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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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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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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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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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


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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.


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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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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


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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

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CHAPTER 7 - ELEMENT LIBRARY