy

σzz

σxy

σyz

σzx

C1 C2 C4 C7 C11 C16

. C3 C5 C8 C12 C17

. . C6 C9 C13 C18

. . . C10 C14 C19

. . . . C15 C20

. . . . . C21

εxx

εyy

εzz

εxy

εyz

εzx



LOAD TYPES Nodal loads Prescribed displacements Pressure loads (on any face, +ve towards the element centre) Temperature loads Body forces Centrifugal loads Angular accelerations

MASS MODELLING Consistent mass (used by default) Lumped mass

OUTPUT Stresses and strains are available at integration points related to either global or local axes (global by default)

NODE NUMBERING The nodes are listed in a screw sense, clockwise or anti-clockwise, starting on a triangular face

INTEGRATION RULES 1x1x2 Gauss quadrature by default. Higher order rules by request. Appendix -G gives positions of integration points.

LOCAL AXES At any point local X’ coincides with the (straight) line L1=0 +ve in the direction 1, 2. Local Y’ lies in the triangular plane L1L2L3 +ve towards node 3. Local Z’ forms a right-handed set with local X’ and local Y’. See Appendix -G for explanation of curvilinear axes.

SIGN CONVENTIONS Direct stresses σxx, σyy, σzz +ve for tension Shear stresses σxy, σyz, σzx +ve as shown

REFERENCE A. 2

BRK6



Isoparametric Brick Element with Quasi-linear Strain Variation

NUMBER OF NODES 8







- Hyperelastic

PLASTIC - von Mises, Tresca, Mohr-Coulomb, Drucker-Prager Tension cut, yield criteria. Isotropic, Kinematic (Prager or Ziegler) or Combined Hardening.

CREEP - von Mises.


BRK8

12

34

56

78

=

σxx

σyy

σzz

σxy

σyz

σzx

C1 C2 C4 C7 C11 C16

. C3 C5 C8 C12 C17

. . C6 C9 C13 C18

. . . C10 C14 C19

. . . . C15 C20

. . . . . C21

εxx

εyy

εzz

εxy

εyz

εzx








LOCAL AXES At any point local X’ is coincident with curvilinear ξ. Local Y’ lies in the curvilinear ξη plane, +ve in the +ve η direction. Local Z’ forms a right-handed set with local X’ and local Y’. See Appendix -G for explanation of curvilinear axes.


REFERENCE A. 2

BRK8



Isoparametric Brick Element with Quasi-quadratic Strain Variation

NUMBER OF NODES 15 (6 corner, 9 mid-side)

NODAL COORDINATES x, y, z (may be omitted for mid-side nodes on straight edges). The position of each mid-side node has a tolerance of side-length/10 about the true mid-side position.






- Hyperelastic

PLASTIC - von Mises, Tresca, Mohr-Coulomb, Drucker-Prager Tension cut, yield criteria Isotropic, Kinematic (Prager or Ziegler) or Combined Hardening.

CREEP - von Mises.


BR15

=

σxx

σyy

σzz

σxy

σyz

σzx

C1 C2 C4 C7 C11 C16

. C3 C5 C8 C12 C17

. . C6 C9 C13 C18

. . . C10 C14 C19

. . . . C15 C20

. . . . . C21

εxx

εyy

εzz

εxy

εyz

εzx






NODE NUMBERING The nodes are listed in a screw sense, clockwise or anti-clockwise, starting on a triangular face at a corner node


LOCAL AXES At any point local X’ is tangential to curvilinear L1 = constant +ve in the direction 1 to 2. Local Y’ is tangential to the curvilinear L1L2L3 surface, +ve towards node 5. Local Z’ forms a right-handed set with local X’ and local Y’. See Appendix -G for explanation of curvilinear axes.


REFERENCE A. 2

BR15



Isoparametric Brick Element with Quasi-quadratic Strain Variation








- Hyperelastic

PLASTIC - von Mises, Tresca, Mohr-Coulomb, Drucker-Prager Tension cut, yield criteria. Isotropic, Kinematic (Prager or Ziegler) or Combined Hardening.

CREEP - von Mises.


BR20

=

σxx

σyy

σzz

σxy

σyz

σzx

C1 C2 C4 C7 C11 C16

. C3 C5 C8 C12 C17

. . C6 C9 C13 C18

. . . C10 C14 C19

. . . . C15 C20

. . . . . C21

εxx

εyy

εzz

εxy

εyz

εzx






NODE NUMBERING The nodes are listed in a screw sense, clockwise or anti-clockwise, starting at a corner node


LOCAL AXES At any point local X’ is tangential to and in the direction of curvilinear ξ. Local Y’ is tangential to the curvilinear ξη surface, +ve in the +ve η direction. Local Z’ forms a right-handed set with local X’ and local Y’. See Appendix -G for explanation of curvilinear axes.


REFERENCE A. 2

BR20



Isoparametric Field Brick Element with Quasi-linear Variation of Field Variable

NUMBER OF NODES 6


DEGREES OF FREEDOM T at each node


MATERIAL MODELS FIELD

PIER

Material properties can be temperature dependent if required

LOAD TYPES Nodal value related to field variable type Prescribed field variable Temperature Flux density - surface or internal

OUTPUT Fluxes per unit area (analogous to stresses) and field variable gradient (analogous to strains) are available at integration points related to either global or local axes (global by default)



LOCAL AXES At any point local X’ coincides with the (straight) line L1=0 +ve in the direction 1, 2. Local Y’ lies in the triangular plane L1L2L3 +ve towards node 3. Local Z’ forms a right-handed set with local X’ and local Y’. See Appendix -G for explanation of curvilinear axes.

SIGN CONVENTIONS Fluxes and gradients positive when in the positive axis direction.

BRT6

12

3

4 5

6



NOTES

1. Temperature loading does not produce thermal loading and does not imply prescribed temperature but

simply allows temperature dependent material properties to be specified. This is not required for heat

conduction analysis.

2. The element allows linear analysis only except for heat conduction analysis.

3. Field elements allow a variety of field problems to be analysed eg. heat conduction, fluid seepage and

electrical conduction.

See Reference A. 4A. 4A. 4, Chapter 7 for full details

REFERENCE A. 2, A. 4

BRT6



Isoparametric Field Brick Element with Quasi-linear Variation of Field Variable

NUMBER OF NODES 8





PIER


LOAD TYPES Nodal values related to the field variable type Prescribed field variable Temperature Flux density - surface or internal

OUTPUT Fluxes per unit area (analogous to stresses) and field variable gradients (analogous to strains) are available at the integration points related to either the local or global axes (global by default)



LOCAL AXES At any point local X’ is coincident with curvilinear ξ. Local Y’ lies in the curvilinear ξη plane, +ve in the +ve η direction. Local Z’ forms a right-handed set with local X’ and local Y’. See Appendix -G for explanation of curvilinear axes.

SIGN CONVENTIONS Fluxes and gradients are positive when in the positive axis direction

BRT8



NOTES







See Reference A. 4, Chapter 7 for full details


BRT8



Isoparametric Field Brick Element with Quasi-quadratic Variation of Field Variable






PIER






LOCAL AXES At any point local X’ is tangential to curvilinear L1 = constant +ve in the direction 1 to 2. Local Y’ is tangential to the curvilinear L1L2L3 surface, +ve towards node 5. Local Z’ forms a right-handed set with local X’ and local Y’. See Appendix -G for explanation of curvilinear axes.

SIGN CONVENTIONS Fluxes and gradients are positive when in the positive axis direction

BT15



NOTES









BT15



Isoparametric Field Brick Element with Quasi-quadratic Variation of Field Variable






PIER






LOCAL AXES At any point local X’ is tangential to and in the direction of curvilinear ξ. Local Y’ is tangential to the curvilinear ξη surface, +ve in the +ve η direction. Local Z’ forms a right-handed set with local X’ and local Y’. See Appendix -G for explanation of curvilinear axes.


BT20



NOTES









BT20



Straight Field Axial Element with Linear Variation of Field Variable

NUMBER OF NODES 2

NODAL COORDINATES x, y, z z should be omitted for 2D problems

DEGREES OF FREEDOM T at each node.

GEOMETRIC PROPERTIES A1 Cross-sectional area at node 1 A2 Cross-sectional area at node 2 (The cross-sectional area varies linearly between node 1 and node 2. The value A2 may be omitted for an element with uniform area A1).


PIER

CVEC

RADI


LOAD TYPES Nodal values related to the field variable type Prescribed field variable Temperature

OUTPUT Fluxes per unit area (analogous to stresses) and field variable gradients (analogous to strains) are available at the integration points related to the local axes

INTEGRATION RULE Not appropriate, explicit integration assuming constant field variable is used.

LOCAL AXES Local X’ lies along the element from node 1 towards node 2.


FAT2

1

2



NOTES








4. For heat conduction analysis, this element may be used to model convection by specifying directive FLNS

in the PROB/TITL or GROUP commands. In this case, the first material property specified will have the

meaning of a heat transfer (or film) coefficient and the length of an element will not enter into the heat flow

calculations. All FAT2 elements in the same group are so treated.

5. The convective and radiant heat transfer can be modelled directly using the CVEC and RADI material

models, respectively. The length of an element will not enter into the calculations with these 2 models.

6. The area required for the RADI model is the direct interchange area. This is defined to the product of the

geometric view factor and the emitting surface area.

REFERENCE A. 1, A. 2, A. 4

FAT2



Curved Axial Field Element with Quadratic Variation of Field Variable

NUMBER OF NODES 3



GEOMETRIC PROPERTIES A1 Cross-sectional area at node 1 A2 Cross-sectional area at node 2 A3 Cross-sectional area at node 3 (The cross-sectional area varies quadratically between node 1, node 2 and node 3. The values A2 and A3 may be omitted for an element with uniform area A1).


PIER


LOAD TYPES Nodal values related to the field variable type Prescribed field variable Temperature

OUTPUT Fluxes per unit area (analogous to stresses) and field variable gradients (analogous to strains) are available at the integration points related to the local axes

INTEGRATION RULE 2 point integration assuming linear variation of the field variable

LOCAL AXES Local X’ lies along the element axis from node 1 towards node 3.


FAT3

1

32



NOTES









FAT3



Straight Axial Element with Constant Strain

NUMBER OF NODES 2

NODAL COORDINATES x, y, z z should be omitted 2D problems

DEGREES OF FREEDOM X, Y, (Z) at each node. Option TWOD converts to 2-D form, freedoms X, Y only.

GEOMETRIC PROPERTIES There are two types of geometric properties available:

(a) Cross-sectional areas at nodes 1 and 2, no keyword required with geometric property data

A1 Cross-sectional area at node 1 A2 Cross-sectional area at node 2 (The cross-sectional area varies linearly between node 1 and node 2. The value A2 may be omitted for an element with uniform area A1).

(b) Cross-sectional areas at nodes 1 and 2 plus keyword CABL on a continuation line to invoke the conversion to a tension only (cable formulation)

A1 Cross-sectional area at node 1 A2 Cross-sectional area at node 2 (The cross-sectional area varies linearly between node 1 and node 2. The value A2 may be omitted for an element with uniform area A1).

The geometric property data required following the keyword CABL are:

Te - erection tension m - mass unit per length g - acceleration due to gravity Cd - coefficient of drag ρa - mass per unit volume for air d - cable diameter V - magnitude of wind velocity α - bearing of V from the global XZ plane β - bearing of V from the global XY plane a - load stiffness

FLA2

1

2



MATERIAL MODELS ELASTIC - Isotropic - Hyperelastic

PLASTIC - von Mises, Tresca, Mohr-Coulomb, Drucker-Prager, Tension cut, yield criteria Isotropic, Kinematic (Prager or Ziegler) or Combined Hardening.

CREEP - von Mises.


LOAD TYPES Nodal loads Prescribed displacements Temperature loads (Not valid with CABL properties) Body forces Centrifugal loads Angular accelerations

MASS MODELLING Lumped mass (used by default) Consistent mass

OUTPUT Stresses and strains are available for the centre of the element (in local axes).

INTEGRATION RULE Not appropriate, explicit integration assuming constant stress is used.

LOCAL AXES Local X’ lies along the element from node 1 towards node 2.

SIGN CONVENTION Axial stress +ve for tension.

NOTES

1. Any group containing FLA2 elements must contain only FLA2 elements.

2. The stiffness E(A1 + A2)/2L of the element can be set to E(A1 + A2)/2, thereby allowing the elastic (natural)

stiffness to be unchanged by large deformations. This is accomplished by directive FLNS using the

PROB/TITL or GROUP commands. All FLA2 elements in the same group are so treated.


FLA2



Interface/Gap Element with Sliding Capacity

NUMBER OF NODES 2


DEGREES OF FREEDOM X, Y, (Z) at each node. Option TWOD converts to 2-D form, freedoms X, Y only.

GEOMETRIC PROPERTIES GAP The initial size of the gap. (GAP ≤ 0.0 assumes an initial gap closed condition and GAP will be reset to zero internally) MUY Coefficient of friction in local Y’-direction MUZ Coefficient of friction in local Z’-direction, zero for TWOD XG X component of vector defining the gap reference axis YG Y component of vector defining the gap reference axis ZG Z component of vector defining the gap reference axis KN Normal contact stiffness factor (see note 4) KT Tangential stick stiffness factor (see note 5) KR Gap residual stiffness factor (see note 6) C Damping coefficient

MATERIAL MODELS Elastic only. K - the effective contact stiffness is given in the material property data (see note 3)

LOAD TYPES Nodal loads Prescribed displacements

OUTPUT The gap size, GAP, in the X’-direction and sliding displacements SLIDE-Y and SLIDE-Z are related to local axes. Force across the gap, Fx’x’, and frictional forces Fy’y’ and Fz’z’ are related to the local axes. STATUS refers to the status of the element at the last iteration. Both STRS and STRN should be specified using the corresponding BLOC command to obtain gap output.

GAP2

1

2



LOCAL AXES Local X’ lies along the gap reference axis (see note 1). Local Y’ lies in the global xy plane, perpendicular to local X’. (If local X’ is parallel to global z, then local Y’ lies in the global xy plane in the negative x direction). Local Z’ forms a right-handed set with local X’ and local Y’.

SIGN CONVENTIONS Force Fx’x’ tending to open gap is positive. GAP is positive if gap is open.

NOTES

1. The gap reference axis defines the direction of the gap surface, which is assumed to be in a plane

perpendicular to this axis. If this is specified as {0.0, 0.0, 0.0}, the gap reference axis will be assumed to

lie along the element from node 1 to node 2. In this case, nodes 1 and 2 must not be coincident.

2. GAP elements cannot be placed with other types of element in the same group.

3. The effective stiffness (K) required in the material property data can be estimated as E√A, where E is the

elastic modulus and A is the effective area at the contact node.

4. When the gap is closed, the normal stiffness between the two nodes is computed as KN*K. If KN ≤ 0.0 is

specified, it will be set equal to the value of the parameter GAPSTF in the PARA command (default 1000).

5. When the gap is closed and stick, the tangential stick stiffness betweeen the two nodes is computed as

KT*K. If KT ≤ 0.0 is specified, it will be set equal to the value of the parameter GAPSTF in the PARA

command (default 1000).

6. When the gap is open, a residual stiffness is used in order to maintain numerical stability. This is given by

KR*K. If KR < 0.0 is specified, it will be set equal to the value of the parameter GAPSMA in the PARA

command (default 10-8).

GAP2



Radial Gap Element with Sliding Capacity

NUMBER OF NODES 2


DEGREES OF FREEDOM X, Y, Z

MATERIAL MODELS Elastic only - the effective stiffness, K (see note 4)

GEOMETRIC PROPERTIES GAP Gap parameter (see note 2) MUY Coefficient of friction in local Y’ direction MUZ Coefficient of friction in local Z’ direction XG X component of vector defining the gap reference axis YG Y component of vector defining the gap reference axis ZG Z component of vector defining the gap reference axis KN Normal contact stiffness factor (see note 5) KT Tangential stick stiffness factor (see note 6) KR Gap residual stiffness factor (see note 7) C Damping coefficient


OUTPUT The gap size, GAP in the X’ direction and sliding displacements SLIDE-Y and SLIDE-Z are related to the local axes. Forces across the gap Fx’x’ and frictional forces Fy’y’ and Fz’z’ are related to the local axes. STATUS refers to the status of the element at the last iteration. STATUS = 1 for no contact, = 2 for contact and stick, = 5 for contact and slide. Both STRS and STRN should be specified using the corresponding BLOC command to obtain gap output.

LOCAL AXES Local Z’ axis is the gap reference axis (see note 3). Local X’ lies from node 1 to node 2 and on the normal plane to local Z’. Local Y’ is also on the normal plane to local Z’ and perpendicular to local X’.


Notes

1. Gap elements cannot be placed with other types of element in the same group.

2. The gap parameter is used to define the position and diameter of the tubes (plus any non-structural coatings, etc). a) Tube in Tube configuration. The parameter is used to define the distance (gap) between the outer diameter of the inner tube and the

GAPR

1 2 2

GAP > 0.0 GAP < 0.0



inner diameter of the outer tube. Hence the value entered ought to equal the outer tube’s inner radius less the inner tube’s outer radius. Allowance will be automatically be made if the nodes are not coincident. b) Two separate tubes configuration. To indicate that this is the case, the sign of this parameter must be negative. The magnitude of the parameter is used to define the distance (gap) between nodes below which contact will occur. Hence the the value will be equal to the sum of the two outer radii.

3. The gap reference axis defines the direction that is normal to the contact plane. If this is specified as {0.0, 0.0, 0.0}, the gap reference axis will be assumed to be in the global Z direction (i.e. the contact plane is the global X-Y plane).

4. The effective stiffness (K) required in the material property data can be estimated as E√A, where E is the elastic modulus and A is the effective area at the contact node.

5. When the gap is closed, the normal stiffness between the two nodes is computed as KN*K. If KN ≤ 0.0 is specified, it will be set equal to the value of the parameter GAPSTF in the PARA command (default 1000).

6. When the gap is closed and stick, the tangential stick stiffness betweeen the two nodes is computed as KT*K. If KT ≤ 0.0 is specified, it will be set equal to the value of the parameter GAPSTF in the PARA command (default 1000).

7. When the gap is open, a residual stiffness is used in order to maintain numerical stability. This is given by KR*K. If KR < 0.0 is specified, it will be set equal to the value of the parameter GAPSMA in the PARA command (default 10-8).

GAPR



Axisymmetric Interface/Gap Element with Sliding Capacity

NUMBER OF NODES 2

NODAL COORDINATES r, z (Note that r and z occupy the first and third fields with coordinate data using an unnamed cartesian system).

DEGREES OF FREEDOM R, Z at each node. Any skew system must be 2-D.

GEOMETRIC PROPERTIES GAP The initial size of the gap. (GAP ≤ 0.0 assumes an initial gap closed condition and GAP will be reset to zero internally) MUY Coefficient of friction in local Y’-direction MUZ Coefficient of friction in local Z’-direction (always ignored) XG X component of vector defining the gap reference axis YG Y component of vector defining the gap reference axis (always assumed zero) ZG Z component of vector defining the gap reference axis KN Normal contact stiffness factor (see note 4) KT Tangential stick stiffness factor (see note 5) KR Gap residual stiffness factor (see note 6) C Damping coefficient

MATERIAL MODELS Elastic only. K - the effective contact stiffness is given in the material property data (see note 3)


OUTPUT The gap size, GAP, in the X’-direction and sliding displacements SLIDE-Y are related to local axes. Force across the gap, Fx’x’, and frictional force Fy’y’ are related to the local axes. STATUS refers to the status of the element at the last iteration. Both STRS and STRN should be specified using the corresponding BLOC command to obtain gap output.

GAPX

1

2

Z

R



LOCAL AXES Local X’ lies along the gap reference axis (see note 1). Local Y’ lies in the global rz plane, perpendicular to local X’.


NOTES

1. The gap reference axis defines the direction of the gap surface, which is assumed to be in a plane

perpendicular to this axis. If this is specified as {0.0, 0.0, 0.0}, the gap reference axis will be assumed to

lie along the element from node 1 to node 2. In this case, nodes 1 and 2 must not be coincident.

2. GAP elements cannot be placed with other types of element in the same group.

3. The effective stiffness (K) required in the material property data can be estimated as E√A, where E is the

elastic modulus and A is the effective area at the contact node.

4. When the gap is closed, the normal stiffness between the two nodes is computed as KN*K. If KN ≤ 0.0 is

specified, it will be set equal to the value of the parameter GAPSTF in the PARA command (default 1000)

5. When the gap is closed and stick, the tangential stick stiffness between the two nodes is computed as

KT*K. If KT ≤ 0.0 is specified, it will be set equal to the value of the parameter GAPSTF in the PARA

command (default 1000).

6. When the gap is open, a residual stiffness is used in order to maintain numerical stability. This is given by

KR*K. If KR < 0.0 is specified, it will be set equal to the value of the parameter GAPSMA in the PARA

command (default 10-8).

GAPX



Isoparametric Laminated Brick Element with Quasi-quadratic Strain Variation




GEOMETRIC PROPERTIES Lay up data. See Section 5.2.5.3. The layers are stacked from the bottom surface up. The bottom surface is defined as the first face formed by the local node numbering (the face formed by nodes 1-6 in this case).

MATERIAL MODELS ELASTIC - Laminated

FAIL - Lamina failure law for composites.




OUTPUT Stresses and strains are available at integration points related to the principal material axes of each layer

For failure analysis, the equivalent stress at each integration point is also available. This is defined as:

SEQ=10*mode+f

where f is the failure function value and mode is the failure mode integer.

mode = 0, elastic = 4, fibre failure

LB15



= 5, matrix failure = 6, lamina failure = 7, transverse shear/normal stress failure = 8, modes 5 and 7


INTEGRATION RULES 1x3x1 Gauss quadrature for each layer by default. If the element contains one single layer only, then the default is 1x3x3, where Gauss quadrature is used for the in-plane integration and Newton-Coates for through thickness integration. Other rules by request. Appendix -G gives positions of integration points. Note that the integration order specified in the preliminary data is the rule adopted for each layer.

LB15




REFERENCE A. 2

LB15



Isoparametric Laminated Brick Element with Quasi-quadratic Strain Variation


NODAL COORDINATES x, y, z (may be omitted for mid-side nodes on straight edges). The position of each mid-side node has a tolerance of side/10 about the true mid-side position.


GEOMETRIC PROPERTIES Lay up data. See Section 5.2.5.3. The layers are stacked from the bottom surface up. The bottom surface is defined as the first face formed by the local node numbering (the face formed by nodes 1-8 in this case).

MATERIAL MODELS ELASTIC - Laminated

FAIL - Lamina failure law for composites




OUTPUT Stresses and strains are available at integration points related to the principal material axes of each layer.

For failure analysis, the equivalent stress at each integration point is also available. This is defined as:

SEQ=10*mode+f

where f is the failure function value and mode is the failure mode integer.

mode = 0, elastic = 4, fibre failure = 5, matrix failure = 6, lamina failure

LB20



= 7, transverse shear/normal stress failure = 8, modes 5 and 7


INTEGRATION RULES 2x2x1 Gauss quadrature for each layer by default. If the element contains one single layer only, then the default is 2x2x3, where Gauss quadrature is used for the in-plane integration and Newton-Coates for through thickness integration. Other rules by request. Appendix -G gives positions of integration points. Note that the integration order specified in the preliminary data is the rule adopted for each layer.

LB20




REFERENCE A. 2

LB20



Line-Spring Element Compatible with Quadratic Shell Elements for Modelling Surface Flaws with Symmetry Boundary

NUMBER OF NODES 3


DEGREES OF FREEDOM X, Y, Z, RX, RY, RZ

GEOMETRIC PROPERTIES d1 Crack depth at node 1 t1 Shell thickness at node 1 d2 Crack depth at node 2 t2 Shell thickness at node 2 d3 Crack depth at node 3 t3 Shell thickness at node 3 x1, y1, z1 Orientation node coordinates for node 1 x2, y2, z2 Orientation node coordinates for node 2 x3, y3, z3 Orientation node coordinates for node 3 The orientation node is a node in the plane of the crack, pointing in the direction of the surface from which the crack originates. (Note - d is +ve if a flaw lies on the +ve Z’ side and vice versa)

MATERIAL MODELS ELASTIC - Isotropic only

PLASTIC - von Mises yield criterion Isotropic hardening only


MASS MODELLING No mass

OUTPUT Forces and moments per unit length of flaw for fracture modes I, II and III and the associated relative displacements and rotations are available at all integration points. In addition, the mode I, II and III stress intensity factors, the plastic part of the J-integral and the total J are also printed at each integration point.

INTEGRATION RULES 3 point Simpson’s rule along the flaw (i.e. 3x1x1) and this cannot be changed.

LOCAL AXES Local X’ axis is tangential to the curvilinear ξ axis, positive in the direction of node 1 to node 3. The local Y’ axis lies in the plane through the orientation node and the local X’ axis, positive towards the orientation node. Local Z’ forms a right handed set with local X’ and local Y’.

LSP3

1

23



NOTES

1. The element is written for small displacement analysis only, i.e. large displacement effects are not included

and should not be specified.

2. Thermal strain effects are not included.

3. Plasticity is included for mode I response only, so that elasto-plastic analysis should only be carried out

with LSP3 or with LSP6 when mode I behaviour dominates. Significant approximations have been made

in the plasticity model and therefore this should be used with care.

4. The amount of plastic work of the numerical model can be adjusted using the PARA command FACLSP

(default 0.4) to provide a matching to the experiment results for an edge-cracked specimen.

REFERENCE A. 6 , A. 7

LSP3



2

1

34

56

Line-Spring Element Compatible with Quadratic Shell Elements for Modelling Surface Flaws

NUMBER OF NODES 6


DEGREES OF FREEDOM X, Y, Z, RX, RY, RZ

GEOMETRIC PROPERTIES d1 Crack depth at node 1 t1 Shell thickness at node 1 d2 Crack depth at node 2 t2 Shell thickness at node 2 d3 Crack depth at node 3 t3 Shell thickness at node 3 x1, y1, z1 Orientation node coordinates for node 1 x2, y2, z2 Orientation node coordinates for node 2 x3, y3, z3 Orientation node coordinates for node 3 The orientation node is a node in the plane of the crack, pointing in the direction of the surface from which the crack originates. (Note - d is +ve if a flaw lies on the +ve Z’ side and vice versa)

MATERIAL MODELS ELASTIC - Isotropic only

PLASTIC - von Mises yield criterion Isotropic hardening only


MASS MODELLING No mass

OUTPUT Forces and moments per unit length of flaw for fracture modes I, II and III and the associated relative displacements and rotations are available at all integration points. In addition, the mode I, II and III stress intensity factors, the plastic part of the J-integral and the total J are also printed at each integration point.

INTEGRATION RULES 3 point Simpson’s rule along the flaw (i.e. 3x1x1) and this cannot be changed.

LOCAL AXES Local X’ axis is tangential to the curvilinear ξ axis, positive in the direction of node 1 to node 3. The local Y’ axis lies in the plane through the orientation node and the local X’ axis, positive towards the orientation node. Local Z’ forms a right handed set with local X’ and local Y’.

LSP6



NOTES

1. The element is written for small displacement analysis only, i.e. large displacement effects are not included

and should not be specified.

2. Thermal strain effects are not included.

3. Plasticity is included for mode I response only, so that elasto-plastic analysis should only be carried out

with LSP3 or with LSP6 when mode I behaviour dominates. Significant approximations have been made

in the plasticity model and therefore this should be used with care.

4. The amount of plastic work of the numerical model can be adjusted using the PARA command FACLSP

(default 0.4) to provide a matching to the experiment results for an edge-cracked specimen.

REFERENCE A. 6 , A. 7

LSP6



Quadrilateral Membrane Field Element with Quasi-linear Variation of Field Variable

NUMBER OF NODES 4

NODAL COORDINATES x, y, (z) z should be omitted for 2-D problems.


GEOMETRIC PROPERTIES ti Thickness at node i (i=1,4), t2 to t4 may be omitted for an element with uniform thickness t1.

No geometric property required with PLSN option. In this case, the geometric

property integer in the topology data should also be omitted.


PIER


LOAD TYPES Nodal values related to field variable type Prescribed field variable Temperature Flux density - surface or internal

OUTPUT Fluxes per unit area (analogous to stresses) and field variable gradients (analogous to strains) are available at integration points related to either global or local axes (local by default).

NODE NUMBERING The nodes are listed in cyclic order, clockwise or anti-clockwise.

INTEGRATION RULES 2x2 Gauss quadrature by default. Other rules by request. Appendix -G gives position of integration points.

LOCAL AXES Invariant throughout element. Local X’ lies along the straight line from node 1 towards node 2. Local Y’ is in the plane of the element perpendicular to local X’ and +ve towards node 3. Local Z’ forms a right-handed set with local X’ and local Y’.

SIGN CONVENTION Fluxes and gradients are positive when in the positive axis direction

QMT4

Y'

1 2

3

4 σ�x'y'

σ�x'x'

σ�y'y'X'



NOTES









QMT4



Isoparametric Quadrilateral Membrane Field Element with Quasi-quadratic Variation of Field Variable

NUMBER OF NODES 8

NODAL COORDINATES x, y, (z) z should be omitted for 2D problems. Coordinates may be omitted for mid-side nodes on straight edges, but if given each node must be within side/10 of the true mid-side.


GEOMETRIC PROPERTIES ti Thickness at node i (i=1,8) t2 to t8 may be omitted for an element with uniform thickness t1.




PIER




NODE NUMBERING The nodes are listed in cyclic order, clockwise or anti-clockwise, starting at a corner node.


QMT8

1 23

4

5

67

8



LOCAL AXES Local X’ lies on the element surface. For flat elements, it is a straight line parallel to a line through nodes 1 and 3. For elements curved out-of-plane, it is the intersection of the element surface with the plane containing the surface normal and the straight line through nodes 1 and 3. Local Y’ is in the surface, perpendicular to local X’ and +ve towards node 5. Local Z’ forms a right-handed set with local X’ and local Y’.


NOTES









QMT8



Quadrilateral Membrane Element with Quasi-linear Strain Variation

This element can be used for both plane strain and plane stress applications in two and three dimensions.

REQUIRED OPTIONS PLSN - 2-D Classical Plane Strain (εz = 0.0) EPSN - 2-D Engineering Plane Strain (εz = const.) TWOD - 2-D Plane Stress none - 3-D Plane Stress

NUMBER OF NODES 4

NODAL COORDINATES x, y, (z) z should be omitted for plane strain and 2-D plane stress forms.

DEGREES OF FREEDOM X Y, for Plane Strain and 2-D plane stress forms.

X,Y,Z for 3-D Plane stress. Deformations out-of-plane must be suppressed or restrained by adjacent elements.

GEOMETRIC PROPERTIES Plane strain - None (the geometric property integer with the element topology data should also be omitted)

Plane stress - ti Thickness at node i (i=1,4), t2 to t4 may be omitted for an element with uniform thickness t1.

MATERIAL MODELS ELASTIC - Isotropic - Orthotropic - Woven - Anisotropic Anisotropic matrix C (or C-1) defined in axis system

selected for output.

4 coefficients of thermal expansion αxx, αyy, αxy, αzz, referred to axis system selected for output

- Hyperelastic

QUM4

1 2

34

=

σxx

σyy

σxy

σzz

C1 C2 C4 C7

. C3 C5 C8

. . C6 C9

. . . C10

εxx

εyy

εxy

εzz



PLASTIC - von Mises, Tresca, Mohr-Coulomb, Drucker-Prager yield criteria Isotropic, Kinematic (Ziegler) or Combined Hardening.

CREEP - von Mises.


LOAD TYPES Nodal Loads Prescribed displacements Edge pressure loads (on any side, +ve towards the element centre) Normal pressure loads (+ve for +ve local z’ direction) Distributed load patterns ML1, ML2, ML3 Temperature loads Body forces Centrifugal loads Angular accelerations Tank Loads


OUTPUT Stresses and strains are available at integration points referred to either global or element local axes (local by default). Note global should not be used with elements in the 3-D Plane stress form.



LOCAL AXES Invariant throughout element. Local X’ lies along the straight line from node 1 towards node 2. Local Y’ is in the plane of the element perpendicular to local X’ and +ve towards node 3. Local Z’ forms a right-handed set with local X’ and local Y’.

SIGN CONVENTION Direct stresses σxx, σyy, σzz +ve for tension Shear stress σxy +ve as shown

QUM4



NOTES

1. With the EPSN option, one extra node, with number MAXND+1 (MAXND is the maximum node number

on the structure), is automatically added to the structure. The node has εz as its only freedom, which is

reported in the displacement output. As this extra node is common to all elements, εz is constant for the

entire structure.

2. 2-D elements with global stress output must be used if fracture mechanics processing in POSTNL is

required.

REFERENCE A. 2

QUM4



Isoparametric Quadrilateral Membrane with Quasi-quadratic Strain Variation



NUMBER OF NODES 8

NODAL COORDINATES x, y, (z) z should be omitted for plane strain and 2-D plane stress forms. Coordinates may be omitted for mid-side nodes on straight edges, but if given each node must be within side/10 of the true mid-side.

DEGREES OF FREEDOM X, Y for Plane strain and 2-D Plane stress forms X, Y, Z for 3-D Plane stress. Deformations out-of-plane must be suppressed or restrained by adjacent elements.

GEOMETRIC PROPERTIES Plane strain - None (the geometric property integer with the topology data should also be omitted).

Plane stress - ti Thickness at node i (i=1,8), t2 to t8 may be omitted for an element with uniform thickness t1.


selected for output

4 coefficients of thermal expansion αxx, αyy, αxy, αzz, referred to axis system selected for output.

- Hyperelastic

QUM8

1 23

4

5

67

8

=σxx

σyy

σxy

σzz

C1 C2 C4 C7

. C3 C5 C8

. . C6 C9

. . . C10

εxx

εyy

εxy

εzz



PLASTIC - von Mises, Tresca, Mohr-Coulomb, Drucker-Prager yield criteria Isotropic, Kinematic (Ziegler) or Combined Hardening.

CREEP - von Mises.


LOAD TYPES Nodal Loads Prescribed displacements Edge pressure loads (on any side, +ve towards the element centre) Normal pressure loads (+ve for +ve local z’ direction) Distributed load patterns ML1, ML2, ML3 Temperature loads Body forces Centrifugal forces Centrifugal loads Angular accelerations Tank Loads





LOCAL AXES Local X’ lies on the element surface. For flat elements, it is a straight line parallel to a line through nodes 1 and 3. For elements curved out-of-plane, it is the intersection of the element surface with the plane containing the surface normal and the straight line through nodes 1 and 3. Local Y’ is in the surface, perpendicular to local X’ and +ve towards node 5. Local Z’ forms a right-handed set with local X’ and local Y’.

SIGN CONVENTION Direct stresses σxx, σyy, σzz +ve for tension Shear stress σxy +ve as shown

QUM8



NOTES


on the structure), is automatically added to the structure. The node has εz as its only freedom, which is

reported in the displacement output. As this extra node is common to all elements, εz is constant for the

entire structure.


required.

REFERENCE A. 2

QUM8



Quadrilateral Element with Linearly Varying Thickness for Modelling Thin or Thick Shells

NUMBER OF NODES 4


DEGREES OF FREEDOM X, Y, Z, RX, RY, RZ at each node.

GEOMETRIC PROPERTIES ti Thickness at node i (i = 1,4), t2 to t4 may be omitted for an element with uniform thickness t1. Additional lay-up data is required for laminated material option. See Section 5.2.5.3 for the LAMI command.

MATERIAL MODELS ELASTIC - Isotropic - Orthotropic - Woven - Anisotropic Anisotropic matrix C (not C-1) defined in element

material axes. (see Appendix B.1.2) Coefficients C1-C24 required. Note that they do not contain the thickness.

3 coefficients of thermal expansion αxx, αyy, αxy referred to local axes.

PLASTIC - von Mises, Tresca, Mohr-Coulomb, Drucker-Prager yield criteria. Isotropic, Kinematic (Ziegler) or Combined Hardening. Ivanov yield criterion with Isotropic hardening.

CREEP - von Mises

FAIL - lamina failure law for composites


QUS4

1 2

34

=

Nx’x’

Νy’y’

Νx’y’

Mx’x’

My’y’

Mx’y’

Qx’z’

Qy’z’

C1t C2t C4t C7t2 C11t2 C16t2 0 0 . C3t C5t C8t2 C12t2 C17t2 0 0 . . C6t C9t2 C13t2 C18t2 0 0 . . . C10t3 C14t3 C19t3 0 0 . . . . C15t3 C20t3 0 0 . . . . . C21t3 0 0 . . . . . . C22t C23t . . . . . . . C24t

εx’x’

εy’y’

εx’y’

yx’x’

yy’y’

yx’y’

εx’z’

εy’z’



LOAD TYPES Nodal loads Prescribed displacements Pressure loads (+ve for +ve local Z’ direction) Distributed load patterns ML1, ML2, ML3 Temperature loads Face temperature loads (Face 1 is on the -ve local Z’ side) Body forces Centrifugal loads Angular accelerations Tank Loads

QUS4




OUTPUT Stresses, strains and stress resultants are available at all integration points referred to element local axes. For Ivanov (full section) models only stress and strain resultants are available. In addition, the stress indicators are printed for plastic points.


INTEGRATION RULES 1 point Gaussian integration in the plane and 3 point Newton-Cotes through thickness by default. 2x2 Gauss rule in the plane by request. Other in-plane rules not recommended. See Appendix -G for positions of integration points.

LOCAL AXES Local X’,Y’,Z’ form a right- handed orthogonal system which, in general, varies in orientation from point to point within the element. At any point P in the element, X’ and Y’ lie in the tangent plane at P. The tangent plane is the plane containing the vectors PR and PS which are vectors tangent to the curvilinear ξ and η directions respectively. X’ and Y’ are positioned in the tangent plane such that the angle between PR and X’ equals the angle between PS and Y’.

SIGN CONVENTIONS Direct forces/unit width Νx’x’, Νy’y’, Νx’y’ +ve as shown. Bending moments/unit width Μx’x’, Μy’y’, Μx’y’ +ve as shown. Shear forces/unit width Qx’z’, Qy’z’ +ve as shown.

REFERENCE A. 3

QUS4



Axisymmetric Quadrilateral Element With Straight Sides

NUMBER OF NODES 4

NODAL COORDINATES r, z (Note that r and z occupy the first and third fields with coordinate data using an unnamed cartesian system)

DEGREES OF FREEDOM R, Z at each node (Any skew system must be 2-D. Of the six direction cosines R’R, R’θ, R’Z, Z’R, Z’θ, Z’Z, the values R’θ and Z’θ must be zero).


MATERIAL MODELS ELASTIC - Isotropic - Orthotropic - Woven - Anisotropic Anisotropic matrix C (or C-1) - referred to axis system

selected for output (global by default)

4 coefficients of thermal expansion αrr, αzz, αθθ, αrz, referred to axis system selected for output

- Hyperelastic

PLASTIC - von Mises, Tresca, Mohr-Coulomb, Drucker-Prager yield criteria. Isotropic, Kinematic (Prager or Ziegler) or Combined Hardening.

CREEP - von Mises.


QUX4

Z

1 2

34

=

σrr

σzz

σθθ σrz

C1 C2 C4 C7

. C3 C5 C8

. . C6 C9

. . . C10

εrr

εzz

εθθ εrz



LOAD TYPES Nodal Loads (must be defined per radian) Prescribed displacements Pressure loads (on any side, +ve towards the element centre) Temperature loads Body forces Centrifugal loads


OUTPUT Stresses and strains are available at integration points in global or local element axes (global by default)


INTEGRATION RULES 2x2 rule used by default. Higher order rules by request. Appendix -G gives position of integration points.

LOCAL AXES Invariant throughout the element. Local R’ lies along the line from node 1 to node 2. Local Z’ is perpendicular to local R’, in the global rz plane, and lies counter clockwise from R’.

SIGN CONVENTIONS Direct stresses σrr, σzz, σθθ +ve for tension Shear stress σrz +ve as shown

NOTE Global stress output must be used if fracture mechanics processing in POSTNL is required.

REFERENCE A. 2

QUX4

z

r



Axisymmetric Isoparametric Quadrilateral Element

NUMBER OF NODES 8

NODAL COORDINATES r, z (may be omitted for mid-side nodes on a straight edge). Note that r and z occupy the first and third fields with coordinate data using an unnamed cartesian system.

DEGREES OF FREEDOM R, Z at each node (Any skew system must be 2-D. Of the six direction cosines R’R, R’θ, R’Z, Z’R, Z’θ, Z’Z, the values R’θ and Z’θ must be zero)


MATERIAL MODELS ELASTIC - Isotropic - Orthotropic - Woven - Anisotropic Anisotropic matrix C (or C-1) - referred to axis system

selected for output (global by default)


- Hyperelastic


CREEP - von Mises.


QUX8

Z

1 2 3

45

678

=

σrr

σzz

σθθ σrz

C1 C2 C4 C7

. C3 C5 C8

. . C6 C9

. . . C10

εrr

εzz

εθθ εrz



LOAD TYPES Nodal Loads (must be defined per radian) Prescribed displacements Pressure loads (on any side, +ve towards the element centre) Temperature loads Body forces Centrifugal loads


OUTPUT Stresses and strains are available at integration points in global or local element axes (global by default)




SIGN CONVENTIONS Direct stresses σrr, σzz, σhh +ve for tension Shear stress σrz +ve as shown


REFERENCE A. 2

QUX8

z

r



Axisymmetric Quadrilateral Field Element with Quasi-linear Variation of Field Variable

NUMBER OF NODES 4

NODAL COORDINATES r, z (Note that r and z occupy the first and third fields with coordinate data using an unnamed cartesian system)




PIER



OUTPUT Fluxes per unit area (analogous to stresses) and field variable gradients (analogous to strains) are available at integration points related to either global or local axes (global by default).





