Finite Element Reference Guide

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Finite Element

Reference Guide

Version 5 Release 16

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Special Notices

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All other company names and product names mentioned are the property of their respective owners. Certain portions of this product contain elements subject to copyright owned by the following entities: Copyright © Dassault Systemes

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The 2D/2.5D Display analysis function, the MSC.Nastran interface and the ANSYS interface are based on LMS International technologies and have been developed by LMS International

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Finite Element Reference Guide

Overview

Conventions

What's New?

Objects & Characteristics

Elements Linear Triangle Parabolic Triangle Linear Quadrangle Parabolic Quadrangle Linear Tetrahedron Parabolic Tetrahedron Linear Pentahedron Parabolic Pentahedron Linear Hexahedron Parabolic Hexahedron Beam Linear Bar Parabolic Bar Spring Coincident Contact Rod Tightening Beam Periodic Condition Rigid Beam Rigid Spider Smooth Spider Fastened Join Slider Join Contact Join Tightening Join Fitting Join Physical Properties Shell Property Membrane Property Shear Panel Property Solid Property

Beam Property Bar Property Spring Property

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Contact Property Tightening Property Periodic Property

Rigid Body Motion Property Smooth Body Motion Property Slider Property

Pressure Fitting Property

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Overview

Welcome to the Finite Element Reference Guide. This guide is intended for users who wants to be familiar with the finite elements used in the Analysis products.

This overview provides the following information:

● Finite Elements in a nutshell ● Before reading this guide

● Getting the most out of this guide ● Conventions used in this guide

Finite Element in a Nutshell

The Finite Element Reference Guide provides reference information on the elements used in the Analysis workbenches and the physical properties which are associated with those

elements.

Name of the finite element Type Physical Property Mesh Connectivity

Linear triangle Surface element shell membrane shear panel TR3 Parabolic triangle TR6 Linear quadrangle QD4

Parabolic quadrangle shell

membrane QD8

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Solid element solid

Parabolic tetrahedron TE10

Linear pentahedron WE6

Parabolic pentahedron WE15

Linear hexahedron HE8

Parabolic hexahedron HE20

Beam

Lineic element

beam

BAR

Linear Bar bar

Parabolic Bar bar

Spring spring

Coincident rigid body motion

Contact rod contact

Tightening beam tightening

Periodic condition periodic

Rigid Beam rigid body motion

Rigid spider

Spider element

rigid body motion

SPIDER

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Fastened join

Join element

smooth body motion

SPIDER

Slider join slider

Contact join contact

Tightening join tightening

Fitting join pressure fitting

Before Reading this Guide

Before reading this guide, we recommend that you read the Generative Structural Analysis User's Guide.

Getting the Most Out of this Guide

To get the most out of this guide, we suggest that you read the Objects and Characteristics

section. This section gives a table with all the elements and several characteristics you can find in this Reference Guide and contains two chapters: Elements and Physical Properties.

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Conventions

Certain conventions are used in CATIA, ENOVIA & DELMIA documentation to help you recognize and understand important concepts and specifications.

Graphic Conventions

The three categories of graphic conventions used are as follows:

● Graphic conventions structuring the tasks

● Graphic conventions indicating the configuration required ● Graphic conventions used in the table of contents

Graphic Conventions Structuring the Tasks

Graphic conventions structuring the tasks are denoted as follows:

This icon... Identifies...

estimated time to accomplish a task a target of a task

the prerequisites

the start of the scenario a tip a warning information basic concepts methodology reference information

information regarding settings, customization, etc. the end of a task

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functionalities that are new or enhanced with this release allows you to switch back to the full-window viewing mode

Graphic Conventions Indicating the Configuration Required

Graphic conventions indicating the configuration required are denoted as follows:

This icon... Indicates functions that are...

specific to the P1 configuration specific to the P2 configuration specific to the P3 configuration

Graphic Conventions Used in the Table of Contents

Graphic conventions used in the table of contents are denoted as follows:

This icon... Gives access to...

