Download - CHAPTER 7 - ELEMENT LIBRARY
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Introduction to Lagrange
Chapter 7 - Element Library MSC.Dytran Seminar Notes
CHAPTER 7 - ELEMENT LIBRARYCHAPTER 7 - ELEMENT LIBRARY
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Introduction to Lagrange
Chapter 7 - Element Library MSC.Dytran Seminar Notes
APPLICABILITY AND ELEMENTS
ELEMENT DEFINITIONS
COORDINATE SYSTEMS
SOLID ELEMENTS
SHELL ELEMENTS
BEAM/ROD ELEMENTS
SPRINGS AND DAMPERS
DAMPERS
LUMPED MASSES
CONTENTS
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Introduction to Lagrange
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Used to model structures
Elements available:
SolidsQuadrilateral ShellsTriangular ShellsTriangular MembranesBeamsRodsSprings and DampersLumped MassesRigids
APPLICABILITY AND ELEMENTS
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ELEMENT DEFINITIONS
Entities defining an element are:
• Grid point locations
The coordinates of a grid point are defined using a GRID card
• Connectivity
The shape of an element is described by a Cxx card
• Property
A Pxx card specifies the mathematical element formulation
• Material
A DMATxx, DYMATxx or a MATxx card specifies the material type and parameters
Identification Numbers (IDs):
Each card is referred to by its ID, which must be unique in the corresponding entity.The cards can be referred to as often as you like.
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DMATEP, 15, 7850., 210E9, .3
PSHELL, 5, 15, .1
CTRIA3, 55, 5, 1, 2, 10
GRID, 1, , 0., 1., 0.
GRID, 2, , 0., 2., 0.
GRID, 10, , 1., 1.,` 1.
Hierarchy of References by IDs
Relating cards by referring to their IDs can be visualized by a tree:
Example: Triangular Shell Element Definition
Connectivity
Grids Property
Material
Failure ModelYield Model Shear Model ...
ELEMENT DEFINITIONS (continued)
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Basic coordinate system
This is the default reference, rectangular coordinate system (coordinate system 0). All other coordinate systems and geometry must ultimately be defined relative to this system.
Element geometry definition in basic coordinate system
Calculations performed in (local) element system
Output by default in basic coordinate system
Local coordinate system
Grid points can be defined in a user defined local coordinate system
Some constraints and loading can be defined in a user defined local coordinate system
Types of coordinate system
Rectangular (x, y, z)Cylindrical (R, , Z)Spherical (R, , )
COORDINATE SYSTEMS
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Used to model volumetric parts of structures
Consist of 8 grid points (hexagonal element)
PENTA and TETRA hexagonal elements are degenerated forms of the 8 node HEXA element
Grid points have only 3 DOFs
Standard solids use global coordinate system for numerical calculations
The Lagrangian solids with orthotropic material use a local element coordinate system
SOLID ELEMENTS
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PSOLID - Single point quadrature
The element uses one point Gauss integration to determine the stresses and is very cheap to use.
PSOLID, 10, 20
Avoid PENTA and TETRA
The PENTA and TETRA elements are degenerate forms of the HEXA element and give very poor performance. TETRA is particularly bad.
SOLID ELEMENTS
CPENTA CTETRA
CHEXA
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Use the entities
GRIDCHEXAPSOLID
Example of the definition of the Lagrangian solid 71 with property id 100 and material 200
GRID, 1, 0., 0., 0.GRID, 2, 1., 0., 0.GRID 3 to 8CHEXA, 71, 100, 1, 2, 3, 4, 5, 6, ++, 7, 8PSOLID, 100, 200
SOLID GEOMETRY DEFINITION
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Used to model thin structures, where the thickness is small compared to the length
Shell grid points have 6 DOFs
Quadrilateral shell element coordinate system
Belytschko-Tsay and Hughes-Liu
Key-Hoff
G1 G2
G3G4
Xelem
YelemZelem
G1 G2
G3G4
Xelem
YelemZelem
SHELL ELEMENTS
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SHELL ELEMENTS (continued)
CQUAD4
Belytschko-Tsay
• Constant strain element based on the C0-Mindlinshell formulation with one point Gauss quadrature.
• Very efficient element which gives good results at large strains in bending.
• Element geometry is assumed to be flat and the results in warping can become inaccurate.
• Thickness is constant over the element.
PSHELL1, 10, 20, BLT, , , , , , ++, 0.8
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SHELL ELEMENTS (continued)
CQUAD4
Hughes-Liu
• Constant strain element based on the C0 Mindlin shell formulation with one point Gauss quadrature.
• More complex and more expensive to use than the Belytschko-Tsay element.
• Element geometry is assumed to be curved, but can become inaccurate in warping mode.