NOTES





QXT4

Z

1 2

34



Axisymmetric Isoparametric Quadrilateral Field Element with Quasi-quadratic Variation of Field Variable

NUMBER OF NODES 8

NODAL COORDINATES r, z (may be omitted for mid-side nodes on a straight edge). Note that r and z occupy the first and third fields with coordinate data using an unnamed cartesian system.




PIER








QXT8

Z

1 2 3

45

678



NOTES









QXT8



Linear Axisymmetric Rigid Surface Contact Element

NUMBER OF NODES 3

NODAL COORDINATES r, z

DEGREES OF FREEDOM R, Z

GEOMETRIC PROPERTIES No basic geometric property. RIGS required to define the geometry of rigid surface. (See Section 5.2.5.4)

MATERIAL MODELS ELASTIC - K is the normal contact stiffness (stress/penetration) PLASTIC - Coulomb friction

Frictionless surface is assumed if no plastic material data.

LOAD TYPES Nodal loads, Prescribed displacements

OUTPUT The gap size, GAP in the X’-direction and sliding displacement SLIDE-Y are related to local axes. Stress across the gap, STRESS-XX and frictional stress, STRESS-YY are related to the local axes.

INTEGRATION RULES 2 point Newton-Cotes (Trapezoidal rule) along the interface at nodes 1 and 2 (i.e. 2x1x1)

LOCAL AXES Local X’ lies normal to the rigid surface and passes through the integration point. Local Y’ lies in the global rz plane, perpendicular to local X’ (ie tangential to the rigid surface).

SIGN CONVENTIONS σx’x’ is positive when compressive. σy’y’ is positive when it acts in negative y’ direction GAP is positive when penetrated SLIDE- Yis positive when sliding in the +ve Y’ direction

RGX3

1

2

3

1

2

X'

Y' +ve direction of rigid surface



NOTES

1. Node 3 is the rigid body reference node and should always be either suppressed or prescribed. Nodes 1 and

2 should be on the deforming body.

2. It is always assumed that the structure is separated from the rigid surface at the beginning of an analysis

and therefore care must be taken to ensure that singularity is not present at time t=0.0. If the structure is

not properly supported initially, the user will have to put in sufficient boundary conditions to avoid the

singularity. These boundary conditions can then be removed once the contact condition with the rigid

surface is established.

3. If contact is made at the very first step, it is assumed that no sliding or frictional stress will be developed

during this step. Because of this restriction, it is advisable to solve at t=0.0 first before proceeding the

analysis further.

4. Augmented Lagrangian procedure is invoked by specifying the maximum number of augmentation steps

required, MXAUGM, in the PARA command. See also Appendix C.6.

REFERENCE A. 8

RGX3



Quadratic Axisymmetric Rigid Surface Contact Element

NUMBER OF NODES 4

NODAL COORDINATES r, z

DEGREES OF FREEDOM R, Z

GEOMETRIC PROPERTIES No basic geometric property. RIGS required to define the geometry of rigid surface. (See Section 5.2.5.4)


Frictionless surface is assumed if no plastic material data



INTEGRATION RULES 3 point Newton-Cotes (Simpson’s rule) along the interface at nodes 1, 2 and 3 (i.e. 3x1x1)

LOCAL AXES Local X’ lies normal to the rigid surface and passes through the integration point. Local Y’ lies in the global rz plane, perpendicular to local X’ (ie tangential to the rigid surface).

SIGN CONVENTIONS σx’x’ is positive when compressive. σy’y’ is positive when it acts in negative y’ direction GAP is positive when penetrated SLIDE-Y is positive when sliding in the +ve Y’ direction

RGX4

4

1

2 3

X'

Y'

1

2 3

+ve direction of rigid surface



NOTES

1. Node 4 is the rigid body reference node and should always be either suppressed or prescribed. Nodes 1, 2

and 3 should be on the deforming body.








analysis further.



REFERENCE A. 8

RGX4



Linear 2-D Rigid Surface Contact Element

NUMBER OF NODES 3


DEGREES OF FREEDOM X, Y

GEOMETRIC PROPERTIES (i) Basic Properties Plane stress - ti thickness at node i (i=1,2) (>0.0) t2 may be omitted for an element with uniform thickness t1. Plane strain - no basic geometric property

(ii) RIGS required to define the geometry of the rigid surface (see Section 5.2.5.4)





INTEGRATION RULES 2 point Newton-Cotes (Trapezoidal rule) along the interface at nodes 1 and 2 (i.e. 2x1x1)

LOCAL AXES Local X’ lies normal to the rigid surface and passes through the integration point. Local Y’ lies in the global xy plane, perpendicular to local X’ (ie tangential to the rigid surface).

SIGN CONVENTIONS σx’x’ is positive when compressive. σy’y’ is positive when it acts in negative Y’ direction GAP is positive when penetrated SLIDE-Y is positive when sliding in the +ve Y’ direction

RG23

1

2

3

1

2

X'




NOTES

1. Node 3 is the rigid body reference node and should always be either suppressed or prescribed. Nodes 1 and

2 should be on the deforming body.








analysis further.



REFERENCE A. 8

RG23



Quadratic 2-D Rigid Surface Contact Element

NUMBER OF NODES 4


DEGREES OF FREEDOM X, Y

GEOMETRIC PROPERTIES (i) Basic Properties Plane stress - ti thickness at node i (i=1,3) (>0.0) t2 and t3 may be be omitted for an element with uniform thickness t1. Plane strain - no basic geometric property

(ii) RIGS required to define the geometry of the rigid surface (see Section 5.2.5.4)





INTEGRATION RULES 3 point Newton-Cotes (Simpson’s rule) along the interface at nodes 1, 2 and 3 (i.e. 3x1x1)

LOCAL AXES Local X’ lies normal to the rigid surface and passes through the integration point. Local Y’ lies in the global xy plane, perpendicular to local X’ (ie tangential to the rigid surface).

SIGN CONVENTIONS σx’x’ is positive when compressive. σy’y’ is positive when it acts in negative Y’ direction GAP is positive when penetrated SLIDE-Y is positive when sliding in the +ve Y’ direction

RG24

1

2

4

3

1

2 3

X'




NOTES

1. Node 4 is the rigid body reference node and should always be either suppressed or prescribed. Nodes 1, 2

and 3 should be on the deforming body.








analysis further.



REFERENCE A. 8

RG24



Translational Spring/Dashpot Element

NUMBER OF NODES 2

NODAL COORDINATES x, y, (z) z should be omitted for TWOD option

DEGREES OF FREEDOM X, Y, (Z), at each node

GEOMETRIC PROPERTIES (i) Global coordinates of a point defining line of action of spring (ii) Linear stiffness K or tabulated values of displacement and force (iii) Linear damping factor C or tabulated values of velocity and force

MATERIAL PROPERTIES ELASTIC - Isotropic (Not used but material integer must be specified.) PLASTIC - Inelastic spring, SPRG

LOAD TYPES Nodal loads Prescribed displacements.

MASS MODELLING No mass (use added mass).

OUTPUT Spring force, relative displacement, damping force and relative velocity in spring direction.

LOCAL AXES If the global coordinates P specified in the geometric properties data are all zero, local X’ lies along the element from node 1 to node 2. For other cases, local X’ is defined by the position vector OP, where O is the origin of the global axes.

SIGN CONVENTIONS Forces are positive in tension. Displacements are positive when node 2 moves positively relative to node1.

NOTES

1. If the coordinates of P are all zero, nodes 1 and 2 must not be coincident.

2. Elastic behaviour is always assumed for damping.

SPR1

1

2

K

C



Rotational Spring/Dashpot Element

NUMBER OF NODES 2


DEGREES OF FREEDOM RX, RY, RZ, at each node

GEOMETRIC PROPERTIES (i) Global coordinates of a point, P, defining line of action of spring (ii) Linear rotational stiffness K or tabulated values of moment and rotation and moment. (iii) Linear damping factor C or tabulated values of moment and angular velocity and moment.

MATERIAL PROPERTIES ELASTIC - Isotropic (Not used but material integer must be specified.) PLASTIC - Inelastic spring, SPRG.

LOAD TYPES Nodal loads Prescribed displacements.

MASS MODELLING No mass (use added mass).

OUTPUT Spring moment, relative rotation, damping moment and relative angular velocity.

LOCAL AXES If the global coordinates P specified in the geometric properties data are all zero, local X’ lies along the element from node 1 to node 2. For other cases, local X’ is defined by the position vector OP, where O is the origin of the global axes.

SIGN CONVENTIONS Rotations are positive when node 2 rotates positively relative to node 1.

NOTES

1. If the coordinates of P are all zero, nodes 1 and 2 must not be coincident.

2. Elastic behaviour is always assumed for damping.

SPR2



Isoparametric Beam/Stiffener Element having Thin-walled Open Cross-sections of Arbitrary Shape (no warping)

NUMBER OF NODES 4 (2 end, 1 mid-length and 1 auxiliary node).

NODAL COORDINATES X, Y, Z (may be omitted for mid-length node on a straight element). The mid-length node has tolerance of length/10 about the true mid-length. The auxiliary node is only used to define the local axes (see below).

DEGREES OF FREEDOM X, Y, Z, RX, RY, RZ.

GEOMETRIC PROPERTIES The element can have any open thin-walled cross-section made up of straight sided segments, connected at median points. The element has special geometric properties (see Geometric Property Section 5.2.5.1).

RMUL - Rigidity multiplier (= 1.0 - to represent full cross-section, or = 0.5 to represent half symmetric cross-section). s,t - Local coordinates to define median points in plane of cross-section. IA,IB - Local connectivity.

NSTAT - Number of integration stations along the segment. NLAY - Number of integration layers through segment thickness. T - Segment thickness.

The cross-section of the element is assumed constant along the length (Geometric Properties at nodes 2 and 3 need not be supplied).

MATERIAL MODEL ELASTIC - Isotropic PLASTIC - von-Mises

Isotropic Hardening


SST4

2

34

s

tr

1

Repeat this for each segment



LOAD TYPES Nodal loads Prescribed displacements. Body forces Centrifugal loads Angular accelerations


OUTPUT Direct stress σrr, shear stress σrm, (referred to segment axes) and stress resultants (in element local axes) are available as follows.

STRS: stresses at all integration points on element SSTR: smoothed stresses for all integration points at 2 cross-sections corresponding to 2 point Gauss rule on length. ESTR: smoothed stresses for top and bottom layers at end of each segment (ie extreme fibrepoints) at 2 cross-sections corresponding to 2 point Gauss rule on length. SRES: stress resultants at all 4 Gauss points along the length SSRE: smoothed stress resultants at 2 cross-sections corresponding to 2 point Gauss rule on length Strains and strain resultants are not available For elastic analysis, only stress resultants (i.e. SRES or SSRE) are available.

INTEGRATION RULES 4 Point Gauss Quadrature along length (invariant and independent of stress output). User defined trapezoidal rule for each segment. (NO DEFAULT) - see Geometric Properties Data. As a guide the following are suggested:

Elastic - 2 stations, 1 layer Plastic - 5 stations, 4 layers

NODE NUMBERING Node 3 is always the MID-LENGTH node and 4 the auxiliary node.

LOCAL AXES r, s, t Independent of cross-sectional shape - ie s, t do not have to coincide with principal axes of the cross-section. Local r is tangential to the curvilinear nodal axis, positive in the direction node 1 to node 2. s is normal to the plane containing the r-axis and node 4. t is orthogonal to r and s and points away from node 4, ie positive t and the auxiliary node are on opposite sides of the r axis.

SST4



SIGN CONVENTIONS Axial force +ve tension Axial stress +ve tension

Generalised stress resultants, +ve as shown

Fr - axial force Qrs - shear along s Qrt - shear along t Ms - moment about s Mt - moment about t Tsv - St. Venant Torque

NOTES

1. This element requires special Geometry Property and Residual stress input data (see Sections 5.2.5.1 and

5.6.3).

2. Note that the element topology definition and local axes are not the same as the STF4 beam stiffener.

3. Segment number 1 must start at free edge of the beam cross-section. Each subsequent segment must start

from the end of any previously numbered segment.

4. Stress and stress resultant outputs always correspond to the full cross-section.

REFERENCE A. 5

SST4

Mt

Qrt

t

sQrs

Ms

rFr

Tsv



Curved Beam Element with Transverse Shear and Offset Nodes for use with the TCS Family of Thick Shell Elements

NUMBER OF NODES 4 (2 end, 1 mid-length and 1 auxiliary node, see Note).

NODAL COORDINATES x, y, z (may be omitted for mid-length node on a straight element). The mid-length node has a tolerance of length/10 about the true mid-length. The auxiliary node defines the local axes.

DEGREES OF FREEDOM X, Y, Z, RX, RY, RZ at nodes 1, 2, 3.

GEOMETRIC PROPERTIES There are three types of cross sections available:

(a) Solid rectangular cross-section RECT (or blank) with the geometric property data

For nodes 1, 2 and 3, in turn: aY’ cross-sectional dimension of local Y’ direction aZ’ cross-sectional dimension of local Z’ direction eX’ nodal offset in local X’ direction eY’ nodal offset in local Y’ direction eZ’ nodal offset in local Z’ direction

(b) Thin tubular cross-section TUBE - with the geometric property data

For nodes 1, 2 and 3, in turn: ro outer radius t wall thickness (ro/t should be ≥ 10) eX’ nodal offset in local X’ direction eY’ nodal offset in local Y’ direction eZ’ nodal offset in local Z’ direction

Note that +ve θ is the rotation from local Y’ towards local Z’.

STF4

1

Y' 4

X'

Z'

2

3

Y'

Z'aY'

aZ'

X' axis into paper



(c) Thin hollow rectangular cross-section (Box-section) BOX - with the geometric property data.

For nodes 1, 2 and 3, in turn: ao outer dimension of box in local Y’ axis. bo outer dimension of box in local Z’ axis. t1 thickness of segment 1 t2 thickness of segment 2 t3 thickness of segment 3 t4 thickness of segment 4 eX’ nodal offset in local X’ direction eY’ nodal offset in local Y’ direction eZ’ nodal offset in local Z’ direction

In this case again thin section assumption is made, ao/(t2 or t4)>10 and bo/(t1 or t3)>10. The hollow section is divided into four segments for integration purposes. Numbering of segments is shown above. Segment 1 is numbered where positive Y’ axis crosses the segment and segment 3 is numbered where the negative Y’ axis crosses. Similarly segments 2 and 4 are numbered where +ve and -ve Z’ axis crosses respectively.

MATERIAL MODEL ELASTIC - Isotropic PLASTIC - von Mises, Tresca, Mohr-Coulomb, Drucker-Prager

yield criteria. Isotropic, Kinematic (Ziegler) or Combined Hardening.

CREEP - von Mises


LOAD TYPES Nodal loads Prescribed displacements Distributed load pattern CB1 Temperature loads Body forces Centrifugal loads Angular acceleration


OUTPUT Stresses, strains and stress resultants are available at integration points referred to element local axes. Stress point indicators for plastic points are also printed.

STF4

Y'

Z'

bo

X' axis into paper

aot4

t1 t2

t3

1

23

4



INTEGRATION RULES (1) Rectangular cross-section.

2 point Gauss quadrature along length and 3 x 3 Newton-Cotes rules on cross-section by default (2 x 3 x 3). Other rules, by request, using the INTEgration command in Preliminary data. Newton-Cotes points are equally spaced and Appendix -G gives the positions of the Gauss integration points.

Examples

From the above examples it may be noted that the numbering of integration points always start from the negative quadrant of Y’ Z’ axis. Points are numbered in the local Z’ axis direction (from -ve to +ve direction) first. Then points are numbered in the local Y’ axis direction (from -ve to +ve direction) as shown above.

(2) Tube cross-section

2 point Gauss quadrature along length and 8 points (Trapezoidal) equally spaced around the tube periphery by default (ie 2x8x1 = NGX*NGY*NGZ). Other rules, by request, using the INTEgration command in Preliminary data. (Note that NGZ must be given but is not used) NGY should be a multiple of 4.

Examples

STF4

Y'

7 8 9

4 5 6

1 2 3

Z'

Y'

1 3 5

Z'

2 4

Y'

7 8 9 Z'

10 12

13 1514

1 32

4 6

Y'

13 14 15 Z'

22 24

25 2726

1 32

9

19 2116 18

107

4

12

6

3x3=9 1x5=5 5x3=15 9x3=27(default)

5

11

5

811

1720

23



The numbering of the integration points always start from the negative quadrant of the Y’ Z’ axes as shown above. The points are equally spaced on the circumference.

(3) Box cross-section

2 point Gauss quadrature along length and 12 point Newton-Cotes on cross-section by default (2x12x1). Other orders, by request, using the INTEgration command in Preliminary data. NGY must be a multiple of 4 with a minimum of 12.

Examples

Take NGY = 4n ; n = number of integration points for each segment

For the box section, there are the two stresses at each point on the segment. These are the normal stress and the shear stress along the segment.

NODE NUMBERING Node 2 is always the mid-length node and node 4 is the auxiliary node.

LOCAL AXES Local X’ axis is tangential to the curvilinear centroidal axis, positive in the direction of node 1 to node 3. The local Y’ axis lies in the plane through node

STF4

NGY = 20, n = 5

Y'

5

1

1 2 53 4

CL

1 2 53 4

CL

43

2

Y'

5

1

CL

43

2

CL

Z'

Z'



4 and the local X’ axis, positive towards node 4. Local Z’ forms a right-handed set with local X’ and local Y’.



SIGN CONVENTIONS Axial force +ve for tension Axial stress +ve for tension Torque +ve in positive direction of local axis Bending Moment +ve for sagging Shear force +ve in the local axes Y’ Z’ +ve direction

OFFSETS Offsets eX’, eY’, eZ’ +ve as shown. Note that the mid-length node cannot be offset in the local X’ direction.

NOTE The auxiliary node must be a dummy node and NOT a node on the structure.

STF4

1 2

4

3

eX'eX'

X'

eZ' Y'

4

1Z'

eY'



Generally Curved Degenerate Triangular Thick Shell Element with Varying Thickness and Transverse Shear Capable of

Modelling Discontinuities in Curvature and Thickness

NUMBER OF NODES 6 (3 corner, 3 mid-side) NODAL COORDINATES x, y, z (may be omitted for mid-side nodes

on straight edges). Each mid-side node has tolerance of side/10 about the true mid-side.


GEOMETRIC PROPERTIES ti Thickness at node i (i = 1,6), t2 to t6 may be omitted for an element with uniform thickness. Additional lay-up data is required for laminated material option. See Section 5.2.5.3 for the LAMI command.

MATERIAL MODELS ELASTIC - Isotropic - Orthotropic - Woven - Laminated - Anisotropic Anisotropic matrix C (not C-1) defined in element

material axes. (See Appendix B.1.2) Coefficients C1-C24 required. Note that they do not contain the thickness.



CREEP - von Mises FAIL - lamina failure law for composites


TCS6

=

Nx’x’

Νy’y’

Νx’y’

Mx’x’

My’y’

Mx’y’

Qx’z’

Qy’z’


εx’x’

εy’y’

εx’y’

yx’x’

yy’y’

yx’y’

εx’z’

εy’z’



LOAD TYPES Nodal Loads Prescribed displacements Pressure loads (+ve for +ve local Z’ direction) Distributed load patterns ML1, ML2, ML3 Temperature loads Face temperature loads (Face 1 is on the -ve local Z’ side) Body forces Centrifugal loads Angular accelerations Tank Loads

TCS6






INTEGRATION RULES 3 point triangular rule in plane and 3 point Newton-Cotes rule through thickness (1x3x3) by default. Other rules by request, but only the through thickness integration rule may be altered. See Appendix -G for positions of integration points.

LOCAL AXES Local X’, Y’, Z’ form a right-handed orthogonal system which, in general, varies in orientation from point to point within the element. At any point P in the element, X’ and Y’ lie in the tangent plane at P. The tangent plane is the plane containing the vectors PR and PS which are vectors tangent to the curvilinear ξ and η directions respectively. X’ and Y’ are positioned in the tangent plane such that the angle between PR and X’ equals the angle between PS and Y’.



TCS6



Generally Curved 8-Node Quadrilateral Thick Shell Element with Varying Thickness and Transverse Shear,

Capable of Modelling Discontinuities in Curvature and Thickness

NUMBER OF NODES 8 (4 corner, 4 mid-side). NODAL COORDINATES x, y, z (may be omitted for mid-side nodes



GEOMETRIC PROPERTIES ti Thickness at node i (i = 1,8), t2 to t8 may be omitted for an element with uniform thickness t1. Additional lay-up data is required for laminated material option. See Section 5.2.5.3 for the LAMI command.





CREEP - von Mises FAIL - lamina failure law for composites Material Properties may be temperature dependent if required.

TCS8

=

Nx’x’

Νy’y’

Νx’y’

Mx’x’

My’y’

Mx’y’

Qx’z’

Qy’z’


εx’x’

εy’y’

εx’y’

yx’x’

yy’y’

yx’y’

εx’z’

εy’z’



LOAD TYPES Nodal Loads Prescribed displacements Pressure loads (+ve for +ve local Z’ direction) Distributed load patterns ML1, ML2, ML3 Temperature loads Face temperature loads (Face 1 is on the -ve local Z’ side) Body forces Centrifugal loads Angular accelerations Tank Loads

TCS8






INTEGRATION RULES 2x2 Gauss quadrature in plane and 3 point Newton-Cotes through thickness (2x2x3) by default. Other rules by request, but only the through thickness integration rule may be altered. See Appendix -G for positions of integration points.

LOCAL AXES Local X’, Y’, Z’ form a right handed orthogonal system which, in general, varies in orientation from point to point within the element. At any point P in the element, X’ and Y’ lie in the tangent plane at P. The tangent plane is the plane containing the vectors PR and PS which are vectors tangent to the curvilinear ξ and η directions respectively. X’ and Y’ are positioned in the tangent plane such that the angle between PR and X’ equals the angle between PS and Y’.



TCS8



Generally Curved 9-Node Quadrilateral Thick Shell Element with Varying Thickness and Transverse Shear,

Capable of Modelling Discontinuities in Curvature and Thickness

NUMBER OF NODES 9 (4 corner, 4 mid-side, 1 centre). NODAL COORDINATES x, y, z (may be omitted for mid-side nodes


DEGREES OF FREEDOM X, Y, Z, RX, RY, RZ at each node. GEOMETRIC PROPERTIES ti Thickness at node i (i = 1,9),

t2 to t9 may be omitted for an element with uniform thickness t1. Additional lay-up data is required for laminated material option. See Section 5.2.5.3 for the LAMI command.





CREEP - von Mises FAIL - lamina failure law for composites

TCS9

=

Nx’x’

Νy’y’

Νx’y’

Mx’x’

My’y’

Mx’y’

Qx’z’

Qy’z’


εx’x’

εy’y’

εx’y’

yx’x’

yy’y’

yx’y’

εx’z’

εy’z’




LOAD TYPES Nodal Loads Prescribed displacements Pressure loads (+ve for +ve local Z’ direction) Distributed load patterns ML1, ML2, ML3 Temperature loads. Face temperature loads (Face 1 is on the -ve local Z’ side) Body forces Centrifugal loads Angular accelerations Tank Loads




INTEGRATION RULES 2x2 Gauss quadrature in plane and 3 point Newton-Cotes through thickness (2x2x3) by default. Other in-plane rules not recommended although 3x3 rule may be adopted in special circumstances. Other through thickness rules by request. See Appendix -G for positions of integration points.

LOCAL AXES Local X’, Y’, Z’ form a right handed orthogonal system which, in general, varies in orientation from point to point within the element. At any point P in the element, X’ and Y’ lie in the tangent plane at P. The tangent plane is the plane containing the vectors PR and PS which are vectors tangent to the curvilinear ξ and η directions respectively. X’ and Y’ are positioned in the tangent plane such that the angle between PR and X’ equals the angle between PS and Y’.


TCS9




TCS9



Triangular Membrane Field Element with Linear Variation of Field Variable

NUMBER OF NODES 3

NODAL COORDINATES x, y, (z) z should be omitted for 2-D problems.


GEOMETRIC PROPERTIES ti Thickness at node i (i=i,3) t2, t3 may be omitted for an element with uniform thickness t1




PIER





INTEGRATION RULES Single point rule by default (1x1). 3 point rule by request. Appendix -G gives position of integration points.

LOCAL AXES Local X’ lies along the straight line from node 1 towards node 2. Local Y’ is in the plane, perpendicular to X’ and positive towards node 3. Local Z’ forms a right-handed set with local X’ and local Y’.


TMT3

Y'

1 2

3

σ�x'y'σ�x'x'

σ�y'y'

X'



NOTES









TMT3



Isoparametric Triangular Membrane Field Element with Quasi-quadratic Variation of Field Variable

NUMBER OF NODES 6

NODAL COORDINATES x, y, (z) z should be omitted for 2-D problems. Coordinates of mid-side nodes may be omitted for straight edges but, if given, each node must be within side/10 of the true mid-side.


GEOMETRIC PROPERTIES ti Thickness at node i (i=1,6) t2, to t6 may be omitted for an element with uniform thickness t1.




PIER





INTEGRATION RULES 3 point rule by default (1x3). One point rule by request. See Appendix -G for positions of integration points.

TMT6



LOCAL AXES Local X’ lies on the element surface. For flat elements it is a straight line parallel to a line, through nodes 1 and 3. For elements curved out-of-plane, it is the intersection of the element surface with the plane containing the surface normal and the straight line through nodes 1 and 3. Local Y’ is in the surface, perpendicular to local X’ and +ve towards node 5. Local Z’ forms a right-handed set with local X’ and local Y’.


NOTES









Y'

1 2

3

4

σ�x'y'

σ�x'x'

σ�y'y'

5

6

X'

TMT6



Triangular Membrane Element with Constant Strain



NUMBER OF NODES 3

NODAL COORDINATES x, y, (z) z should be omitted for plane strain and 2-D plane stress forms.

DEGREES OF FREEDOM X, Y, for Plane strain and 2-D Plane stress forms (see note 2)

X, Y, Z for 3-D Plane stress. Deformations out-of-plane must be suppressed or restrained by adjacent elements

GEOMETRIC PROPERTIES Plane strain - None (the geometric property integer with the element topology data should also be omitted)

Plane stress - ti Thickness at node i (i=i,3) t2, t3 may be omitted for an element with uniform thickness t1


selected for output


- Hyperelastic

PLASTIC - von Mises, Tresca, Mohr-Coulomb, Drucker-Prager yield criteria. Isotropic, Kinematic (Ziegler) or Combined Hardening.

TRM3

=

σxx

σyy

σxy

σzz

C1 C2 C4 C7

. C3 C5 C8

. . C6 C9

. . . C10

εxx

εyy

εxy

εzz



CREEP - von Mises.


LOAD TYPES Nodal loads Prescribed displacements Edge pressure loads (on any side, +ve towards the element centre) Normal pressure load (+ve local z’ direction) Distributed load patterns ML1, ML2, ML3 Temperature loads Body forces Centrifugal loads Angular accelerations Tank Loads

MASS MODELLING Consistent Mass (used by default) Lumped Mass



INTEGRATION RULES Single point rule by default (1x1). 3 point rule by request. Appendix -G gives position of integration points.

LOCAL AXES Local X’ lies along the straight line from node 1 towards node 2. Local Y’ is in the plane, perpendicular to X’ and positive towards node 3. Local Z’ forms a right-handed set with local X’ and local Y’.

SIGN CONVENTIONS Direct stresses σxx, σyy, σzz +ve for tension Shear stress σxy +ve as shown

NOTES


on the structure), is automatically added to the structure. This node has εZ as its only freedom, which is

reported in the displacement output. As this extra node is common to all elements, εZ is constant for the

entire structure.


required.

TRM3

Y'

1 2

3

σ�x'y'σ�x'x'

σ�y'y'

X'



REFERENCE A. 2

TRM3



Isoparametric Triangular Membrane Element with Linear Strain Variation



NUMBER OF NODES 6

NODAL COORDINATES x, y, (z) z should be omitted for plane strain and 2-D plane stress forms. Coordinates of mid-side nodes may be omitted for straight edges but, if given, each node must be within side/10 of the true mid-side.

DEGREES OF FREEDOM X, Y, for Plane strain and 2-D Plane stress forms (see note 2)

X, Y, Z for 3-D Plane stress. Deformations out-of-plane must be suppressed or restrained by adjacent elements

GEOMETRIC PROPERTIES Plane strain - None (the geometric property integer with the element

topology data should also be omitted)

Plane stress - ti Thickness at node i (i=1,6) t2, t3 may be omitted for an element with uniform thickness t1


selected for output


- Hyperelastic

TRM6

=σxx

σyy

σxy

σzz

C1 C2 C4 C7

. C3 C5 C8

. . C6 C9

. . . C10

εxx

εyy

εxy

εzz



PLASTIC - von Mises, Tresca, Mohr-Coulomb, Drucker-Prager yield criteria. Isotropic, Kinematic (Ziegler) or Combined Hardening.

CREEP - von Mises.


TRM6



LOAD TYPES Nodal loads Prescribed displacements Edge pressure loads (on any side, +ve towards the element centre) Normal pressure load (+ve for +ve local z’ direction) Distributed load patterns ML1, ML2, ML3 Temperature loads Body forces Centrifugal loads Angular accelerations Tank Loads




INTEGRATION RULES 3 point rule by default (1x3). One point rule by request. See Appendix -G for positions of integration points.

LOCAL AXES Local X’ lies on the element surface. For flat elements it is a straight line parallel to a line, through nodes 1 and 3. For elements curved out-of-plane, it is the intersection of the element surface with the plane containing the surface normal and the straight line through nodes 1 and 3. Local Y’ is in the surface, perpendicular to local X’ and +ve towards node 5. Local Z’ forms a right-handed set with local X’ and local Y’.

SIGN CONVENTIONS Direct stresses σxx, σyy, σzz +ve for tension Shear stress σxy +ve as shown

TRM6



NOTES


on the structure), is automatically added to the structure. This node has εZ as its only freedom, which is

reported in the displacement output. As this extra node is common to all elements, εZ is constant for the

entire structure.


required.

REFERENCE A. 2

TRM6



Axisymmetric Triangular Element with Straight Sides

NUMBER OF NODES 3

NODAL COORDINATES r, z (Note that r and z occupy the first and third fields on lines using an unnamed cartesian system. The second field must be input as zero.)

DEGREES OF FREEDOM R, Z at each node (Any skew system must be defined by the six direction cosines R’R, R’θ, R’Z, Z’R, Z’θ, Z’Z. The values R’θ and Z’θ must be zero)



selected for output


- Hyperelastic


CREEP - von Mises.


TRX3

Z

1 2

3

=

σrr

σzz

σθθ σrz

C1 C2 C4 C7

. C3 C5 C8

. . C6 C9

. . . C10

εrr

εzz

εθθ εrz



LOAD TYPES Nodal loads (must be defined per radian) Prescribed displacements Pressure loads (on any side, +ve towards the element centre) Temperature loads Body forces Centrifugal loads


OUTPUT Stresses and strains are available at integration points either in global or local element axes (global by default).

NODE NUMBERING The nodes may be listed either clockwise or anti-clockwise.

INTEGRATION RULES Single point rule used by default. Higher order rules by request. Appendix -G gives position of integration points.

LOCAL AXES Local R’ is a straight line from node 1 to node 2. Local Z’ is perpendicular to local R’ in the RZ plane and lies counter clockwise from R’.

SIGN CONVENTION Direct stresses σrr, σzz, σθθ +ve for tension Shear stress σrz +ve as shown


REFERENCE A. 2

TRX3

z

r



Axisymmetric Isoparametric Triangular Element

NUMBER OF NODES 6

NODAL COORDINATES r, z (may be omitted for mid-side nodes on a straight edge). Each mid-side node has a tolerance of side/10 about the true mid-side. Note that r and z occupy the first and third fields with coordinate data using an unnamed cartesian system.

DEGREES OF FREEDOM R,Z at each node (Any skew system must be 2-D. Of the six direction cosines R’R, R’θ, R’Z, Z’R, Z’θ, Z’Z. The values R’θ and Z’θ must be zero)



selected for output


- Hyperelastic


CREEP - von Mises.


TRX6

Z

1 23

45

6

=

σrr

σzz

σθθ σrz

C1 C2 C4 C7

. C3 C5 C8

. . C6 C9

. . . C10

εrr

εzz

εθθ εrz



LOAD TYPES Nodal loads Prescribed displacements Pressure loads (on any side, +ve towards the element centre) Temperature loads Body forces Centrifugal loads


OUTPUT Stresses and strains are available at integration points either in global or local element axes (global by default).

NODE NUMBERING The nodes are listed in cyclic order, clockwise or anti-clockwise, starting at a corner.

INTEGRATION RULES 3 point rule used by default (1x3). Single point rule by request. Appendix-G gives positions of integration points.

LOCAL AXES Invariant throughout the element. Local R’ is a straight line parallel to a line through nodes 1 and 3. Local Z is perpendicular to local R’ in the global RZ plane, and lies counter clockwise from R’.

SIGN CONVENTION Direct stresses σrr, σzz, σθθ +ve for tension Shear stress σrz +ve as shown


REFERENCE A. 2

TRX6

z

r



Three-dimensional Beam Bending Element with Uniform Circular Cross-section

NUMBER OF NODES 2



GEOMETRIC PROPERTIES D External diameter (>0.0) (uniform) t Wall thickness (D/2>t>0.0) Local Axis definition -May be omitted. See Section 5.2.5.5 and Appendix A.2.1.







FORCE OUTPUT The forces are exerted by the nodes on the element, and related to the local axes. Note that for an offset beam the forces output are related to the element centroidal axes.


TUBE



LOCAL AXES A beam element has two local axes systems. The X’Y’Z’ local axes are associated with end nodes of the element. The X”Y”Z” local axes are associated with the end points of the centroidal axis of the element, taking account of any non-zero rigid offsets.

If all offsets are zero, X’Y’Z’ and X”Y”Z” are coincident.

If local axis data is supplied, local X” lies along the centroidal axis from end 1 towards end 2. Local Y” lies in the plane defined by the two nodes (ends) and a third point defined in the geometric properties list. Local Z” forms a right handed set with local X” and localY”.

If local axis data is not supplied, local X” lies along the centroidal axis from end 1 towards end 2. Local Z” must lie in the global XY plane with +ve local Y” on the +ve side of the global XY plane. In the special case where local Y” is also in the global XY plane, local Y” must lie in the global Y direction. BM3D should be used for a beam with general orientation of local Z”.

See also Section 5.2.5 and Appendix A.2.1.

SIGN CONVENTIONS Axial force positive for tension Shear force positive for end 2 sagging relative to end 1 Torque positive for clockwise rotation of end 2 relative to end 1, looking from end 1 toward end 2 Bending moment positive for sagging

Shear QY” +ve Shear QZ” +ve

Moment Z”Z” +ve Moment Y”Y” +ve

DATA EXAMPLES ELEM

MATP 4

TUBE 4 1 17

END

GEOM

17 TUBE 20000.0 17.5

END

REFERENCE A. 1

TUBE

Y''

X''

1 2

Z''

X''1 2



Axisymmetric Triangular Field Element with Linear Variation of Field Variable

NUMBER OF NODES 3

NODAL COORDINATES r, z (Note that r and z occupy the first and third fields on lines using an unnamed cartesian system. The second field must be input as zero.)




PIER




NODE NUMBERING The nodes may be listed either clockwise or anti-clockwise.

INTEGRATION RULES Single point rule used by default. Higher order rules by request. Appendix -G gives position of integration points.

LOCAL AXES Local R’ is a straight line from node 1 to node 2. Local Z’ is perpendicular to local R’ in the RZ plane and lies counter clockwise from R’.


NOTES





TXT3

Z

1 2

3



Isoparametric Axisymmetric Triangular Field Element with Quasi-quadratic Variation of Field Variable

NUMBER OF NODES 6

NODAL COORDINATES r, z (may be omitted for mid-side nodes on a straight edge). Each mid-side node has a tolerance of side/10 about the true mid-side. Note that r and z occupy the first and third fields with coordinate data using an unnamed cartesian system.




PIER




NODE NUMBERING The nodes are listed in cyclic order, clockwise or anti-clockwise, starting at a corner.

INTEGRATION RULES 3 point rule used by default (1x3). Single point rule by request. Appendix-G gives positions of integration points.

LOCAL AXES Invariant throughout the element. Local R’ is a straight line parallel to a line through nodes 1 and 3. Local Z is perpendicular to local R’ in the global RZ plane, and lies counter clockwise from R’.

SIGN CONVENTION Fluxes and gradients are positive when in the positive axis direction.

TXT6

Z

1 23

45

6



NOTES









TXT6



Isoparametric Beam/Stiffener Element having Thin-walled Open Cross-sections of Arbitrary Shape (allowing warping)

NUMBER OF NODES 4 (2 end, 1 mid-length and 1 auxiliary node).

NODAL COORDINATES X, Y, Z (may be omitted for mid-length node on a straight element). The mid-length node has tolerance of length/10 about the true mid-length. The auxiliary node is only used to define the local axes (see below).

DEGREES OF FREEDOM X, Y, Z, RX, RY, RZ, WRR.

GEOMETRIC PROPERTIES The element can model any open thin-walled cross-section made up of straight sided segments, connected at median points. The element has special geometric properties (see Geometric Property Section 5.2.5.1).

ISEC - Median point number to be used as warping origin RMUL - Rigidity multiplier (= 1.0 - to represent full cross-section, or = 0.5 to represent half symmetric cross-section). s,t - Local coordinates to define median points in plane of cross-section. IA,IB - Local connectivity. NSTAT - Number of integration stations along the segment. NLAY - Number of integration layers through segment thickness. T - Segment thickness.

The cross-section of the element is assumed constant along the length (Geometric Properties at nodes 2 and 3 need not be supplied).


PLASTIC - von-Mises Isotropic Hardening.


LOAD TYPES Nodal loads Prescribed displacements. Body forces Centrifugal loads Angular accelerations

WST4

2

34

s

tr

1

Repeat this for each segment




OUTPUT Direct stress σrr, shear stress σrm, (referred to segment axes) and stress resultants (in element local axes) are available as follows.

STRS: stresses at all integration points on element SSTR: smoothed stresses for all integration points at 2 cross-sections corresponding to 2 point Gauss rule on length. ESTR: smoothed stresses for top and bottom layers at end of each segment (ie extreme fibrepoints) at 2 cross-sections corresponding to 2 point Gauss rule on length. SRES: stress resultants at all 4 Gauss points along the length SSRE: smoothed stress resultants at 2 cross-sections corresponding to 2 point Gauss rule on length Strains and strain resultants are not available For elastic analysis, only stress resultants (i.e. SRES or SSRE) are available.

INTEGRATION RULES 4 Point Gauss Quadrature along length (invariant and independent of stress output). User defined trapezoidal rule for each segment. (NO DEFAULT) - see Geometric Properties Data. As a guide the following are suggested:

Elastic - 2 stations, 1 layer Plastic - 5 stations, 4 layers

NODE NUMBERING Node 3 is always the MID-LENGTH node and 4 the auxiliary node.

LOCAL AXES r, s, t Independent of cross-sectional shape - ie s, t do not have to coincide with principal axes of the cross-section. Local r is tangential to the curvilinear nodal axis, positive in the direction node 1 to node 2. s is normal to the plane containing the r-axis and node 4. t is orthogonal to r and s and points away from node 4, ie positive t and the auxiliary node are on opposite sides of the r axis.

WST4



SIGN CONVENTIONS Axial force +ve tension Axial stress +ve tension

Generalised stress resultants, +ve as shown

Fr - axial force Qrs - shear along s Qrt - shear along t Ms - moment about s Mt - moment about t Mw - warping moment Tsv - St. Venant torque Tw - warping torque Twag - Wagner torque T = Tsv + Tw + Twag

T - total torque

NOTES

1. This element requires special Geometry Property and Residual stress input data (see Sections 5.2.5.1 and

5.6.3).

2. Note that the element topology definition and local axes are not the same as the STF4 beam stiffener.

3. Segment number 1 must start at free edge of the beam cross-section. Each subsequent segment must start

from the end of any previously numbered segment.

4. Stress and stress resultant outputs always correspond to the full cross-section.

REFERENCE A. 5

WST4

Mt

Qrt

t

sQrs

Ms

rFr

Tsv

Mw



A.4 References

A. 1 Przemieniecki, J.S., Theory of Matrix Structural Analysis, McGraw-Hill, 1968.

A. 2 Zienkiwicz, O.C and Taylor, R.L., The Finite Element Method, 4th Edn., Volumes 1 and 2, McGraw-Hill, 1989.

A. 3 Kebari, H., A one point integrated assumed strain 4-node Mindlin plate element. Eng. Comp. 1990, Vol. 7, December, pp 284-290.

A. 4 Bathe, K-J., Finite Element Procedures in Engineering Analysis, Prentice-Hall, 1982.

A. 5 Bates, D.N., The Mechanics of Thin Walled Structures with Special Reference to Finite Rotations. PhD Thesis, University of London, 1987.