Site Map

Split View Mode What's New? Overview Getting Started Basic Tasks

User Tasks or Advanced Tasks Interoperability

Workbench Description Customizing

Administration Tasks Reference

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Methodology

Frequently Asked Questions Glossary

Index

Text Conventions

The following text conventions are used:

● The titles of CATIA, ENOVIA and DELMIA documents appear in this manner throughout the text. ● File -> New identifies the commands to be used.

● Enhancements are identified by a blue-colored background on the text.

How to Use the Mouse

The use of the mouse differs according to the type of action you need to perform.

Use this

mouse button... Whenever you read...

● Select (menus, commands, geometry in graphics area, ...)

● Click (icons, dialog box buttons, tabs, selection of a location in the document

window, ...)

● Double-click ● Shift-click ● Ctrl-click

● Check (check boxes) ● Drag

● Drag and drop (icons onto objects, objects onto objects)

● Drag ● Move

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What's New?

No enhancements in this release.

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Objects and Characteristics

This table gives you the name of a finite elements, the type of this element, the physical property which is associated with this element and finally, the mesh connectivity of this element.

Name of the finite element Type Physical Property Mesh Connectivity

Linear triangle Surface element shell membrane shear panel TR3 Parabolic triangle TR6 Linear quadrangle QD4

Parabolic quadrangle shell

membrane QD8

Linear tetrahedron

Solid element solid

TE4

Parabolic tetrahedron TE10

Linear pentahedron WE6

Parabolic pentahedron WE15

Linear hexahedron HE8

Parabolic hexahedron HE20

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Lineic element BAR

Linear Bar bar

Parabolic Bar bar

Spring spring

Coincident rigid body motion

Contact rod contact

Tightening beam tightening

Periodic condition periodic

Rigid Beam rigid body motion

Rigid spider

Spider element

rigid body motion

SPIDER

Smooth spider smooth body motion

Fastened join

Join element

smooth body motion

SPIDER

Slider join slider

Contact join contact

Tightening join tightening

Fitting join pressure fitting

Elements Physical Properties

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Elements

This section provides a description of the elements used in the Analysis workbenches. You will find the following information: type, associate physical property, mesh connectivity, number of nodes, degrees of freedom and type of behavior of those elements.

Linear Triangle Parabolic Triangle Linear Quadrangle Parabolic Quadrangle Linear Tetrahedron Parabolic Tetrahedron Linear Pentahedron Parabolic Pentahedron Linear Hexahedron Parabolic Hexahedron Beam Linear Bar Parabolic Bar Spring Coincident Contact Rod Tightening Beam Periodic Condition Rigid Beam Rigid Spider Smooth Spider Fastened Join Slider Join Contact Join Tightening Join Fitting Join

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Linear Triangle

Linear Triangle is a three-nodes plate finite element with flexing and transverse shear based on the Reissner/Mindlin theory (thick plates).

Type surface element

Physical property _shell

membrane shear panel Mesh connectivity TR3 Number of nodes 3 Degrees of freedom (per node)

6 (3 translations and 3 rotations)

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Parabolic Triangle

Parabolic Triangle is a six-nodes surface element based on the Degenerate Solid theory.

membrane shear panel Mesh connectivity TR6 Number of nodes 6 Degrees of freedom (per node)

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This element has three gauss points with intrinsic coordinates: P1 (1/6 ; 1/6) P2 (2/3 ; 1/6) P3 (1/6 ; 2/3)

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Linear Quadrangle

Linear Quadrangle is a four-nodes surface element based on the Reissner/Mindlin theory.

membrane shear panel Mesh connectivity QD4 Number of nodes 4 Degrees of freedom (per node)

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This element has four gauss points:

P1 (-

_{/2 ; -}

_/2

) P2 (

/2 ; -

/2

) P3 (

/2 ;

/2

) P4 (-

/2 ;

/2

)

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Parabolic Quadrangle

Parabolic Quadrangle is a eight-nodes surface element based on the Reissner/Mindlin theory.

membrane

Mesh connectivity QD8

Number of nodes 8

Degrees of freedom (per node)

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P1 (-

_{/2 ; -}

_/2

) P2 (

/2 ; -

/2

) P3 (

/2 ;

/2

) P4 (-

/2 ;

/2

)

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Linear Tetrahedron

Linear Tetrahedron is a four-nodes isoparametric solid element.