• Thickness may vary over the element
• Especially used for large bending when the material used is elastic plastic (with failure)
PSHELL1, 10, 20, HUGHES, , , , , , ++, 0.8
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SHELL ELEMENTS (continued)
CQUAD4
Key-Hoff
• Same element definition as Belytschko-Tsay with improvements.
• Warped element geometry• ”Transverse shear” option provides physical
stiffness in warping mode
• Accurate results at very large strains in bending as well as warping mode.
• No hourglass control needed for the warping mode.
• About twice as expensive as the Belytschko-Tsay element.
PSHELL1, 10, 20, KEYHOFF, , , , , , ++, 0.8
The PSHELL entry, when used with CQUAD4 elementsassumes Key-Hoff formulation.
PSHELL, 10, 20, 0.1
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CTRIA3
C0-triangle
Efficient, accurate triangular element giving good results in bending. It is stiffer than a quad formulation and so should only be used for transition regions, or in problems dominated by bending.
PSHELL1, 10, 20, C0-TRIA, , , , , , ++, 0.8
The PSHELL entry, when used with CTRIA3 elements assumes C0-triangle formulation.
PSHELL, 10, 20, 0.8
Membrane
Formulation specifically for membrane action only (the element can not carry bending).
PSHELL1, 10, 20, MEMB, , , , , , ++, 0.8
SHELL ELEMENTS (continued)
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Use the entities
-GRID-CQUAD/CTRIA-PSHELL/PSHELL1/PCOMP
Example of the definition of the Belytschko-Tsay shell element 71 with PID = 100, material 200 and thickness .1
Grid 1, 1, 0., 0., 0.Grid 2, 2, 1., 0., 0.Grid 3, 2, 0., 1., 0.Grid 4, 4, 1., 1., 0.CQUAD, 71, 100, 1, 2, 3, 4PSHELL1, 100, 200, BLT, , , , , , ++, .1
SHELL GEOMETRY DEFINITION
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Used to model very slender structural components
Beam consist of 2 grid points (1D element)
Beam grid points have 6 DOFs
Beam element coordinate system
-X-axis through grid G1 and G2
-XY-plane defined by external point G3 with y-axis normal to x-axis.
-Z-axis normal to x-axis and y-axis.
G1
G2
G3
Xelem
YelemZelem
BEAM ELEMENTS
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BEAM ELEMENTS (continued)
CBAR, CBEAM
Belytschko-Schwer (default)
Resultant Plasticity
This is a very efficient bar element, using resultant plasticity. This means that the whole section yields at once and the element goes from elastic to the full plastic moment. It is not suitable if the partially yielded behavior is important.
Linear Moment
A linear variation of bending moment is modeled. The element can yield at either end.
There is no difference in element formulation in MSC.Dytran between using CBAR and CBEAM unlike in MSC.Nastran.
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Definition of beam properties
The following data must be defined
Area: A
Inertias: Iyy, Izz
Torsion constant: J
Plastic moduli: Zy, Zz (only if plastic)
Example:
PBAR, 10, 20, 49.3, 10054.0, 333.0, 5193.0
PBEAM1, 10, 20, BELY,,,,, ++, 49.3, 10054.0, 333.0, 5193.0, 651.8, 85.07
For PBAR is used, the plastic moduli for a rectangular section are used.
BEAM ELEMENTS (continued)
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BEAM ELEMENTS (continued)
CBAR, CBEAM
Hughes-Liu
General Sections, Partial Yielding
The Hughes-Liu element is much more expensive to use, but can model partial yielding. It also allows general cross-sections to be defined and can model more complex material models. Only use it if you need one of its features.
Constant Moment
Only a constant variation of bending moment is represented.
Define Shape and Size of Section
The shape can be rectangular, circular, Z, T, hat, C or U shaped.
Example of a rectangular beam 200mm x 100mm
PBEAM1, 10, 20, HUGHES, , , , RECT,,++, 200.0, 200.0, 100.0, 100.0
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BEAM ELEMENTS (continued)
CBAR, CBEAM
Composite Beam
Shape and materials used can be arbitrary.
Based upon Hughes-Liu element formulation.
Example of a rectangular beam 200mm x 100mm
PBCOMP, 10, 20, …
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Integration of Beam Elements
Two types of integration:
Gauss (default)PBEAM1, 10, 20, , GAUSS, , , , , ++, 200.0, 200.0, 100.0, 100.0
LobattoPBEAM1, 10, 20, , LOBATTO, , , , , ++, 200.0, 200.0, 100.0, 100.0
BEAM ELEMENTS (continued)
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CROD
Tension/Compression only
This is a simple tension/compression element.
Efficient
The rod element is very efficient. Only the area is defined.