A. 6 Rice, J.R., The Line-Spring Model for Surface Flaws, in the Surface Crack: Physical Problems and Computational Solutions, ed. J.L. Swedlow, ASME, 1972.

A. 7 Parks, D.M., and White, C.S., Elastic-Plastic Line-Spring Finite Elements for Surface-Cracked Plates and Shells, Trans ASME, Journal of Pressure Vessel Technology, Vol. 104, 1982, pp287-292.

A. 8 Laursen, T.A. and Simo, J.C., On the Formulation and Numerical Treatment of Finite Deformation Frictional Contact Problems, in Non-linear Computational Mechanics - State of the Art, ed. Wriggers, P. and Wagner, W., Springer-Verlag, 1991, pp716-736.

Appendix B ASAS (Non-Linear) User Manual

Page B-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - B Material Models

B.1 Linear Elasticity

B.1.1 Isotropic Material

An isotropic, linear elastic material is characterised by two independent elastic constants, namely the Young’s modulus and the Poisson’s ratio. As the material properties are invariant under coordinate transformation, the choice of material reference axis system becomes irrelevant. Explicit forms of the elastic material matrix for an isotropic material can be found in Ref B.1.

B.1.2 Anisotropic Material

For a completely anisotropic material, 21 independent elastic constants are necessary to define the 3-dimensional stress-strain relationship. For finite element types other than 3-D solids, the number of constants required will be different. The exact forms of the anisotropic material matrix for individual elements are given in Appendix -A.

Unlike isotropic material, the coefficients of the material matrix for anisotropic materials are strongly dependent on the choice of material reference axis system. The specification of material coefficients that are consistent with the definition of material axis system are important to ensure the correct modelling of the material behaviour.

By default, the material axis system coincides with the stress output axis system defined in Appendix -A. The only exception is for shell elements where the default material Xm–axis is defined as the projection of global X-axis onto the shell surface with Ym lying on the tangent plane of the shell and orthogonal Xm. The user can override this default by specifying a material skew integer in the material properties data. In this case, the material constants should be provided with respect to the skew system. For bricks, plane stress/strain membranes and axisymmetric solids, the skew axis system should be defined relative to the output axis system, ie the direction cosines are those between the skew axes and the output axes. For shells, however, a different definition of the skew system is adopted. The skew system is defined relative to the global axis system instead, and Xm will become the projection of the skew X-axis onto the shell surface. Since the procedure for defining the default material axis system will fail when the shell surface is normal to the global X, a skewed material system must be specified in this situation.

B.1.3 Orthotropic Material

Orthotropic material is a special form of the general anisotropic material. It is completely defined by the Young’s modulii, shear modulii and Poisson’s ratio in 3 principal material directions. From the 9 principal elastic constants specified, the program will internally convert them into the equivalent anisotropic material matrix format as described in Appendix -A. Because of the different numbers of stress components for each element type, the conversion process is element dependent. As an example, the anisotropic matrix for a shell element is given by:



where νν 2112

1111 -1

E = C , νν

ν2112

221212 -1

E = C , νν 2112

2222 -1

E = C

and E = E 11212212 νν

The default material axis system is defined in the same way as for anisotropic materials. Again, the user can specify a material skew system to provide more general orientation of the material. Refer to B.1.2 for definitions of the material axis system with and without skewing.

B.1.4 Laminated Material for Shell Elements

Laminated material is available to model shell structures constructed by assembling several layers of materials with different properties such as fibre reinforced composites. Detailed discussion of laminated material and composite analysis can be found in Ref B.2.

Based on the layup configuration specified, the equivalent anisotropic material properties for the laminate are then obtained by integrating the properties for each individual layer through the thickness. This computation is automatically carried out in PRENL and the results stored. The terms in the processed material matrix for a composite laminate are defined as follows:



where Q = 3x3 in-plane material stiffness matrix calculated for each lamina in the laminate reference axis system S = 2x2 transverse shear material stiffness matrix in the laminate reference system t = thickness of the laminate z = axis of the laminate reference system normal to the plane of the laminate



The laminate reference axes are defined such that the 0° fibre direction is parallel to the material Xm–axis and the 90° fibre direction is parallel to the material Ym–axis. By default, the material Xm–axis is defined as the projection of global X-axis onto the shell surface with Ym lying on the tangent plane of the shell and orthogonal to Xm. When skew system is specified, Xm will become the projection of the skew Xonto the shell surface. Since the procedure for defining the default material axis system will fail when the shell surface is normal to the global X, a skewed material system must be specified in this situation.

Unlike isotropic material where a single transverse shear correction factor of 5/6 can be applied throughout, the shear correction factors for a laminated shell depend on both the layup sequence and the material properties of each constitutive layer. Herein, the procedure outlined in Ref B.3 for orthotropic laminate has been adopted for determining the shear correction factors.

The transverse shear constitutive relations for orthotropic laminates take the form

where k21 , k2

2 = shear correction factors T11 = C22t T22 = C24t

From Ref 0, k21 is evaluated from

∫ dz(z)gT = k i

12t

2t-

11

-1

21

where

z)A-B(2

D2Q+G

S

1=(z)g 1111x

i11i

1

2

i11

i1

and i = for all layers in the laminate

Gi1 = constants determined from interface continuity conditions and the requirement that

shear stresses σxz’s vanish on the bottom surface of the plate.

Dx = (D11A11-B112)

with A11=C1t , B11=C7t2 and D11=C10t3

Similarly, k22 can be determined with all suffix 1 replaced by 2.

B.1.5 Woven Material

The woven material considered is of 2-dimensional plain weave structure only. Thus, the fabric is assumed to be composed of two sets of interlacing, mutually orthogonal yarns of the same material. The equivalent anisotropic material properties of a woven layer are determined from the yarn properties (orthotropic) using the parallel mosaic model (Ref B.8). The key simplification of the mosaic model is the omission of the fibre undulation and

Qxz

Qyz 0

0 εxz

εyz

= Tk 11

21

Tk 2222



continuity that exist in the actual fabric. Effectively, a woven layer is treated as an assemblage of cross-ply unidirectional laminae. The equivalent properties obtained can in general be written as:

D = ν0C0 + ν90C90

where ν = the volume fraction C = the material stiffness of the unidirectional sub-lamina subscripts 0 and 90 = the yarn orientation

The definitions of the material axis system with and without skewing are identical to those for anisotropic material. Refer to B.1.2 for details.

B.2 Non-Linear Elasticity

B.2.1 Hyperelastic Material

Hyperelastic material is used to model rubber-like materials which have high elastic deformability and near incompressible behaviour. The material behaviour is characterised by a single scalar strain energy density function in terms of the strain components. In ASAS-NL, a modified form of the classical Mooney-Rivlin model has been implemented. The strain energy density, U, for this model can be written as:

)Jf(+3)-J(C+3)-J(C=U 3201110

where C10, C01 = Mooney-Rivlin material constants J1 , J2, J3 = a set of modified invariants defined by

I=J II=J , II=J 321

33 32-

223 31-

11 ∧

I1 , I2 and I3 are, respectively, the first, second and third invariants of the left Cauchy-Green stretch tensor, b=F·Ft , and F is the deformation gradient. These invariants are given by:

I1 = Tr (b)

I2 = [ ]b).Tr(b-I21 2

1

I3 = Det (b)

The first two terms on the r.h.s. of the expression for U correspond to the deviatoric part of the strain energy density while f(J3) corresponds to the volumetric part which allows the near incompressible behaviour to be modelled. The function f(J3) is given by:

[ ])Jln(+)1-J(K 21=)Jf( 2

32

33

where K = the bulk modulus

Stresses and material stiffnesses are obtained by differentiating U with respect to strains, ie



δεδεδ

δεδσ U=D , U=

B.3 Plasticity

B.3.1 Yield Criteria

The yield criterion in a hypothesis which defines the limit of elasticity under any combination of stresses. The following yield criteria are available.

B.3.1.1 Von Mises

Yield occurs when the elastic distortional energy reaches a critical value (Ref B.4), ie in terms of the equivalent stress when

σ = σy where σy is the uniaxial yield stress in tension

The equivalent stress, reported in the output, is calculated as

J3= 2σ

where J2, the second invariant of the deviatoric stress, is given as

( )σσσσσσσσσ 2zx

2yz

2xy

2xxzz

2zzyy

2yyxx2 6+6+6+)-(+)-(+)-(

61=J

B.3.1.2 Tresca

Yield occurs when the maximum shear stress reaches a critical value (Ref 0), ie in terms of principal stresses σ1,

σ2, σ3, with

σ1 > σ2 > σ3 then

σ =σ1-σ3=σy

where σy = the uniaxial yield stress in tension and σ the equivalent stress reported in the output

B.3.1.3 Ivanov

This (approximate) principle is based on the instantaneous plastification of the shell section (rather than examining individual layers as for the other criteria) (Ref B.5). The stress resultants (direct forces and moments) of the mid-plane are used directly in the yield criterion in conjunction with the flow rule. The criterion, which does not include the effect of transverse shear stress resultants, has the form

( )1=

)Q0.48+Q(Q-QQ

41- Q+Q

41+Q

21+Q=f

mt

2tmmt2

tm2mmt



where Qt, Qm, Qtm = functions of the stress resultants as follows:

NMNM=Q ;

MM=Q ;

NN=Q

00tm2

0m2

0t

where

N3+NN-N+N= N 2xyyx

2y

2x

M3+MM-M+M= M 2xyyx

2y

2x

NM3+NM21-NM2

1-NM+NM= MN xyxyxyyxyyxx

=t= N 00 σ uniaxial yield force / unit width

4t= M

20

0σ = uniaxial yield moment / unit width

= 0σ yield stress in tension

=t thickness of shell section

The modified Ivanov criterion is simply the Ivanov criterion with M0 replaced by αM0, thus giving a better approximation for the uniaxial moment/plastic curvature relationship with increasing equivalent plastic curvature. The multiplier α is defined as:

e0.4-1.0= )(-2.6 psχα

where χps is the non-dimensional plastic curvature. This is obtained by summing the incremental equivalent

plastic curvatures;

∆∆∆∆∆•

∆

∆

4+++

34

3Et=

3Et=

2pxy

pypx2py

2px

o

22ps

o

22

ps

χχχχχ

σχ

σχ

In which E is the Youngs Modulus and ∆χpx, ∆χpy, ∆χpxy are the incremental plastic curvatures.

In the program the yield function f is converted to an equivalent stress σ reported by the program as

σ =σ0f (where σ0 is the initial yield stress as before)

B.3.1.4 Mohr-Coulomb

This criterion is based on a generalisation of Coulomb’s failure theory for soils, and may be viewed as resulting from the addition of a dependence on the mean stress into the Tresca yield criterion. Failure occurs when (Ref B.4)



φσσφσσ sin)+(-cos c 2=)-( 3131

where σ1, σ3 = maximum and minimum principal stresses

c = the cohesion

φ = angle of friction

In this case the equivalent stress reported by the program is:

φσσσσσ sin)+(+)-(= 3131

B.3.1.5 Drucker-Prager

The Drucker-Prager yield criterion is a generalisation of the von Mises yield criterion into which a dependence on mean stress has been added. Failure occurs at an equivalent stress given by (Ref B.4)

k=J+I= 21ασ

where I1 = σ1 + σ2 + σ3 (the 1st stress invariant)

where J2 = 2nd invariant of the deviatoric stress defined in Section B.1.1

α = )sin-(33

sin2φ

φ

k = )sin-(33

cos c 6φ

φ

where c, φ = the cohesion and angle of friction respectively as before

B.3.1.6 Stress Resultant Plasticity for Beams

The stress resultant plasticity models BEM2, BEM3 and BEAM are only available with engineering beam elements BM2D, BM3D and TUBE. The theory assumes that the whole beam cross-section will plastify instantaneously when a combination of the stress resultants at the point of interest reaches a critical value. It is also assumed that the material behaviour is elastic-perfectly plastic and that all plastic deformation of an element is concentrated at the nodes, while the inside of the element remains elastic. When plasticity develops, a plastic interaction relationship between various stress resultant components is strictly satisfied and the plastic displacement associated with each stress resultant component is defined according to the flow rule. Further details about the so-called “plastic node method” can be found in Ref B.6.

Three types of yield surfaces are available in ASAS-NL and these are defined as follows:

(i) BEM2

1=MM+

PP

pz

z

2

o

2



(ii) BEM3

1=MM+

MM+

PP

py

y2

pz

z

2

o

2

(iii) BEAM

1=MM

C+MMC+

PP

Cpy

yC

5pz

zC

3o

C

1

642

where P0 = yield force Mpz = yield moment about beam local z-axis Mpy = yield moment about beam local y-axis C1 to C6 = yield function constants

B.3.1.7 Coulomb Friction

The Coulomb friction model is available for use with rigid surface elements (and implicitly with gap elements). Slip occurs when

0 = - || || = f lt σσ

and ) , (min = onl τσµσ

where σt = tangential stress σn = normal stress µ = coefficient of friction τo = shear stress limit

B.3.1.8 Tension Cut-off

The tension cutmodel assumes that failure occurs when the principal stress reaches a critical value, i.e.

si=σy (i=1,3)

where σy is the uniaxial tensile strength

This material is suitable for modelling cracking in plain or reinforced concrete.

B.3.1.9 Inelastic Spring

The figure below shows a typical skeleton curve that is used to represent the inelastic spring model. The spring initially deforms in a linear elastic manner until the initial yield force fy1 is reached. Plastic yielding will start to develop when further loading is applied. If the loading is reduced or its direction reversed, the spring will unload elastically.



The unloading/reloading stiffness after yielding occurred may be different from the initial elastic stiffness. This

is controlled by the material parameter α1. By default, the unloading stiffness is assumed to be the same as the

initial stiffness (i.e. α1 is set to 1.0 if it is specified.

The hysteretic behaviour is modelled through shifting of the spring curve origin. Origin shift takes place when

unloading continues beyond a limit point (point P above). When this happens, P will become the new origin of

the spring curve. The materials parameter α2 defines the location of point P and it allows for the modelling of

different kinematic hardening behaviour. By default, α2 = 0.0 and thus the shifted origin is always along the

displacement axis. The setting α2 = 1.0 is almost equivalent to the pure kinematic hardening model in

continuum elements. Normally, α2 should be set between 0.0 and 1.0.

B.3.2 Hardening Rules

Hardening Rules define how the yield criterion is modified by plastic deformation. Various hardening rules are available by giving suitable directives with the material property commands in the structural description data. The rules are given below.

B.3.2.1 Isotropic

The yield surface expands uniformly about the origin and a uniaxial model would yield at the same value in both tension and compression. No Bauschinger effect is reproduced.



B.3.2.2 Kinematic

The yield locus translates as a rigid body when plastic deformation occurs. The Bauschinger effect is modelled. Two types of kinematic hardening are available. Prager hardening assumes that the yield locus translates as a rigid body in the direction of the normal to its surface at the point concerned, ie

dα = c dεp

where c = a constant

dα = the instantaneous change in the position of the locus

dεp = the instantaneous plastic strain

Ziegler hardening assumes that the yield locus translates in the direction of the load vector, ie

dα = e(σ-α)

where e = a constant

σ = the current stress state

α = the current centre of yield (ie back stress)

Prager hardening cannot be used in reduced stress spaces, ie for plane stress, plates, shells and beams. For these elements Ziegler hardening must be used.

B.3.2.3 Combined

Both types of kinematic hardening may be combined with isotropic hardening. The ratio of kinematic to isotropic hardening is chosen by specifying a parameter h to have a value between zero and one (h=0 gives kinematic and h=1 gives isotropic hardening). h is given with the material property data.

The various hardening rules are displayed in Figure B.3.1.



Figure B.3.1 Hardening Rules

B.3.3 Equivalent Strain

The equivalent (or effective) strain reported by the program is defined as:

I34 = 2ε

where I2, the second invariant of the strains vector is defined as

′′′ εεεεεε 2zx

2yz

2xy

2zz

2yy

2xx2 2

1+21+

21+++

21 = I

εεεεεεεεε 2zx

2yz

2xy

2xxzz

2zzyy

2yyxx 2

3+23+

23+)-(+)-(+)-(

61 =

B.4 CREEP

All time dependent material behaviour is represented in the program by the description ‘Creep’ and the analysis of this is explained fully in Appendix -J.

Currently the creep model is limited to the von Mises potential function and associative flow rule when extending the uniaxial creep description to multiple axes. No yield limit is used in the uniaxial creep description (ie the yield stress is effectively zero) and so the combination of creep and conventional time independent



plasticity is not possible in any one load step. There are a number of creep laws in-built to the program. Alternatively, a creep law can be defined directly in a user supplied subroutine. Any uniaxial description which is a function of stress, equivalent strain, time, temperature and any user-supplied constants may be defined using the user creep subroutine.

B.4.1 In-Built Creep Laws (i) NORT

tc= CC1c

32σε

This is a Norton law in which

σ = equivalent stress

t = time

εc = equivalent creep strain rate

and constants C1, C2, C3 are supplied by the user with the creep material properties data. Additional

versatility is possible by allowing C1-C3 to be temperature-dependent. In this case the constants for each

specified temperature are listed.

(ii) LAW2

exptC+exptC= /T)C(-CC5

/T)C(-CC1c

876432 σσε

This law thus has both primary and secondary creep components with time hardening.

Note that the temperature T is absolute Kelvin, ie that defined by any current temperature loading plus

273°. Therefore if this temperature dependence is used (ie non-zero C4 or C8) the temperature loading

should be defined in °C.

(iii) LAW3

expC+expC= /T)C(-C5

/T)C(-Cc

C1c

76432 σεσε

This is a strain hardening formulation with the accumulated equivalent creep strain εc participating in the

definition of the primary creep rate.

Note that the temperature T is as defined for LAW2.

(iv) LAW4

This is a Blackburn law, implementing the creep data for 316 stainless steel for temperature ranges

between 450°C and 700°C according to the reference “Isochronous stress-strain curves for austenitic

stainless steel” Blackburn Trans ASME (1972).

supplied by program



Note that the units for LAW4 are N, mm, °C and secs.

B.4.2 User Supplied Creep Laws

A user defined creep law is associated with a particular material type via the appropriate 4 character directive USE1, USE2, USE3, USE4 and USE5. Up to five user define laws can be added to the program. Users should specify their creep law in the form of a FORTRAN subroutine which can then be compiled and linked into the program. This subroutine must be named as indicated below and should be written in double precision.

4 character directive with CREEP properties data

Subroutine name

USE1 CRPUS1

USE2 CRPUS2

USE3 CRPUS3

USE4 CRPUS4

USE5 CRPUS5

The subroutine should define the uniaxial (equivalent) creep strain rate with an argument list and format as follows.

SUBROUTINE CRPUS1 (STRESS, SIGEQ, TEMP, DTIME, TOTIME, CRPTOT,

1 CRATE, PRICRP, MOUT, IELMAT, EQSTRN, NST,

2 DCRATE, CR)

LOGICAL PRICRP

DOUBLE PRECISION STRESS(NST), CRPTOT(NST), TEMP, DTIME,

TOTIME, CRATE, EQSTRN, SIGEQ, DCRATE, CR (9)



User supplied code defining an expression for uniaxial (equivalent) creep strain rate

CRATE and, if OPTIon VISC is to be used, an expression for DCRATE (see

definition below)

IF(.NOT.PRICRP) GO TO 9999

CALL PRINT (1)

WRITE (MOUT, 2000)

2000 FORMAT (19H ** CREEP USER LAW 1)

9999 CONTINUE

RETURN

END

The variables in the argument list are defined as follows

Input:

STRESS - Stress Vector

SIGEQ - Equivalent Stress (von Mises)

TEMP - Temperature

DTIME - Time increment

TOTIME - Total creep time

CRPTOT - Total creep strain vector

PRICRP - A flag having a value TRUE on the first pass through the user subroutine and a value FALSE on all subsequent passes

MOUT - Variable defining the output device number. All WRITE statements in the user supplied code should take the form WRITE(MOUT, format label)

IELMAT - Material Property Integer

EQSTRN - Equivalent creep strain (total)

NST - Dimension of stress and creep strain vectors STRES and CRPTOT

CR - Vector of creep law constants C1 to C9, if supplied.

Output:

CRATE - Uniaxial (equivalent) creep strain rate

DCRATE - Derivative of CRATE with respect to SIGEQ. Only required if OPTIon VISC is to be used.

The value of NST and the nature of the stresses and strains contained in vectors STRESS and CRPTOT depend on the type of element according to the following table:



Element Type NST Locations in Vector

1 2 3 4 5 6

Uniaxial 1 XX - - - - -

Plane Stress / Plane Strain 4 XX YY XY ZZ - -


3D Solids 6 XX YY ZZ XY YZ ZX

Thick Beams (STF4) 3 XX XY(XT)* XZ(-)*


* For tube or box section beams

B.5 Composite Failure

Failure of a composite laminate can be analysed by specifying failure criteria in the failure material properties data. Depending on the nature of an analysis, the data supplied may have the following different definitions:

(i) When FAIL data are specified for a constitutive layer within a laminate and the element is elastic, these

will define the lamina strength and strain limits.

(ii) When FAIL data are specified after the LAMInated material properties data, they will define the failure

limits of the whole laminate.

(iii) When FAIL data are specified for a constitutive layer within a laminate and the element is plastic, these

will define the failure limits of the lamina and any failure law constants required to model the post-failure

behaviour.

B.5.1 Lamina Failure Criteria

Lamina failure criteria are applied to individual layers within a laminate. A number of lamina failure criteria for elastic laminated composite elements are evaluated in POSTNL when options FEMV→LAMI are selected. These are reported in the form of failure indices, F. The surface F=1 defines the failure envelope and encloses the stress states that the material can sustain without failure. In other words,

F≥ 1 failed

F<1 safe



The lamina failure indices are computed from the stresses or strains in each layer together with the specified unidirectional strength properties. For laminated brick elements, the layer stresses and strains are directly computed in ASASNL. For shell elements, however, these are obtained through a stress recovery process in POSTNL. Also, in this case, a plane stress condition has been assumed in the failure criteria, and therefore only 3 in-plane stress components (σ1, σ2 and σ12) are relevant. Note that the stresses are given in the principal directions 1, 2 and 3, ie in the fibre direction and directions perpendicular to fibre.

Let Xt, ε1t be the tensile stress and strain limits, respectively, in the 1-direction Xc, ε1c be the compressive stress and strain limits, respectively, in the 1-direction Yt, ε2t be the tensile stress and strain limits, respectively, in the 2-direction Yc, ε2c be the compressive stress and strain limits, respectively, in the 2-direction Zt, ε3t be the tensile stress and strain limits, respectively, in the 3-direction Zc, ε3c be the compressive stress and strain limits, respectively, in the 3-direction and S12, γ12 be the shear stress and strain limits, respectively, in the 12-plane S23, γ23 be the shear stress and strain limits, respectively, in the 23-plane S31, γ31 be the shear stress and strain limits, respectively, in the 31-plane and Zl be the interlaminar tensile stress limit Sl be the interlaminar shear stress limit



The various lamina failure criteria evaluated in POSTNL are defined as follows:

(i) Azzi-Tsai

σσσσσσσ3222221222

32

22

12

X1-

Z1+

Y1-

Z1-

Y1+

X1-

Z+

Y+

X=F

S+

S+

S+

Y1-

X1+

Z1-

31

312

23

232

12

122

31222σσσσσ

where X=Xt , σ1≥0 Y=Yt , σ2≥0 Z=Zt , σ3≥0

X=Xc , σ1<0 Y=Yc , σ2<0 Z=Zc , σ3<0

(ii) Norris

S+

XY+

Y+

X=F

12

122

2122

12

1σσσσσ

S+

YZ+

Z+

Y=F

23

232

3232

22

2σσσσσ

S+

XZ+

Z+

X=F

31

312

3132

12

3σσσσσ

F = MAX {F1, F2, F3}


X=Xc , σ1<0 Y=Yc , σ2<0 Z=Zc , σ3<0

(iii) Hoffman

( ) )-(XX

1-ZZ

1+YY

121+-

ZZ1-

YY1+

XX1

21=F 2

32ctctct

212

ctctctσσσσ

( ) σσσσσ 3ct

2ct

1ct

132

ctctct Z1-

Z1+

Y1-

Y1+

X1-

X1+-

YY1-

XX1+

ZZ1

21+

S+

S+

S+

31

312

23

232

12

122

σσσ

(iv) Tsai-Wu

σσσσσσ3

ct2

ct1

ctct

23

ct

22

ct

21

Z1-

Z1+

Y1-

Y1+

X1-

X1+

ZZ+

YY+

XX=F



σσσσσσσσσ311332232112

31

312

23

232

12

122

F2+F2+F2+S

+S

+S

+



F12, F23, and F13 are experimentally determined coefficients and it is necessary that they satisfy the

stability condition

0>F-ZZ

1XX

1 0,>F-ZZ

1YY

1 0,>F-YY

1XX

1 213

ctct

223

ctct

212

ctct

At present, F12, F23, and F13 are always set to zero and this has been shown to give good results.

(v) Von-Mises

( )σσσσσσσσσσσσ 231

223

212313221

23

22

21

ct

+3+3+---++XX

1=F

This criterion has assumed that Xt=Xc=X, where X is the uniaxial failure stress of an isotropic material.

All other strength properties are related to X and therefore the input values will be ignored. Because of

the special assumptions, this criterion is only applicable in certain situations.

(vi) Maximum Stress

S,

S,

S,

Z,

Y,

XMAX=F

31

312

23

232

12

122

32

22

12

σσσσσσ


X=Xc , σ1<0 Y=Yc , σ2<0 Z=Zc , σ3<0

(vii) Delamination

0>for Z

=F 3l

32

1 σσ

0<=for 0= 3σ

( )S+=F 2

l

231

223

2σσ

F = MAX {F1, F2}

Delamination is only checked at the interface between adjacent layers.

B.5.2 Laminate Failure Criteria

Unlike lamina failure criteria, the laminate failure criteria are applied directly to the entire laminate, which is considered homogeneous but anisotropic. Thus, the global stresses and strains (or resultants) for the laminate and their strength characterisation are required to evaluate the failure indices. A total of five failure indices are



reported when POSTNL options FEMV→GFAI are selected labelled GFAIL01 to GLFAIL05. Of these five indices, only the first is in-built and the remaining four are user defined.

Let ε xx be the direct strain limit in the laminate x direction (i.e. in the 0° direction) ε yy be the direct strain limit in the laminate y direction (i.e. in the 90° direction) ε xy be the shear strain limit in the laminate xy plane ψ xx be the bending curvature limit in the laminate x direction ψ yy be the bending curvature limit in the laminate y direction ψ xy be the torsional curvature limit in the laminate xy plane ε xz be the shear strain limit in the laminate xz plane and ε yz be the shear strain limit in the laminate yz plane

The global laminate failure criterion evaluated in POSTNL is defined as follows:

4. Maximum strain resultant criterion

|ˆ|||

=F ; |ˆ|||

=F ; |ˆ|||=F

xy

xy3

yy

yy2

xx

xx1

εε

εε

εε

|ˆ|||

=F ; |ˆ|||

=F ; |ˆ|||=F

xy

xy6

yy

yy5

xx

xx4 ψ

ψψψ

ψψ

|ˆ|||

=F ; |ˆ|||=F

yz

yz8

xz

xz7

εε

εε

1,8=i }FMAX{=F i

In addition, users may specify their laminate failure criterion in the form of a FORTRAN function which can then be compiled and linked into the program POSTNL. This function must be named as indicated below.

Laminate Failure Type Name

Laminate failure criterion 1 (in-built) -

Laminate failure criterion 2 (User) GLFC02






The function should evaluate the failure index with an argument list and format as follows:

DOUBLE PRECISION FUNCTION GLFC02 (SRES,ERES,NSRES,FAIL,NFAIL) DOUBLE PRECISION STRES(NSRES), ERES(NSRES),FAIL(NFAIL) C**** C**** USER CODE C**** . . . GLFC02=... RETURN END

The variables in the argument list are defined as follows:

Input:

SRES - Stress resultants in laminate reference axis system

ERES - Strain resultants in laminate reference axis system

NSRES - Number of stress/strain resultants

FAIL - Failure properties

NFAIL - Number of failure properties (=14)

Output:

GLFC02 - Failure index for laminate failure criterion 2

B.5.3 Failure Laws

Failure laws are used to study the behaviour of composite laminate beyond the point of first ply failure. It is assumed that the material behaves linearly up to failure. The failure surface and the post-failure degradation in material properties are then defined by the failure law. It should be noted that the failure model currently assumes a plane stress hypothesis, ie the transverse shear components must always remain elastic with no degradation in material stiffness. A total of five failure laws (FLW1, FLW2, FLW3, FLW4 and FLW5) are available in the program, of which laws FLW1 and FLW2 are pre-defined and the other three are user defined.

B.5.3.1 In-Built Failure Law

FLW1

This law checks material failure via a combination of maximum stress criterion in the fibre direction and a choice of criteria from Tsai-Wu, Azzi-Tsai, Hoffman, Norris, von-Mises or maximum stress. From the governing failure criterion, the mode of failure, ie fibre or matrix failure, can be determined. The maximum stress criterion in fibre direction can clearly be identified as an indicator of fibre cracking whereas the other criterion selected predicts the layer strength for stress states with relatively large transverse stress components



and therefore can be treated as matrix failure. The post-failure material stiffness will depend on the mode of failure and its form for fibre and matrix failure are given as follows:

In the above, subscripts 1 and 2 denote fibre and transverse direction, respectively. 2β is a material parameter defining the reduction in fibre stiffness after fibre failure. If not specified, 1- 2β =E22/E11 which means that only matrix stiffness remains after fibre failure. Delamination is checked using the formula stated in Appendix B.5.1. When this failure is detected, it is assumed that the lamina will lose all its stiffness. β is a material parameter defining the reduction in fibre stiffness after matrix failure. Full details of the theory are given in Ref B.7.

FLW2

For this law, failure is deemed to occur when the selected failure function is exceeded. The six available failure criteria are Tsai-Wu, Azzi-Tsai, Hoffman, Norris, von-Mises and maximum stress. This failure law has distinct failure modes that correspond to failures in each of the principal material direction (i.e. 11,22,33,12,23,31 for 3-D). When failure occurs, the dominant failure mode is determined from the stress component that has the largest contribution towards failure.

The post-failure stiffness degradation factors for all six possible failure modes are tabulated below. These factors have been made very general so that the law may be applied to laminae with different material definitions.

Mode Reduction Factors for Diagonal Terms on Material Stiffness 11 22 33 12 23 31

11 β1 β2 β2 β3 1.0 β3 22 β4 β1 β8 β5 β5 1.0

33 β4 β8 β1 1.0 β5 β5



12 β6 β7 1.0 β1 1.0 1.0

23 1.0 β 7 β7 1.0 β1 1.0

31 β6 1.0 β7 1.0 1.0 β1

The defaults for all the βs are zero and, if specified, they must lie within the range 0.0≤ β ≤ 1.0. When more than one failure modes is active, the reduction factor taken for a term will be the smallest among all the active failure modes. Off-diagonal terms in the stiffness are assumed to have reduction factors of min {βi, βj}, where βi and βj are the reduction factors for the associated diagonal terms.

Delamination is checked using the formula stated in Appendix B.5.1. When this failure is detected, it is assumed that all the failure modes in the above table will be active.

B.5.3.2 User-Defined Failure Laws

For user-defined failure laws FLW3, FLW4, and FLW5, users should specify a set of two FORTRAN subroutines for each of their own failure laws. One of these routines is for the formation of the material stiffness matrix, both tangent and secant, while the other is for the evaluation of the failure index. The user routines must be named as indicated below:

Failure law type Material stiffness routine name Failure index routine name

FLW3 DFAIL3 SFAIL3

FLW4 DFAIL4 SFAIL4

FLW5 DFAIL5 SFAIL5

(i) Material Stiffness Routine

This routine should form the material stiffness matrix as a function of stress and/or strain states. Both secant and tangent stiffnesses are required and the appropriate matrix should be set according the the value of input argument IOPT. The following argument list and format should be adhered to.

SUBROUTINE DFAIL5 (DEP ,DE ,STRS ,STRN ,FAIL ,

1 ISF ,NDIM ,NSTV ,NFAIL ,IOPT)

DIMENSION ISF(6)

DOUBLE PRECISION STRS(NSTV),DE(NDIM,NDIM),DEP(NDIM,NDIM),

1 STRN(NSTV),FAIL(NFAIL)

CALL SENTRY (4HDFAI,2HL5)

C

C**** USER CODE

C

.

.

.



CALL SEXIT

RETURN

END


Input:

DE - Elastic material matrix in fibre axis system (ie along fibre and normal to fibre)

STRS - Stress vector in fibre axis system

STRN - Strain vector in fibre axis system


ISF - Failure indicator for each stress component (0 - not failed, 1 - failed) ISF(1) - Component 11 ISF(2) - Component 22 ISF(3) - Component 33 ISF(4) - Component 12 ISF(5) - Component 23 ISF(6) - Component 31

NDIM - Dimension of material matrix (=5 for shells)

NSTV - Size of stress vector (=6 for shells, the last position being the ‘equivalent’ quantity)

NFAIL - Number of failure properties (=14)

IOPT - Option code for material matrix type (1 - tangent, 2 - secant)

Output:

DEP - Failed material matrix in fibre axis system, tangent or secant according to IOPT

(ii) Failure Index Routine

This routine should evaluate the failure index and also report the cause of failure. The user routine should have the following argument list:

SUBROUTINE SFAIL5 (F,IFAIL,ISFLG,STRS,STRN,FAIL,NSTV,NFAIL)

DIMENSION ISFLG(6)

DOUBLE PRECISION STRS(NSTV),STRN(NSTV),FAIL(NFAIL),F

CALL SENTRY(4HSFAI,2HL5)

C

C**** USER CODE

C

.

.

.



CALL SEXIT

RETURN

END


Input:

IFAIL - Failure status at end of last iteration (0 - elastic, 4 - fibre failure, 5 - matrix failure, 6 - lamina failure, 7 - transverse shear/normal stress failure, 8 - modes 5 and 7)

STRS - Stress vector

STRN - Strain vector


NSTV - Size of stress vector

NFAIL - Number of failure properties

Output:

F - Value of failure index (F=1 defines the failure surface)

ISFLG - Failure indicator for each stress component (0 - not failed, 1 - failed) ISFLG(1) - Component 11 ISFLG(2) - Component 22 ISFLG(3) - Component 33 ISFLG(4) - Component 12 ISFLG(5) - Component 23 ISFLG(6) - Component 31

B.6 User Material

The user material interface enables users to define their own constitutive behaviour for a material. A set of two FORTRAN subroutines are required, of which one is for the formation of material stiffness matrix and the other is for the computation of stresses. The user is cautioned that this is an advanced capability and it generally requires considerable expertise to develop a realistic material model. The user must also ensure that the numerical scheme implemented is stable so as to avoid numerical instability.

(i) User Material Stiffness Routine

This user routine should have the following argument list and format:

SUBROUTINE USERDM (DMAT ,ELSTR ,ESTRN ,PSTRN ,STRSB , 1 STATEV,EDAT ,TEMP ,DTEMP ,TIME , 2 DTIME ,ISP ,NSTAT ,NED ,NSTV , 3 NST ,IELTNO ,IMATNO ,LNCNO ,ITER ) INTEGER ISP,NSTAT ,NED , NSTV ,NST ,IELTNO ,IMATNO ,LNCNO ,ITER



DOUBLE PRECISION DMAT(NST,NST),ELSTR(NSTV),ESTRN(NSTV), 1 PSTRN(NSTV),STRSB(NSTV),STATEV(NSTAT), 2 EDAT(NED),TEMP,DTEMP,TIME,DTIME CALL SENTRY(4HUSER,2HDM) C C**** USER CODE C . . . CALL SEXIT RETURN END

Input variables:

ELSTR - Stress vector

ESTRN - Elastic strain vector

PSTRN - Plastic strain vector

STRSB - Back stress vector

STATEV - State variables

EDAT - Elastic material properties

TEMP - Current temperature

DTEMP - Temperature increment

TIME - Current time


ISP - Stress point indicator (0 - elastic, 1 - elastic unloading, 2 - plastic)

NSTAT - Number of state variables (=3)

NED - Number of elastic material properties (=24)

NSTV - Dimension of stress vector

NST - Number of stress components for element (=NSTV-1)

IELTNO - User element number

IMATNO - User material property integer

LNCNO - Load increment number

ITER - Iteration number

Output variables:

DMAT - Material stiffness matrix

(ii) User Stress Computation Routine



This user routine should have the following argument list and format:

SUBROUTINE USERST (ELSTR ,STSDEL ,ELSTN ,ESTRN ,PSTRN ,

1 STRNI ,STNDEL ,STRSB ,STATEV ,EDAT ,

2 WORK ,TEMP ,DTEMP ,TIME ,DTIME ,

3 ISP ,NSTAT ,NED ,NSTV ,NST )

4 IELTNO ,IMATNO ,LNCNO ,ITER )

INTEGER ISP,NSTAT,NED ,NSTV ,NST ,IELTNO ,IMATNO ,LNCNO,ITER

DOUBLE PRECISION ELSTR(NSTV),ELSTN(NSTV),STSDEL(NSTV),

1 STNDEL(NSTV),STRNI(NSTV),ESTRN(NSTV),

2 PSTRN(NSTV),STRSB(NSTV),STATEV(NSTAT),

3 EDAT(NED),TEMP,DTEMP,TIME,DTIME,WORK

CALL SENTRY(4HUSER,2HST)

C

C**** USER CODE

C

.

.

.

CALL SEXIT

RETURN

END

Input variables:

STRNI - Total strain increment vector

STNDEL - Mechanical strain increment vector

EDAT - Elastic material properties

TEMP - Current temperature

DTEMP - Temperature increment

TIME - Current time


NSTAT - Number of state variables

NED - Number of elastic material properties

NSTV - Dimension of stress vector

NST - Number of stress components for element (=NSTV-1)

IELTNO - User element number

IMATNO - User material property integer

LNCNO - Load increment number



ITER - Iteration number

Output variables:

STSDEL - Stress increment vector

Updated variables:

ELSTR - Current stress vector

ELSTN - Current strain vector

ESTRN - Elastic strain vector

PSTRN - Plastic strain vector

STRSB - Current back stress vector

STATEV - State variables

WORK - Incremental work

ISP - Stress point indicator (0 - elastic, 1 - elastic unloading, 2 - plastic)

Notes

1. User material interface cannot be used for creep or field analysis.

2. User material interface cannot be applied to laminated shells.

3. All variables are defined in the stress output axis system as specified in Appendix -A for individual element types.

4. For shell analysis, the first two user material properties specified must correspond to the Young’s modulus and Poisson’s ratio of the material.

5. In transient analysis, the stiffness damping factor for a user material must be set to zero.

6. The updated variables in S/R USERST will be passed in as the values at the beginning of the current increment and all incremental variables will be the incremental changes during the increment.

7. Only the following element types are allowed to have user material. The number of stress components (NST) and their orders are given in the following table:



Element type NST Location in vector

1 2 3 4 5 6 Uniaxial 1 XX - - - - -

Plane Stress 3 XX YY XY - - -

Plane Strain 4 XX YY XY ZZ - -


3-D solids 6 XX YY ZZ XY YZ ZX

Thick beams, STF4 3 XX XY(XT)* XZ(-)* - - -


Springs 1 XX

* for tube or box sections, XT is the tangential shear stress component

8. The last location (ie NSTVth position) in the stress and strain vectors should only be used to store the equivalent values. For spring elements, NST=NSTV=1 and thus the location for equivalent values in not available.



B.7 References

B.1 Zienkiewicz, O.C. and Taylor, R.L., ‘The Finite Element Method, Vol. 1’, McGraw Hill, 1989 (4th Edition).

B.2 Jones, R.M., ‘Mechanics of Composite Materials’, McGraw-Hill, 1975.

B.3 Whitney, J.M., ‘Shear Correction Factors for Orthotropic Laminate Under Static Load’, Tran. ASME, J. Appl. Mech., 1973, pp303-304.

B.4 Hinton, E. and Owen, D.R.J., ‘Finite Elements in Plasticity’, Pineridge Press, 1981.

B.5 Crisfield, M.A., ‘Ivanov’s Yield Criterion for Thin Plates and Shells Using the Finite Element Method’. TRRL Rep. 919, D.O.E., 1979.

B.6 Ueda, Y., and Yao, T., ‘The Plastic Node Method: A New Method of Plastic Analysis’, Comp. Meth. Appl. Mech. Eng., Vol. 34, 1982, pp1089-1104.

B.7 Dorninger, K. and Rammerstorfer, F.G., ‘A Layered Composite Shell Element for Elastic and Thermoelastic Stress and Stability Analysis at Large Deformations’, International Journal for Numerical Methods in Engineering, Vol. 30, 1990, pp833-858.

B.8 Chou, T.W. and Ishikawa, T., ‘Analysis and Modelling of Two-Dimensional Fabric Composites’, Ch.7 of Textile Structural Composites, Composite Materials Series, Vol, 3, Eds. Chou and Ko, Elsevier, 1989, pp209-277.

Appendix C ASAS (Non-Linear) User Manual

Page C-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - C Solution Strategies in ASAS-NL

C.1 Introduction

The fundamental problem of structural analysis is to solve the equilibrium equations. In the finite element idealization these equations are presented in the matrix form.