Type solid element

Physical property solid

Mesh connectivity TE4

Number of nodes 4

3 (translations)

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This element has only one gauss point: the gravity center (P1) of the tetrahedron. There are only three translations.

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Parabolic Tetrahedron

Parabolic Tetrahedron is a ten-nodes iso-parametric solid element.

Type solid element

Mesh connectivity TE10

Number of nodes 10

3 (translations)

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P1 (0,138 ; 0,138 ; 0,138) P2 (0,138 ; 0,138 ; 0,585) P3 (0,138 ; 0,585 ; 0,138) P4 (0,585 ; 0,138 ; 0,138) There are only three translations.

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Linear Pentahedron

Linear Pentahedron is a six-nodes solid element.

Type solid element

Mesh connectivity WE6

Number of nodes 6

3 (translations)

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P1 (0,138 ; 0,138 ; 0,138) P2 (0,138 ; 0,138 ; 0,585) P3 (0,138 ; 0,585 ; 0,138) P4 (0,585 ; 0,138 ; 0,138) There are only three translations.

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Parabolic Pentahedron

Parabolic Pentahedron is a fifteen-nodes solid element.

Type solid element

Mesh connectivity WE15

Number of nodes 15

3 (translations)

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This element has eight gauss points:

P1 (0,1667 ; 0,1667 ; 0,577) P2 (0,6667 ; 0,1667 ; 0,577) P3 (0,1667 ; 0,6667 ; 0,577) P4 (0,1667 ; 0,1667 ; -0,577) P5 (0,6667 ; 0,1667 ; -0,577) P6 (0,1667 ; 0,6667 ; -0,577) There are only three translations.

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Linear Hexahedron

Linear Hexahedron is a eight-nodes solid element.

Type solid element

Mesh connectivity HE8

Number of nodes 8

3 (translations)

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P1 (0,5774 ; 0,5774 ; 0,5774) P2 (0,5774 ; 0,5774 ; -0,5774) P3 (0,5774 ; -0,5774 ; 0,5774) P4 (0,5774 ; -0,5774 ; -0,5774) P5 (-0,5774 ; 0,5774 ; 0,5774) P6 (-0,5774 ; 0,5774 ; -0,5774) P7 (-0,5774 ; -0,5774 ; 0,5774) P8 (-0,5774 ; -0,5774 ; -0,5774) There are only three translations.

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Parabolic Hexahedron

Parabolic Hexahedron is a twenty-nodes solid element.

Type solid element

Mesh connectivity HE20

Number of nodes 20

3 (translations)

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P1 (0,5774 ; 0,5774 ; 0,5774) P2 (0,5774 ; 0,5774 ; -0,5774) P3 (0,5774 ; -0,5774 ; 0,5774) P4 (0,5774 ; -0,5774 ; -0,5774) P5 (-0,5774 ; 0,5774 ; 0,5774) P6 (-0,5774 ; 0,5774 ; -0,5774) P7 (-0,5774 ; -0,5774 ; 0,5774) P8 (-0,5774 ; -0,5774 ; -0,5774) There are only three translations.

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Beam

Beam is a two-nodes straight beam element with transverse shear based on the Timoshenko theory.

Type lineic element

Physical property beam

Mesh connectivity BAR

Number of nodes 2

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Linear Bar

Bar element is a two-nodes bar element with stiffness along their axis.