Example:
CROD, 1, 10, 2, 3PROD, 10, 20, 10.73
ROD ELEMENTS
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Use the entities:
-GRID-CBAR/CBEAM/CROD-PBAR/PBEAM/PBEAM1/PROD
Example of the definition of beam element 71 with PID = 100 and material 200.
Grid, 1, 0., 0., 0.Grid 2, 1., 0., 0.Grid 3, 0., 0., 1.CBEAM, 71, 100, 1, 2, 3.PBEAM, 100, 200, 100., 25., 25.,, 30.
BEAM/ROD GEOMETRY DEFINITION
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Used to model structural behavior that can be described by a spring or damper behavior
Springs and dampers consist of two grid points
Grid points can have 3-6 DOFs
Available are the following elements with linear as well as non-linear behavior
- Springs with orientation - CSPR- Scalar springs - CELAS- Dampers with orientation - CVISC- Scalar dampers - CDAMP
SPRINGS AND DAMPERS
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SPRING ELEMENTS
CSPR - Springs with Orientation
CSPR springs connect two grid points. The force in the element always acts in the direction of the two grid points. If the element undergoes large rotations, the direction of the force will change during the analysis.
CELASn - Scalar springs
CELAS1 and CELAS2 springs can connect one or two grid points. The force in the element always acts in the specified direction regardless of the relative positions of the grid points.
CELAS1 elements reference PELASn property entries and can be linear or nonlinear. The property data forCELAS2 elements is included on the element definition. These elements can only be linear.
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Three Types of springs selected by the PSPRn/PELASn entry
1 - Linear Elastic (PSPR, PELAS)
The force is linearly proportional to the displacement.
Failure on tension/compressionYou must give the stiffness
PSPR, 30, 2.7E6
2 - Nonlinear Elastic (PSPR, PELAS1)
The force is not proportional to the displacement, but there is no permanent deformation.
You must give the force displacement characteristic on a TABLED1 entry.
It can be of any shape.
PELAS1, 30,32TABLED1,32,,,,,,,,++,-1.,-1.E6,0.,0.,1.,1.E9,ENDT
Displacement
Force
K = 2.7E6
DisplacementForce
SPRING DEFINITION
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SPRING DEFINITION (continued)
3 - User Defined Springs (PSPREX, PELASEX)
Spring characteristics defined with user subroutines.
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Gaps
PSPR1, 100, 110TABLED1,110,,,,,,,,++,-1,-1.0E6,0.,0.,1.,0.,ENDT
Cables
PSPR1, 30,32TABLED1,32,,,,,,,,++,-1.,0.,0.,0.,1.,1.E6,ENDT
Component Failure
PSPR1, 30,32TABLED1,32,,,,,,,,++,-1.,-1.E6,1.,1.E6,1.,0.,2.0,0.,++,ENDT
Displacement
Force
Displacement
Force
Displacement
Force
APPLICATION OF NONLINEAR SPRINGS
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DAMPER ELEMENTS
CVISC - Dampers with Orientation
CVISC dampers connect two grid points. The force in the element always acts in the direction of the two grid points. If the element undergoes large rotations, the direction of the force will change during the analysis.
CDAMPn - Scalar dampers
CDAMP1 and CDAMP2 dampers can connect one or two grid points. The force in the element always acts in the specified direction regardless of the relative positions of the grid points.
CDAMP1 elements reference PDAMPn property entries and can be linear or nonlinear. The property data for CDAMP2 elements is included on the element definition. These elements can only be linear.
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Three types of dampers selected by the PVISCn/PDAMPn entry
Velocity
Force
C = 0.3
Velocity
Force
1 - Linear (PVISC, PDAMP)
The force is linearly proportional to the relative velocity of the end points in the direction of the damper.
Failure on tension/compressionYou must give the damping constant, C.
PDAMP, 30, 2.7E6
2 - Nonlinear (PVISC1, PDAMP1)
The force is not proportional to the velocity.
You must give the force-velocity characteristic on a TABLED1 entry.
It can be of any shape.
PVISC1, 30,32TABLED1,32,,,,,,,,++,-1.,-1.E6,0.,0.,1.,1.E9,ENDT
DAMPER DEFINITION
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3 - User Defined (PVISCEX)
Damper characteristics defined with user subroutines.
DAMPERS
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CONM2
Used to add mass and/or inertia to a Lagrangian grid point
All grid points must have mass, either by virtue of the properties of the structural elements attached to thegridpoints, or by using a CONM2.
Example of the definition of a CONM2 id 7 adding mass of .1 to grid point 9:
CONM2,7, 9,, .1
REMINDER - ALWAYS USE MASS UNITS IN DYTRAN !!!!
LUMPED MASSES
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Using TAB characters in the input deck
COMMON PROBLEMS