P=QK* (C.1.1)

and relate the vector of external loads P to the displacement vector Q utilising the structural stiffness matrix K. For non-linear problems the equation (C.1.1) no longer holds, since K is a function of stress and deformation states. However if a piecewise linearisation of the equilibrium equation (C.1.1) is applied as follows

dP=dQK* (C.1.2)

where dQ and dP are increments in the displacement and force vectors, the solution of the problem may be obtained in a sequence of steps.



Figure C.1.1 Main Program Flow Chart

The explicit form of the equation (C.1.2) depends on the type of non-linearity and formulation adopted. In ASAS-NL this applies to non-linear material relations and large displacements. The latter are treated using the Updated Lagrangian formulation, which implies that all state variables are referred to the current configuration of the deformed structure. A flow chart illustrating corresponding algorithm of calculations is shown in Figure C.1.1.

From the methodological point of view the strategy employed in ASAS-NL to calculate the solution of (C.1.2) is a combined incremental - iterative approach. This part of solution process may be considered as global calculation and numerous versions of the solution strategy will be discussed in Section C.2.

During the global calculations there is another set of non-linear equations which is to be solved locally, that is in a number of specified points within an element. This local set of equations relates stresses and strains as follows

dED*=dS (C.1.3)

where dS represents stress vector increment, dE is strain vector increment and D is the material stiffness matrix (modulus matrix). The solution of (C.1.3), which is often referred to as “stress recovery” has twofold objective. The first is to provide a state of stress corresponding to certain load level and the second to contribute to

strains and stress computation unbalanced load calculation

calculation of updated geometry

calculation of displacements

solution of incremental equilibrium equations

data preparation

load generation

stiffness generation



calculation of unbalanced load which is represented by dP vector during the iteration process. The solution methods specific to the stress recovery will be discussed in Section C.3.

C.2 Incremental - Iterative Procedures

C.2.1 Introduction

The solution to the non-linear problem provided by ASASNL is obtained using incremental solution procedures with a possibility of iterative correction within each increment. Two main types of procedures are incorporated into the program. The first ones (code named SOLV) are the classical Newton-Raphson incremental - iterative procedures, which provide the solution (displacements) corresponding exactly to the originally specified load. Using the second type of procedures (code named SOLU) load level as well as displacements are adjusted according to the response of the structure. Those procedures are often referred to as ‘structural response’ or ‘variable load’ methods. However despite the differences both types of procedures can be described using the same general formulation, and in order to avoid unnecessary repetitions this method of presentation is adopted here.

Numerical execution of the solution process within each increment is performed in two stages. During the first stage a type of increment and its size is selected and incremental prediction dQi,1 (subscript ‘i’ denotes increment number) is obtained from the equations

Pd=QdK* 1i,1i, (C.2.1)

Qd*a=dQ 1i,i1i,

Pd*a=dP 1i,i1i,



Figure C.2.1 Constraint Surface of Solution Process

solution points

dP

dPi,1 dPi,2 dP2

constraint surface

dQi,1 dQi,2 dQ

load - deflection curve (true equilibrium path)



where K is the stiffness matrix, Pd 1i, is an increment of the load vector of arbitrary size and ai is a scalar multiplier used to obtain requested increment size. During the second stage an iteration procedure is applied, which is aimed at the improvement of initial incremental prediction. To describe in a general but precise manner the procedures employed by ASAS-NL a concept of constraint surface is introduced. The characteristic feature of this surface is that it contains points representing a sequence of solutions obtained during subsequent iterations, Figure C.2.1. Exact definition of this surface will be given later. The operations performed at this stage include choice of the type of constraint surface, application of an iteration technique of specified type and then calculation of an iterative correction dQj (subscript ‘j’ denotes iteration number) from the equation.

dP=QdK* jj (C.2.2)

where dPj is the residual force vector. Next the current incremental values dQ ji, and dP ji, of the displacement and load vectors respectively are calculated using the following formulae

dQ+dQ*b+1-dQ=dQ j1i,jji,ji, (C.2.3)

dP*b+1-dP=dP 1i,jji,ji,

where bj is a multiplier determined according to the adopted constraint as discussed later. A flow chart showing

the idea of the described above incremental - iterative method is shown in Figure C.2.2.



Figure C.2.2 Flow Chart of Incremental/Iterative Solution Process

FINISH

conv?

First stage

Second Stage

Qd ji, Pd ji,

Qd 1i, Pd 1i,

START

Qd 1,i

ai

dPj

dQj

bi

Y

N

unscaled incremental prediction (type of increment)

scaling multiplier (size of increment)

scaled incremental vectors

unbalanced load (path dependent or path independent approach)

iterative correction (type of iteration method)

constraint multiplier (type of constraint surface)

corrected incremental vectors

convergence check



C.2.2 Basic Definitions

The selection of increment type and the definition of constraint surface is based on the scalar function fi,j which

is defined in two alternative forms:

as a linear function

dP*H+dQ*G=f ji,iji,iji, (C.2.4)

or as a quadratic function

dQ*G*)dQ((=f ji,iT

ji,ji, dP*H*)dP(+ ji,iT

ji, )dP*L*)dQ(+ ji,iT

ji, (C.2.5)

where Gi, Hi, Li are diagonal matrices which in general may vary between increments. Prescribing the value of the scalar fi,j at the beginning of the increment and then keeping its value constant during the iteration process provides two additional equations, which are used to calculate the multipliers ai and bj .

The constraint surface can now be defined as a subspace in the load/displacement space which is characterized

by a constant value of fij within the i-th increment. The position of this surface is determined by the size of the i-

th increment. In mathematical terms these two conditions are expressed as follows

dl=f i1i, (C.2.6)

where dli is the required length of incremental vector, and

0=f-f 1ji,ji, − (C.2.7)

Taking into account (C.2.3) and (C.2.4) or (C.2.5) the above constraint becomes )dP*b+(dP*H+)dQ+dQ*b+(dQ*G i,1j1j-i,iji,1j1j-i,i

0=dP*H-dQ*G- 1ji,i1ji,i −− (C.2.8)

or

)dQ+dQ*b+dQ(*G*)dQ+dQ*b+dQ( j1i,i1ji,iT

j1i,j1ji, −−

)dP*b+dP(*H*)dP*b+dP(+ 1i,j1ji,iT

1i,h1ji, −−

)dP*b+dP(*L*)dQ+dQ*b+dQ(+ 1i,j1ji,iT

j1i,j1ji, −−

dP*H*)dP(-dQ*G*)dQ(- 1ji,iT

1ji,1ji,iT

1ji, −−−−

0=dP*L*)dQ(- 1ji,iT

1ji, −− (C.2.9)

respectively for linear or quadratic formulation.



The following values of matrices Gi, Hi and Li are available in ASASNL

(a) G = [0], H = [I], L = [0] (C.2.10)

where [I] is the identity matrix

(b) G = [I], H = [0], L = [0] (C.2.11)

(c) G(n,n) = 0 for n = m, G(m,m) = 1

where ‘n’ is from 1,N. ‘N’ is the total number of displacements and ‘m’ is the number of a

specified displacement

H = [0], L = [0] (C.2.12)

(d) G(n,n) = K(n,n), H(n,n) = 1/K(n,n) for ‘n’ from 1,N

L = [0] (C.2.13)

(e) G = [0], H = [0], L = [I] (C.2.14)

In the following sections it will be shown how the choice of matrices Gi, Hi and Li determines the character of

numerical procedure.

C.2.3 Incrementation procedures

As mentioned before, during the first stage a prescribed value of dli is adopted which together with one of the above options gives the required type and size of the increment. This is realised as follows in ASAS-NL.

(a) Load vector increment (proportional), obtained using (C.2.4), (C.2.6), and (C.2.10), which gives

),Pd/(I*dl=a 1iii (C.2.15)

Requested by SOLV or SOLU LOAD

with the values of dli (for i = 1,2...) are either specified using a list of pseudo-times or automatically

generated.

For the automatic procedure, the pseudo-time step size is given by

tf=t 1i-i ∆∆

where f = FINCMX if the solution has converged in less than ITERD iterations in KSIGNL consecutive

steps and f = 1.0 otherwise. The default value of FINCMX is 1.5.

(b) Specified displacement increment, obtained using (C.2.4), (C.2.6), and (C.2.12), which gives



)(mQ/ddl=a 1i,ii (C.2.16)

Requested by SOLU CONSIT

with the initial value of dli (for i = 1) specified using INCDIS and then (for i 1) controlled by ITERD

via

2/1

1i-i ITERITERD

dl=dl

and ITER is the number of iterations for convergence in the (i-1)th step.

(c) Displacement vector increment, obtained using (C.2.5), (C.2.6), and (C.2.11), which gives

)Qd*)Q((d/dl=a ,1iT

,1iii (C.2.17)

Requested by SOLU ARCL

with the initial value of dli (for i = 1) specified using INITPR or INCDIS and then (for i 1) controlled

by ITERD as in (b).

C.2.4 Iteration procedures

C.2.4.1 Type of constraint surface

The general definition of the constraint surface has the form of either equation (C.2.8) or (C.2.9). This combined with one of the options for the matrices Gi, Hi and Li provides a wide selection of the constraint surfaces. Substituting the current displacement and load vectors into the surface equation during the second stage gives the formula which is a basis for the determination of the multiplier bj used in (C.2.3). This in detail is presented below together with ASAS-NL realization.

(a) Plane of constant load, defined by the equation

0=bj (C.2.18)

obtained from (C.2.8) and (C.2.10).

Requested by SOLV or SOLU LOAD

(b) Plane of constant displacement, defined by the equation

0=)dQ(m*b+)dQ(m ,1ijj (C.2.19)




Requested by SOLU CONSIT

or by SOLU CONSIT AUTO

In the later case displacement number ‘m’ is automatically selected from the condition

))(nQ(dmax =)dQ(m ,1i,1i (C.2.20)

(c) Cylindrical surface of constant length of incremental displacement vector, defined by the equation

0=3a+b*2a+b*1a j2j (C.2.21)

where

,1iT

,1i dQ*)dQ(=1a (C.2.22)

)dQ+dQ(*)dQ(*2=2a j1j-,iT

,1i

)dQ+dQ*(2*)dQ(=3a j1j-,iT

j


Requested by SOLU ARCL

(d) Piecewise plane envelope of the above, defined by the equation

0=dQ*)dQ(*b+dQ*)dQ( 1j-,iT

,1ij1j-,iT

j (C.2.23)

Obtained from truncated combination of (C.2.8) and (C.2.11). Serving as back-up for the previous case.

Requested by SOLU TARCL

(e) Piecewise plane envelope of ellipsoidal surface of constant length of combined weighted incremental/load

vector, defined by the equation

0=dQ*G*)dQ(*b+dQ*G*)dQ( 1j-,iiT

,1ij1j-,iiT

j (C.2.24)

obtained from truncated combination of (C.2.9) and (C.2.13).

Serving as back-up for the case (c) when scaled convergence is used (see Section C.4).

(f) Surface of constant work, defined by the equation

0=3a+b*2a+b*1a j2j (C.2.25)



where

,1iT

,1i dP*)dQ(=1a (C.2.26)

1j-,iT

,1i,1iT

j1j-,i dP*)dQ(+dP*)dQdQ(=2a

1j-,ij dP*dQT=3a


Requested by SOLU ARCL WORKC

(g) Piecewise plane envelope of the above, defined by the equation

0=dP*)dQ(*b+dP*)dQ( ,1iT

,1ij,1iT

j (C.2.27)

obtained from linearised combination of (C.2.9) and (C.2.14).

Requested by SOLU CONSIT WORKC

C.2.4.2 Iteration techniques

The following iteration techniques are available in ASASNL

(a) Standard Newton-Raphson, Figure C.2.3

This involves formation and reduction of the stiffness matrix K and solution of the equilibrium equation

on each iteration. In this case equations (C.2.1)1 and (C.2.2) are as follows

,1i,1i,1i Pd=Qd*K (C.2.28)

Pd=Qd*K jjj,i

It is requested by UPDA STIF ITER ALL



Figure C.2.3 Standard Newton-Raphson

(b) Modified Newton-Raphson, Figure C.2.4

It involves updating and reduction of the stiffness matrix K only once during an increment. The solution

of the equilibrium equation, calculated at each iteration is obtained using the most recently formulated

stiffness matrix.

The equations (C.2.1)1 and (C.2.2) are now

,1i,1i,1i Pd=Qd*K (4.12)

Pd=Qd*K jj,1i

It is requested by UPDA STIF INCR ALL

or UPDA STIF KT1 ALL

which results in updating of K at the beginning of an increment (i = 1),

or by UPDA STIF KT2 ALL

which results in K being updated at the 2nd iteration.

dP

dPi,1

dPi,2

constraint surface

dQi,1 dQi,2 dQ

load - deflection curve



Figure C.2.4 Modified Newton-Raphson

(c) Initial stiffness, Figure C.2.5

The original structural stiffness matrix Ko is used at all iterations which results in the following form of

the equations (C.2.1)1 and (C.2.2)

,1i,1io dP=dQ*K (4.13)

dP=dQ*K jjo

This method is not suitable if the structure exhibits a high degree of non-linearity. This is the default

method.

dP

dPi,1

dPi,2

constraint surface

dQi,1 dQi,2 dQ




Figure C.2.5 Initial Stiffness

(d) Accelerations

The modified Newton-Raphson and initial stiffness techniques may be ‘accelerated’ by obtaining a new

correction of the displacement increment using a combination of current and previous displacements

rather than repeating the solution of the equilibrium equation. Two acceleration techniques are available

in ASAS-NL, namely

the Secant-Newton, requested by

OPTI SECN

and line search approach requested by

OPTI LINS

C.2.5 Solution methods

A number of solution methods are available in ASAS-NL by which the non-linear problem is solved in step by step manner. They can be obtained using various combinations of incremental and iteration techniques described in the previous sections.

C.2.5.1 Euler-Cauchy method

The simplest method is the Euler-Cauchy integration scheme during which no iterative corrections are calculated and unbalanced load from previous step is neglected. This method is also called the ‘tangent’ stiffness method,

dP constraint surface

dQi,1 dQi,2 dQ




since the evaluation of the tangent stiffness matrix K, based on the state at the beginning of the step is required. It is realised using the following commands.

JOB STAT

PROB/TITL NRES LARG . . . .

SOLV or SOLU . . . .

UPDA STIF INCR ALL

UPDA GEOM

ITER 1 TO END

OPTI OVIT

C.2.5.2 Self-correcting Euler-Cauchy

The Euler-Cauchy method can be considerably improved by taking into account the unbalanced (residual) load due to non-linear effect. In structural analysis this method is also called “the initial load” method. It is realised by

JOB STAT

PROB/TITL LARG . . . .


UPDA STIF INCR ALL

UPDA GEOM

ITER 1 TO END

OPTI OVIT

C.2.5.3 Full incremental - iterative method

This method is a combination of incremental process with an iterative technique. In ASAS-NL this combination is defined by the user and no restrictions are imposed. Also the iteration techniques chosen can be combined with any of the constraint surfaces available. It is realised by

JOB STAT

PROB/TITL LARG . . . .


UPDA STIF . . . .

UPDA GEOM . . . .

However the type of increment and the type of constraint surface must be of the same nature since they are defined using the same command for both. For example

SOLU ARCL

results in incrementation of the displacement vector and use of cylindrical surface. Graphical representation of this method is shown in Figure C.2.6.



Figure C.2.6 Arclength Solution Procedure with Cylindrical Constraint Surface

C.2.6 Conclusions

Two purely incremental methods described above constitute cheap but inaccurate way of tracing a non-linear equilibrium path. In practice the solution should be rather calculated using full incremental-iterative approach, exploiting to the best advantage a variety of options available within that method.

First a choice between SOLV or SOLU method has to be made. Having in mind full large displacement elasto-plastic analysis, including possible bifurcation or snap through phenomena the arclength type method is recommended as well suited to trace load-displacement path which contains limit points of both load and displacement character. SOLV method should be used when solution to precisely specified load is necessary. Therefore making first approach to obtain a solution of general non-linear problem involving both material and geometrical non-linearities, the following procedure is recommended

1. For non-proportional loading

JOB STAT

PROB/TITL LARG PLAS . . . .

SOLU LOAD . . . .

UPDA STIF ITER ALL

UPDA GEOM

Load

Displacement



2. If limit point is expected and proportional loading

JOB STAT

PROB/TITL LARG PLAS . . . .

SOLU ARCL nn . . . .

(or SOLU CONSIT nn AUTO . . . .)

UPDA STIF ITER ALL

UPDA GEOM

This procedure may then be changed during the course of analysis allowing to ‘tailor’ the type of non-linear strategy to the problem being solved, thus increasing computational efficiency. This can be done using Restarts and redefining controlling commands.

The termination of iteration within each increment is based upon satisfaction of certain criteria. This as well as possibility of automatic restart in the case of converging solution is discussed in the later section.

C.3 Computation of Stresses

In the previous section global strategies for solution of non-linear equilibrium equations and calculation of displacements were discussed. Separate problem which has to be dealt within each solution cycle is the calculation of strain and stress states. As already mentioned those calculations are performed at a number of integration points within each element according to the following algorithm.

First using geometrical relations vector of total strains E is obtained from current displacements. Then vector of strain increments dE is calculated and applying constitutive relations vector of stress increments dS is evaluated. In the elastic case this relation has the linear form

dED*=dS (C.3.1)

In the case of plasticity the constitutive relation is in general of non-linear character

)dE(dE-D*=dS p (C.3.2)

where dEp is the vector of plastic strain increments and is a function of the stress state.

In ASAS-NL, there are two different approaches to integrate the incremental elastic-plastic constitutive relationship and these are called the Forward Euler and Backward Euler schemes, respectively. Forward Euler scheme is the default in the program and Backward Euler scheme is activated by OPTION BAKE.

C.3.1 Forward Euler Integration Scheme

The single step Forward Euler scheme is an explicit method that uses the plastic flow direction and yield condition at the beginning of a step as the reference. Due to its explicit nature, the scheme is only conditionally stable and will fail if very large increments of plastic strain occur within a step. To make the solution process more stable and to improve accuracy, a technique known as sub-incrementation can be adopted where the strain



increment is divided into a number of sub-increments and the stresses accumulated accordingly. Illustrations of the Forward Euler scheme with and without sub-incrementation are given in Figure C.3.1.

The number of sub-increments NSUB for each strain increment can be determined either by setting it explicitly using

PARA SUBINC NSUB (default to 1)

or by setting the required size of strain sub-increment using

PARA SUBTOL tolerance value

Figure C.3.1 Forward Euler Integration Scheme

The number of sub-increments is then determined by

/SUBTOL|dE*dE=|NSUB T (C.3.3)

The appropriate value of SUBTOL may be difficult to predict, thus giving it the value 0.0 results in

10*|))dE(1)*(1)dE/(||)dE(i)*(i)dE((|=NSUB TT (C.3.4)

S

E

dS

NSUB

dE

no sub-increment

NSUB sub-increments

stress-strain relation curve



During the iteration process the element strains and stresses are calculated after each iteration. In ASAS-NL this calculation is approached by the “path independent” scheme. The flow chart for the stress computation is shown in Figure C.3.2.

Figure C.3.2 Flow Chart of Path Independent Stress Calculation

In the path independent scheme strain increment is calculated as the difference between the current strains and those obtained from the previous step (increment), related therefore to converged solution. Corresponding stress increment as well as total stress are then calculated. But until a convergence is satisfied the total stress contribute only to recalculation of unbalanced load (residuals) used in the next displacement iteration. The final state, being a sum of the previous converged solution and the current increment does not depend directly on the solution path.

The main advantage of the path independent scheme is that it reduces the risk of incorrectly predict unloading during plasticity analysis. It is particularly suitable to be used in combination with variable load methods. In situations where the strain increment may have relatively large values, it is more effective to use the path independent scheme in combination with sub-incrementation or with the Backward Euler Integration Scheme in the next section.

C.3.2 Backward Euler Integration Scheme

The Backward Euler scheme is a fully implicit method where the plastic conditions are enforced at the end of a load step. It is unconditionally stable and is therefore capable of handling large plastic strain increments. It has been shown that rapid convergence of the global set of non-linear equilibrium equations can be achieved if the Backward Euler scheme adopts a path independent strategy and a “consistent” tangent modulus that takes into

j,iE

current total displacements j,iQ

E-E=Ed 1i-j,ij,i

)dEf(=dS j,ij,i

j,i1i-j,i dS+S=S

current total strains

incremental strains

constitutive law

current total stresses



account the effect of finite step size is employed in the stiffness calculation. This procedure will be in force when OPTION BAKE is specified

At present, the Backward Euler scheme is only available for von Mises yield criterion with isotropic and/or kinematic hardening. For plane stress, beam and shell elements, there is an additional requirement that any non-linear hardening must be isotropic. Other types of yield surfaces must use the Forward Euler scheme.

C.4 Convergence and Auto-Recovery

C.4.1 Convergence Check

The convergence criteria specify what level of accuracy of the iterative solution is acceptable. Convergence check is performed after each iteration using the following inequality

tolerance<= )q( /NORM)dq( NORM j,ij

where dqj is j-th iterative correction of selected quantity, calculated during i-th increment, and qi,j is the total

incremental value of this quantity obtained after j-th iteration of i-th increment. Several state variables can be

used in the convergence criteria, such as; displacements, residual forces, strains and stresses. NORM used in the

left hand side of the above inequality may be selected as one of the following; Absolute, Euclidean, or Maximum

value. In addition if displacements or residual forces are used in the convergence criteria, its components can be

scaled according to the formula

dQ)D**dQ( T

or

dP)*D*dP( -1T

for displacements or residual forces respectively, where D is the matrix of diagonal stiffness terms.

After the convergence requirement is satisfied the run is terminated or the next increment can be started. Otherwise the iterative process is repeated and new values of state variables are calculated. However the number of iterations within one increment is limited (to default number of 10, or to the user specified number). If convergence test is not satisfied within that limit the run is terminated.

C.4.2 Auto-Recovery

In some cases the iteration process may not be converging fast enough or even diverging. A facility is available in the SOLU procedures to break out of diverging (or slowly converging) iteration process and restart a new one from last converged solution. For restarted increment standard Newton-Raphson iteration procedure will be automatically invoked and step size will be reduced

new step = STEPRF * old step



The multiplier STEPRF has the default value 0.5, but if required can be redefined using the PARAMETER command. The number of auto-recoveries is 3 by default, but it again can be adjusted using the PARAMETER command and specifying required number after parameter MXAUTO.

C.5 Eigenvalue Analysis

In ASAS-NL three separate applications of eigenvalue analysis are available. First is to a stability analysis which provides the information about a buckling load. The buckling (or bifurcation) point is defined as the intersection between two distinct equilibrium paths; primary and secondary. Two situations may be distinguished

(a) Linear prebuckling behaviour, where the primary path is linear (e.g. Euler column).

(b) Non-linear prebuckling behaviour characterized by non-linear primary path (e.g. shallow circular arch

under central point load).

The second application is to spectral analysis of the small displacement stiffness matrix.

The third application is for natural frequency analysis to evaluate the vibration characteristics of a loaded or unloaded structure.

C.5.1 Linear Pre-buckling Case

To obtain the bifurcation point for the situations where the pre-buckling (or primary path) is linear, the following eigenvalue problem is solved

0=*)K*+K( Go φλ (C.5.1)

where Ko is the current small deflection stiffness, KG(σ) the geometric stiffness, λ is the eigenvalue and φ is eigenmode.

The buckling (critical) load Pc, is given by

P*=Pc λ (C.5.2)

where P is the applied load.

C.5.2 Non-linear Pre-buckling Case

In this case the buckling problem may be derived from an incremental displacement relation

dP=dQK* ii (C.5.3)

or in expanded form

Pd=dQ*)K+K( iiGo (C.5.4)



Assuming locally linear behaviour, buckling occurs if it is possible to find a displaced state φdQ+ without change in load dP. In other words there exist a neighbouring configuration φdQ+ that is also in equilibrium with load dP. The incremental load deflection relationship is thus

0=*)K*+K( Gio φλ (C.5.5)

in which we seek values of the multiplier λi which yields a non-zero solution for φ . It is possible to carry out an eigenvalue analysis at any point in the load history once a converged state has been reached i.e. at the end of an increment.

The buckling (critical) load is again calculated from the formula

P*=Pic λ (C.5.6)

Figure C.5.1 Critical Load Evaluation using Eigenvalue Analysis

Figure C.5.1 illustrates the procedure, where the solid curve is the load-deflection curve (the so called primary

path). The dashed curve is the locus of critical loads Pic. The point of intersection between these two curves

occurs at λ = 1 and coincides with the bifurcation point. However because in many practical cases the critical

load curve is almost straight, it is not necessary to carry out costly eigenvalue analysis at every increment. Often

two or three points on that curve are sufficient to determine the bifurcation point (Ref.C.1).

C.5.3 Spectral Analysis

This is a standard eigenproblem written in the form

P

Q

λ�=1λ�>1

critical load curve

primary path

secondary path

bifurcation point

λ<1



0=I)+K( o φλ (C.5.7)

where I is the unit matrix. The solution of (C.5.7) is used in the evaluation of an element stiffness matrix or in the calculation of the condition number of a structure stiffness matrix.

C.5.4 Natural Frequency Analysis

In this case the eigenproblem can in general be written as

φλφφ iii2iiCGo M=Mw=)K+K+K( (C.5.8)

where Ko and KG are as defined before Kc is the centrifugal stiffness and is a function of the angular velocity M is the mass matrix λi is the ith eigenvalue and is equal to the square of angular velocity, wi

φ i is the corresponding mode shape

Once the eigenproblem is solved, the natural frequency of vibration, fi, can be obtained from

π2w=f i

i

Note that if the structure is not spinning or loaded in any way, both KG and Kc will be zero and equation (C.5.8) becomes

φφ i2iio Mw=K

which is the standard generalised eigenvalue problem for unloaded structures.

C.6 Contact Analysis

Two types of solution procedures for contact analysis are available in ASAS-NL; namely the penalty method and the augmented Lagrangian method. The penalty method is used for both gap elements and rigid surface elements while the augmented Lagrangian method is only available to rigid surface elements on request (by specifying a positive integer for PARAmeter MXAUGM).

C.6.1 Penalty Method

In this method, penalty springs of very high stiffness are introduced at regions where contact occurs to enforce the necessary impenetrability and stick (if any) conditions. The contact constraints can be more strongly satisfied by increasing the penalty stiffness but this may also create matrix conditioning problems. On the other hand, the contact conditions may not be properly enforced if the penalty is too small. Thus, the choice of suitable penalty parameters for the solution is very important.

In ASAS-NL, the penalty stiffness for the gap elements is specified through the effective stiffness from the material property data and the parameter GAPSTF. These two parameters can be adjusted to give the desired



penalty effect. Magnitudes of the penalty stiffness for the rigid surface elements in both the normal and tangential directions are supplied as elastic and Coulomb friction material data.

C.6.2 Augmented Lagrangian Method

The augmented Lagrangian method (Ref C.2) can be viewed as a combined Lagrange multiplier and penalty method. It has been shown that this method can provide added robustness to the penalty approach because of its ability to correct under-penalised solutions while maintain good numerical conditioning. In essence, the augmented Lagrangian method assumes that the contact forces are decomposed into the penalty and Lagrange multiplier parts. Instead of treating the Lagrange multipliers as additional global variables, they are fixed during the global solution stage and thus the entire solution process works in the same way as the penalty method, with the appropriate consideration of the multiplier contributions. Augmentation of the multipliers is performed only after a new global solution is obtained and when the following conditions are met:

1. The maximum number of augmentations, MXAUGM, has not been reached, and

2. Contact conditions have not been completely satisfied, i.e. penetration > GAPCVG at any of the contact positions, or relative tangential displacement > TANCVG at any of the stick positions.

MXAUGM, GAPCVF and TANCVG are parameters which may be reset using the PARA command.

C.7 References

C.1 Chang, S.C. and Chen, J.J., ‘Effectiveness of Linear Bifurcation Analysis for Predicting the Non-linear Stability Limits of Structures,’ Int. Jnl. Num. Methods in Eng., Vol.23, pp831-846, 1986.

C.2 Simo, J.C., and Laursen, T.A., ‘An Augmented Lagrangian Treatment of Contact Problems Involving Friction’, Comp. Struct., Vol. 42, pp97-116, 1992.

Appendix D ASAS (Non-Linear) User Manual

Page D-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - D Restarts

D.1 Introduction

Restarts have obvious advantages in economy and convenience compared with re-running an original analysis from the start and are normal practice for most non-linear analyses. The facilities provided in ASAS-NL allow an analysis to be restarted from any previous valid load step with a new set of control instructions and loading if required. For a restarted job, only the Preliminary data, suppressions data, prescribed freedoms data, loading data and additional mass data may be changed.

Restarts may be used for a number of purposes, including:

• running an analysis in a series of controlled stages

• continuing an analysis terminated through lack of resources

• re-running with new loading

• re-running (from previous steps) with new solution strategies

• continuing an analysis from onset of non-linear behaviour after scaling the initial linear analysis with

the SCALE command.

During the course of an analysis, information about the current state of the analysis is saved on two external files, the data manager archive file and element stiffness matrix archive file (see Section 4.4.4), according to instructions specified with the Preliminary data SAVE command. When a restart is attempted, the internal file structure is re-created from these two backing files. Restarts may thus only be performed from load steps at which the two backing files were archived in the initial analysis.

D.2 Initial Analysis

The following action is needed:

(i) Define the names of the (new) stiffness and data manager archive files. This is done by means of FILE

commands (one for each file), together with the directive ‘NEW’ specified with the SAVE command. If

no names are defined explicitly, default names (see Section 6) will be used, but this is not recommended.

(ii) With the SAVE command, give the increments at which data is to be archived.

In the absence of a SAVE command, both files are automatically archived for the last load increment

only.



Note that stiffness matrices are only archived if a change of state has taken place from the previous

archive. Thus, the stiffness file may not be checkpointed at certain load stages, despite the request with

the SAVE command.

D.3 Restarted Jobs

Before restarting an analysis, the user must ensure that the appropriate data manager and stiffness files for the restart are to hand.

If the restarted analysis is to follow the original load history then only Preliminary data should be present, together with a STOP command.

If the load history or boundary conditions are to be redefined, then all data blocks including the STOP command are required. However, in this case the structural description data must be identical to the original model.

The following points apply to Preliminary Data:

(i) The name and title specified with the PROJECT command must be the same as for the initial analysis.

(ii) The name of an existing structure within the same project should be specified with the STRUCTURE

Command.

(iii) The name of the structure to be created in this run should be specified with the NEWSTRUCTURE

command

(iv) The name of the old data manager archive file must be specified with the JOB command together with the

checkpoint number of the restart. The checkpoint number is given preceding the displacements for the

restarted load step on the ASAS-NL output file for the initial analysis.

(v) The name of the old stiffness matrix file may optionally be given with a FILE command.

(vi) The SOLVE command should be replaced by a RESTART command, giving the time from which the

restart is to be made (say Tr), followed by a list of solution times. No solution is attempted at the restart

time Tr. The checkpoint number specified with the JOB command must correspond to the load step Tr.

If the SOLU command was used in the initial analysis it should be replaced by the SREST command,

giving the increment number from which the restart is to be made. No solution is attempted at this

increment.

(vii) Number of groups and their definition must be the same for both initial and restarted runs.

(viii) Archiving during the restart should be defined as before using the SAVE command.



(ix) If the option ‘NEW’ is specified on the SAVE command, then new backing files will be created during

the restarted analysis. The file names should be defined using FILE commands. If the option ‘OLD’ is

specified with the SAVE command, then the old backing files will be used for all archiving during the

restart. Archived information will be appended to previously archived data up to the restart time. Any

previous archives made after the restart time will be overwritten.

In general, it is recommended that ‘NEW’ be used rather than ‘OLD’.

D.4 Examples

Initial Analysis

A sample ASAS-NL data file for performing an initial analysis is given below.


PROJ APRJ * RESTARTS

STRUCTURE ASTR

JOB STAT

TITL PLAS *INITIAL ANALYSIS

SOLV 0.1 0.2 0.3 0.4

FILE ARCH ARCHA

FILE NSTF STIFA

UPDA STIF KT2 0.1 0.3

SAVE NEW ALL

END

Structural description data

Boundary conditions data

Loading data

Additional mass data

(Initial conditions data)

STOP

Checkpoints are written to the new archive files ARCHA and STIFA for each load increment as follows:

Increment Time File Checkpoint

1 0.1 STIFA ARCHA

1 2

2 0.2 ARCHA 3

3 0.3 STIFA ARCHA

3 4



4 0.4 ARCHA 5

The two files are checkpointed separately. Checkpoint 1 is written to ARCHA by PRENL. STIFA is not checkpointed for load steps 0.2 and 0.4 as the stiffness matrices are not reformed in these load steps (see UPDA command).

Restarted Analysis

The ASAS-NL data file for performing a restart from the conclusion of the second load step is as follows:


PROJ APRJ *RESTARTS

STRUCTURE ASTR

NEWSTRUCTURE BSTR

JOB STAT ARCHA (3)

TITL PLAS *EXAMPLE RESTART

REST 0.2 0.3 0.4 0.5 0.6

FILE OSTF STIFA

FILE NSTF STIFB

FILE ARCH ARCHB

UPDA STIF INCR 0.2

SAVE NEW 0.4 0.5

END

STOP

Checkpoint 3 is used on the data manager archive file. New backing files ARCHB and STIFB are created in the restarted analysis. The checkpoints written during the restarted analysis are:


4 0.4 ARCHB 5

5 0.5 ARCHB 6

6 0.6 ARCHB 7

No solution is attempted at the first solution time specified with REST command. The file STIFB was not created as the element stiffness matrices are not reformed during the analysis.

Re-Restart Analysis

A further restart continuing the analysis from the end of the previous restart is obtained with the following:


PROJ APRJ *RESTARTS



STRUCTURE BSTR

NEWSTRUCTURE CSTR

JOB STAT ARCHB (7)

TITL PLAS *EXAMPLE RE-RESTART

REST 0.6 0.7 0.8

UPDA STIF KT2 ALL

END

STOP

The archived element stiffness matrices are read from STIFA and data manager file from checkpoint 7 on ARCHB created in the previous restart analysis. The new checkpoints created are:


8 0.8 STIFA ARCHB

8 9

As no SAVE command was given, the original backing files were overwritten (in this case the restart continued

from the end of the previous restart and thus the extra checkpointed information would be appended to the

original backing file).

Appendix E ASAS (Non-Linear) User Manual

Page E-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - E Example Data Files

E.1 Example 1: BM3D Plasticity Model (T0574) Description

Data


PROJ *VALIDATION TEST FOR PLASTICITY MODEL FOR BM2D AND BM3D

JOB STAT

TITL PLAS * 3D FRAME COLLAPSE - SHI ET AL (EX.3)

TEXT ASAS-NL TEST FILE - T0574PRE.DAT

TEXT CREATED - 23/07/90

SOLV 10.0 12.0 14.0 16.0 17.0 17.5 17.75 18.0 18.25 18.5 18.75 19.0

SOLV 19.25 19.5 19.75 20.0 20.15

UPDA STIF ITER ALL

PARA SUBINC 5

OUTP 1 ALL

BLOC 1 SRES

OPTI PIND

END

COOR

1

2 0 0 2500

3 0 0 5000

4 5000 0 0



5 5000 0 5000

6 0 5000 5000

7 0 10000 5000

8 0 10000 0

9 5000 10000 5000

10 5000 10000 0

END

ELEM

MATP 1

BM3D 1 2 1

BM3D 3 5 1

BM3D 5 4 1

BM3D 6 7 1

BM3D 5 9 1

BM3D 8 7 1

BM3D 7 9 1

BM3D 9 10 1

MATP 2

BM3D 2 3 1

BM3D 3 6 1

END

MATE

1 ISO 207000 0.3

1 PLAS BEAM 8.1127E6 8.4582E8 8.4582E8

: 1.0 2.0 1.0 2.0 1.0 2.0

2 ISO 207000 0.3

2 PLAS BEAM 8.1127E6 9.0E8 9.0E8

: 1.0 2.0 1.0 2.0 1.0 2.0

END

GEOM

1 BM3D 2.3628E4 3.17376E8 3.17376E8 6.34752E8 2500 5000 0

END

SUPP

ALL 1 4 8 10

END

LOAD

SET 1 VERT AND HORIZ LOAD

NODAL LOAD

X 49050. 2

X 24525 6

Z -49050. 3 5 7 9

END

STOP



E.2 Example 2: TCS9 Geometric non-linearity (T0533) Description

Data


PROJ * FOUR AND NINE NODE SHELLS

JOB STAT

TITL LARG * SHELL ROOF UNDER VERTICAL PRESSURE

TEXT PRENL TEST DATA - T0533PRE.DAT


SOLV .001 .002 .003 .004

UPDA GEOM ITER ALL

UPDA STIF ITER ALL

PARA PENFUN 1.E-3 DRILF 1.E-6 SHEARL 0.0

END

COOR

CYLI AXES RAD

DCOS 1. 0.0 0.0 0.0 0.0 -1.

ORIG 0.0 0.0 0.0

//

/

1 7600. 4.71238898 0.0

RP 9 1 0.0 .087266462 0.0

RRP 9 9 0.0 0.0 950.

END

ELEM

//

/

TCS9 1 2 3 12 21 20 19 10 11 1 1



RP 4 2

RRP 4 18

END

MATE

1 ISO 2.1E4 0.0 0.0 1.3412736E-6

END

GEOM

1 TCS9 76.

END

SUPP

X 1 10 19 28 37 46 55 64 73

X 2 3 4 5 6 7 8 9

Y 73 74 75 76 77 78 79 80 81

Z 1 2 3 4 5 6 7 8 9

RX 73 74 75 76 77 78 79 80 81

RY 1 2 3 4 5 6 7 8 9

RY 10 19 28 37 46 55 64 73

RZ 1 10 19 28 37 46 55 64 73

RZ 74 75 76 77 78 79 80 81

END

LOAD

SET 1

BODY FOR

0.0 0.0 -9810.