Type lineic element

Physical property bar

Number of nodes 2 nodes

3 translations

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Parabolic Bar

Bar element is a three-nodes bar element with stiffness along their axis.

Type parabolic element

Physical property bar

Number of nodes 3 nodes

3 translations

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Spring

Spring represents three translation and three rotational springs of stiffness, coupling two coincident points of a structure.

Type lineic element

Physical property spring

Number of nodes 2

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Coincident

Coincident is a two-nodes finite element that has no sense if the two nodes are not coincident.

Type lineic element

Physical property rigid body motion

Number of nodes 2

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Contact Rod

Contact Rod element with two nodes is used to impose a minimal clearance between the nodes in the direction joining these two nodes.

Type lineic element

Physical property contact

Number of nodes 2

3 (translations)

Type of behavior kinematics

The nodes of this element can support rotation but only the three translations at each node are used.

If during the computation, the minimum clearance is reached, there are two cases: 1. The clearance increases.

2. The relative displacement is orthogonal to the direction of the contact (given either in input or by the element).

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The use of contact rod is recommended when some part of a structure may be brought into contact with some other part of the structure.

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Tightening Beam

Tightening Beam element with two nodes, used to impose a minimum overlap between two nodes.

Type lineic element

Physical property tightening

Number of nodes 2

The relations are obtained in the following way:

1. Link the displacement of the two nodes (N1 and N2) according to the rigid body motion equations, except for the translation in the direction N1N2.

2. Impose a minimal overlap between the two nodes in the direction N1N2 If the length of the beam is null, the direction given by the property is used. Tightening elements generate a two-steps computation:

1. Submit a tightening force,

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Periodic Condition

Periodic Condition element is a two-nodes element.

Type Lineic element

Physical property periodic

Number of nodes 2

The displacements of the node N2 are equal to the transformation of the displacements of the node N1.

If the two plans are not parallel, the 3D transformation is a rotation.

If the two plans are parallel, the 3D transformation is a translation. In this case, the Periodic Condition becomes the traditional Rigid Beam element and the displacements of the node N2 are equal to the displacement of the node N1.

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Rigid Beam

Rigid Beam connects a node to a set of nodes in a rigid fashion.

Type beam element

Number of nodes 2 (1 master, 1 slave)

The degrees of freedom of the master node (N1) are linked to the degrees of freedom of the slave node (N2) according to rigid-body equations.

As a consequence, the displacement of the slave node depends to the rigid-body motion. Any direction can be relaxed in the rigid-body equations.

If there is more that one slave node, this Rigid Beam element becomes the traditional Rigid Spider element.

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Rigid Spider

Rigid Spider connects a node to a set of nodes in a rigid fashion.

Type spider element

Mesh connectivity SPIDER

Number of nodes 1 master, n-1 slaves

The degrees of freedom of the master node (N1) are linked to the degrees of freedom of each slave node (N2 to Nn) according to rigid-body equations.

As a consequence, the displacements of the slave nodes are linked among themselves according to rigid-body motion.

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Any direction can be relaxed in the rigid-body equations.

If there is only one slave node, this Rigid Spider element becomes the traditional Rigid Beam element.

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Smooth Spider

Smooth Spider connects a node to a set of nodes in a smooth fashion.

Type spider element

Physical property smooth body motion

Number of nodes 1 slave, n-1 masters

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The displacement of the slave node (N1) is linked to the displacement of the center of gravity of the n-1 master nodes. This linkage does not introduce any additional stiffness between the master nodes.

The relations are obtained in the following way:

1. Compute the center of gravity of the master nodes using the same weight for all the nodes.

The average displacement (translations and rotations) of the center of gravity of the master nodes is computed using the Mean Squares method.

2. The slave node is linked to the center of gravity of the n-1 master nodes according to the rigid-body equations.

The master nodes should not be aligned, otherwise the rotation along the axis of alignment can not be transmitted.