END

STOP

E.3 Example 3: QUX4 Incompressible behaviour (T0540) Description

Sphere under internal pressure 1. 16 QUX4 elements with constant volumetric dilatation (i.e. PINO 1) 2. ν=0.49999

Inner radius = 0.5 Outer radius = 1.0



Data


PROJ * HYPERELASTICITY AND INCOMPRESSIBILITY

JOB STAT

TITL * ISOTROPIC SPHERE UNDER INTERNAL PRESSURE (QUX4)

TEXT ASAS-NL TEST FILE - T0540PRE.DAT


SOLV 1.0

PINO 1 (16) (1,1)

OUTP 1 ALL

BLOC 1 DISP (5)(1,1) (5)(33,1)

OUTP 2 ALL

BLOC 2 STRS STRN 1 2 3 4

END

COOR

CYLI XXXX

DCOS 1.0 0.0 0.0 0.0 0.0 1.0

ORIG 0.0 0.0 0.0

//

/

1 0.5 0.0

RP 5 1 0.125 0.0

RRP 4 8 0.0 22.5

FIN

CART

/

33 0.0 0.0 0.5

RP 5 1 0.0 0.0 0.125

END

ELEM

MATP 1

/

QUX4 1 2 10 9

QUX4 2 3 11 10

QUX4 3 4 12 11

QUX4 4 5 13 12

RP 4 8

END

MATE

1 ISO 20000.0 0.49999

END

SUPP

/



Z 1

R 33

RP 5 1

END

LOAD

SET 1 ’INTERNAL PRESSURE’

PRESSURE

/

U 1.0 1 9

RP 4 8

END

STOP

E.4 Example 4: QUS4 Elasto-plastic stiffened shell (T0553) Description

Data


SYSPAR LPGSIZ 256

PROJ * FOUR AND NINE NODE SHELLS

JOB STAT

TITL PLAS LARG *STRINGER STIF. CYL. - IMP. COLL. PROB. F10

TEXT PRENL TEST FILE - T0553PRE.DAT


TEXT

TEXT CYLINDRICAL PANEL WITH FLAT BAR STRINGER STIFFENER

TEXT R=400.0 L=200.0 T=1.0 STIFFENER D=10.0 T=1.0

TEXT E=2.1E5,PR=0.3 SIGY 350

TEXT IMPERIAL COLLEGE PROBLEM - F10

TEXT DRILF 1.E-6 PENFUN 1.E-3 FLATOL 90.0

R D L=200

R=400 L=200 t=1 (shell) stiffener depth=10=D thickness (stiffener)=1 E=2.1x105, ν=0.3, σy=350 96 QUS4 elements 47 increments 181 iterations 54 stiffeners



TEXT INTE 1 1 5

TEXT

SOLU ARCL 50 INITPR 14.25 ITERD 4 MAXDIS 3 Z 0.4

UPDA STIF KT2 ALL

UPDA GEOM ITER ALL

PARA DRILF 1.E-6 PENFUN 1.E-3 FLATOL 90.0

OUTP 1 ALL

BLOC 1 DISP 3

ITER 20 TO END

INTE 1 1 5 (96)(1,1)

CONV EUCN DISP 0.001

OPTI GOON PIND AUTO OVIT

FILE POST T0553PST

POST DISP ALL

END

COOR

CART

1 395.0753 -62.5738 0.0000

2 398.7669 -31.3836 0.0000

3 400.0000 0.0000 0.0000

4 398.7669 31.3836 0.0000

5 395.0753 62.5738 0.0000

6 395.0020 -62.5622 16.6667

7 400.0000 0.0000 16.6667

8 395.1487 62.5854 16.6667

9 394.9299 -62.5508 33.3333

10 398.6631 -31.3755 33.3333

11 400.0000 0.0000 33.3333

12 398.8707 31.3918 33.3333

13 395.2208 62.5968 33.3333

14 394.8603 -62.5397 50.0000

15 400.0000 0.0000 50.0000

16 395.2904 62.6079 50.0000

17 394.7944 -62.5293 66.6667

18 398.5664 -31.3679 66.6667

19 400.0000 0.0000 66.6667

20 398.9675 31.3994 66.6667

21 395.3563 62.6183 66.6667

22 394.7332 -62.5196 83.3333

23 400.0000 0.0000 83.3333

24 395.4174 62.6280 83.3333

25 394.6779 -62.5108 100.0000

26 398.4833 -31.3613 100.0000



27 400.0000 0.0000 100.0000

28 399.0505 31.4060 100.0000

29 395.4727 62.6367 100.0000

30 394.6295 -62.5032 116.6667

31 400.0000 0.0000 116.6667

32 395.5212 62.6444 116.6667

33 394.5887 -62.4967 133.3333

34 398.4196 -31.3563 133.3333

35 400.0000 0.0000 133.3333

36 399.1143 31.4110 133.3333

37 395.5620 62.6509 133.3333

38 394.5561 -62.4916 150.0000

39 400.0000 0.0000 150.0000

40 395.5946 62.6560 150.0000

41 394.5325 -62.4878 166.6667

42 398.3795 -31.3531 166.6667

43 400.0000 0.0000 166.6667

44 399.1544 31.4141 166.6667

45 395.6182 62.6598 166.6667

46 394.5182 -62.4855 183.3333

47 400.0000 0.0000 183.3333

48 395.6325 62.6620 183.3333

49 394.5133 -62.4848 200.0000

50 398.3658 -31.3521 200.0000

51 400.0000 0.0000 200.0000

52 399.1680 31.4152 200.0000

53 395.6373 62.6628 200.0000

54 397.5 0.0 0.0

55 397.5 0.0194 33.3333

56 397.5 0.0375 66.6667

57 397.5 0.0531 100.0000

58 397.5 0.0650 133.3333

59 397.5 0.0725 166.6667

60 397.5 0.0750 200.0000

61 395.0 0.0 0.0

62 395.0 0.0195 16.6667

63 395.0 0.0388 33.3333

64 395.0 0.0574 50.0000

65 395.0 0.0750 66.6667

66 395.0 0.0913 83.3333

67 395.0 0.1061 100.0000

68 395.0 0.1190 116.6667

69 395.0 0.1299 133.3333



70 395.0 0.1386 150.0000

71 395.0 0.1449 166.6667

72 395.0 0.1487 183.3333

73 395.0 0.1500 200.0000

74 392.5 0.0 0.0

75 392.5 0.0583 33.3333

76 392.5 0.1125 66.6667

77 392.5 0.1591 100.0000

78 392.5 0.1949 133.3333

79 392.5 0.2174 166.6667

80 392.5 0.2250 200.0000

81 390.0 0.0 0.0

82 390.0 0.0390 16.6667

83 390.0 0.0777 33.3333

84 390.0 0.1148 50.0000

85 390.0 0.1500 66.6667

86 390.0 0.1827 83.3333

87 390.0 0.2122 100.0000

88 390.0 0.2380 116.6667

89 390.0 0.2598 133.3333

90 390.0 0.2772 150.0000

91 390.0 0.2898 166.6667

92 390.0 0.2974 183.3333

93 390.0 0.3000 200.0000

201 398.7147 -31.3795 16.6667

203 398.8191 31.3877 16.6667

209 398.6138 -31.3715 50.0000

211 398.9200 31.3958 50.0000

217 398.5234 -31.3644 83.3333

219 399.0104 31.4029 83.3333

225 398.4495 -31.3585 116.6667

227 399.0843 31.4088 116.6667

233 398.3973 -31.3544 150.0000

235 399.1366 31.4129 150.0000

241 398.3703 -31.3522 183.3333

243 399.1636 31.4150 183.3333

301 397.5000 0.0097 16.6667

302 397.5000 0.0287 50.0000

303 397.5000 0.0457 83.3333

304 397.5000 0.0595 116.6667

305 397.5000 0.0693 150.0000

306 397.5000 0.0744 183.3333

307 392.5000 0.0293 16.6667



308 392.5000 0.0861 50.0000

309 392.5000 0.1370 83.3333

310 392.5000 0.1785 116.6667

311 392.5000 0.2080 150.0000

312 392.5000 0.2231 183.3333

END

ELEM

MATP 1

/

QUS4 1 6 201 2 1

QUS4 2 201 7 3 1

QUS4 3 7 203 4 1

QUS4 4 203 8 5 1

QUS4 6 9 10 201 1

QUS4 201 10 11 7 1

QUS4 7 11 12 203 1

QUS4 203 12 13 8 1

RP 6 8

/

QUS4 3 7 301 54 2

RP 6 8 8 1 1

/

QUS4 54 301 62 61 2

RP 6 1 1 2 2

/

QUS4 7 11 55 301 2

RP 6 8 8 1 1

/

QUS4 301 55 63 62 2

RP 6 1 1 2 2

/

QUS4 61 62 307 74 2

RP 6 2 2 1 1

/

QUS4 74 307 82 81 2

RP 6 1 1 2 2

/

QUS4 62 63 75 307 2

RP 6 2 2 1 1

/

QUS4 307 75 83 82 2

RP 6 1 1 2 2

END



MATE

1 ISO 210000.0 0.3

1 PLAS MISE 350.0 0.0

END

GEOM

1 QUS4 1.0

2 QUS4 1.0

END

SKEW

1 0.9877 -0.1564 0.0 0.1564 0.9877 0.0

2 0.9969 -0.0785 0.0 0.0785 0.9969 0.0

3 0.9969 0.0785 0.0 -0.0785 0.9969 0.0

4 0.9877 0.1564 0.0 -0.1564 0.9877 0.0

END

SUPP

/

1 Y RX RZ 1

RP 7 8

/

1 Y RZ RX 6

RP 6 8

/

4 Y RX RZ 5

RP 7 8

/

4 Y RX RZ 8

RP 6 8

1 X Y RX RZ 1

2 X Y RX RZ 2

X Y RX RZ 3

3 X Y RX RZ 4

4 X Y RX RZ 5

1 Z RX RY 49

2 Z RX RY 50

Z RX RY 51

3 Z RX RY 52

4 Z RX RY 53

/

X Y RZ 54

RP 2 20

/

X Y RZ 61

RP 2 20



/

Z RX RY 60

RP 2 20

/

Z RX RY 73

RP 2 20

END

LOAD

SET 1

NODAL LO

1 Z 1 15.705 1

2 Z 1 31.41 2

Z 1 32.66 3

3 Z 1 31.41 4

4 Z 1 15.705 5

Z 1 2.5 54

Z 1 2.5 61

Z 1 2.5 74

Z 1 1.25 81

END

LOAD-FUN

1 0.0 0.0 350000.0 350000.0

END

STOP

E.5 Example 6: QUS4 transient dynamics (T0591) Description

Impulse loaded clamped plate (one quarter model)

0.6

5.0

v1 v2

Lines of Symmetry

t = 0.125 ρ = 2.61x10-4

E = 10.4x106

ν = 0.3 σy = 41.4x103

Initial velocities v1 = 5000 v2 = 3904

Features: 1. 5 QUS4 elements 2. 1x1x5 integration 3. LARG+PLAS 4. TALPHA = -0.05



Data


PROJ *AUTOMATIC TIMESTEPPING TEST

JOB TRAN

TITL LARG PLAS * IMPULSE LOADED CLAMPED PLATE (1/4 MODEL)

TEXT PRENL TEST FILE - T0591PRE.DAT


SOLU DOMFRQ 26 FIRTIN 1.0E-5 MAXTIM 1.0E-3

TEMP TALPHA -0.05 KSIGNL 3 FINCMX 1.5

UPDA GEOM ITER ALL

UPDA STIF ITER ALL

INTE 1 1 5 (5)(1,1)

OPTIONS GOON PIND SAVJ BAKE

OUTP 1 ALL

BLOC 1 DISP 11

END

COOR

CART

//

/

1 0.0 0.0 0.0

RP 6 1 1.0 0.0 0.0

RRP 2 10 0.0 0.6 0.0

END

ELEM

MATP 1

/

QUS4 1 2 12 11 1

RP 5 1

END

MATE

1 ISO 10.4E06 0.3 0.1E-05 2.61E-4

1 PLAS MISE 41.4E3 0.0

END

GEOM

1 QUS4 0.125

END

SUPP

ALL 6 16

X RY RZ 1 11

Y RX 11

Y RX RZ 12 13 14 15

END



LOAD

SET 1 DUMMY NODAL LOAD

NODAL LO

Z 1 1.0 11

END

LOAD-FUN

1 0.0 0.0 2.0 0.0

END

INIT

Z 0.0 5000.0 1 11

Z 0.0 3904.0 2 12

END

STOP

Appendix F ASAS (Non-Linear) User Manual

Page F-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - F List of Freedom Names

A three-character alphanumeric name is used to indicate each of the freedoms at a node. The direction of the freedoms is determined by the current orientation of the global axes, for the particular node (i.e. the axes established after any skewed suppression constraint or prescribed displacement has been applied).

The following list gives the freedom names used. Names with one or two characters must always be right-justified in a three character field for fixed format data input.

ALL All freedoms at the node

X Displacement along the x-axis

Y Displacement along the y-axis

Z Displacement along the z-axis

RX Rotation about the x-axis

RY Rotation about the y-axis

RZ Rotation about the z-axis

R Displacement radially

WRR Curvature about local r-axis

EZZ Strain in z direction

T Field variable

Appendix F ASAS (Non-Linear) User Manual

Page F-2 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix G ASAS (Non-Linear) User Manual

Page G-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - G Isoparametric Elements

G.1 Curvilinear Axes

Isoparametric elements employ curvilinear coordinates l, m, n (or for triangular faces L1L2L3) which result from ‘mapping’ the element from its parent regular form to the actual distorted shape, see Figure G.1. Note that the direction of each curvilinear axis is determined by the order in which the element nodes are listed. They do not necessarily form a right handed system.

An element’s local axes (which is often the reference frame for stress and strain calculations) are usually defined with respect to the curvilinear axes.

G.2 Integration Rules

All continuum elements in ASAS-NL use Gaussian quadrature; structural elements (i.e. shell and beam) use Gaussian quadrature in the plane (axis) of the shell (beam) and closed Newton-Cotes rules for through thickness effects.

The user is free to select the order of the rule used, but cannot change the type (e.g. from Gaussian to Newton-Cotes). The order of rule required is specified by giving the number of integration points in each of the elements’ local directions with INTEgration rule commands in the Preliminary data. (For elements with triangular faces the number of points in the triangular plane is given.) If an INTEgration rule command is not present for an element the default rule (given on the element description sheet) is used.

For continuum elements integration points for each element are numbered sequentially from 1 in the order given by (((X=1,NGX), Y=1,NGY),Z=1,NGZ) where NGX, NGY and NGZ are the number of integration points in directions l, m, and n respectively. (For elements with triangular faces NGX is conventionally 1 and NGY is the number of points in the triangular point rule.)

For beam and shell elements, all integration points with the same planar coordinates (i.e. l for beams, l, m, for shells) are numbered sequentially from the bottom surfaces towards the top surface. Thus, for shell elements for example, Surface 1 is the bottom surface and surface NGZ is the top suface.

Figure G.2 illustrates the above conventions.

The coordinates of all integration points can be printed at the start of the analysis by using option GAUS with the OPTIons command. The position of each point within an element can be obtained from Table G.1.



Figure G.1 Curvilinear Axes for Shells and Beams



Figure G.1 Curvilinear Axes for Continuum Elements (...cont.)



Figure G.2 Sample Point Numbering for Shells and Beams



Figure G.2 Sample Point Numbering for Continuum Elements (...cont.)

1

1 2

3

(1 x 1 x 1)

1

1 2

3

(1 x 3 x 1)3 2

43

1 2

m

l

1 2

34

(2 x 2 x 1)

4 6

1 3

m

l

1 2

34

(3 x 2 x 1)

5

2

11 12

7 8

m

l

(2 x 3 x 2)

9 10

5 6

1 2

m

l3 4

4 5

6

1 2

5

4

8 7

6

3

1

3

2

4

56

1

23

(1 x 3 x 2)



Note, P is the integration point and a its position from the mid point of the curvilinear line AB, length 2c

No. of Integration Points

GAUSS +/- a/c

NEWTON-COTES +/- a/c

1 0.0 0.0 2 0.57735 1.0

3 0.77459 0.0

1.0 0.0

4 0.86113 0.33998

1.0 0.33333

5 0.90617 0.53846 0.0

1.0 0.5 0.0

6 0.93246 0.66120 0.23867

1.0 0.6 0.2

7

0.94910 0.74153 0.40584 0.0

1.0 0.66667 0.33333 0.0

8

0.96028 0.79666 0.52553 0.18343

1.0 0.71429 0.42857 0.14285

9

0.96816 0.83603 0.61337 0.32425 0.0

1.0 0.75 0.5 0.25 0.0

10

0.97390 0.86506 0.67940 0.43339 0.14887

1.0 0.77778 0.55556 0.33333 0.11111

11

0.97822 0.88706 0.73015 0.51909 0.26954 0.0

1.0 0.8 0.6 0.4 0.2 0.0

Table G.1 Integration Point Positions for Different Rules (cont...)

A B

aP

c c



No. of Integration Points

GAUSS +/- a/c

NEWTON-COTES +/- a/c

12

0.98156 0.90411 0.76990 0.58731 0.36783 0.12523

1.0 0.81818 0.63636 0.45455 0.27273 0.09091

13

0.98418 0.91759 0.80157 0.64234 0.44849 0.23045 0.0

1.0 0.83333 0.66667 0.5 0.33333 0.16667 0.0

Table G.1 Integration Point Positions for Different Rules (...cont)

Appendix H ASAS (Non-Linear) User Manual

Page H-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - H ASAS/ASAS-NL Compatibility

ASAS/ASAS-NL Differences

The following ASAS Data are not appropriate to ASAS-NL.

Preliminary Data ASAS has its own commands for this data

Structural Description Component Topology

Boundary Conditions Link freedoms

Master freedoms

Freedom Releases (Global)

Special Freedom Directions

Gaps

Loading Component loads

Additional Mass Consistent mass input

Component Recovery All

Stiffness Input All

Combined Loadcases All

All other ASAS data blocks are fully compatible with ASAS-NL subject to the following:

Structural Description

Element Topology

Group numbers are assigned in the Preliminary data in ASAS-NL, not in the topology data as in ASAS.

Material Properties

Elastic material behaviour is defined as in ASAS. Additional data is required to define non-linear materials.

When defining anisotropic material properties in ASAS-NL, 30 properties are always required. This is not the case with ASAS.



Loading Data

Load cases used in ASAS are treated as Load Sets in ASAS-NL. In general, a load function number may be specified with ASAS-NL data, which is not required by ASAS.

Temperature Loads

Temperature values are construed as absolute temperatures and thermal loads are calculated due to the difference between these and the reference temperature, TREFLD, defined in the Preliminary data (PARAMETER command).

Face Temperature Loads

Similar to temperature loads.

Additional Mass

Lumped Mass Input

FULL MAS option is not available in ASAS-NL.

Appendix I ASAS (Non-Linear) User Manual

Page I-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - I POSTNL General Post-Processor Interface Program

I.1 Introduction

POSTNL is an interface program required by all ancillary post-processing programs. It converts the post-processing file (or “porthole” file) produced by ASAS-NL when the POST command is used, into a suitable format for the post-processor. It has the following uses (or “output options”)

1. to interface with FEMVIEW

2. to interface with PATRAN

3. to produce time histories of one or more quantities for plotting

4. to print selective element stress strain and associated quantities, and nodal displacements, eigenvectors etc.

POSTNL will also, if appropriate to the output interface and requested by the user, perform certain additional post-processing calculations

1. calculation of principal stresses, stress resultants, strains etc.

2. extrapolation of element integration point quantities (eg stresses & strains) to nodes. Principal quantities, if requested, are not extrapolated but are recomputed from nodal quantities

3. averaging of element nodal stresses at common nodes for all elements in a group. The averaging is done across groups if specifically requested (except for the PATRAN interface where it is done automatically). Note that no account is taken of any difference in the local axes system; thus it is up to the analyst to ensure that the averaging is meaningful.

4. recalculation of equivalent quantities (e.g. equivalent stress) at nodes following nodal averaging

5. unskewing of any displacements or reactions in a local skew axis to the common global axis system (this option is automatically enforced for PATRAN and FEMVIEW)

6. recovery of layer stresses and strains for laminated shells and calculation of failure indices (for FEMVIEW only)

7. calculation of fracture mechanics parameters (for PRINT only)

I.2 Usage

The program is an interactive one which will prompt the user for the required response. The input commands are echoed both to the terminal and also to a file named ZZZMONIT.



The program requires the name of the porthole file created by the ASAS-NL run. If this was not explicitly named on a FILE command it will default to ZZZPORTF. POSTNL also requires to know whether any shell or beam elements are to be post-processed (this information is needed in order to allocate space efficiently).

The program then asks for the “output option” required. The following 4 character options are valid

FEMV - to interface with FEMVIEW (see I.3)

PATN - to interface with PATRAN (see I.4)

PRIN - to print selected quantities (see I.5)

TIME - to obtain time histories of selected quantities (see I.6)

INDX - to obtain a list of the output types on the named porthole file for each increment (see below)

NEW - to post-process output on another porthole file (see below)

STOP - to terminate the POSTNL session

On completion of the processing in one of the above ‘output options’ POSTNL prompts the user for a further ‘output option’. To exit from the program at this stage enter STOP.

To obtain a catalogue of the quantities saved on the porthole at each increment enter INDX. Identifiers are listed together with pseudo-times.

On completion of the current post-processing, output on a different porthole file can be processed by entering NEW. The program then asks for the name of the new post-processing file. Note that this has to be on the same project, as identified with the ASAS-NL JOB command.

I.3 FEMVIEW Interface

The interface between POSTNL and FEMVIEW consists of a single formatted file containing details of both the model (ie coordinates and element topology) and all the results to be displayed. POSTNL will either append the results to an existing model file, or create it as required. In the former case the model file will have been created by a FEMGEN run or by specifying FEMV with the ASAS-NL OPTIONS command, or in a previous session of POSTNL.

After entering FEMV to request the FEMVIEW interface, the program asks for the ‘model name’ and an ‘operation code’ to indicate whether the model file is to be created anew (C) and the results added, or that the results are to be appended to an existing model file (A). In the latter case the model name should correspond to that on the existing model file (if this was created in the ASASNL run then the name is the first 6 characters of the title specified with the TITLE/PROBLEM command).



If A is input POSTNL creates a file (with no structure data) which may be used to append to an existing FEMVIEW data base for this model name. The program then asks for the filename to which results are to be written. This name should be unique to avoid the possibility of deleting existing output files.

If operation code C was entered the filename must be the name of the existing model file (if created in the ASAS-NL run this will be ZZZMODEL by default or otherwise as named with a FILE command).

The program then asks for the four character label identifying the output type and increment. Valid output type

labels are given in Table I.1. The next prompt determines the format in which quantities are output to the

FEMVIEW neutral file. Note that all element based quantities do not involve any averaging process across

element boundaries. Having transferred data for the current output type, the program prompts for the next output

type and increment. To exit, enter END. This will result in a prompt for a further output file name. To exit from

this level enter FIN.

Primary Nodal Variables

DISP Displacements VELO Velocities

ACCN Accelerations REAC Reactions

EIGN Eigenvector

Primary Element Based Variables

STRS Element stresses STRN Element (total) strains

ELAS Element elastic strains INST Element plastic strains

CRSN Element creep strains TEMP Element temperatures

SRES Element stress resultants (beams & shells only)

RESN Element strain resultants (beams & shells only)

Secondary Element Based Variables

LAMI Lamina stress/strains and failure indices SFAI Shell surface failure indices

GFAI Shell global failure indices

Table I.1 Output Types for FEMGEN



The various prompts encountered using the FEMV option are detailed below.

Enter FEMV at the prompt for an output option.

ENTER MODEL NAME AND OP. CODE (C,CREATE A,APPEND) (6A1,1X,A1)

Type in a 6 character name, followed by C or A.

If A is entered the name should match that given before and the file created may be used to append to an existing FEMVIEW database.

ENTER NAME OF OUTPUT FILE OR FIN (12A1)

Enter a unique name of up to 12 characters beginning with a letter. (The filename should be unique even though operation Code A has been entered in the previous command since any existing output file with the same name would be overwritten).

Enter FIN to exit from the FEMV option.

ENTER CURC FOR PLOTTING RESULTS ON CURRENT CONFIGURATION ELSE BLANKS

If the create option (C) has been entered for the operation code and CURC is entered for this prompt then the coordinates written to the FEMVIEW neutral file will be the original coordinates plus the displacements for the increment selected. The CURC option has to be selected if it is required to rotate any shell stresses/strains and/or stress/strain resultants into a common axis system.

ENTER OUTPUT TYPE AND INCREMENT, ELSE END (A4,FREE)

Type in 4 character keyword for one of the FEMVIEW output types (see Table I.1) and the increment number for output. Currently the data for one increment only may be processed.

Various prompts will appear depending on the output type selected. The prompts divide into two basic sets; those dealing with primary nodal variables, ie DISP, VELO, ACCN, REAC and EIGN and the remainder which are all element based variables, eg STRS and STRN.

I.3.1 Primary Nodal Variables

If any of the output types DISP,VELO,ACCN or REAC are selected then the displacements, velocities, accelerations or reactions respectively are unskewed (if necessary) and copied directly to the output file. If output type EIGN is selected then the following prompt will appear:

ENTER REQUIRED MODE NUMBER/GENERATOR OR ALL

Enter eigenvector mode number, list of modes optionally using topological format (see Section 4.2.3) or all modes to be transferred. Examples are:

1 mode 1 only 1 3 5 7 modes 1, 3, 5 and 7



(4) (1,2) modes 1, 3, 5 and 7 ALL all modes

I.3.2 Primary Element Based Variables

The primary element based variables are stresses and strains, stress and strain resultants (beams and shells only) and stress point indicators. For most element types these variables are only stored as Gauss point quantities. If element by element nodal values are required an extrapolation process has to be carried out. Some shell and beam element results (e.g. Stresses) contain more than one surface. The surface number corresponds to the sequence in which the integration points are numbered through a section. For shells, these are from 1 (bottom) to NGZ (top) (see Appendix G). Note that this definition is opposite to the convention adopted by FEMVIEW and thus care must be taken when displaying the TOP SURFACE and BOTTOM SURFACE results in FEMVIEW. Additionally for shell elements there are a variety of options for rotating stresses into a common axis system, extracting individual layer data from a non-linear material analysis and the computation and output of subsidiary data such as failure indices for laminated composite structures. The various prompts which may be encountered are as follows:

ENTER GAUS, NODE OR ELND FOR OUTPUT POSITION (A4)

Results may be output to the FEMVIEW neutral file in ‘Element at Gauss points’ format (enter GAUS), ‘Element at Nodes’ format (enter ELND or NODE, both have the same effect).

I.3.2.1 Rotation of Shell Element Based Variables

If shell elements are being processed it is possible to instruct POSTNL to rotate stresses/strains and stress/strain resultants into a common local axis system. The necessary data required to carry out these rotations is prompted for with the following instructions. Full details of the theory behind the computations carried out are given in Section I.77 of this Appendix.

ENTER ROTA IF ‘output type’ VALUES ARE TO BE ROTATED, ELSE BLANKS

If output type STRS,STRN,SRES or RESN have been selected the option to rotate the values is given.

ENTER RADI FOR RADIAL DEFINITION OF NEW LOCAL X DIRECTION, ELSE BLANKS

The values may be rotated into a common axis system where all element local x and y directions are parallel. Alternatively, a radial axis system may be selected, by entering RADI, where all the element local x directions point to a common central point.

ENTER GLOBAL COORDINATES OF POINT DEFINING NEW LOCAL X DIRECTION

The common local x direction for each element is parallel to a vector starting at the global origin (X=Y=Z=0.0) and terminating at the point whose coordinates are prompted for here.

ENTER GLOBAL COORDINATES OF CENTRE POINT FOR RADIAL AXIS SYSTEM

If RADI is selected the user is required to enter the global X,Y,Z coordinates of the common central point.



ENTER GLOBAL COORDINATES OF THE REFERENCE POINT FOR THE CONTROL VECTOR

To ensure the top and bottom surface for each shell is correctly aligned the user is requested to input the coordinates of a reference point. The control vector is constructed from this reference point to any integration (Gauss) point. This control vector enters the element through the bottom surface and exits through the top surface.

ENTER GROUP NUMBERS FOR WHICH VALUES ARE TO BE ROTATED (FREE)

As it may only be sensible to rotate values for certain groups of elements the choice of selecting only certain groups is available. Enter ALL if all element groups are to be rotated.

INPUT FILENAME FOR FILE TO HOLD ROTATION ANGLES (12A1)

The calculation of the necessary rotations at each integration point can be time consuming, particularly for large structures with many elements. To avoid repetition, various data is stored on a disc file. The user is asked to provide the name of this file as, by default, it is not deleted on completion of the POSTNL session.

I.3.3 Secondary Element Based Variables

Various facilities exist within the FEMVIEW interface to calculate subsidiary data from the primary element based variables.

I.3.3.1 Laminated Composite Shells

Two basic types of laminated composite shell analysis are available in ASAS-NL; elastic and ‘plastic’ or failure analysis. Both types require the user to supply material and geometric property data defining the layup sequence and the material properties of each layer.

For an elastic analysis, it is not necessary to continually monitor and/or update the change in stress for each lamina. Hence, recovery of lamina stresses and strains and the calculation of failure indices (according to several different theories) is carried out, on request, in POSTNL. These calculations are currently only available in the FEMVIEW interface and are obtained by requesting output type LAMI. The LAMI option is only valid if stress resultants (SRES) have been saved onto the porthole file. It should also be noted that output positions other than GAUS are also not currently available. On entering GAUS the following prompt will be obtained:

ENTER USER LAYER NUMBER (0 IF NON-LAMI DATA, -1 IF ALL LAYERS)

Enter a layer number or -1 for all layers or 0 if non-laminate data are to be processed. With LAMI requested, a 0 user layer number means that no processing will be carried out.

For a laminated composite analysis employing a non-linear material failure law, information concerning the state of stress and strain are available using the output types STRS and STRN in the usual manner. The same user layer number prompt will appear on entering GAUS so that the user may request output at a particular layer or all layers within the laminate. If an analysis contains both laminated and homogeneous shell elements, entering a 0 at this prompt will cause the program to process the results of homogeneous shell only. Note also that, in this case, it is not possible to process both the laminated and homogeneous sets of results simultaneously.



Similarly, when there is a mixture of elastic and plastic shell elements in the same run, the user should use LAMI to recover the lamina stresses/strains of the elastic elements and STRS/STRN to process the plastic elements separately.

I.3.3.2 Surface and Global Failure Indices

The surface failure index, Fs, is a single value computed at each shell surface integration point and is defined as follows;

Note that this index is available for both homogeneous and laminated shells. For homogeneous or ‘plastic’ laminate analysis only a single value will be output at each surface integration point. For elastic laminate analysis, ten surface failure indices, corresponding to the ten lamina failure indices computed for each lamina, will be output.

To obtain the surface failure indices, specify output type SFAI. Again, this option is currently only available with output position GAUS.

Global failure indices are for laminated shells only and are obtained by using output type GFAI with output position GAUS. Up to five global failure indices are computed, the first being in-built (see Appendix B.5.2 for details) and the remaining four being user-defined.

It should be noted that the SFAI and GFAI options are only valid if stress resultants (SRES) have been saved onto the porthole file.

I.3.3.3 Laminated Composite Bricks

The calculations available for laminated bricks are very similar to those for laminated shells. In this case, however, the lamina stresses and strains are computed in ASASNL and therefore it is not necessary to distinguish between elastic and failure analysis.

The lamina failure indices can be obtained by requesting output type LAMI as before. The LAMI option is only valid if stresses (STRS) have been saved onto the porthole file.

If only the lamina stresses or strains are required, these can be obtained using the output types STRS and STRN in the usual manner.

The surface failure indices are obtained by specifying output type SFAI. Again, stresses (STRS) should be saved onto the porthole file. Note that surface failure indices are only available for an elastic laminated brick analysis.

Global failure indices are not available to laminated bricks as stress resultants are not calculated.

Fs = No. of through-thickness integration points that have failed

Total no. of through-thickness integration points



I.4 PATRAN Interface

The interface between ASAS-NL and PATRAN consists of the so-called PATRAN model file containing coordinate and element topological data, and a set of neutral results files, one for each required output type (e.g. STRS at increment 2). The model file is created by a PATRAN pre-processing run, or by specifying PATN with the ASAS-NL OPTIONS command. The results files are created by POSTNL. They are in binary form but their formatted contents are put to the command file ZZZMONIT by entering ECHO after an appropriate prompt. After entering PATN for the PATRAN interface the program asks for the name of the output file which is to be created. This must be unique to the output type it is to contain. The program then asks for the 4 character label identifying the output type and the increment number. Valid type labels are given in Table I.2.

Integration point quantities cannot be handled by PATRAN and all such data is therefore extrapolated to nodes and averaged across common elements. Principal quantities, if requested, are computed from extrapolated nodal values and then averaged; equivalent values are computed from averaged nodal data.

Shell elements require each layer to be treated separately. The layer number corresponds to the sequence in which the integration points are numbered through the shell thickness (1 to NGZ see Appendix -G). However the mid surface can also be identified by the label 0 and top surface by the label 999.

Having written the selected output to the neutral file, the program returns with a further prompt for the name of the output file for the next output type. To exit enter FIN.

The various prompts encountered using the PATN option are detailed below.

STRS Element stress vectors

STRN Element (total) strain vectors

ELAS Element elastic strain vectors

INST Element plastic strain vectors

CRSN Element creep strain vectors



ISP Element stress point indicators

EIGN Eigen vectors

DISP Displacement vectors

REAC Reactions

TEMP Element temperatures

Table I.2 Output Types for Patran



4.1 ENTER NAME OF OUTPUT FILE OR FIN (12A1)

Give a unique name for the results file of up to 12 characters, or type in FIN to exit from the PATN option.

Next prompt 4.2.

4.2 ENTER ECHO FOR PATRAN O/P ECHOING ELSE BLANKS

Type in ECHO to cause all the Patran data to be echoed to ZZZMONIT, or press return.

4.3 ENTER O/P TYPE AND INCREMENT ELSE END (A4, FREE)

STRS 3.4, 3.5, (3.6, 3.7)

STRN 3.4, 3.5, (3.6, 3.7)

ELAS 3.4, 3.5, (3.6, 3.7)

INST 3.4, 3.5, (3.6, 3.7)

CRSN 3.4, 3.5, (3.6, 3.7)

SRES 3.4, 3.5, (3.6, 3.7)

RESN 3.4, 3.5, (3.6, 3.7)

ISP 3.4, 3.5, (3.6, 3.7)

EIGN 3.8

DISP all disp/reac unskewed then transferred

REAC 3.1

TEMP 3.4, 3.5, (3.6, 3.7)

All return to prompt 4.1.

4.4 ENTER PRINC TO CALCULATE PRINCIPAL QUANTITIES FOR 2D AND SHELL

ELEMENTS, ELSE BLANKS

Type in PRINC or press return.

4.5 ENTER EQUIV TO RECALCULATE EQUIVALENT QUANTITIES AT NODES, ELSE

BLANKS

Enter EQUI for recalculation of equivalent quantities following nodal averaging.

Next prompt 4.6

Press return for no recalculation

4.6 ENTER YIELD FUNCTION TYPE (1 VON MISES, 2 TRESCA, 4 MOHR-COULOMB, 5

DRUCKER-PRAGER)

Enter number for yield function to be used. If 4 or 5, then prompt 4.7.

4.7 ENTER ANGLE OF FRICTION



Enter angle in degrees.

4.8 ENTER REQUIRED MODE NUMBER

Enter mode number for the eigenvector to be transferred.

I.5 Printer Interface

Any of the data on the porthole can be selectively printed. In addition the following quantities are also available.

• displacements, velocities, accelerations, reactions and/or eigenvectors in the global axis system

• displacements, velocities, and/or accelerations at any, arbitrary, user defined point

• nodal element quantities, obtained by extrapolation of integration point values

• element quantities at any, arbitrary, user defined point

• principal quantities at integration points

• principal quantities at any, arbitrary, user defined point

• principal quantities at nodes calculated from nodal quantities rather than by extrapolation of

integration point values

• fracture mechanics processing (J, J*, C or C*) (see also I.88)

• create nodal load data from reaction results

• create prescribed displacement data from displacement results

• create temperature load data from heat analysis results

• create eigenvector perturbated coordinate data

All output requested is automatically printed to the monitor file ZZZMONIT. POSTNL prompts for the word VIEW if, in addition, the data is to be displayed on the screen. The program then asks for the keyword PLOT if data concerning stress/strain resultants for beams is to be output to a file.

The user is then asked to enter the output type and increment, or type END to exit from the printer interface. Valid output types are given in Table I.3.

The output type labels are similar to those specified with the ASAS-NL POST command. Where displacements are stored (DISP), as shown on the index, reactions are also stored. Similarly for stress resultants and strain resultants. Any number of output types may be printed to the monitor file.



Nodal quantities (displacements, reactions and eigenvectors) can be transformed from any local skew systems to the common global system if required.

Element quantities can be the original integration (Gauss) point quantities or the same quantities extrapolated to the nodes. In either case they relate to the axis system chosen for the ASAS-NL calculation. Nodal principal quantities (requested by entering PRIN at the appropriate prompt) are calculated from the nodal components after extrapolation from the integration points. Element stress point indicators are always printed with any element quantities.

Both displacements and element quantities may be requested to be output at any arbitrary user defined point.

STRS Element stress vectors

STRN Element (total) strain vectors

ELAS Element elastic strain vectors

INST Element plastic strain vectors

CRSN Element creep strain vectors




EIGN Eigen vectors

DISP Displacement vectors

VELO Velocity vectors

ACCN Acceleration vectors

REAC Reactions

WORK Sum of element work for each group


JAY J integral

JAYS J* integral

CEE C integral

CEES C* integral

HEAT Create temperature load data from thermal results

Table I.3 Output Types for the Printer Interface

The various prompts encountered using the PRIN option are detailed below.

5.1 ENTER VIEW FOR SCREEN COPY ELSE BLANKS

Type in VIEW for data to be echoed to the screen as well as ZZZMONIT, or press return to continue.



5.2 ENTER ‘PLOT’ IF PLOT FILE IS REQUIRED FOR NODAL BEAM RESULTANTS ELSE

BLANKS

Type in PLOT to open a plot file, next prompt 5.3. Each data set written to the plot file contains the user element number, node number, followed by beam resultants as given in Table I.6.

Press return to continue to 5.4.

5.3 INPUT C(CREATE)/A(APPEND) AND FILENAME FOR PLOT FILE (A1,1X,12A1)

ELSE BLANKS

Enter C or A and a filename or press return to continue to prompt 5.4. (C to create a new plotfile and A to append to an existing one).

5.4 ENTER ‘PERT’ IF EIGENVECTOR COORDINATE PERTURBATION IS REQUIRED,

ELSE BLANKS

Enter PERT if the global nodal coordinates are to be recovered from the porthole file and scaled eigenvectors are to be added to the coordinates subsequently.

5.5 ENTER O/P TYPE AND INCREMENT ELSE END (A4, FREE)

Enter an output type or END.

STRS 5.6, 5.7, (5.10.1, 5.10.2, 5.10.3), 5.8

STRN 5.6, 5.7, (5.10.1, 5.10.2, 5.10.3), 5.8

ELAS 5.6, 5.7, (5.10.1, 5.10.2, 5.10.3), 5.8

INST 5.6, 5.7, (5.10.1, 5.10.2, 5.10.3), 5.8

CRSN 5.6, 5.7, (5.10.1, 5.10.2, 5.10.3), 5.8

TEMP 5.6, 5.7, (5.10.1, 5.10.2, 5.10.3), 5.8

SRES 5.6, 5.7, (5.10.1, 5.10.2, 5.10.3, (5.10.4, 5.10.5)), 5.8

RESN 5.6, 5.7, (5.10.1, 5.10.2, 5.10.3), 5.8

DISP 5.9, 5.10, (5.10.1, 5.10.2, 5.10.3), 5.12, 5.14, (5.18)

VELO 5.9, 5.10, (5.10.1, 5.10.2, 5.10.3), 5.12

ACCN 5.9, 5.10, (5.10.1, 5.10.2, 5.10.3), 5.12

REAC 5.9, 5.10, 5.12, 5.15, (5.18)

EIGN 5.9, 5.10, (5.10.1, 5.10.2, 5.10.3), 5.11, 5.12, (5.17, 5.18,

5.19)

JAY 5.13

JAYS 5.13

CEE 5.13

CEES 5.13

HEAT 5.16, 5.18

WORK

END

All options return to 5.5 after printing.



5.6 ENTER PRINC TO CALCULATE PRINCIPAL QUANTITIES FOR 2D AND SHELL ELEMENTS,

ELSE BLANKS

Enter PRINC or press return if inapplicable.

5.7 ENTER GAUS OR NODE OR POIN FOR OUTPUT POSITION (A4)

Type in GAUS to output data at the integration points

Type in NODE to output data extrapolated to the nodes

Type in POIN if element values at a user defined point are required. For GAUS and NODE, the next prompt is 5.8. For POIN, the next prompt is 5.10.1

5.8 ENTER USER ELEMENT NUMBER(S)/GENERATOR (O TO FINISH) OR ALL

Type in either a list of 1 or more element numbers, use the free format generator (see Section 4.2.3) or ALL to output data for all elements. The free format generator may only be used to generate up to 80 elements. Next prompt is 5.5 after data has been transferred.

5.9 ENTER ‘GLOBAL’ IF VECTORS ARE TO BE SKEWED TO COMMON GLOBAL AXES

ELSE BLANKS FOR OUTPUT IN SKEW SYSTEMS

Enter GLOBAL or press return.

5.10 ENTER ‘POINT IF DISPLACEMENTS AT USER DEFINED POINT ARE REQUIRED,

ELSE BLANKS

Press return to continue to 5.12 (5.11 for output type EIGN). If POINT is entered, the following prompts are made:

5.10.1 ENTER ELEMENT NUMBER WITHIN WHICH THE POINT LIES

Enter user element number (or system element number if no user element numbers specified).

5.10.2 ENTER ‘GLOB’ OR ‘CURV’ FOR INPUT OF GLOBAL OR CURVILINEAR

COORDINATES OF POINT

The position of the point within the element may be specified using global cartesian coordinates or in terms of the element curvilinear coordinate system. See Appendix -G for definitions of the element curvilinear coordinate systems.

5.10.3 ENTER GLOBAL (CURVILINEAR) COORDINATES OF POINT

Sufficient coordinate values must be given to specify the point. One, two or three values will be required depending on the element and the coordinate system specified. Next prompt is 5.5 for all output types except EIGN and SRES. For output type EIGN, the next prompt is 5.11, after which the program returns to prompt 5.5. If output type SRES has been specified and the current element is a shell element, the following prompt is made.



5.10.4 ENTER ‘TTVL’ IF THROUGH THICKNESS STRESSES ARE REQUIRED, ELSE BLANKS

Press return to continue to prompt 5.5. If TTVL is entered, the following prompt is made.

5.10.5 ENTER THROUGH THICKNESS COORDINATE (ZITA) AT POINT

The value entered for zita should be between +/- 1.0. Next prompt is 5.5.

5.11 ENTER REQUIRED MODE NUMBER

Enter a list of 1 or more mode numbers for this increment for which the eigenvector is to be printed.

5.12 ENTER NODE NO / GENERATOR OR ALL

Type in either a list of 1 or more node numbers, use the free format generator (see Section 4.2.3) or ALL to output data for all nodes.

5.13 ENTER NAME OF CONTOUR DEFINITION FILE (12A1)

Enter the name of the contour definition file, up to 12 characters beginning with a letter. See Appendix I.88 for format of this file.

5.14 ENTER PRES TO CONVERT DISPS TO LOADS, ELSE BLANKS

Enter PRES to create prescribed displacement data from the displacement results obtained or press return.

If PRES is entered, a DISP data block is created for all freedoms at all nodes selected except those which have a displacement ‘exactly’ equal to zero. These freedoms are assumed to be suppressed. Also, PRESCRIB load data is created with the non-zero displacements as prescribed values. All output is to a user defined text file. Enter return to obtain normal printed output.

5.15 ENTER NODA TO CONVERT REACS TO LOADS, ELSE BLANKS

Enter NODA to create nodal load data from the reaction results obtained or press return.

If NODA is entered, all reactions at all nodes selected are converted into NODAL LO data except

Type in a list of group numbers, use the free format generator (see Section

those freedoms where the reactions are ’exactly‘ equal to zero which are ignored. All output is to a user defined text file. Enter return to obtain normal printed output.

5.16 ENTER GROUP NO/GENERATOR OR ALL

4.2.3) or ALL to output data for all groups.

5.17 ENTER ‘EIGV’ IF EIGENVECTOR IS TO BE ADDED TO COORDINATES

If PERT has been entered in response to prompt 5.4, the above prompt will be displayed. Press return if the current requested eigenvector is to be ignored, in which case the next prompt is 5.5. Entering EIGV causes the prompts for a coordinate data filename and scaling factor for the perturbation to be displayed.



5.18 ENTER 4 CHARACTER IDENTIFIER FOR .AAA FILE

Type in a 4 character identifier for the load data file to be created. In the above prompt, AAA will appear as LOD for nodal load data, as DIS for prescribed displacement data, as TEM for temperature load data, and as COR for perturbated coordinate data. The name of each output file produced is XXXXnnnn.AAA, where XXXX is the file identifier, nnnn is the increment number. It should be noted that two files are created for prescribed displacement data. The .DIS file contains the DISP data while the .PRD file contains the PRESCRIB data.

5.19 ENTER NODE, DOF (1, 2 OR 3) AND ABSOLUTE VALUE

Before adding the eigenvector to the current global nodal coordinates, the eigenvector is scaled such that the specified degree of freedom (translational only) at the specified node will have a magnitude equal to the absolute value specified. This prompt is repeated for each requested mode and then each requested increment.

I.6 Time Histories

Tabulated time histories of up to 10 selected quantities can be extracted and listed. They are formatted in a form suitable for importing into a spreadsheet program for plotting.

Quantities are identified by 4 character labels. Valid identifiers are listed in Table I.4.

After entering TIME to obtain the Time history interface the user is prompted for VIEW if screen copy is required and a filename if the output is to be plotted. The program next asks for a list of increments (or ALL for all increments on the porthole file) for which quantities are to be obtained, followed by the number of time histories (or identifiers). Each identifier is then requested in turn.

Nodal quantities (displacements, velocities, accelerations, reactions and eigenvectors) require the freedom to be identified by an integer label 1-10. This requires users to know the number of degrees of freedom at the node. The sequence follows that given in the ASAS-NL output and is given in Table I..

Element quantities (e.g. stresses, strains) are normally integration point quantities as calculated in ASAS-NL (i.e. no principal and/or nodal values can be selected). They are identified by their element number, integration point number (see Appendix -G) and the component number. The latter corresponds to the column number of the printed output and varies from element to element. Details are given in Table I..

Output types DISP, VELO, ACCN, REAC, DMAX, RSUM, PSUM have an option to input rotation and translation factors A and B such that the value output is A*value + B.

Both displacements and element quantities may be requested to be output at any arbitrary user defined point.



DISP+ Nodal displacements

VELO+ Nodal velocities

ACCN+ Nodal accelerations

STRS Element stresses (or fluxes for field element)

STRN Element (total) strains (or field gradients for field element)

INST Element plastic strains

ELAS Element elastic strains

SRES Element stress resultants (beams and shells only)

RESN Element strain resultants ( ” ” ” ” )

CRSN Element creep strains



NULL Null vector

TMSN Element (total) mechanical strains

REAC+ Nodal reactions

ADD Form new identifier by adding any 3 quantities already selected

SUB Form new identifier by subtracting any 2 quantities from a third, all of which have already been selected

DMAX*+ Maximum displacement

VMAX*+ Maximum velocity

AMAX*+ Maximum acceleration

RSUM*+ Reaction sum

PSUM*+ Sum of reactions associated with prescribed displacements

ITER* Accumulated iterations to date

ISTF* Accumulated stiffness reformations to date

ILIN* Accumulated line searches to date

NTER* No. of iterations in current increment

NSTF* No. of stiffness reformations in current increment

NLIN* No. of line searches in current increment



* These quantities are saved using the identifier ‘SUMR’ with the POST command in the Preliminary data. + With option to input rotation and translation factors.

Table I.4 Valid Identifiers for Time Histories

Component number 1 2 3 4 5 6 7 8 9 10 Freedom X Y Z RX RY RZ WRR EZZ R T

Table I.5 Nodal Component Numbers

Notes

1. For axisymmetric solid analysis only. Component number 1 may also be used to represent freedom R.

2. For field analysis only. Component number 1 may also be used to represent freedom T.

Element Type

Component Number

1 2 3 4 5 6 7 8 9 10 11 12

QUM4

QUM8 XX YY XY ZZ EQ - P1 P2

TRM3

TRM6

QUX4

QUX8 RR ZZ HH RZ EQ P1 P2

TRX3

TRX6

BRK6

BRK8 XX YY ZZ XY YZ ZX EQ

BR15

BR20

LB15

LB20

TCS6 XX YY XY XZ YZ EQ P1 P2

TCS8 NXX NYY NXY MXX MYY MXY SXY SXZ PN1 PN2 PM1 PM2

QUS4

XX XY XZ EQ

STF4 FXX TXX MYY MZZ SXY SXZ

FLA2 XX EQ

GAP2 RG23 RG24

XX YY

GAPX RGX3 RGX4

RR ZZ

SST4 RR RM



Element Type

Component Number

1 2 3 4 5 6 7 8 9 10 11 12

WST4 FRR SRS SRT MSS MTT MWP TSV TWP TRQ

Table I.6 Element Quantity Component Numbers

Element Type

Component Number

1 2 3 4 5 6 7 8 9 10 11 12

SPR1 XREL VREL

SPR2

BM2D FXX SQY MZZ

BM3D FXX SQY SQZ TXX MYY MZZ

LSP3 N1 M1 N2 M2 N3 M3 JP JTOT

LSP6

QMT4

QMT8 XX YY

TMT3

TMT6

QXT4

QXT8 RR ZZ

TXT3

TMT6

BRT6

BRT8 XX YY ZZ

BT15

BT20

FAT2 XX

FAT3

Table I.6 Element Quantity Component Numbers (continued)



The various prompts encountered using the TIME option are detailed below.

6.1 ENTER VIEW FOR SCREEN COPY ELSE BLANKS

Type in VIEW for plotting data to be echoed to the screen, or press return.

6.2 ENTER C(CREATE)/A(APPEND) AND FILENAME FOR PLOT FILE (A1,1X,12A1),

ELSE BLANKS

Enter C and a filename to create a new plotfile.

Enter A and an existing filename to append to a plotfile.

Press return to continue without opening a plotfile.

6.3 INPUT INCREMENT NOS/GENERATOR, OR ALL

Type in a list of increments to be plotted, use the free format generator (see Section 4.2.3) or ALL to select all increments on the interface file.

6.4 ALLOWABLE IDENTIFIERS

DISP STRS STRN INST ELAS SRES RESN CRSN ISP TEMP NULL TMSN

REAC ADD SUB DMAX RSUM PSUM ITER ISTF ILIN NTER NSTF NLIN

INPUT NO OF IDENTIFIERS MAX = 10

Enter the number of identifiers to be plotted.

6.5 INPUT IDENTIFIER NO ‘n’ (OR NULL)

Input identifier n

DISP 6.6, 6.7, 6.7.1, (6.7.2, 6.7.3, 6.7.4, 6.7.5), 6.8, (6.9)

VELO 6.6, 6.7, 6.7.1, (6.7.2, 6.7.3, 6.7.4, 6.7.5), 6.8, (6.9)

ACCN 6.6, 6.7, 6.7.1, (6.7.2, 6.7.3, 6.7.4, 6.7.5), 6.8, (6.9)

REAC 6.6, 6.7, 6.8, (6.9)

STRS 6.13, (6.14, 6.15, 6.16, (6.17, 6.18)), (6.10)

STRN 6.13, (6.14, 6.15, 6.16, (6.17, 6.18)), (6.10)

INST 6.13, (6.14, 6.15, 6.16, (6.17, 6.18)), (6.10)

ELAS 6.13, (6.14, 6.15, 6.16, (6.17, 6.18)), (6.10)

SRES 6.13, (6.14, 6.15, 6.16, (6.17, 6.18)), (6.10)

RESN 6.13, (6.14, 6.15, 6.16, (6.17, 6.18)), (6.10)

CRSN 6.13, (6.14, 6.15, 6.16, (6.17, 6.18)), (6.10)

ISP NOT CURRENTLY AVAILABLE

TEMP

NULL No further prompt

TMSN NOT CURRENTLY AVAILABLE

ADD 6.11

SUB 6.11



DMAX 6.12, 6.7, (6.9)

BMAX 6.12, 6.7, (6.9)

AMAX 6.12, 6.7, (6.9)

RSUM 6.12, 6.7, (6.9)

PSUM 6.12, 6.7, (6.9)

ITER No further prompt

ISTF No further prompt

ILIN No further prompt

NTER No further prompt

NSTF No further prompt

NLIN No further prompt

All return to 6.5 until the number of identifiers requested have been input. The program then exits from the TIME option and returns to the main menu.

6.6 INPUT ‘GLOBAL’ FOR VECTORS TO BE UNSKEWED, ELSE BLANKS

Type in GLOBAL or press return for output in skew systems.

6.7 INPUT ‘FACT’ IF ROTATION AND TRANSLATION FACTORS TO BE INPUT, ELSE

BLANKS

Type in FACT or press return.

6.7.1 INPUT ‘POINT’ IF DISPLACEMENTS AT USER DEFINED POINT ARE REQUIRED,

ELSE BLANKS

Press return to continue to 6.8. If POINT is entered, the following prompts are made:

6.7.2 ENTER ELEMENT NUMBER WITHIN WHICH THE POINT LIES


6.7.3 ENTER ‘GLOB’ OR ‘CURV’ FOR INPUT OF GLOBAL OR CURVILINEAR

COORDINATES OF POINT

The position of the point within the element may be specified using global cartesian coordinates or in terms of the element curvilinear coordinate system. See Appendix -G for definitions of the element curvilinear coordinate systems.

6.7.4 ENTER GLOBAL (CURVILINEAR) COORDINATE OF POINT

Sufficient coordinate values must be given to specify the point. One, two or three values will be required depending on the element and the coordinate system specified.

6.7.5 INPUT COMPONENT NO. (1-7)

Type in the component number (depends on the nodal freedoms, see Table I..



6.8 INPUT COMPONENT NO (1-7), NODE NO

Type in the component no (depends on nodal freedoms, see Table I.) and the node number e.g. 1,2.



6.9 INPUT ROTATION FACTOR A AND TRANSLATION FACTOR B

Input two values A,B such that value output will be

A*VALUE+B

6.10 INPUT COMPONENT NO., USER EL. NO., INTEGRATION POINT NO.

Enter the component number (depends on element type, see Table I.7), user element number and the integration point number for which data is to be output.

6.11 INPUT 3 IDENTIFIER NO.S (OR ZEROS)

Input three numbers of columns A,B,C such that for ADD, VALUE = A+B+C and for SUB, VALUE = A-B-C

6.12 INPUT FREEDOM NAME (A3)

Enter name of freedom for which maximum values are to be plotted.

6.13 INPUT ‘POINT’ IF VALUES AT A USER DEFINED POINT ARE REQUIRED, ELSE

BLANKS

Press return to continue to 6.10. If POINT is entered, the following prompts are made:

6.14 ENTER ELEMENT NUMBER WITHIN WHICH THE POINT LIES


6.15 ENTER ‘GLOB’ OR ‘CURV’ FOR INPUT OF GLOBAL OR CURVLINEAR COORDINATES

OF POINT

The position of the point within the element may be specified using global cartesian coordinates or in terms of the element curvilinear coordinate system. See Appendix -G for definitions of the element curvilinear coordinate systems. 6.16 ENTER GLOBAL (CURVILINEAR) COORDINATES OF POINT

Sufficient coordinate values must be given to specify the point. One, two or three values will be required depending on the element and the coordinate system specified. Next prompt is 6.7.5 for all output types except SRES. If output type SRES has been specified and the current element is a shell element, the following prompt is made.

6.17 ENTER ‘TTVL’ IF THROUGH THICKNESS STRESSES ARE REQUIRED, ELSE BLANKS

Press return to continue to prompt 6.5. If TTVL is entered, the following prompt is made.

6.18 ENTER THROUGH THICKNESS COORDINATE (ZITA) AT POINT

The value entered for zita should be between +/- 1.0. Next prompt is 6.5.



I.7 Rotation of Element Based Variables for Shells

I.7.1 Introduction

Generally curved finite elements are most effectively formulated using a reference frame that follows the naturally curved shape of the element. Stresses and strains (and stress resultants for structural elements) are calculated with respect to this reference frame at the integration points for each element. As this reference frame changes orientation (with respect to some other fixed reference frame) not just from element to element but from integration point to integration point, so the directions of the stresses and strain vary. A graphical representation of stresses and strains may be achieved in many ways but one of the most popular is to draw a contour map where each contour line is the locus of points of equal stress or strain. As stresses and strains are vectors, such contour maps are only meaningful if the stresses and strains are oriented in a consistent manner over the area of interest. For simple geometries, this can often be achieved by judicious meshing and ordering of the element topology. In general, however, a facility is needed to transform the stresses and strains into a predefined direction before contouring is carried out. This section details the procedures implemented into POSTNL, to achieve these transformations.

I.7.2 Restrictions

The procedures outlined here are applicable to membrane, axisymmetric solid and shell elements. In the current version of POSTNL, these procedures are only implemented for the shell elements TCS6 and TCS8 with the default surface integration rule.

I.7.3 The Plane Stress Transformation

The transformation of interest here is the rotation about a surface normal of the stresses in each layer of a shell. In the thick shell elements these are the plane stress components σxx, σyy and τxy and the two orthogonal transverse shear stresses τyz and τzx. The rotation of a general state of plane stress through an angle θ is a standard exercise in mechanics (reference 0) and the stresses in the new (primed) system are given by:

σ′xx = (cos2 θ) σxx + (sin2θ) σyy + (2 sin θ cos θ) τxy

σ′yy = (sin2 θ) σxx + (cos2θ) σyy - (2 sin θ cos θ) τxy

τ′xy = (sin θ cos θ) (σyy - σxx) + (cos2 θ - sin2 θ) τxy (1)

The transverse shear components transform according to the usual transformation rule for vectors, that is:

τ′yz = (cos θ) τyz + (sin θ) τzx

τ′zx = (-sin θ) τyz + (cos θ) τzx (2)

Exactly the same transformations may be employed for the corresponding strain components except that the definition of the in-plane shear strain requires a factor of one half to be applied to this term.

Similarly for the stress resultants the in-plane forces and in-plane shear and the bending moments and twist may all be transformed using the same relationships. Also, the transverse shear forces will transform like the transverse shear stresses.



I.7.4 Determination of the Rotational Angle, θ

The direction into which the stresses are to be rotated is defined by the user. There are several ways in which this direction may be specified and these will be dealt with in the following section. For the purposes of deriving a suitable algorithm to compute the angle of rotation, θ, it is assumed that a unit vector in the required direction, p ( i , j , k ) where i , j , and k are unit vectors in the global (fixed) reference frame, has been defined. The stress state before rotation is given with respect to a local orthogonal cartesian system x,y,z (see Figure I.7.1.) with unit vectors x ( i , j , k ), y ( i , j , k ), z ( i , j , k ) respectively.

Figure I.7.1. Local axis system

The projection of p on the x,y plane, q, is given by

yy + xx = q

where x and y are determined from the dot products

x.p = x

y.p = y

A further dot product between a unit vector in the direction of q, q , and the local x direction unit vector x , yields the angle θ, i.e.

cos θ = x.q

where

q = q / |q|

I.7.5 User Definition of New Local Axes Direction

Two different methods of defining the local axes directions are available to the user of POSTNL. The first, and simplest, requires the user to define the coordinates of a point P, with respect to the global reference frame. Taking P as the terminal point of a vector starting at the origin of the global reference frame and denoting it as P( i , j , k ) then a unit vector in the direction of P, p , is given by



p = P / |P|

Using this method, the local x′ axis direction is constant for all elements in the groups specified (see FigureI.7.2.) i.e. all parallel to p and in the direction of p .

Figure I.7.2. Rotated directions in global axis system

The second method requires the user to define the coordinates of a point, P, with respect to the global reference frame which acts as the centre point for a radial axis system. Using this method, the local x′ axis direction points from the global position at which the stresses are defined, i.e. the integration point, towards the point P.



Denoting the position vector of the integration point G as g (see Figure I.7.3.) and the position vector of the point P as P then a vector, p, from the integration point G to the point P is given simply as

p = P - g

and a unit vector in this direction, p , is obtained by normalisation in the usual manner.

Figure I.7.3. Rotated directions with radial option

This method is invoked by responding RADI to the required prompt when using POSTNL.

I.7.6 User Definition of Element Top and Bottom Surfaces

The definition of the top and bottom surface of 2-D finite elements such as membranes, shells and axisymmetric solids is associated with the node order in which the element topology is specified in the analysis. In general, adjacent elements in a mesh may have a mismatch of surfaces, i.e. the top surface of one element is coincident with the bottom surface of an adjacent element. Thus when post-processing the element results, a consistent convention must be adopted if meaningful plotting of, for example, stress contours is to be carried out.

In POSTNL, the specification of the top surface of an element is achieved by prompting the user to define the global coordinates of a reference point, R, which is used to define a control vector, d (see Figure I.7.4.). This control vector starts at R and terminates at the integration point, G, at which results are being processed. The convention adopted is that the control vector enters the element at the bottom surface and exits through the top surface. Computationally, this procedure is very simple. Knowing the global coordinates of G (interpolated from the element nodal coordinates using the element shape functions).



Figure I.7.4. Construction of Control Vector for Element Surface Definition

the vector d is determined as

d = g - r

and a unit vector in this direction, d , is obtained by normalisation in the usual manner. The angle θ between the vector d and the unit normal to the shell surface, z , is easily calculated from the definition of the dot product, i.e.

cos θ = z.d

If 1 ≥ cos θ ≥ 0, then the top surface defined in the analysis is assumed to coincide with that specified by the user in POSTNL. However, if cos θ < 0, it is assumed that the surfaces need to be reversed or flipped.

I.7.7 References

I.1 Timoshenko, S.P. and Gere, J.M., Mechanics of Materials, van Nostran Reinhold, 1973.

G

R

Gθ�

g

r

d

kZ, jY,

iX,

d z

y x



I.8 Fracture Mechanics Processing

I.8.1 Introduction

The facility to request the calculation of the fracture mechanics parameters J and J* and creep fracture parameters C and C* is available in POSTNL.

To enable fracture mechanics processing, results for displacements (DISP), stresses (STRS), total strains (STRN), elastic strains (ELAS) and, if PLAS, inelastic strains (INST) must be saved on the post-processing file. For C and C*, creep strains (CRSN) must also be saved. In addition, all the results for C and C* must be saved for a neighbouring state as well as the required increment in order to enable the calculation of rate quantities. The facility is invoked via the PRINT option. When the user is prompted for output type and increment, the output type should be either:

JAY for J integral calculation

JAYS for J* integral calculation

CEE for C integral calculation

CEES for C* integral calculation

Having made the appropriate response, the user is then prompted for the name of the contour definition file. This file must be created before the POSTNL run. The contour definition file is a formatted ASCII file, details of which are given in Section I.8.4.

Once the contour definition file name has been entered, POSTNL echoes the data to the screen and then computes and prints out J and/or J* or C and/or C* as requested. From this point on the process may be repeated for further contour definitions.

I.8.2 Restrictions

The fracture parameter calculations in POSTNL are currently subject to a number of restrictions. These are:

(a) Elements on and within the contour must be axisymmetric solid elements or membrane elements in 2-D.

Surface flaws on shells can be analysed using the line-spring elements.

(b) Elements on and within the contour must not be subject to body forces (including centrifugal loading).

(c) The analysis must be carried out using global stresses, i.e. stress calculation for the elements must be

related to the global axis system. Note that this is the default for the axisymmetric solid elements.



I.8.3 Notes on the use of Fracture Parameters

It is assumed that the user is fully conversant with the theory and application of the J(C) and J*(C*) integrals. The following offers some practical guidance to their use within the finite element method.

For linear elastic fracture mechanics, J(C) is path independent and should thus give the same value regardless of the contour specified. This is only approximately true with a finite element discretisation. However, providing the variation of stresses and strains within the elements on the contour is not too severe (as they are at the crack tip), the value of J(C) should not vary by more than a few percent. The further the contour is from the crack tip, the more path independent J(C) should be in a finite element discretisation. It is also advisable to avoid distorted elements (which in themselves may cause a sharp variation in the stress field) or unstressed elements which, in effect, increase the length of the contour path but add nothing to the strain energy.

For elasto-plastic fracture mechanics, J(C) is path independent only if the entire contour passes through an elastic region. It is for this reason that J*(C*) was introduced and this integral should be independent of the path and area of integration. It is well known that including the elements surrounding the crack-tip in the evaluation of J*(C*) introduces significant errors and therefore these elements should be excluded from the area of integration.

I.8.4 Format of Contour Definition File

The contour definition file contains the information required to define the contour for the J(C) integral calculation and the elements to be included in the J*(C*) integral calculation. It also contains the angle of orientation of the crack with respect to the global axis directions. The format of the file is as follows:

THETAD (EN)

NODS

NODCNT(1) NODCNT(2)........

............................

...........NODCNT(NODS)

NELS

NELCNT(1) NELCNT(2)........

...........NODCNT(NELS)

THETAD is the angle the crack x1 axis direction makes with the global R (or X) direction and is specified in degrees. EN is only required for C and C* calculation and is the Creep law exponent, n, in the expression

σε ncr B = . NODS is the number of nodes defining the contour. Element mid-side nodes should not be

included. NODCNT(I) are the node numbers lying on the contour, from one end to the other end. Note that the contour integration is always performed in an anti-clockwise fashion inside the program. NELS is the number of elements lying on the contour for J(C) and on and within the contour for J*(C*). NELCNT(I) are the user element numbers.

I.8.5 Example

The following example demonstrates the form of the data required.



Figure I.8. shows the section of interest in an axisymmetric model with the crack angle and contour path. Figure I.9. shows the finite element mesh used with node and element numbers. The contour data definition file for J integral calculation would be as follows:

220.0

19

251 217 183 181 179 177

175 173 207 241 292 326

328 330 332 334 336 302 268

14

49 50 51 52 53 57 61

65 69 73 74 75 76 77

If J* also was to be calculated, the above data file could be used with the addition of 2 elements, 60 and 68. Note that the elements surrounding the crack tip have been excluded from this J* calculation.

Figure I.8. Crack Angle and Contour Path



Figure I.9. Finite Element Mesh Node and Element Numbers

Appendix J ASAS (Non-Linear) User Manual

Page J-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - J Creep Analysis

J.1 Overview

The following data are required in addition to the normal description of a model when conducting a creep analysis.

1. A creep analysis is initiated by the four character directive CREP with the PROBLEM/TITLE command in the Preliminary data. The job type should also be set to TRAN (time dependent analysis) with the JOB command. Currently only one material non-linearity can be modelled in any one restart stage, i.e. any instantaneous (‘plasticity’) effects must be isolated from time dependent (‘creep’) effects and treated in a separate restart.

2. For creep analysis the ‘pseudo’ times used for the ASAS-NL incremental solution procedure become real times, representing the period for which creep behaviour is to be calculated. The solution must therefore be controlled by SOLVE and RESTART commands with lists of real times at which solutions are to be calculated. In addition to the times at which results are desired it is likely that a number of intermediate times should also be requested in order to achieve acceptable accuracy and stability. This can be done either manually (simply by defining a list of solution times) or automatically by the program (see Section J.4).

3. Three solution methods are available for creep and are explained in Section J.2. They are set as follows:

Explicit: This is the default and so no additional information is necessary.

Implicit, elastic stiffness: Specify a non-zero implicit weighting factor VALPHA with the TEMPORAL command.

Implicit, updated stiffness: Specify a non-zero implicit weighting factor VALPHA with the TEMPORAL command, and set OPTION VISC.

4. If automatic selection of timesteps (see Section J.4) is required then OPTION AUCR should be set. A sufficient number of timestep controlling parameters should also be selected to achieve the desired control. If AUCR is not set the program defaults to manual timestep selection and only solves at the times specified with the SOLVE or RESTART command.

5. The creep material behaviour is defined by specifying a creep law for each material type in the creep material properties data block, see Section 5.2.4.3. For any particular material type there is a choice of four laws in-built to the program, NORT, LAW2, LAW3, LAW4. Alternatively a creep law can be defined directly in a user supplied subroutine, directives USE1, USE2, USE3, USE4, USE5 on the creep material-properties data block. Details of the various creep material models are given in Appendix B.4.



J.2 Creep Solution Methods

The three creep time integration methods currently available in the program are:

(i) Explicit

This is also known as the Euler Forward Method or Forward Difference Method. The incremental

equivalent creep strains are calculated simply from the equation

t= (i)cc ∆εε c

Where the superscript (i) denotes that the equivalent creep rateεc is calculated using the values of stress,

strain, temperature and time at the start of the timestep, and ∆ t is the time increment.

No iteration is necessary for this calculation because it is based entirely on known quantities at the start of

the timestep.

(ii) Implicit, elastic stiffness

For this method the equivalent incremental creep strains are calculated from

t (VALPHA)t+ VALPHA)-(1= 1)(i+c

(i)cc ∆∆ εεε

Where the superscript (i+1) denotes that the creep rate is calculated using the values of stress, strain,

temperature and time at the end of the timestep.

Stresses and strains are not known a priori for the end of the timestep and so iteration is necessary over

the increment, each time using the latest estimate of these quantities, until no change is observed in

consecutive iterations.

If VALPHA is set to 1.0 this method is known as the Euler Backward Method or Backward Difference

Method. If VALPHA is 0.5 this is known as the Central Difference Method. If VALPHA is zero it

defaults to the Explicit method.

(iii) Implicit, updated stiffness

This method uses the implicit equation in (ii) above except that the solution is estimated without iteration,

by calculating a tangential material stiffness each increment. This effectively approximates the change to

the creep rate from changing stress over the increment but does not account for any such changes due to

changing total creep strain, temperature or time.

This method is derived as a Viscoplastic solution procedure in reference J.1.



Currently the creep model is limited to the von Mises potential function and associative flow rule when extending the above uniaxial creep descriptions to multiple axes. The term ‘equivalent’ therefore always denotes von Mises equivalent quantities.

Note that for all three methods there is no need for the user to specify any UPDATE information if creep is the only non-linearity being considered. The first two methods use the elastic material stiffness exclusively and the third method automatically UPDATES the stiffness on all iterations. If large displacements are considered concurrently with creep then additional updating should be requested as required, see the UPDATE command.

Note also that because creep analysis is a timestepping procedure modelling transient behaviour through real time, solution is always by the SOLVE method with pseudo times representing real times. The special solution (SOLU) methods are therefore not available for creep.

J.3 Convergence of Creep Solutions

Although the type of Norm and the tolerance value specified with the CONVERGENCE command can in general be specified freely for creep analysis, control of the Reference Variable is limited as follows.

(i) Explicit method

The Residual Forces (RESF) Variable remains the default as with other types of analysis. No residual

forces are present for creep increments when other non-linearities are not involved and so in such cases

no iteration will take place. The DISP variable may be selected but STRN and STRS may not.

(ii) Implicit Method, elastic stiffness

Two convergence checks are made:

(a) Convergence of the creep rate calculations is automatically monitored by a STRS check

with EUCN. The convergence tolerance is 0.001.

(b) The RESF (or alternatively DISP) check described in (i) above is also made and again the

residual forces will always be zero unless other non-linearities are involved. STRS and

STRN may not be selected with the CONVERGENCE command.

(iii) Implicit Method, updated stiffness

Convergence checking is the same as for the Explicit Method.

J.4 Automatic Timestepping

The purpose of the automatic control of timestepping is to enable the program to choose timestep lengths according to user supplied criteria so as to achieve consistent accuracy over the period of solution. The basic



philosophy is that the program solves at all times specified with the SOLVE or RESTART commands and additionally at as many intermediate times as is necessary for the given criteria. The automatic timestep facility operates independently of the selection of creep solution method.

Note that although solutions at intermediate times follow identical theory to those at SOLVE or RESTART times, they are hidden to the user with the exception of a brief summary of each step. Thus OUTPUT, POST, SAVE, RESTART etc. commands may only refer to SOLVE or RESTART times. If ‘ALL’ is specified on such a command then all times specified with the SOLVE or RESTART command will be inferred (but no intermediate times).

The automatic timestepping facility is controlled by the following OPTION and TEMPORAL identifiers:

Controlling Options using the OPTION command

AUCR Autocreep. This activates the automatic control facility (Default: manual control, solutions only at SOLVE or RESTART times).

FCRO Full Creep Output. A half page performance summary is printed for each automatically selected timestep (Default: a two line summary is printed).

Controlling parameters using the TEMPORAL command

Any number of these parameters may be set to control the timestep length. After each solution the next solution time will be chosen from the shortest time implied by all of the parameters, or the next SOLVE or RESTART time; whichever is the sooner.

DCSTMX Maximum change of creep strain. In each timestep the maximum equivalent change of creep strain for all integration points is recorded. If this quantity for the previous step (step size t(i)) is denoted MAX then the new timestep length t(i+1) will be:

MAXDCSTMX . t=t (i)1)(i+ ∆∆

DCESMX Maximum relative change of creep strain. The same method of control as for DCSTMX is used but in this case the control quantity is the ratio of equivalent incremental creep strain to current equivalent elastic strain.

DSIGMX Maximum relative change of stress. The same method of control as for DCSTMX is used but in this case the control quantity is the ratio of equivalent change of stress to current equivalent stress.

FINCMX Maximum ratio of new timestep length to previous timestep length.

TINCMX Maximum timestep length.



Supplementary parameters

FIRSTP First timestep length. Specifies the first solution time in a run. If omitted the first solution will be at the first time given with the SOLVE or RESTART command.

TINCMN Minimum acceptable timestep length. If the controlling parameters imply a timestep length less than TINCMN then the solution will be stopped.

MXINCS Maximum number of timesteps in a run. If this number is exceeded in any run then the solution will be stopped.

J.5 Example Preliminary Data

The following two examples indicate additional Preliminary data used when analysing a model for creep behaviour.

(i) Explicit integration; Manual control (solutions at SOLVE times only); No large displacement effects.

JOB TRAN

TITL CREP * ....

SOLV ..........

(ii) Implicit integration; Weighting factor = 0.7; Updated stiffness method; Automatic timestep control; First

intermediate solution at 10.0 time units; Timesteps to limit incremental creep strain to half of elastic

strain; Results could be printed (or post-processed or saved for further restarts) at times 100.0, 300.0

and/or 1000.0; No large displacement effects.

Note - this example assumes that information is available from a previous analysis for a restart from time

5.0.

JOB TRAN ....

TITL CREP * ....

REST 5.0 100.0 300.0 1000.0

TEMP VALPHA 0.7 FIRSTP 5.0 DCESMX 0.5

OPTI AUCR VISC

J.6 Recommendations for Creep Analysis

The choice of method and parameters for conducting a creep analysis depends strongly on the characteristics of the problem. It is therefore not possible to propose fixed rules. However the following generalisations may be useful.



(i) The accuracy of solution is sensitive to timestep sizes and great caution should be exercised in their

selection. In the limit of diminishing timestep size, all three solution methods will converge on the same

results. These results will be correct within the limitations of the material definition.

(ii) If accuracy of solution is lost through excessive timestep length it should be assumed (in general) that the

solution will not recover subsequently, even if the step length is reduced.

(iii) The implicit method with updated stiffness is much more tolerant of long timesteps than the two other

methods (by an order of magnitude or more for a given accuracy) provided that the only creep rate

variable which changes during the step is stress (i.e. no hardening, no temperature change). This method

is therefore normally to be preferred for such situations.

For rapid changes in temperature loading or hardening the implicit method with elastic stiffness takes best

account of changes during the step. However the convergence of iterations when using this method can

be poor and in general the use of the explicit method with short steps is therefore to be preferred for these

problems.

(iv) The choice of value for the implicit weighting factor (VALPHA) has influence on the results in both of

the implicit methods. (Note that convergence of iterations with the implicit elastic stiffness method is not

convergence to a ‘correct’ solution, but only signifies satisfaction of the weighted creep strain equation in

Section J.2.) A value between 0.5 and 0.8 is recommended.

(v) Given the necessity for consistent accuracy throughout the solution, the use of automatic control of

timesteps is strongly recommended. The values of control parameters depend very much on the problem

being considered but as a rough guide the new user is advised to start by limiting creep strains to the same

order of magnitude as elastic strains for the implicit updated stiffness method and an order of magnitude

lower for the two other methods.

J.7 References J.1 Hinton, E. and Owen, D.R.J., ‘Finite Elements in Plasticity’, Pineridge Press, 1981.

Appendix K ASAS (Non-Linear) User Manual

Page K-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - K Transient Dynamics Analysis

K.1 Overview

The following are particular information concerning the run control of a transient dynamic analysis.

(i) A transient analysis is initiated by setting the job type to TRAN with the JOB command.

(ii) For transient analysis, the ‘pseudo’ times used in ASAS-NL become real times. The times at which

solutions are attempted can be specified manually or automatically determined by the program. When the

SOLV/REST command is specified, solutions will be obtained at times explicitly prescribed by the user

as in a static analysis. If a constant timestep is used throughout an analysis, an automatic time generation

facility TGEN with the SOLV/REST command is available which can significantly reduce the data

preparation work. Alternatively, an analysis can be performed using the automatic timestepping

procedure. This is invoked by setting directive DOMFRQ or MAXFRQ with the SOLU/SREST

command. Further details about the adaptive timestepping schemes are given in Section K.3.

(iii) The time integration algorithm developed for transient dynamics analysis is an element partitioned

implicit-explicit scheme. By default, all element groups are implicit. Groups can be made explicit by

specifying directive EXPL with the GROU/PROB command. It should, however, be noted that the

definitions of implicit-explicit groups cannot be altered during any restart analysis.

(iv) Rayleigh damping is assumed in which the damping matrix C is given by:

C = αmM+αkKL

where M is the mass matrix, KL is the linear stiffness matrix, and αm and αk are mass and stiffness

damping factors, respectively, that are specified as material properties.

The factors αm and αk are usually chosen to give correct damping at two frequencies. For a specified

damping factor ξ (i.e. ratio of actual damping to critical) at a frequency ω, then

+= ωα

ωα

ξ km

21

Typically, for structural materials, the value of ξ is in the range 0.01 to 0.07. The two frequencies selected

should cover all the important response modes. Thus, one value is normally taken at the fundamental

mode, while the other is taken more arbitrarily at some higher frequency mode.

(v) Any non-zero initial displacements and velocities should be specified in data block INIT. Initial loadings

can be given using the load function facility. When any of the above initial conditions is specified,



solution at time 0.0 must be performed in order to compute the consistent acceleration vector to start the

time integration.

(vi) In transient analysis, it is often necessary to predict the response of structures subjected to some known

velocity or acceleration time histories. To facilitate this, the user can use the data block VELO and

ACCN to enter prescribed velocities or accelerations at any specified freedoms. However, there is a

restriction that mixed prescribed types are not allowed in the same analysis. It should also be noted that

any non-zero prescribed value at time 0.0 will lead to erroneous results unless the governing equation of

motion is satisfied.

K.2 Time Integration Algorithm

The time integration algorithm in ASAS-NL is based on the implicit Bossak’s method, Ref K.1, and this is given by the following equations.

F=)v,dN(+aM+Ma)-(1 1n+1n+1n+n1n+ αα K.2.1

]a2+a)2-[(1 2t+vt +d=d 1n+n

2

nn1n+ ββ∆∆ K.2.2

]a+a)-[(1t +v=v 1n+nn1n+ γγ∆ K.2.3

where dn, vn and an are known displacements, velocities and accelerations, respectively, at time tn and dn+1, vn+1 and an+1 are the corresponding unknowns at time tn+1 which are obtained from solutions of equations K.2.1 to K.2.3; M is the mass matrix; N is the internal force vector; Fn+1 is the external force vector at time tn+1; ∆t is the timestep. The time integration parameters α, β,and γ determine the stability and accuracy characteristics of the algorithm and it has been shown that unconditional stability, second-order accuracy and maximal high frequency dissipation are achieved if

0≤α ; αγ -21= ; )-(1

41= 2αβ K.2.4

In ASAS-NL, the default settings of these parameters are α=0, γ=0.5, and β=0.25 which correspond to the trapezoidal rule without any numerical damping. These defaults can be reset by specifying TALPHA (α), TBETA (β) or TGAMMA (γ) with the TEMP command. If only TALPHA is given, the values of β and γ will be computed according to equations K.2.4.

The explicit scheme is constructed from similar governing equations but with the an+1 terms dropped in the expressions for displacements and velocities when solving equation K.2.1. Using a lumped mass matrix, the solution of this equation becomes trivial and no matrix inversion is required. It should, however, be noted that the explicit scheme is only conditionally stable and the timestep size is limited by the stability limit.



Two different methods are available to define the predictor at the beginning of a new time step. The default scheme assumes that the predictor acceleration is zero and this works well for linear problems. The alternative predictor is constructed by assuming that the predictor displacement is the same as the displacement at the end of the previous time step. This is recommended for non-linear analysis since the convergence is usually faster. The alternative predictor may be selected by specifying IPDICT 2 with the TEMP command. Note, however, that this scheme will break down when β=0.0 and the default scheme must be used in this case. In addition, the alternative predictor is not applicable to explicit time integration algorithms.

K.3 Automatic Timestepping

The purpose of the automatic timestepping procedures is to enable the program to determine the timestep sizes in a manner which will achieve better computational efficiency while maintaining a consistent level of accuracy over the solution period. Schemes based on the control of current dominant frequency and current maximum apparent frequency are available and their definitions are as follows:

(i) Dominant Frequency (Ref K.2, K.3)

The dominant frequency is estimated at each converged timestep using the displacement and internal

force increments by

dMdFd

dMddKd=

T

T

T

T2n ∆∆

∆∆≈

∆∆∆∆

ω

where ∆d is the incremental displacement vector, K is the current stiffness matrix, M is the mass matrix

and F∆ is the incremental internal force vector due to the stiffness terms.

The dominant frequency obtained above is dictated by spurious mass or stiffness terms when artificially

low or high masses or stiffnesses are used. This adverse effect can be avoided by eliminating all

displacement components in ∆d which have an extremely small or large apparent frequency compared to

the dominant frequency. If we define the modified incremental displacement vector as ∆d*, the modified

dominant frequency is given by:

dTMdFTd=

*

*2n ∆∆

∆∆ω

(ii) Maximum Apparent Frequency (Ref K.4, K.5)

The apparent frequency of the ith freedom is defined as

dMF

dMaM=

ii

2i ∆

∆≈

∆∆

ω

where ∆a is the incremental acceleration vector and all other quantities have their previously defined

meanings.

The maximum apparent frequency is the highest frequency value among all the apparent frequencies.

Thus,



}max{= 2i

2max ωω

When directive DOMFRQ is specified with the SOLU command, the automatic timestepping procedure

will be activated using ω2n as the controlling factor and this is applicable to implicit time integrations.

Alternatively, the maximum apparent frequency adaptive scheme will be activated by specifying

MAXFRQ with SOLU and this is suitable for explicit time integrations. Note that because the nature of

implicit and explicit schemes are quite different, the timestepping control procedure for one type of time

integration scheme should not be applied to the other.



Upon determining ω2 from the response (ω2 can be ω2n or ω2

max depending on the control parameter

selected), the desired timestep for the next step is

ωπ2 x FP=t*∆

where FP is the desired timestep factor which is expressed as a fraction of the controlling period.

However, the continuous adjustment of the step size at every timestep is not effective because it requires

excessively frequent matrix decompositions even for linear problems. To overcome this deficiency and

to account for the effect of non-linearities on the solution convergence, the timestep adjustment is made

according to the following formula instead:

where

ITER is the number of iterations for convergence in the nth step and ITERD is the user specified desired

number of iterations as in a static analysis. The function f(ξ) which determines the timestep adjustment is

shown diagrammatically as follows:

The form of f(ξ) indicates that there is a range of ξ (between ξlo and ξhi) in which the timestep will remain

unchanged. This avoids the need for making small adjustments. In addition, fmax defines the maximum



timestep ratio which is used to limit the size of increase between steps and ξrj defines the lower limit on ξ

for accepting the current solution as a good one. It is often desirable that a time adaptive scheme is

conservative on making timestep increases in order to maintain better numerical stability. In this respect,

any increase in timestep will only be made after the increasing signals have been recorded for KSIGNL

consecutive steps, where KSIGNL is a user input parameter.



The current solution is rejected when convergence cannot be obtained or ξ is less than ξrj. The analysis

will then be restarted from the previous converged solution with a reduction in step size. The reduction

factor, RF, will depend on the reason for rejecting the solution and is given by

(i) RF=ξrj for ξ<ξrj

(ii) RF=STEPRF for convergence failure

where STEPRF has the same meaning of the auto-recovery factor in static analyses. The timestep used

for restart is thus given by

tRF*=t nn ∆∆

Similar to the static load adaptive scheme, the number of possible restarts within a step is governed by the

parameter MXAUTO.

There are a number of control parameters for automatic timestepping and these are listed below together

with their default values:

Parameter Default

TINCMN Minimum timestep 0.0

TINCMX Maximum timestep 1.0x1015

FINCMX Maximum timestep ratio 10.0

TFACLO Lower limit of plateau in f(ξ) 0.75

TFACHI Upper limit of plateau in f(ξ) 1.35

TFACRJ Limit on ξ below which the current solution will be rejected 0.10

FRAPRD Desired fraction of the characteristic period for the timestep 0.05

KSIGNL The number of consecutive timestep increasing signals required before the increase is made

2

MXAUTO Limit for number of restarts in any step 3

STEPRF Step reduction factor after convergence failure 0.5

To a certain extent, the performance of the automatic timestepping scheme will depend on the setting of

the control parameters. Although it is not possible to propose fixed rules because of the possible different

characteristics of each new problem, the following general guidelines may be useful.