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Fastened Join

Join element allows connecting a node and a face of an element.

Type join element

Physical property smooth body motion

depend of the dimension

Mesh visualization:

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1. Compute the projection of the slave node (N1) on the surface defined by n-1 master nodes.

2. Interpolate the displacement of the projected point (P) using the shape function of the face defined by the master nodes.

3. Link the displacement of the slave node to the displacement of the projected point (P) using rigid-body equations.

The projected point (P) is a conceptual point, that means it is never created. The displacement of this point is always expressed in terms of displacement of the master nodes through interpolation.

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Slider Join

Type join element

Physical property slider

3 translations

Mesh visualization:

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3. Impose a relative displacement of master nodes and projected point (P) to be null in the direction given by the property (or in the direction of the projection if the property does not contain any direction information).

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Contact Join

Type join element

Physical property contact

depend of the dimension

Mesh visualization:

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3. Impose a minimal clearance between the slave node (N1) and the projected node (P) in the direction given by the property.

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Tightening Join

Type join element

Physical property tightening

3 translations

Mesh visualization:

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3. Link the displacement of the slave node (N1) to the displacement of the projected point (P) using rigid-body equations, except for the translation in the direction of the tightening given by the property.

4. Impose a minimum overlap in the direction given by the property between the slave node (N1) and the projected point (P).

Tightening elements generate a two-steps computation: 1. Submit a tightening force,

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Fitting Join

Type join element

Physical property pressure fitting

3 translations

Mesh visualization:

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2. Interpolate the displacement of the projected point (P) using the shape functions of the face defined by the master nodes.

3. Link the translations normal to the direction given by the property (or direction ) according to rigid body equations.

4. Impose a minimum clearance between the slave node (N1) and the projected point (P) in the direction given by the property.

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Physical Properties

This section provides a description of the physical properties which are associated with the reference elements.

Shell Property Membrane Property Shear Panel Property

Solid Property Beam Property Bar Property Spring Property Contact Property Tightening Property Periodic Property Rigid Body Motion Property Smooth Body Motion Property

Slider Property Pressure Fitting Property

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Shell Property

Shell property is a physical property assigned to a surface part.

A shell property references a material assigned to the surface part and describes a thickness associated to this surface part. A shell property is associative to the geometry this property points at.

The input and output characteristics are:

● Input: ❍ Material ❍ Thickness ● Output: ❍ Stress ❍ Strain

❍ Point force vector ❍ Point moment vector ❍ Stress Von Mises ❍ Elastic energy

❍ Elastic energy density ❍ Estimated error ❍ Curvature

❍ Transverse shear strain ❍ Transverse shear stress

Those characteristics can be expressed at the given positions in the elements and in different axis systems:

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Characteristics Center of element

Nodes of element

Gauss

point Global Local

Stress

Strain

Point force vector

Point moment vector

Stress Von Mises

Elastic energy

Elastic energy density

Estimated error Curvature Transverse shear strain Transverse shear stress

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Membrane Property

Membrane property is a physical property assigned to a surface part.

A membrane property references a material assigned to the surface part and describes a thickness associated to this surface part. A membrane property is associative to the geometry this property points at.

Associated to this property, elements (linear or parabolic triangle, linear or parabolic quadrangle) have:

● a plane stress state,

● two degrees of freedom per node (both translations in the finite element plane), ● no transversal stiffness,

● longitudinal shearing,

● tension / compression deformation.

❍ Point force vector ❍ Stress Von Mises ❍ Elastic energy

❍ Elastic energy density ❍ Estimated error

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Position Axis System Characteristics Center of element Nodes of element Gauss

Stress

Strain

Point force vector

Stress Von Mises

Elastic energy

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Shear Panel Property

Shear Panel property is a physical property assigned to a surface part.

A shear panel property references a material assigned to the surface part and describes a thickness associated to this surface part. A shear panel property is associative to the geometry this property points at.