(i) A conservative initial timestep is generally preferred as this provides greater accuracy at the start of the

time integration process.



(ii) In non-linear analysis, it is advisable to set the maximum timestep ratio, FINCMX, to a realistic value, for

example, 2.0. It helps to improve the numerical stability as too drastic a change in step size may cause

divergence due to the presence of non-linearities. The improvement in numerical stability can also be

achieved by increasing the value of KSIGNL.

(iii) The default setting of FRAPRD is adequate for linear analysis. This number may need to be decreased

(ie more steps per characteristic period) for highly non-linear problems.

(iv) When the loading is changing very rapidly (eg in earthquake problems), it may be necessary to limit the

timestep by an upper value TINCMX in order to secure that the load intensity at sufficiently close

intervals is sampled.



K.4 References

K.1 Wood, W.L., Bossak, M. and Zienkiewicz, O.C., ‘An Alpha Modification of Newmark’s Method,’ International Journal for Numerical Methods in Engineering, Vol. 15, 1980, pp1562-1566.

K.2 Bergan, P.G. and Mollestad, E., ‘An Automatic Time-stepping Algorithm for Dynamic Problems,’ Comp. Meth. Appl. Mech. Eng., Vol. 49, 1985, pp299-318.

K.3 Lee, S.H. and Hsieh, S.S., ‘Expedient Implicit Integration with Adaptive Time Stepping Algorithm for Non-linear Transient Analysis,’ Comp. Meth. Appl. Mech. Eng, Vol. 81, 1990, pp151-172.

K.4 Park, K.C. and Underwood, P.G., ‘A Variable-Step Central Difference Method for Structural Dynamics Analysis - Part 1. Theoretical Aspects,’ Comp. Meth. Appl. Mech. Eng., Vol. 22, 1980, pp241-258.

K.5 Underwood, P.G. and Park, K.C., ‘A Variable-Step Central Difference Method for Structural Dynamics Analysis - Part 2. Implementation and Performance Evaluation,’ Comp. Meth. Appl. Mech. Eng., Vol 23, 1980, pp259-279.

Appendix L ASAS (Non-Linear) User Manual

Page L-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - L References

1. ‘ASAS-NL - Theory and Implementation’ Atkins Research and Development, December, 1981.

2. Ahmad, S., Irons, B.M., Zienkiewicz, O.C. ‘Analysis of Thick and Thin Shell Structures by Curved Elements’. Int. J. Num. Meth. Eng., Vol.2, pp.413-451 (1970).

3. Bathe, K.J. ‘Finite Element Procedures in Engineering Analysis’. Prentice-Hall, 1982.

4. Bushnell, D. ‘A Strategy for the Solution of Problems Involving Large Deflections, Plasticity and Creep’. Int. J. Num. Meth. Eng., Vol. 11, pp.683-708 (1977).

5. Bushnell, D. ‘Stress, Stability and Vibration of Complex Branched Shells of Revolution’. Comput. Struct., Vol.4, pp.399-435 (1974).

6. Cook, Robert D. ‘Concepts and Application of Finite Element Analysis’. John Wiley, 1974.

7. Crisfield, M.A. ‘A Fast Incremental/Iterative Solution Procedure that Handles Snap-Through’. Comput. Struct., Vol. 13, pp.55-62 (1981).

8. Crisfield, M.A. ‘Ivanov’s Yield Criterion for Thin Plates and Shells Using the Finite Element Method’. TRRL, Rep. 919, D.o.E., 1979.

9. Gallagher, R.H. ‘Finite Element Analysis Fundamentals’. Prentice Hall, 1972.

10. Gierlinski, J.T. and Graves Smith, T.R. ‘A Variable Load Iteration Procedure for Thin-walled Structures’. Comput. Struct., Vol.21, pp.1085-1094 (1985).

11. Hill, R. ‘The Mathematical Theory of Plasticity’. Clarendon Press, 1980.

12. Hinton E. and Owen D.R.J. ‘Finite Elements in Plasticity’. Pineridge Press, 1981.

13. Irons, B. et al. ‘Analysis of Thick and Thin Shell Structures by Curved Finite Elements’. Int. J. Num. Meth. Eng., Vol. 2, 1970.

14. Johnson, W. and Mellor, P.B. ‘Engineering Plasticity’. Van Nostrand, 1978.

15. Malvern, L.E. ‘Introduction to the Mechanics of Continuous Medium’. Prentice-Hall, 1969.

16. Owen, D.R.J. and Gomez, C.M.B. ‘An Appraisal of Numerical Solution Techniques for Elasto-Plastic and Elasto-Viscoplastic Material Problems’. 6th International Conference SMIRT, Vol. M M3/1.

17. Powell, G. and Simons, J. ‘Improved Iteration Strategy for Non-linear Structures’. Int. J. Num. Meth. Eng., Vol.17, pp.1455-1467 (1981).

18. Przemieniecki, J.S. ‘Theory of Matrix Structural Analysis’. McGraw-Hill, 1968.

19. Riks, E. ‘An Incremental Approach to the Solution of Snapping and Buckling Problems’. Int. J. Solids Struct., Vol. 15, pp 529-551 (1979).



20. Robotnov, Y.N. ‘Creep Problems in Structural Mechanics’. North-Holland, 1969.

21. Smith, I.M. ‘Programming the Finite Element Method with Applications to Geomechanics’. John Wiley, 1982.

22. Stolarski, H. and Belytschko, T. ‘Membrane Locking and Reduced Integration of Curved Elements’. J. Appl. Mech., Vol.49, pp.172-176 (1982).

23. Washizu, K. ‘Variational Methods in Elasticity and Plasticity’. Pergamon Press, 1975 (2nd Edition).

24. Waszczyszyn, Z. ‘Numerical Problems of Non-linear Stability Analysis of Elastic Structures’. Comput. Struct., Vol.17, pp.13-24 (1983).

25. Zienkiewicz, O.C. ‘The Finite Element Method in Engineering Science’. McGraw-Hill, 1977 (3rd Edition).

26. Zienkiewicz, O.C., Too, J., Taylor, R.L. ‘Reduced Integration Techniques in General Analysis of Plates and Shells’. Int. J. Num. Meth. Eng., Vol.3, pp. 235-256 (1971).

27. O.R.N.L. - ‘Guidelines and Procedures for Design of Nuclear System Components at Elevated Temperature’ - RDT Standard F9-5T Division of Reactor Research and Development, United States Atomic Energy Commission, September, 1974.

28. Chang, S.C. and Chen, J.J. ‘Effectiveness of Linear Bifurcation Analysis for Predicting the Non-linear

Stability Limits of Structures’. Int. J. Num. Meth. Eng., Vol. 23, pp. 831-846 (1986).

Appendix M - Wave Loading ASAS (Non-Linear) User Manual

Page M-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - M Wave Loading On Offshore Jacket Structures

M.1 Introduction

The wave loading capability in ASAS-NL is incorporated from the program WAVE within the ASAS-OFFSHORE system. This facility enables the calculation of wave, wind and current loading on fixed offshore structures where the structural members are of relatively small section size compared with the wave length. Only TUBE and BM3D elements will have environmental loads generated and all other element types will be ignored.

For natural frequency or transient dynamics analysis, additional inertia due to various hydrodynamic effects is also included. This is similar to the facility offered by the program MASS.

In addition to the description of the structure, the calculation of wave loading requires environmental data, which defines the position of the jacket relative to the mean water-level and sea-bed together with wave height and direction, current profile and direction, wind direction and velocity. The description also defines the presence of flooded or sealed members, the presence of marine growth, and the drag and inertia force coefficients for the loaded members.

A number of different wave theories have been implemented for the user to select from. These include the linear (Airy), Solitary (Cnoidal), Stokes Vth order and stream function wave theories. For conditions not covered by these theories, a facility exists for supplying the wave kinematics as a grid of velocities and accelerations, together with a free surface profile. Facilities are also provided to permit wave loading to be computed within the requirements of the API codes of practice (RP2A-WSD and RP2A-LRFD) including the effects of apparent wave period, non-linear current stretching, current blockage factor and wave kinematics factor. Extreme wave kinetics may be developed using the Shell New Wave model, which utilises statistical analysis of sea state information. Wave loading may also be generated from a random sea state. For details of various wave theories and the wave force calculation, please refer to the WAVE user manual.

In this Appendix, the descriptions of the valid wave load commands in ASAS-NL are presented. These commands are a subset of the commands available in WAVE and generally have identical meanings (except where noted).

M.2 Water Axes

Water axes Xw, Yw and Zw are defined separately to the structure Global Axes. The position of the water axes relative to the global axes is specified in the ‘WAVE LOAD’ data. All of the ‘hydrodynamic’ quantities such as wave direction, current direction, mean water level, etc. are then defined relative to the Water Axes.

The water axis Zw is always vertical and positive upwards.The water axis Xw lies in a plane parallel to the global plane with the water axis Yw on the positive side of the XY plane, Yw is positive in the direction of positive Y (see also the GRAV and MOVE commands in Appendix M.6).



This facility enables the global structure axes to be defined to ‘best fit’ the structure but, in general, for most offshore structures one axis is nearly always vertical and by convention this is usually denoted as the Global Z axis. For this situation the directions of the global and water axes are related simply by supplying ‘-g’ in the Z field of the wave loading GRAVity data command (where g is the gravitational acceleration in consistent units). The facility of being able to vary the position of the structure relative to the water is used to the full in the LAUNCH program which investigates the behaviour of the structure as it is launched from a barge, tilted and installed.

M.3 Wave Theories

M.3.1 Conventional wave theories

For the wave loading, a suitable wave theory is used to calculate the water particle kinematics. The following wave theories are currently available in ASAS-NL:

• Linear Wave Theory (Airy)

• Solitary Wave Theory (Cnoidal)

• Stokes 5th Order Theory

• Stream Function Theory

For guidance on selection of the appropriate wave theory, reference should be made to Figure M.1.

For conditions not covered by the above wave theories, a facility exists for supplying the wave kinematics in the form of a grid of velocities and accelerations, together with a free surface profile. The program utilises linear interpolation for determining kinematic values at locations between the grid positions. See Section M.6.13 GRID Wave Data for further details.

M.3.2 Shell New Wave

The Shell NewWave wave model is incorporated into WAVE as an alternative to the conventional deterministic wave theories described in Section NO TAG. The NewWave wave model was developed by Shell Research (Reference NO TAG) in order to produce a more realistic description of the physical processes which occur under extreme design waves in real seas, something which cannot be accurately described by traditional deterministic wave theories. NewWave is not appropriate for harmonic analyses.

In the NewWave model, the water particle kinematics are generated from a wave spectrum using linear theory. It uses a statistically-based superposition of linear wavelets to define the wave profile and associated kinematics representing the most likely maximum condition of a real sea. The unique features of the theory are illustrated in Figure 2.1 below. This figure shows that the wave crest is significantly higher than the neighbouring troughs, which is consistent with observations of extreme waves.



By definition the NewWave model is dispersive (or evolving) in that the crest height varies with time. In order that analyses may be undertaken in a similar mode to that employed in deterministic wave studies, the wave may be ‘frozen’ and stepped through the structure in the same way that conventional wave theories are processed.

Key features of the NewWave model in WAVE are:

• Delta stretching of wave kinematics under the crest

• Current blockage may be included using the BLOC command

• Wave spreading for nearly uni-directional seas may be selected using the WPAR command

• Doppler shift effects may be incorporated to account for wave/current interaction using the APIW

option

• Both evolving and non-evolving waves are facilitated

• Morison force coefficients may be specified as a function of the characteristic amplitude to tube

diameter ratio using the AMPL table definition

• Facilities to tune the solution method, where appropriate, using the WPAR command

Figure 2.1 NewWave Surface Profile

M.3.3 Irregular Wave

The irregular wave model provides a facility to analyse loading that takes into full account the randomness of the sea state.

In the irregular wave model implemented, the wave particle kinematics are assumed to be generated from a wave spectrum using linear theory. The wave spectrum can be defined in one of the three forms: JONSWAP, Pierson-Moskowitz or user defined.

M

PSMZ wave surface elevation - Shell NewWave - EVOLVING Distance in wave direction

-500.0 -400.0 -300.0 -200.0 -100.0 0.0 100.0 200.0 300.0 400.0 500.0 -3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0



The irregular wave is created by adding together the parameters (wave height, velocity and acceleration) of a number of regular Airy wavelets with random phases and with amplitudes that correspond to the required spectrum. The default number of wavelets is 50 and this may be re-specified using the WPAR command, subject to an upper limit of 1000.

The wavelet phases are generated by a random number generator. The initial seed (default 1) for this process may be modified using the WPAR command, which will enable a different set of random phases to be generated. On a subsequent run, the same initial seed will generate the same sequence of random phases again.

Delta stretching of kinematics as implemented in the Shell New Wave model is also available in irregular wave.

Figure M.1 The Range of Validity of Various Wave Theories



Notes

1. None of these theories is theoretically correct at the breaking limit.

2. Wave theories intended for limiting height waves should be referenced for waves higher than 0.9Hb when stream function theory may underestimate the kinematics.

3. Stream function theory is satisfactory for wave loading calculations over the remaining range of regular waves. The suggested order of stream function is shown above but should be checked by comparison with the results from a higher order solution.

M.4 Wave load data format

The wave load data generally assigns additional properties to elements, or groups of elements, which are specifically required for the load generation. The data syntax is similar to that employed for the structural data but consists of individual command lines, each of which assigns the additional parameters to the element(s). The typical syntax of a command line is as follows:

Once a command has been defined, the value(s) specified remain assigned to the appropriate element(s) until modified by a subsequent command. Basic data, such as drag and mass coefficients, need only to be supplied once within the data set to remain constant throughout the analysis (unless required to be overridden).

The data values may be assigned to all elements using the keyword ALL or to specific elements using the keywords ELEM, PROP or GROU followed by a list of user element numbers, geometric property numbers or element group numbers. The list may be continued onto subsequent lines using the special symbol : (see Section 4.1.3).

The list may be abbreviated using the keyword TO in the form i TO j to create a list of all values between i and j inclusive.

Not all the element, property or group numbers defined need to exist in the structure. Only those elements in the list which correspond to elements in the structure will be included.

ELEM

PROP

ALL

elem

prop

groupGROUrealKEYWORD



M.5 WAVE LOAD Data

Many of the commands described in this section are optional and merely change default values within the program. Once a default value has been changed, by the input of the appropriate command, it remains at the new value until altered again. A list of the WAVE LOAD commands valid for ASAS-NL is given in Table M.1.



Command Meaning Comments AMAS Additional mass on element Default - none BLOC Current blockage factors Optional for use with API codes (use APIW option) BUOY Buoyancy Default - none CURR Current from any direction DRAG Drag coefficients Default - 0.0, 0.7, 0.7 ELEV Water elevation Mandatory END End of all wave load data Mandatory EXEC Execute Optional. Generally not required FREE Free flooding Default - none GRAV Gravity components Mandatory GRID Grid wave kinematics User defined waves GROW Marine growth Default - none HYDR Hydrodynamic dimensions Optional KC KC dependent drag and mass

coefficients Default - none

KINE Wave kinematics factor Optional for use with API codes (use APIW option) LFUN Wave load function Optional. Default is no scaling MASS Inertia coefficients Default - 0.0, 2.0, 2.0 MOVE Water axes Default - coincident with jacket axes NANG Number of angle steps Optional for use with RENL and KC tables. Default

- 8 NOBO No buoyancy Overrides BUOY command NOFR No free flooding Overrides FREE command NOLO No loads Overrides loading commands. Should be specified

after all loading commands NOSW No self-weight Overrides SLWT command NOWI No wind load Overrides WIND command NOWL No wave load Overrides WAVE command OFFS Member offsets Default - none OUTP Print control Default - jacket totals only PCUR Any current PEXT External pressure for buoyancy Default - pressure computed from sea water density

and elevation including wave action effect PHAS Phase Default - 0.0 PRIN Element printing Default - none RENL Reynolds dependent drag and mass

coefficients Default - none

Table M.1 Command words and their defaults for WAVE



Command Meaning Comments SLWT Self-weight Default - none SPEC Seastate spectrum definition Mandatory for irregular wave or New Wave SPRE Wave spreading power Optional for use with API codes (use APIW option) TIDE Current in wave direction TOLS Tolerance command Default 0.1, 0.0 UNIT Define new units Optional VAXS Define orientations of

hydrodynamic axes Default - water axes

VISC Kinematic viscosity Must be defined if RENL command used VPOS Define reference point for

hydrodynamic data Default - origin of water axes

WAVE Wave data Must not precede ELEV command WIND Wind data Default - none WPAR Wave parameters XMAS Extra mass/unit length Default - none ZONE Define zones for DRAG, MASS

and GROW command

Table M.1 Command words and their defaults for WAVE (continued)

M.6 Description of the Wave Load Data Block

M.6.1 WAVE LOAD Data

Parameters

WAVE LOA : compulsory keyword to denote start of the wave data

data : wave load data

END : compulsory keyword to denote end of the wave data

WAVE LOA

data

END



Notes

1. Wave load data should not be defined more than once in the entire load check. The loading specified will be applied to all load sets.

2. The wave loading generated can be scaled, but using command LFUN only.

3. Arc-length type SOLU procedure can be used but wave load must be attached to the proportional load function using LFUN.

4. If modification of wave environment is required during an analysis, this can be achieved by restarting with modified wave data supplied.

M.6.2 AMAS Command

This facility enables non-structural mass such as stiffening rings, anodes, etc. to be included. Extra mass is input as a value per element.

Parameters

AMAS : keyword

mass : extra mass per element. (Real)

ELEM : keyword to indicate element selection

elem : list of user element numbers. (Integer)

GROU : keyword to indicate group selection

group : list of group numbers. (Integer)

PROP : keyword to indicate geometric property selection

prop : list of geometric property numbers. (Integer)

ALL : keyword to indicate selection of all elements

ELEM

PROP

ALL

elem

prop

groupGROUAMAS mass



Notes

1. Extra mass may be specified per unit length per element using the XMAS command.

2. Masses are not cumulative. Subsequent AMAS definitions for a particular element will overwrite previous values.

3. XMAS may be specified in addition to AMAS for a given element, in which case the XMAS mass and the AMAS mass are cumulative.

M.6.3 BEAM Element Command

The BEAM command is replaced by the HYDR command.

M.6.4 Current BLOCKAGE Factor Command

The BLOC command specifies a user defined current blockage factor for use within the API codes of practice. The factor can be varied at different heights on the structure.

Parameters

BLOC : keyword

FACTOR : keyword to define that a user defined current blockage is to be supplied

factor : current blockage factor. (Real)

zmin : minimum height on structure (in water axes) to which this blockage factor applies. (Real)

zmax : maximum height on structure (in water axes) to which this blockage factor applies. (Real)

Notes

(a) Several BLOC commands can be supplied to vary the blockage factor at different heights on the structure.

(b) If zmin and zmax are omitted, the blockage factor is applied between the seabed and still water level.

(c) A default value of 1.0 is used for any region of the structure not covered by a user defined factor.

(d) BLOC commands are cumulative and a table is built up as each command is read. To reinitialise the table use the RESEt command.

BLOC ( zmin zmax ) FACTOR factor



(e) For a fatigue analysis API requires that a factor of 1.0 be used.

(f) For a factor not within the range 0.7 ≤ factor ≤ 1.0, a warning will be issued but the user defined value will be used.

(g) This command will only be utilised when used in conjunction with the APIW option.

Example

BLOC 1.0

.

EXEC

.

RESE 3

BLOC 0.9 0.0 10.0

BLOC 0.95 10.0 15.0

BLOC 0.97 15.0 20.0

M.6.5 BUOYANCY Command

The BUOY command specifies those members for which buoyancy loads are to be calculated. The elements may be filled, either wholly or partially, with an internal fluid either by specifying the density and proportion of flooding or, where the members are free flooding, using the FREE command (see Note 4 below). The command is optional and no buoyancy is calculated if omitted.

Parameters

BUOY : keyword

density : mass density of internal fluid. (Real)

flood : proportion of flooding of internal fluid. (Real)

elev : elevation used for computing internal pressure. (Real) If elev Zb, the sea bed level, internal

pressure is computed assuming fluid pressure to elevation elev. If elev <Zb, internal pressure is

computed to the elevation of the water surface vertically above the point in question.



ELEM

PROP

ALL

elem

prop

groupGROUBUOY density flood (elev )








Notes

1. The weight of any internal fluid is automatically included in the buoyancy calculation.

2. Buoyancy forces are calculated for members below the sea bed. For members above the water surface only the weight of internal fluid is computed if elev is omitted.

3. The proportion of flooding varies between 0.0 for no flooding and 1.0 for full flooding.

4. If the member is free flooded (FREE) the internal fluid details (density and flood) should be omitted otherwise the mass of the internal fluid may be duplicated.

5. The buoyancy calculations are based on the outer diameter of the members including any marine growth which may be present.

6. There are two methods of applying the buoyancy forces to a member. The choice is governed by the BRIG option. See also Section NO TAG.

7. Internal pressure due to internal fluid is only included for the BRIG option.

8. If elev is omitted in both the BUOY and FREE commands, internal pressure will be ignored. If elev is specified more than once for an element, the last specification will be assumed.

M.6.6 CURRENT Command

The CURR command specifies a predetermined current profile in a given direction.

Parameters

CURR : keyword

CURR iprofile v el-s v el-b elev dir



iprofile : profile type integer 1 linear profile

2 exponential profile

vel-s : current velocity at still water level. (Real)

vel-b : current velocity at sea bed. (Real)

elev : elevation relative to water axis at which current becomes constant. (Real)

dir : direction of current relative to water axis system. (Real)

Notes

1. The current may vary either linearly or exponentially between the seabed and a predefined elevation

above which the current is assumed to remain constant.

2. Direction and elevation are in the ‘water’ axis system. Direction is in degrees around the water Zw axis, zero degrees being in the positive Xw direction, and ninety degrees being in the positive Yw direction.

v el-s

v el-b

elev

v el-s

v el-b

elev

Z w Z w

Linear current variation Exponential current variation

q

Yw

Xw

Current Direction



3. Options exist to modify the current profile using either mass conservation or relative velocities. See Appendix M.7.

4. The CURR command remains operative until overridden by a subsequent TIDE, CURR or PCUR command. If it is required to return to having no current or tide loading then a dummy TIDE command should be provided with zero velocity.

M.6.7 DRAG Coefficients

The DRAG command defines the drag coefficients, Cd, for the members used in the calculation of wave and wind forces.

Parameters

DRAG : keyword

cdx : drag coefficient in element local x-direction. (Real)

cdy : drag coefficient in element local y-direction. (Real)

cdz : drag coefficient in element local z-direction. (Real)

TABL : keyword to indicate that a table is to be utilised for determining the hydrodynamic coefficient

tablename : name of table containing drag coefficients

ZONE : keyword to indicate drag coefficients apply only to elements or part of elements in the zone

zonename : name of zone







ELEM

PROP

ALL

elem

prop

groupGROU

TABL tablename ZONE zonename

DRAG cdx cdy cdz




Notes

1. The command is optional and if omitted the program defaults to the following values:

Axial, x Cd = 0.0 Transverse, y and z Cd = 0.7

2. Drag coefficients may be made dependent on Reynolds number or Keulegan-Carpenter number by use of the TABL keyword. See RENL and KC commands for details of how to set up the tables.

Examples

DRAG 0.0 0.7 0.75 ELEM 10 20 30

DRAG RENL TABLE1 ZONE GROWTH ALL

M.6.8 ELEVATION Command

The ELEV command defines:

(a) The Mean Water Level relative to the Water Axes Origin

(b) The Sea Bed Level relative to the Water Axes Origin

(c) The density of the sea water

(d) The density of the air

This command is mandatory in the first loadcase, but need not reappear thereafter.

Parameters

ELEV : keyword

selev : elevation of mean water level relative to water axes origin. (Real)

belev : elevation of sea bed relative to water axis. (Real)

water density : mass density of sea water (e.g. 1025Kg/m3). (Real)

air density : mass density of air (e.g. 1.23 kg/m3). (Optional). (Real)

ELEV selev belev water density ( air density )



Note

The density is multiplied by the acceleration due to gravity as input by the GRAV command, and so must be input in units of MASS per unit volume e.g. 1025 Kg/m3

Example

ELEV 100 -25 1025

M.6.9 END Command

An END command terminates the WAVE LOAD data block.

Parameters

END : keyword

M.6.10 EXECUTE Command

The EXEC command signifies the end of data for a given wave case. Since there can only be one single case in each ASAS-NL data, the use of EXEC to break up different wave cases is therefore not required and the command is only retained for compatibility with WAVE. If EXEC is specified, this must appear immediately before the END command.

END



Parameters

EXEC : keyword

M.6.11 FREE Flooding Command

The FREE command may be used to specify those members which are flooded with the external fluid up to the actual water surface thus inducing additional loading due to the weight of the contained fluid on the members concerned. The command is optional and no free flooding is assumed if omitted.

Parameters

FREE : keyword

elev : elevation used for computing internal pressure. (Real)

If elev Zb, the sea bed level, internal pressure is computed assuming fluid pressure to elevation

elev. If elev <Zb, internal pressure is computed to the elevation of the water surface vertically

above the point in question.







EXEC

ELEM

PROP

ALL

elem

prop

groupGROUFREE elev




Notes

1. Free flooding effects are calculated for members below the sea bed.

2. If elev is omitted in both the BUOY and Free commands internal pressure will be ignored. If elev is specified more than once for an element, the last specification will be assumed.

3. Internal pressure, if any, is only included for the BRIG option.

M.6.12 GRAVITY Command

The GRAV command defines the relationship of the jacket axes to the water axes by specifying the value and direction of the gravitational acceleration relative to the jacket axis system. This command is mandatory. It must appear only once.

Parameters

GRAV : keyword

gx : gravitational vector component in x direction (global jacket axis). (Real)

gy : gravitational vector component in y direction (global jacket axis). (Real)

gz : gravitational vector component in z direction (global jacket axis). (Real)

Notes

1. If the components of gravitational acceleration are given as (0,0,-g), the jacket and water axes are coincident, with the Z-axis directed vertically upwards.

GRAV gx gy gz



2. The GRAV command defines the direction of the gravitational vector (-Zwater) with respect to the jacket (global) axis system. The convention adopted for the X and Y axes of the water axes system is as follows:

Xwater always lies in the global XY plane with Ywater on the positive side of the global XY plane. In the special case where Ywater is also in the global XY plane Ywater lies in the global Y direction.

Jacket and water axes coincident

ZG YG

XG

XW

YW

ZW

General orientation of water axes

ZG

YG

XG

XW

YW

ZW



M.6.13 GRID Wave Command

This data is used as an alternative means for defining the wave kinematics (i.e. particle velocities and accelerations) instead of adopting one of the wave theories detailed in Section M.6.46 WAVE DATA. Typically this data is used when the structure is to be loaded with waves that are outside of the conventional wave theory applicability limits (see Figure M.1) and an alternative source of wave kinematics has been found. The wave is described by defining the surface profile together with velocities and accelerations at regular intervals or grid points throughout the wave. The location of the horizontal and vertical grid lines may be selected to coincide with oceanographic/measured data. The general form of the data shown below.



GRID Wave Header

SYMM

ASYM

GRID nloc nhgt wav elength

GPHS phase

GLOC location

surface

v alue

v alue

v alue

v alue

height

v alue

v alue

v alue

v alue

SURF

VELH

VELV

ACCH

ACCV

GHGT

VELH

VELV

ACCH

ACCV

SYMM

ASYM

GRID nloc nhgt wav elength



Parameters

GRID : keyword to indicate beginning of grid data

SYMM : keyword. The wave is considered to be symmetric in profile about the crest position. Horizontal velocities and vertical accelerations are assumed symmetric about the crest position. Vertical velocities and horizontal accelerations are antisymmetric about the crest. Only half the wave period needs to be defined (see Note 1 below). This is the default option.

ASYM : keyword. The wave is considered to be asymmetric in both profile and wave kinematics. The whole wave period must be defined.

nloc : number of horizontal grid locations to be defined (see Figure M.2). (Integer)

nhgt : number of vertical grid positions to be defined (see Figure M.2). (Integer)

wavelength : wavelength. This must be supplied in order to establish the phase relationship between the structural elements and the wave. (Real)

Figure M.2 Grid definitions

Example

A symmetric wave of 110 m wavelength is defined using 5 horizontal and 4 vertical grid points.

GRID SYMM 5 4 110.

Horizontal Grid Definition

HEIGHT(5)

HEIGHT(4)

HEIGHT(3)

HEIGHT(2)

HEIGHT(1)PHASE(1) PHASE(2) PHASE(3) PHASE(4) PHASE(5)

SURF(1)SURF(2)

SURF(3)

SURF(4)SURF(5)

nhgtverticalgridlocations

nloc horizontal grid locations



Parameters

GPHS : keyword to indicate that phase angles are to be used in defining the horizontal grid locations

phase : phase angle from crest position. (Real)

nloc values must be supplied to fully define the grid. See Note 2 for sign convention

GLOC : keyword to indicate that distances are to be used in defining the horizontal grid locations

location : distance from the crest position. (Real)

nloc values must be supplied to fully define the grid. See Note 2 for sign convention

Example

Horizontal locations of 9 grid lines are defined.

GPHS 0.0 -10.0 -20.0 -40.0 -60.0 -90.0

GPHS -120.0 -150.0 -180.0

or, assuming the wavelength is 180 m,

GLOC 0.0 5.0 10.0 20.0 30.0 45.0

GLOC 60.0 75.0 90.0

GPHS phase

GLOC location



SURFACE Profiles and Kinematics

Parameters

SURF : keyword to denote that surface elevations and kinematic definitions are to follow

surface : wave surface elevation relative to the water axes for each of the horizontal grid locations defined

on the GPHS or GLOC commands. nloc values in total must be supplied. (Real)

VELH : keyword to indicate horizontal particle velocities

VELV : keyword to indicate vertical particle velocities

ACCH : keyword to indicate horizontal particle accelerations

ACCV : keyword to indicate vertical particle accelerations

value : wave kinematics for the surface for each of the horizontal grid locations defined on the GPHS or

GLOC command. nloc values in total must be supplied. (Real)

Example

Surface profile and kinematics for 4 phase locations.

SURF 8.75 8.65 8.37 8.0

VELH 2.2 1.82 0.93 0.0

VELV 0.0 1.05 1.61 1.51

ACCH 0.0 2.2 3.37 3.29

ACCV -2.44 -1.83 -0.39 1.11

surface

v alue

v alue

v alue

v alue

SURF

VELH

VELV

ACCH

ACCV



GRID Kinematics

This block of data should be repeated nhgt times

Parameters

GHGT : keyword to denote that kinematic definitions for the specific elevation are to follow

height : grid elevation relative to the water axes. (Real)

VELH : keyword to indicate horizontal particle velocities

VELV : keyword to indicate vertical particle velocities

ACCH : keyword to indicate horizontal particle accelerations

ACCV : keyword to indicate vertical particle accelerations

value : wave kinematics for the given grid height for each of the horizontal grid locations defined on the

GPHS or GLOC command. (Real)

Values corresponding to grid positions above the water surface need not be defined. See Note 3.

Example

Velocities and accelerations for elevation 10.0 for 4 phase locations

GHGT 10.0

VELH 0.645 0.558 0.322 0.0

VELV 0.0 0.315 0.553 0.639

ACCH 0.0 0.674 1.17 1.35

ACCV -1.15 -0.974 -0.485 0.185

GHGT height

VELH v alue

VELV v alue

ACCH v alue

ACCV v alue



Notes

1. For symmetric waves, only half the wave period needs to be defined, the program will automatically generate wave kinematics for the symmetric part of the wave. The generated kinematics are shown in FigureM.3 below.

Figure M.3 Generated symmetric wave kinematics

2. In common with all phase definitions in WAVE, a positive phase angle indicates that the wave crest has passed the point of interest; conversely, this corresponds to a negative linear distance, as shown in Figure M.4 below.

Figure M.4 Sign convention of phase and distance definitions

3. Where grid points occur at or above the surface elevation, the kinematic values may be set to zero or, if at the end of the line, may be ignored. Thus only sufficient number of values to define the subsurface grid need be supplied.

VELH

VELV

ACCV

ACCH

ACCV

ACCH

VELV

VELH

PHASE = 0

DEFINEDGENERATED

PHASE = 0DISTANCE = 0

-180+L/2

+180-L/2



M.6.14 Marine GROWTH Command

The GROW command defines the thickness of marine growth. The command is optional and zero thickness is assumed if omitted. A number of such commands may be used to define varying growth thickness with depth. New drag and inertia coefficients may be defined to take account of the roughness of marine growth.

Parameters

GROW : keyword

thick : thickness of marine growth. (Real)

density : saturated density of marine growth. (Real)

ZONE : keyword to indicate growth values apply only to elements or parts of elements in the zone


upper : upper level of growth relative to water axes. (Real)

lower : lower level of growth relative to water axes. (Real)

cd : drag coefficient in element local y and z directions. If not defined the appropriate element drag coefficient is used. (Real)

cm : mass coefficient in element local y and z directions. If not defined the appropriate element mass coefficient is used. (Real)








upper lower

ELEM

PROP

ALL

elem

prop

groupGROUGROW thick density cd cmZONE zonename



Notes

1. The self weight of marine growth is automatically included in the total weight reported. If self weight of the growth is not required then the density should be set to zero.

2. If defined, the drag and inertia coefficients supplied on the GROW command override those defined on the DRAG and/or MASS commands for a given element irrespective of the order of the data.

M.6.15 HYDR Command

The HYDR command defines section dimensions and marine growth values for a part of an element. The command is optional and existing section dimensions and growth values are used if omitted. A number of such commands may be used to define specific section dimensions which will supersede existing dimensions. The same applies for marine growth.

Parameters

HYDR : keyword

DIAM : keyword to indicate that revised section dimensions are supplied

dy : Overall dimension in local-y direction (see Note 3), including marine growth (if present)

dz : Overall dimension in local-z direction (see Note 3), including marine growth (if present)

AREA : keyword to indicate that revised section areas are supplied

at : total area, including marine growth (if present). This is used in Morison’s equation

as : cross-sectional area of element (ie annulus area for a tube). This is used for self-weight

calculations

ai : cross-sectional area of internal void of tube. This is used for buoyancy calculations

SURF : keyword to indicate that a revised surface perimeter is supplied

perimeter : surface perimeter, including marine growth (if present). This is used for axial drag calculations

DENS : keyword to indicate that a revised element material density is supplied

NONE

ELEM

PROP

elem

prop

groupGROUHYDR

as aiatAREA

dzdyDIAM

dgagGROW

perimeterSURF

densityDENS

len1(FACT) len2

ECAP aout ain



density : element material density. This is used for self-weight calculations

GROW : keyword to indicate that revised marine growth data is supplied

ag : cross-sectional area of growth (ie area of annulus of growth on a tube)

dg : saturated density of marine growth. These are used to calculate the weight of the growth for the

section

NONE : keyword to indicate that there is no marine growth on this section

ECAP : keyword to indicate that revised end cap area are supplied

aout : outer enclosed area of end cap. This is used to calculate end cap face due to external pressure

ain : inner enclosed area of end cap. This is used to calculate end cap face due to internal pressure

FACT : keyword to indicate that the lengths following are proportions of the element length (ie a

maximum of 1.0)

len1 : distance along the element to the start of the revised data

len2 : distance along the element to the end of the revised data. If FACT has been specified, then len1

and len2 are the proportion of the element lengths


elem : list of user element numbers. (Integer). ALL may not be specified.


group : list of group numbers. (Integer). ALL may not be specified.


prop : list of geometric property numbers. (Integer). ALL may not be specified.

Notes

1. If a section is to be respecified because of a local change in dimension or area, then the following values MUST be specified. No growth - DIAM, AREA, SURF Growth - DIAM, AREA, SURF, GROW GROW NONE should be included if no growth is required on an element that is within a marine growth zone.

2. If the length information is omitted, the properties are applied along the complete length of the element.

3. The dimensions supplied are given in terms of the local axes of the element, as shown below.



dy

dz

Z Z

Y

Y



4. Beam elements that have sections assigned to them via their geometry definition will automatically adopt appropriate properties for the calculation of wave loading and added mass. The following tables provide information regarding the terms used in the load and mass computations.

where d is beam depth b is beam width tf is flange thickness tw is web thickness t is plate thickness tg is thickness of any attached marine growth

The above assumes that the top and bottom flanges for the BOX and FBI section types are the same. The program will correctly account for different bottom flange dimensions if specified. Any specified fillet radius is ignored in these calculations.

Section type Drag load Inertia load Self weight Buoyancy/ Free flooding

Hydrodynamic mass

End cap force

TUB Cdydyρw Cdzdzρw

Cmyatρw Cmzatρw

ρsas ρwat - ρiai ρw(Cmy - 1)at ρw(Cmz - 1)at

ρi ain-ρo aout BOX RHS WF

Cdydyρw Cdzdzρw

Cmyatρw Cmzatρw

ρsas ρwat ρw(Cmy - 1)at ρw(Cmz - 1)at

N/A CHAN ANGL TEE FBI PRI5

N/A N/A N/A N/A N/A N/A FAB5



5. Prismatic and fabricated sections that are required to be wave loaded must have explicit HYDR commands supplied.

Example

A tube with diameter 1.4 and thickness 0.07 has a marine growth applied of 0.2 and density 1.5 over a length of 1.5 starting 2.1 from the first end. The following commands would need to be specified to reflect this.

HYDR DIAM 1.8 1.8 2.1 3.6 ELEM 3

HYDR AREA 2.5446900 0.2924823 1.2468981 2.1 3.6 ELEM 3

HYDR SURF 5.6548668 2.1 3.6 ELEM 3

HYDR GROW 1.0053096 1.5 2.1 3.6 ELEM 3

where at = π(1.4 + 2 x 0.2)2/4 = 2.5446900 as = π(1.42 - (1.4 - 2 x 0.07)2)/4 = 0.2924823 ai = π(1.4 -2 x 0.07)2/4 = 1.2468981 perim = π(1.4 +2 x 0.2) = 5.6548668 ag = π((1.4 + 2x 0.2)2 - 1.42)/4 = 1.0053096

M.6.16 Keulegan-Carpenter Number Tables

The KC command defines tables of Keulegan-Carpenter numbers with corresponding values of drag and mass coefficients so that for each element the drag and mass coefficients can be calculated as a user-defined function of the Keulegan-Carpenter number. The table can, optionally, be made to be dependent on Reynolds number

allowing bilinear interpolation of drag and mass coefficients.

Parameters

KC : keyword

tablename : name of the Keulegan-Carpenter table (up to 32 alphanumeric characters)

RENL : keyword to indicate Reynolds number is to be supplied

r : Reynolds number. (Real)

DRAG : keyword to indicate drag value is supplied after Keulegan-Carpenter number

MASS : keyword to indicate mass value is supplied after Keulegan-Carpenter number

kc : Keulegan-Carpenter number. (Real)

KC tablename RENL r MASS

DRAG

DRAG kc cd

kc cm

kc cdMASS cm



cd : corresponding drag coefficient. (Real)

cm : corresponding mass coefficient. (Real)

Notes

1. For each element the Keulegan-Carpenter number KC and (optionally) Reynolds number Re are calculated as follows:

Re = Diameter x velocity / Kinematic viscosity KC = Wave period x velocity / Diameter

where the velocity is the maximum water particle velocity throughout a wave cycle normal to the member. The calculated value of KC defines a position in the array of KC commands and linear interpolation is used to obtain values for the drag and mass coefficients for the member. If the Reynolds number is also given, bilinear interpolation is utilised.

2. For values of KC outside the defined range, the related parameter is assumed constant and equal to the

extreme values defined, eg

3. The drag and/or mass coefficients must be in the order of the DRAG and MASS keywords.

4. The kinematic viscosity (VISC) must be specified, if Reynolds number dependency is required.

5. Note that this command is not applicable to the NewWave model.

Examples

KC KCTABLE1 DRAG MASS : 4.0 0.3 1.95 : 8.0 0.48 1.8 : 12.0 0.75 1.6 : 20.0 1.05 1.2

M.6.17 Wave KINEMATICS Factor Command

The KINE command specifies a user defined wave kinematics factor for use within the API codes of practice.

Cd

Kc

•

•

•



Parameters

KINE : keyword

factor : user defined wave kinematics factor. (Real)

Notes

1. If the KINE command is not used, factor = 2power1power+

+ where power is the wave spreading power

defined on the SPREAD command.

2. If neither KINE nor SPREAD command is used, a default factor of 1.0 is used.

3. If both the KINE and SPREAD commands are used, the value of the KINE command takes precedence.

4. This command will only be utilised when used in conjunction with the APIW option.

M.6.18 LFUN Data

The LFUN command enables scaling of the wave load by associating a load function with the wave loading. This command is optional and, if omitted, a unit load factor is assumed.

Parameters

LFUN : keyword

lfunno : load function number

Notes

1. For proportional loading (i.e. PROP), lfunno should be set to 1.

KINE factor

LFUN lfunno



M.6.19 MASS Inertia Coefficients

The MASS command defines the inertia coefficients, Cm, for the members used in the calculation of wave forces.

Parameters

MASS : keyword

cmx : inertia coefficient in element local x-direction. (Real)

cmy : inertia coefficient in element local y-direction. (Real)

cmz : inertia coefficient in element local z-direction. (Real)

TABL : keyword to indicate that a table is to be utilised for determining the hydrodynamic coefficient

tablename : name of table containing mass coefficients

ZONE : keyword to indicate mass coefficients apply only to elements or parts of elements in the zone









Notes

1. The command is optional and if omitted the program defaults to the following values:

Axial, x Cm = 0.0

Transverse, y and z Cm = 2.0

ELEM

PROP

ALL

elem

prop

groupGROU

TABL tablename ZONE zonename

MASS cmx cmy cmz



2. Inertia coefficients may be made dependent on Reynolds number, Keulegan-Carpenter number or A/D ratio by use of the TABL keyword. See RENL and KC commands for details of how to set up the tables.

Examples

MASS 0.0 2.0 2.2 ELEM 10 20 30

MASS RENL TABLE1 ZONE GROWTH ALL

M.6.20 MOVE Command

The MOVE command defines the origin of the Water Axes relative to the structure Global Axes. The command is optional and if omitted, the origins of the Water and the Global axes are assumed coincident.

Parameters

MOVE : keyword

x,y,z : coordinates of origin of water axis in the global coordinate system. (Real)

Example

MOVE 0.0 0.0 -∆z

MOVE x y z



M.6.21 NANG Command

This command defines the number of angle steps a wave is to be divided into for determining the maximum velocity experienced by a submerged element in a wave cycle. The maximum velocity is used for calculating the drag and mass coefficients for an element if Reynolds or Keulegan-Carpenter tables are used. See the notes in M.6.16 and M.6.35 on how the computed velocity is utilised.

Parameters

NANG : keyword

nangle : the number of equal phase angles a wave is to be divided into for evaluating the maximum velocity. The angle increment used is 360/nangle degrees

Example

NANG 20

Notes

1. The value for nangle must be greater than zero.

2. The default value for nangle is 8.

3. No more than one NANG command is allowed for each wave case.

Water axis relative to jacket axis

ZG YG

XG

∆�Z

ZW

YW

XW

NANG nangle



M.6.22 NOBM Command

The NOBM command is replaced by the NOLO command.

M.6.23 NOBO Command

The NOBO command specifies elements for which buoyancy loads are excluded. The command overrides any previous BUOY command associated with the specified elements. The buoyancy loading may be reactivated at any later stage by using another BUOY command.

Parameters

NOBO : command keyword








Note

Any number of BUOY and NOBO commands may be used to activate and deactivate loading for different elements. The commands are processed in user input order.

M.6.24 NOFR Command

The NOFR command specifies elements for which free flooding loads are excluded. The command overrides any previous FREE command associated with the specified elements. The free flooding loading may be reactivated at any later stage by using another FREE command.

ELEM

PROP

ALL

elem

prop

groupGROUNOBO



Parameters

NOFR : keyword








Note

Any number of FREE and NOFR commands may be used to activate and deactivate loading for different elements. The commands are processed in user input order.

M.6.25 NOLO Command

The NOLO command specifies elements for which all loads are excluded. The command overrides any previous load command associated with the specified elements. The loading may be reactivated at any later stage by using appropriate load commands.

ELEM

PROP

ALL

elem

prop

groupGROUNOFR

ELEM

PROP

ALL

elem

prop

groupGROUNOLO



Parameters

NOLO : keyword








Note

Any number of LOAD and NOLO commands may be used to activate and deactivate loading for different elements. The commands are processed in user input order.

M.6.26 NOSW Command

The NOSW command specifies elements for which structural self weight loads are to be ignored. The command overrides any previous SLWT command associated with the specified elements. The self weight loading may be reactivated at any later stage by using another SLWT command.

Parameters

NOSW : keyword




ELEM

PROP

ALL

elem

prop

groupGROUNOSW







Notes

1. Any number of SLWT and NOSW commands may be used to activate and deactivate loading for different elements. The commands are processed in user input order.

2. The weight of marine growth is automatically calculated if a GROW command is present. It is unaffected by SLWT/NOSW commands.

3. The weight of any internal fluid is automatically calculated if BUOY/FREE commands are present. It is unaffected by SLWT/NOSW commands.

M.6.27 NOWI Command

The NOWI command specifies tubular elements for which wind loads are excluded. The command overrides any previous WIND command for the specified elements. The wind loading may be reactivated at any later stage by using another WIND command.

Parameters

NOWI : keyword






ELEM

PROP

ALL

elem

prop

groupGROUNOWI





Note

The NOWI command is overridden by subsequent WIND definitions. It is important, therefore, to respecify the NOWI commands after each use of the WIND command.

M.6.28 NOWL Command

The NOWL command specifies tubular elements for which wave loads are excluded. The command overrides any previous WAVE command for the specified elements. The wave loading may be reactivated at any later stage by using another WAVE command.

Parameters

NOWL : keyword








Notes

1. The NOWL command is overridden by subsequent WAVE definitions. It is important, therefore, to respecify the NOWL commands after each use of the WAVE command.

ELEM

PROP

ALL

elem

prop

groupGROUNOWL



2. Use of NOWL ALL does not nullify the existing WAVE definition. The wave surface profile is still applied and this may affect other loading such as buoyancy. To return to the still water condition, a WAVE command with zero wave height must be specified.

M.6.29 OFFSET Command

The OFFS command defines offsets of member ends from the nodal positions. In this way the thicknesses of joints can be taken into account when calculating the loading on these members. The offset is taken as a shortening of the member along its axis.

Parameters

OFFS : keyword

off1 : offset at end one of element. (Real)

off2 : offset at end two of element. (Real)








Note

The offsets defined on this command are additive to any member offsets which may have been defined in the Geometric Properties data. See ASAS User Manual for details.

ELEM

PROP

ALL

elem

prop

groupGROUOFFS off1 off2



M.6.30 OUTPUT Control Command

The OUTP command controls the amount of printed output for each wave case.

Parameters

OUTP : keyword

iout : output control integer 0 No output

1 Total forces and moments and total jacket mass are reported

(default)

2 Total forces and masses on each member are reported

3 Water particle velocities, accelerations, drag and mass

coefficients and the individual forces on each member

are reported. Individual masses on each section of a member

are reported.

Notes

1. Output 3 produces a large quantity of output and should be used with caution.

M.6.31 PEXT Command

The PEXT command specifies those members where the external pressures are to be calculated from the given density and elevation. The command is optional and, if omitted, the external pressure (if applicable) will be

calculated from the sea water density and surface elevation including the effect of wave action.

Parameters

PEXT : keyword

density : mass density of external fluid (Real)

OUTP iout

PEXT density elev

ELEM

GROU

PROP

ALL

elem

group

prop



elev : elevation used for computing external pressure (Real)

If elev Zb the sea bed level, external pressure is computed assuming fluid pressure to elevation

elev. If <Zb, external pressure is computed to the elevation of the water surface vertically above

the point in question.


elem : list of user element numbers (Integer)


group : list of group numbers (Integer)


prop : list of geometric property numbers (Integer)


Notes

1. External pressure calculation is only carried out for the BRIG option

M.6.32 POINT Current Command

The PCUR command specifies a user defined current profile. Each PCUR (point current) command defines a single point on a current profile. The profile may vary in both magnitude and direction with depth.

Parameters

PCUR : keyword

velocity : current velocity. (Real)

direction : current direction relative to water axis system. (Real)

elevation : elevation of this point value relative to water axis. (Real)

PCUR v elocity direction elev ation



Notes

1. Direction and elevation are in the ‘water’ axis system. Direction is in degrees around the water Zw axis, zero degrees being in the positive Xw direction and ninety degrees being in the positive Yw direction.

2. PCUR commands are cumulative and a table is built-up as each command is read. To reinitialise the table, supply another type of current command (i.e. TIDE or CURR), which can have magnitude zero, or use the RESEt command.

elevation

Zw

q

Yw

Xw

Current Direction

SWL

current velocity



3. All locations above the uppermost level defined have a constant current magnitude and direction equal to the defined values. Similarly, the values below the lowest defined value are constant. Thus one PCUR command will define a constant current magnitude and direction at all water depths.

4. Options exist to modify the current profile using either mass conservation or relative velocities (see Appendix M.7).

M.6.33 PHASE Command

The PHAS command determines the position of the wave crest relative to the origin of the water axis system. The command is optional and an initial phase position of zero will be assumed if not specified.

Parameters

PHAS : keyword

npos : number of wave positions in this case. (Integer) (Always set to 1)

pos : position of wave crest relative to water axis (degrees). (Real)

Notes

1. A phase position of zero corresponds to the wave crest at the origin of the water axis system. A positive

wave position indicates that the wave crest has passed the water origin.

PHAS npos pos inc

...........

...........

Direction ofwave advance

-10°�

ZW

+30º



2. There is no phase increment in a static analysis (i.e. the phase position will remain unchanged even if a solution is attempted at more than one pseudo-time).



3. In a transient dynamics analysis, the phase increment at each solution step is given by

T2t= π

∆φ∆

∆φ phase increment ∆t time increment T wave period

4. The PHASE command is not available for irregular wave analysis since the wave kinematics at a given time are no longer sinusoidal.

M.6.34 PRINT Command

The PRIN command may be used to override the OUTP command for specific elements.

Parameters

PRIN : keyword

iout : output control integer 1 No elemental information is reported

2 Total forces and masses on each member are reported

3 Water particle velocities, accelerations, drag and mass

coefficients, and the individual forces on each member are

reported. Individual masses on each section of a member are

reported.

elem : user element number. (Integer)

Note

Option 3 produces a large quantity of output and should be used with caution.

M.6.35 Reynolds Number Tables

The RENL command defines tables of Reynolds numbers with corresponding values of drag and mass coefficients so that for each element the drag and mass coefficients can be calculated as a user-defined function of Reynolds number. The table can, optionally, be made to be dependent on the Keulegan-Carpenter number allowing bilinear interpolation of drag and mass coefficients.

PRIN iout elem



Parameters

RENL : keyword

tablename : name of the Reynolds table (up to 32 alphanumeric characters)

KC : keyword to indicate Keulegan-Carpenter number is to be supplied

kc : Keulegan-Carpenter number. (Real)

DRAG : keyword to indicate drag value is supplied after Reynolds number

MASS : keyword to indicate mass value is supplied after Reynolds number

r : Reynolds number. (Real)

cd : corresponding drag coefficient. (Real)

cm : corresponding mass coefficient. (Real)

Notes

1. For each element the Reynolds number Re and (optionally) Keulegan-Carpenter number KC are calculated as follows:

Re = Diameter x velocity / Kinematic viscosity KC = Wave period x velocity / Diameter

where the velocity is the maximum water particle velocity throughout a wave cycle normal to the member. The calculated value of Re defines a position in the array of RENL commands and linear interpolation is used to obtain values for the drag and mass coefficients for the member. If the Keulegan-Carpenter number is also given, bilinear interpolation is utilised.

2. For values of Re outside the defined range, the related parameter is assumed constant and equal to the extreme values defined, eg

RENL tablename KC kc MASS

DRAG

DRAG r cd

r cm

r cdMASS cm

Cd

Re

•

•

•



3. The drag and/or mass coefficients must be in the order of the DRAG and MASS keywords.

4. The kinematic viscosity (VISC) must be specified.


Examples

RENL REYNOLD1 KC 10 DRAG MASS 20000 1.6 1.0 : 30000 1.2 1.15 : 40000 1.0 1.3 : 80000 0.8 1.65 : 100000 0.65 1.70 : 200000 0.6 1.75

M.6.36 SLWT Command

The SLWT command may be used to include the structural weight of members. If the command is omitted then no structural weight will be calculated.

Parameters

SLWT : keyword

density : structural material density of member(s). (Real)








ELEM

PROP

ALL

elem

prop

groupGROUSLWT density



Notes

1. To prevent the calculation of element self weight use the NOSW command.

2. The calculation of the self-weight of any marine growth or internal fluid is not affected by this command. See BUOY, GROW, NOFR and NOBO commands.

M.6.37 SPECTRAL Command

This command is used to define the wave spectrum to be employed in a New Wave or irregular wave analysis.

Parameters

SPEC : keyword

JONS : keyword to select a JONSWAP wave spectrum

PMOS : keyword to select a Pierson Moskowitz wave spectrum

UDEF : keyword to indicate that a user defined spectrum is to be supplied

UWAV : keyword to indicate that user defined wavelet details are to be supplied

peak : peak period (Tp) for the spectrum. (Real)

gamma : enhancement factor for the spectrum. Defaults to 3.3 if not defined. (Real)

freq : frequency ordinate (Hz) for user defined spectrum

energy : corresponding energy density ordinate (length2/Hz) for user defined spectrum

height : height of wavelet. (Real)

period : period of wavelet. (Real)

phase : phase of wavelet. (Real)

wavelength:length of wavelet. If zero, the wavelength will be computed internally by the program. (Real)

UDEF freq

peakPMOS

SPEC peak

energy

JONS gamma

UWAV height period phase wav elength



Notes

1. Only one such command should be defined for a given New Wave / irregular wave case.

2. For user defined spectra sufficient pairs of ordinates must be provided to adequately define the sea state.

3. For UWAV spectrum, phase is unused in a New Wave analysis.

4. For UWAV spectrum, the number of wavelet data defined in this command determines the number of wavelets to be used to model the wave spectrum. This will override any WPAR WAVELET data specified.

Example

SPEC PMOS 10.0

SPEC UDEF

: 0.04 0.004 0.0477 0.458 0.0547 3.089

: 0.0654 7.650 0.0724 8.2405 0.0794 7.4185

: 0.0865 6.1053 0.0936 4.8084 0.1006 3.7133

: ....

M.6.38 Wave SPREADING Command

The SPRE command specifies a user defined wave spreading power for use with the API codes of practice. This command is used to enable the program to compute a wave kinematics factor.

Parameters

SPRE : keyword

power : user defined wave spreading power. (Real)

Notes

1. If the SPRE command is used, wave kinematics factor = 2)(power+1)(power+

2. If the SPRE command is not used (and KINE is not used) a default value of 1.0 is used for the wave kinematics factor.

3. If both the KINE and SPREAD commands are used, the value of the KINE command take precedence.

4. This command will only be utilised when used in conjunction with the APIW option.

SPRE power




M.6.39 STOP Command

A STOP command is needed to signify the end of the data.

Parameters

STOP : keyword

M.6.40 TIDE Command

The TIDE command specifies a predetermined current profile in the same direction as an associated wave.

Parameters

TIDE : keyword

iprofile : profile type integer 1 linear profile

2 exponential profile

vel-s : current velocity at still water level. (Real)

vel-b : current velocity at sea bed. (Real)

elev : elevation relative to water axis at which current becomes constant. (Real)

Notes

1. The tide current may vary either linearly or exponentially between the seabed and a predefined elevation above which the current is assumed to remain constant.

STOP

TIDE iprofile v el-s v el-b elev



v el-s

v el-b

elev

v el-s

v el-b

elev

Linear current variation Exponential current variation

ZW ZW

SWL



2. Options exist to modify the current profile using either mass conservation or relative velocities (see Appendix M.7).

3. The TIDE command remains operative until overridden by a subsequent TIDE, CURR or PCUR command. If it is required to return to having no current or tide loading then a dummy TIDE command should be provided with zero velocity.

M.6.41 TOLERANCE Command

The TOLS command defines the tolerances to be used to decide between linear and quadratic distributed loads and for the subdivision of elements. The command is optional and, if omitted, a default value of 0.1 is used to decide between linear and quadratic and no sub-division will occur.

The water particle force is calculated at the centre point of the element or subdivision and compared with a value interpolated linearly between the end values. If this lies within the given tolerance then linear distributed loads are used and no subdivision occurs. If the calculated force lies outside the given tolerance, quadratic distributed loads are used and the second tolerance is checked to decide whether or not to subdivide the element. If the value lies outside the second tolerance then both halves of the element have separate quadratic distributed loads.

Parameters

TOLS : keyword

tload : tolerance for linear/quadratic distributed loads. (Real)

tsub : tolerance for element subdivision. (Real)

Note

If tsub is omitted then no subdivision occurs.

M.6.42 UNITS Command

If global units have been defined using the UNITS command in the Preliminary data (Section 5.1.42) the wave input data units may be locally overridden by the inclusion of an UNITS command.

TOLS tload tsub



Parameters

UNITS : keyword


Notes

1. Force, length, and angular units may be specified. Only those terms which are required to be modified need to be specified, undefined terms will default to those currently active.

2. The default input angular unit for waveload data is degrees.

3. A list of valid unit names can be found in Section 5.1.42.1.

4. The mass unit is derived from the force and length unit currently defined. In order to determine the consistent mass unit the force and length terms must both be either metric or imperial. This requirement is only necessary where mass or density data is being specified, in other cases inconsistencies are permitted.

M.6.43 VAXS Command

This command defines the orientations of the hydrodynamic axes with respect to the water axes. By default, the hydrodynamic axes are assumed to be coincident with the water axes.

Parameters

VAXS : keyword

x’x : direction cosine of the hydrodynamic x’ axis w.r.t. the water x axis. (Real)

x’y : direction cosine of the hydrodynamic x’ axis w.r.t. the water y axis. (Real)

x’z : direction cosine of the hydrodynamic x’ axis w.r.t. the water z axis. (Real)

y’x : direction cosine of the hydrodynamic y’ axis w.r.t. the water x axis. (Real)

y’y : direction cosine of the hydrodynamic y’ axis w.r.t. the water y axis. (Real)

UNITS unitnm

VAXS x’x x’y x’z y’x y’y y’z



y’z : direction cosine of the hydrodynamic y’ axis w.r.t. the water z axis. (Real)

Notes

1. Since both the AQWA hydrodynamic and ASAS water z axis are vertically upwards, the direction cosines should define a transformation in the x-y plane, i.e. x’z=y’z=0.0.

2. The hydrodynamic data (e.g. RAO) are given in the hydrodynamic axis system.

M.6.44 VISCOSITY Command

The VISC command defines the kinematic viscosity for the sea water for Reynolds number calculations.

Parameters

VISC : keyword

viscosity : kinematic viscosity

Note

This command must be present if Reynolds numbers (RENL commands) are used in the definition of drag and mass coefficients.

Example

VISC 1.3E-06

M.6.45 VPOS Command

This command defines the reference positions (typically the CoG) for the hydrodynamic data (e.g. RAO and phase). If not specified, the reference points are assumed to be at the origin of the water axes.

VPOS xg yg zg xpoff ypoff zpoff

Parameters

VPOS : keyword

xg : x reference position for RAO in water axis system. (Real)

VISC viscosity



yg : y reference position for RAO in water axis system. (Real)

zg : z reference position for RAO in water axis system. (Real)

xpoff : x offset of phase origin from the RAO reference origin in water axis system. (Real)

ypoff : y offset of phase origin from the RAO reference origin in water axis system. (Real)

zpoff : z offset of phase origin from the RAO reference origin in water axis system. (Real)

Note

The RAO and phase origins are assumed to be identical if the hydrodynamic information is provided by AQWA. In this case, the phase origin offset data are always ignored

M.6.46 WAVE Command

The WAVE command defines the wave theory, and the Height, Period and Direction of the wave. This command is optional, but if it appears must come after the ELEV command.

Parameters

WAVE : keyword

theory : wave theory keyword

AIRY Linear wave theory (Airy)

CNOIDAL Solitary wave theory (Cnoidal 1st)

STOKE5 Stokes 5th order theory

GRID Grid wave

STREAMn Stream function theory of order n (3 ≤ n ≤ 9)

height : wave height. (Real)

period : wave period in seconds. (Real)

direction : wave direction. (Real)

NEWW : keyword to denote the New Wave wave model is to be used

crest : maximum crest elevation measured from the mean water level. (Real)

WAVE theory height period direction

IRRE sigheight direction

directioncrestNEWW



IRRE : keyword to denote an irregular wave spectrum is to be used.

sigheight : significant wave height of the spectrum. (Real)

Notes

1. Direction and elevation are in the ‘water’ axis system. Direction is in degrees around the water Zw axes, zero degrees being in the positive Xw direction and ninety degrees being in the positive Yw direction.

2. For backward compatibility, the theory may be given as an integer with the following correspondence:

1 AIRY 2 CNOIDAL 5 STOKES 10 GRID WAVE -n Stream function theory of order n

3. New Wave is a dispersive wave, i.e. it is not cyclic as with the other deterministic waves. The crest height given is the maximum that can occur when the linear wavelets which constitute the wave are all in place at their respective peaks.

4. Irregular wave, by definition, is a dispersive wave, i.e. it is not cyclic as with the other deterministic waves.

5. For a user defined wave spectrum (i.e. UDEF specified in the SPECTRAL command), the significant wave height is computed from the area under the defined spectrum. In this case, sigheight specified here is used for the stretching depth calculation only.

M.6.47 WIND Command

The WIND command enables wind loading to be input on members above the water surface. This command is optional, but if omitted no wind loads are applied.

Wave Direction

q

Yw

Xw

WIND v elocity direction density



Parameters

WIND : keyword

velocity : wind velocity. (Real)

direction : wind direction. (Real)

density : mass density of air. (Real)

Notes

1. Direction is in the ‘water’ axis system. Direction is in degrees around the water Zw axes, zero degrees being in the positive Xw direction and ninety degrees being in the positive Yw direction.

2. The wind velocity is assumed constant for all elevations. Should a variation with elevation be required this can be modelled by modifying the drag coefficients of the appropriate elements.

M.6.48 WPAR Command

This command permits user control over the default parameters adopted for the NewWave and/or irregular wave computations. Unless guided otherwise, it is suggested that the default values embodied within WAVE are adopted.

q

Yw

Xw

Wind Direction

SPREAD

EVOLVING

alpha

deltaDELTA

WPAR

OFFSET offset

thetaSHIFT

STRETCH dsa

WAVELET

SEED

nwave

iseed



Parameters

WPAR : keyword

STRETCH : keyword to indicate that the delta stretching depth parameter is to be defined. If this parameter is not defined a default value of 0.5 is used (New Wave and irregular wave)

dsa : stretching depth factor. (Real). Stretching begins at a depth of dsa.Hs below the mean water level (MWL) up to the water surface, where Hs is the maximum crest elevation or significant wave height measured from MWL and is specified in the WAVE command. No stretching occurs below this depth, or if the wave surface is below MWL

DELTA : keyword to indicate that the delta stretching parameter is to be defined. If this parameter is not defined a default value of 0.3 is adopted (New Wave and irregular wave)

delta : delta parameter. (Real). A value of 0.0 corresponds to Wheeler stretching under wave crests, 1.0 corresponds to linear extrapolation of kinematics at mean water level to crest (0.0 ≤ delta ≤ 1.0)

SPREAD : keyword to indicate that the wave spreading constant is to be defined. If this parameter is not defined no wave spreading will be considered (alpha = 0.0). See Note 2 below. (New Wave only)

alpha : wave spreading constant in degrees (0.0 ≤ alpha ≤ 40.0). (Real)

SHIFT : keyword to indicate that a common phase shift is to be applied to all the component wavelets. If this parameter is not defined then no phase shift will be applied, and all the wave frequency components will come into phase at x = t = 0.0 (New Wave only)

theta : phase shift to be applied in degrees. (Real)

OFFSET : keyword to denote an offset is to be applied to an evolving wave to define where the wave crests come into phase along the direction of wave propagation. If this parameter is not defined for an evolving wave then no offset will be applied (New Wave only)

offset : offset distance from the origin in the direction of the wave. (Real)

EVOLVING : keyword to indicate that an evolving wave is required. If this keyword is not specified then a non-evolving wave is generate (New Wave only)

WAVELET : keyword to denote the number of regular wavelets to be used to model the wave spectrum. If this parameter is not defined, the default value is 50 (New Wave and irregular wave)

nwave : number of regular wavelets used to model the wave spectrum (1 ≤ nwave ≤ 1000) (Integer)

SEED : keyword to denote the random seed is to be defined. If this parameter is not defined, the default seed is 1

iseed : seed to start the generation of random phases (Integer)

Notes

1. Before utilising any of the options described above for shell New Wave, the user is directed to Reference NO TAG



2. The SPREAD constant alpha is used to modify the horizontal wave kinematics for nearly uni-directional seas. It must not be confused with the SPREAD command used for API analyses which utilises a quite different parameter and methodology to determine the spreading characteristics.

3. The SPREAD command must not be used in conjunction with the NewWave model.

Example

WPAR SPREAD 10.0

WPAR EVOLVING

WPAR WAVELET 100

M.6.49 XMAS Data

This facility enables distributed masses such as that due to the effects of internal fluids where buoyancy loading is being ignored. Extra mass is input per unit length of each selected element.

Parameters

XMAS : keyword

mass : extra mass per unit length. (Real)








ELEM

PROP

ALL

elem

prop

groupGROUXMAS mass



Notes

1. Extra mass may be specified per element using the AMAS command.

2. Masses are not cumulative. Subsequent XMAS definitions for a particular element will overwrite previous values.

3. AMAS may be specified in addition to XMAS for a given element.

M.6.50 ZONE Data

The ZONE command defines the limits of a specified zone in any or all of the X, Y and Z directions.

Parameters

ZONE : keyword

zonename : name of zone (up to 32 alphanumeric characters)

limname : keyword which may be one of the following: XMIN, XMAX, YMIN, YMAX, ZMIN, ZMAX

limit : coordinate value associated with the corresponding limname. Values must be specified in the water axis system. (Real)

Notes

1. Undefined values are assumed to be at +/- infinity.

2. The zonenames can be used with the DRAG, MASS and GROW commands.

Examples

ZONE ZONE1 ZMIN -2.0 ZMAX 27.5

ZONE ZONE2 ZMIN 1.5 ZMAX 31.7 YMAX 147.5 XMIN -25.5

ZONE zonename limname limit



M.7 Valid Options Controlling Wave Load Calculation

In addition to the options listed below, which affect the WAVE or MASS run, options which are valid for ASAS will also be accepted but no action will be taken. For further details see the ASAS User Manual.

Option Name

Application

HYDR Requests detailed elemental hydrodynamic information for each wave case. This is useful for ensuring that complex data assignments have been correctly applied.

APIW/AP20 Selects analysis to the requirements of API RP2A.

MCON For current loads (CURR, TIDE, PCUR) vary the current profile to maintain mass conservation. The input current profile must relate to the still water. The velocities are scaled with depth to give a constant transfer of mass, for the instantaneous surface height, whilst retaining the overall shape of the profile. This is not recommended for use with API analyses.

RELC For current loads (CURR, TIDE, PCUR) vary the current profile such that the velocities are not at absolute depths, but relative depths. This does not give mass conservation. The current velocities at x% of the water depth are the same for still water as for water with waves.

APIC

VEXT For current loads (CURR, TIDE, PCUR) the current profile is not modified in the presence of a wave, simple vertical extrapolation is used above still water level.

This is the default option for all non-APIW analyses, and is provided to override the standard non-linear stretching when APIW is active.

For current loads (CURR, TIDE, PCUR) vary the current profile using non-linear stretching as recommended in the API RP2A Code of Practice. The relationship is given by

where z is the elevation of the point of interest z’ is the effective elevation corresponding to z d is the still water depth λn is the wave length η is the wave surface elevation above the point of interest z, z’, η are measured from the mean still water level

)d/(2sinh /d) + z((2sinh + z = zn

n

λπλπη

′′

This is the default option when APIW is selected.



BRIG The default method of calculating buoyancy loads is to determine the volume of fluid displaced by a member and to apply the equivalent force as a distributed load in an upward direction ( z - water ). An alternative approach is available using the BRIG option. With this more rigorous approach the hydrostatic forces are calculated at the member ends and are applied as nodal forces in the direction of the member. Thus all components of hydrostatic force are included.

CONV API RP2A states that the convective acceleration components of the wave kinematics should be ignored. If APIW option is selected the convective acceleration terms are removed by default. The CONV option allows these terms to be included when APIW is operative. For all non-APIW analyses this is the default.

RVOF The wave drag forces in a transient analysis are calculated using the relative velocity formulation of Morison’s equation by default. This option switches off the relative velocity effect, thus ignoring the structural velocities in the load calculations

Appendix N ASAS (Non-Linear) User Manual

Page N-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - N Heat Analysis

N.1 Introduction

Heat analysis is used to determine the temperature distribution on a structure. ASAS(NL) is capable of modelling all three major modes of heat transfer: conduction, convection and radiation. ASAS(NL) can perform both steady state and transient heat analyses.

N.2 Heat Equations

The finite element transient thermal equations can be written in the form:

where C is the heat capacity matrix, H is the conductivity matrix, F is the applied heat flux vector and T is the nodal temperature vector. Both C and H can be functions of temperature and the equations will become non-linear in such circumstances.

Discretising the governing equations in time, the nodal temperatures can be solved incrementally in time by the direct time integration method as follows:

where the subscripts n and (n+1) denote the step number, ∆t is the time step and Yh is the transient thermal

time integration parameter.

The time integration parameter Υh controls the accuracy and stability of the solution. For linear problems,

the solution is unconditionally stable if 1/2 ≤γh ≤ 1. The scheme with γh = 1/2 is called the Crank-Nicholson

scheme or the trapezoidal rule. It is second order accurate but may suffer from wild oscillations. The

choice γh = 1 is called the backward Euler scheme. It provides the desirable numerical damping to damp

out the unwanted oscillations but is only first order accuate. The backward Euler is the only scheme that is

unconditionally stable in non-linear problems. In ASAS(NL), the default setting for γh is 1.0, i.e. the

backward Euler scheme. Other setting may be specified using parameter HGAMMA in the TEMP

command. The HGAMMA value specified must be between 0.5 or 1.0 or else a warning will be flagged and

the value of HGAMMA will be reset to the nearest value in the valid range.

For steady state problems, the governing equations simplify to the form:

HT = F

F=+HTdtdTC

F=HT+dt

dTC 1+n1+n1+n

]dt

dT+dt

dT)-t[(1+T=T 1+nh

nhn1+n γγ∆



This form is identical to that for a static stress analysis and thus both can be solved using the same non-linear solution procedure.

N.3 Convection

The heat flow per unit area for a general convection law is given by:

q = h (T2 - T1)r

where h is the film coefficient, r is the power index of the heat tranfer law, T1 and T2 are temperatures on surfaces 1 and 2.

This heat transfer law is implemented as material CVEC in ASAS(NL) (see Sec 5.2.4.1.10). At present, CVEC material can only be used with FAT2 element.

N.4 Radiation

The heat flow per unit area for radiation is given by:

q=σε(Τ24-Τ14)

where σ is the Stefan-Boltzmann constant, ε is the effective surface emissivity, Τ1 and Τ2 are temperatures on surfaces 1 and 2. Note that Τ1 and Τ2 are values relative to absolute zero temperature.

In general, the effective surface emissivity is equal to the product of surface emissivity on both surfaces, i.e. ε = ε1.ε2. If the two surfaces are directly opposed and close to each other, the effective emissivity is given by:

This heat transfer law is implemented as material RADI in ASAS(NL) (see Sec 5.2.4.1.11). At present, RADI material can only be used with FAT2 element.

N.5 Controlling a Heat Analysis

The following run control information is relevant for a heat analysis:

1. A steady state job is invoked by setting job type to HEAT in the JOB command. The job type should be set to HTRA for a transient heat job.

2. Only field element types are valid for heat analysis but the program will also accept stress elements defined in the element topology deck and automatically convert them into corresponding field

εεεεεεε

21-2+1

21=



elements (e.g. BRK8 beomces BRT8). This conversion is carried out as soon as all the element topology data are read in and therefore all the material and geometric properties data supplied must refer to the field element type.

3. Three different types of heat input (c.f. loading in stress analysis) may be specified in a heat analysis. These are nodal flux, prescribed field variable and flux density.

4. In transient thermal analysis, the initial temperature distribution on the structure is defined in the INIT data block. All nodes without initial condition specified (including those with prescribed temperatures) are assumed to have an initial temperature equal to the reference temperature TREFLD. If any non-zero initial condition (heat flux or temperature) is specified, a solution should be performed at the initial time in order to provide a consistent set of starting conditions for the time integration process.

5. The parameter TREFLD specifies the temperature assumed initially at all nodes on the model for evaluating the material properties and hence the conductivity matrix. If not given, TREFLD is assumed to be zero.

6. The parameter TAZERO specifies the absolute zero temperature. By default, TREFLD is assumed to be equal to -273.15, which is consistent with temperature measures specified in Centigrade. If other temperature units are used in an analysis, the absolute zero temperature in the appropriate units must be defined using the PARA TAZERO command in order to incorporate the radiation effect correctly.

7. Option LOWE reduces any higher order elements defined in the data to their corresponding low order element types (e.g. BT20 becomes BRT8). In this case, however, any reference to element mid-side nodes in the boundary conditions or load data is also invalid.

8. Option SURF asks the program to use the surface temperatures on the structure to determine temperature dependent material properties. If not specified, the average element temperature will be assumed instead. This option only has effect on FAT2 elements with FLNS option or CVEC/RADI material.

9. Units command will only have effect on input variables with temperatue or length units. All heat associated properties (e.g. conductivity) do not have units conversion facility implemented and therefore they must be supplied in consistent units.

N.6 Saving Heat Analysis Results

Like all other analysis types, the results from a thermal analysis can be saved using the RESU command. The table below shows the types of results saved together with the keywords required.

Result name Keyword on RESU Result type on database Temperature DISP FIELD VARIABLE Temperature rate VELO VELOCITY



Heat flux STRS FLUX Heat field STRN FIELD Reactive heat flow REAC REACTION

N.7 Interfacing with Stress Analysis

A thermal analysis is very often followed by a stress analysis that studies the effect of thermally induced stresses on the structure. A facility is available in the program to allow import of temperature distribution obtained in a heat analysis into the subsequent stress analysis.

In the stress analysis, the temperature results are read in from the results database via a GRES command within the nodal temperature (i.e. TEMPERAT) data block (see Sec 5.4.7.1). In order to use this feature, it is essential to have the temperature results saved using RESU in the thermal analysis.

It is also a requirement that the thermal and stress runs must come from the same project. This means that the stress job must be an old job, i.e. JOB OLD, with the same project name as defined in the thermal run.

As the results database file is standard across the ASAS suite, the stress job can be performed using either ASAS or ASAS(NL).

Appendix O ASAS (Non-Linear) User Manual

O-1 Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Appendix - O Coupled Wind and Wave Load Analysis of Offshore Wind Turbine

O.1 Introduction

This Appendix describes the facilities available within ASAS(NL) that enable it to perform integrated wind and wave load analyses for offshore wind turbines with a specialised wind loading software package called Flex 5. The purpose of using ASAS(NL) is to provide a realistic foundation model that can accurately model the foundation structural behaviour under the influence of wave loading. Note that foundation here refers to the whole sub-structure that is under the influence of wave loading, i.e. from the sea surface down.

The Appendix is presented as an addendum to the main ASAS-NL User Manual, and reference should be made to the main sections of that manual where appropriate.

The following sections are included:

The Analysis .................................................................................................................. O.2 Data for FLXG job ......................................................................................................... O.3

JOB command ................................................................................................................ O.3.1

Generalized Mode Definition ......................................................................................... O.3.2

Output from FLXG job .................................................................................................. O.4

Generalized Matrix Files ................................................................................................ O.4.1

Generalized External Force File ..................................................................................... O.4.2

O.2 The Analysis

The integrated wind and wave load analysis is carried out with the following series of runs: 1. An initial ASAS(NL) static analysis of the foundation structure is carried out to determine the

deflected shapes that define the transformation between nodal freedoms of the foundation model

and the generalized freedoms required by Flex 5 In this run, unit deflection and rotation load cases

(a total 6 cases) are applied at the foundation top node using normal ASAS prescribed

displacement loading data. Displacements from these load cases form the transformation matrix

and therefore these must be saved to the database using the RESU DISP command to ensure that

they can be assessed in the subsequent runs

2. A second ASAS(NL) analysis is run to produce the generalized mass, damping and stiffness

matrices of the foundation structure together with a time series of the generalized foundation

external loading. Wave and other external loadings on the foundation are applied as normal

loading data in this run. The generalized matrices are written to 3 separate files (one each for

mass, damping and stiffness) and the generalized load time series is written to another file. The

job type of this analysis is called FLXG to indicate its special nature.



3. A Flex 5 solution is then carried out with the foundation effects included through utilising the

generalized matrices and loading vector derived in step 2. The forces or displacements at the

foundation top node at each solution time step are written to a file.

4. A final ASAS(NL) analysis is performed to recover the member forces in the foundation structure

by applying the foundation top node force or displacement time series obtained from Flex 5

together with the foundation external loading as specified in step 2. The analysis can be carried

out statically or dynamically.

• The transformation matrix required in the FLXG job is formed from the displacements of unit

deflection load cases in the initial static analysis. In order to read back these results, both runs

must come from the same project. This means that the FLXG job must be an old job, i.e. job

status is either OLD or REPL, with the same project name as specified the initial static run.

• The generalized matrices (stiffness etc) are computed based on the initial undeformed

geometry and assuming small displacement, linear behaviour. It is thus implicitly assumed that

the foundation is linear with small deformations throughout the entire solution.

• Likewise, when computing the generalized foundation external load time history in step 2, it is

assumed that the structural displacement and velocity are zero since such information is not

available when the loading is generated.

• The hydrodynamic mass in ASAS(NL) is formed assuming that the water elevation is at the

still water level.

• If the foundation internal forces are recovered statically in step 4, the dynamic forces (e.g.

inertial force) in the foundation will be ignored. The dynamic effects can be accounted for by

running this step as a transient job. However, it should be noted that the following effects may

affect the accuracy of the solution: The following points should be noted for this analysis

approach:

1. The generalized mass used in Flex 5 is only an approximation to the true mass matrix

(static reduction is exact but not dynamic).

2. Different time integration schemes are adopted by Flex 5 and ASAS(NL). Hence,

while the displacement time histories are identical in both runs (for the prescribed

displacement case), it may not be the case for the velocity and acceleration time

histories.

• There should be little difference between applying forces or displacements to recover the

foundation forces. The two methods should yield identical results in a linear static analysis.



O.3 Data for FLXG job

The following commands and data sets are supplement to those required for undertaking a conventional structural analysis. Reference should be made to Section 5 of this manual for the main data definitions.

O.3.1 JOB Command Defines analysis type and for restart jobs the old archive file name and required checkpoint number on the old archive file. Compulsory.

Parameters

JOB : compulsory keyword

OLD : optional keyword indicating that this run will add to an existing project database

REPL : optional keyword indicating that this run will replace a previous run of the same structure

on the project database

FLXG : keyword indicating an analysis to generate data for Flex 5

oldarch : old archive name up to 8 characters. This is only required for restarts.

(nchkpt) : number of the required restart checkpoint on the old archive file (brackets must appear). If

omitted the highest checkpoint on the old archive file is taken. This is only required for

restarts. (Integer)

Notes

1. The default project status for FLXG job is old.

O.3.2 Generalized Mode Definition This data defines the generalized modes. The data block must be the last in the data file before the STOP command.

Parameters

oldarchJOB

(OLD)(REPL)

(nchkpt)

TVEC

sname

END

(isub)lc



TVEC : compulsory header keyword to denote the start of the generalized mode definition data

sname : 4 character structure name that contains deflected shape of the generalized mode.

lc : user load case number where displacements are required. (Integer)

isub : load sub-case number. Default is 0. (Integer)

END : compulsory keyword to denote the end of the generalized mode definition data

Notes

1. Since the foundation has six generalized degrees of freedom in Flex 5, there should always be six modes defined in the TVEC data.

2. The defined generalized mode must have been saved in a previous analysis under the same project.

3. The model used for generating the generalized modes must have identical structural properties with the model created in the present analysis.

4. The order in which the load cases are specified defines their order in the transformation matrix, i.e. the first load case defines the first generalized mode etc.



Example

An example of utilising the displacements from user load cases 1 to 6 of structure S001 as the generalized modes.

TVEC S001 1 0 S001 2 0 S001 3 0 S001 4 0 S001 5 0 S001 6 0 END

O.4 Output from FLXG job

Four formatted ASCII files will be generated from each FLXG job. These are:

4. xxxx.gnm generalized mass matrix file 5. xxxx.gnc generalized damping matrix file 6. xxxx.gnk generalized stiffness matrix file 7. xxxx.gnf generalized external force time series file

where xxxx is the 4 character structure name of the FLXG job that produces the files.

O.4.1 Generalized Matrix Files In the very first load step, the generalised mass, damping and stiffness matrices are calculated and written to 3 separate files. The files are written with the following format:

ngenfr (1x, I6) (val(i,1), i=1,ngenfr) (6(1x,E12.5)) (val(i,2), i=2,ngenfr) (6(1x,E12.5)) . . (val(i,ngenfr), i=1,ngenfr) (6(1x,E12.5))

where ngenfr is the number of generalized freedoms, which is always 6 at present and val is the generalized matrix.

The row and column order in the generalized matrix corresponds to the order in which the generalized modes are defined in the TVEC data.

Note that there is currently a restriction that the generalized damping matrix ignores contributions from damping specified for the spring elements SPR1/2.

O.4.2 Generalized External Force File A time series of the generalized foundation external loading vector is written to a force file. At each solution time, the time (t) and the associated generalized load vector (f) will be output to this file. The force file has the following format:

ngenfr (1x, I6) t1 (1x,E12.5) (f1(i), i=1,ngenfr) (6(1x,E12.5)) t2 (1x,E112.5) (f2(i), i=1,ngenfr) (6(1x,E12.5)) .



.

.

. tn (1x,E12.5) (fn(i), i=1,ngenfr) (6(1x,E12.5))

As before, the load values are ordered in the same way as the columns of the transformation matrix are arranged.

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