Associated to this property, elements (linear or parabolic triangle, parabolic quadrangle) have:

● a plane stress state,

● two degrees of freedom per node (both translations in the finite element plane), ● no transversal stiffness,

● longitudinal shearing.

❍ Point force vector ❍ Elastic energy

❍ Elastic energy density ❍ Estimated error

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Gauss

Stress

Strain

Point force vector

Elastic energy

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Solid Property

Solid property is a physical property assigned to a 3D part.

A solid property references a material assigned to this 3D part. A solid property is associative to the geometry this property points at.

● Input: ❍ Material ● Output: ❍ Stress ❍ Strain ❍ Estimated error ❍ Stress Von Mises ❍ Elastic energy

❍ Elastic energy density ❍ Point force vector ❍ Pressure (optional)

The output characteristics can be expressed at the given positions in the element and in different axis systems:

Position Axis System

Characteristics Center of element Nodes of element Gauss point Face of

element Global Local

Stress

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Estimated error

Stress Von Mises

Elastic energy

Point force vector

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Beam Property

Beam property is a physical property assigned to a section of a part (1D).

● Input: ❍ Material

❍ Local Axis (optional) ❍ Cross-sectional Area

❍ Moment of inertia (tree values or six values in the case of variable beam) ❍ Shear Factor (two values )

❍ Shear Center (two values or two values equal to zero in the case of variable beam) ● Output:

❍ Point force vector ❍ Point moment vector

Gauss

Point force vector

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Bar Property

Bar property is a physical property assigned to a section of a part (1D).

● Input: ❍ Material

❍ Cross-sectional Area ● Output:

❍ Point force vector ❍ Stress

❍ Strain

Gauss

Point force vector

Stress

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Spring Property

Spring property is a physical property assigned to a section of a part (1D).

● Input:

❍ Translational stiffness ❍ Rotational stiffness ● Output:

The output characteristics can be expressed at the given positions of the element and in different axis system:

Gauss

Point force vector

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Contact Property

Contact property is a physical property assigned to a connection between two 3D parts. The relative translation of the slave node with respect to the master nodes set is

orthogonal to the direction joining the slave node to the set of master nodes.

● Input:

❍ Direction (optional) ❍ Local Axis (optional) ❍ Initial clearance (optional) ● Output:

❍ Point force vector ❍ Final clearance

The output characteristics can be expressed at the given position in the element:

Gauss

Point force vector

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Tightening Property

Tightening property is a physical property assigned to a section of a part (1D).

● Input:

❍ Orientation vector (optional) ❍ Local axis (optional)

❍ Tightening force ● Output:

The output characteristics can be expressed at the given positions in the element and in different axis system:

Gauss

Point force vector

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Periodic Property

Periodic property is a physical property assigned to a section of a part (1D).

● Input:

❍ 3D Transformation ● Output:

Gauss

Point force vector

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Rigid Body Motion Property

Rigid Body Motion property is a physical property assigned to a connection. Rigid Body motion behavior.

● Input:

❍ Degrees of freedom: relaxation of some relations (optional) ❍ Local Axis (optional)

● Output:

Gauss

Point force vector

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Smooth Body Motion Property

Smooth Body Motion property is a physical property assigned to a connection. Smooth Body motion behavior.

The set of slave nodes (there is generally only one slave node) is linked to the center of gravity of the set of master nodes according to rigid-body motion.

● Input:

❍ Degrees of freedom: relaxation of some relations (optional) ❍ Local Axis (optional)

● Output:

Gauss

Point force vector

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Slider Property

Slider property is a physical property assigned to a connection between two parts.

The relative translation of the slave node with respect to the master nodes set is orthogonal to the direction joining the slave node to the set of master nodes.

● Input:

❍ Direction (optional) ❍ Local Axis (optional) ● Output:

❍ Point force vector

Gauss

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Pressure Fitting Property

Pressure Fitting property is a physical property assigned to a section of a part (1D).

● Input:

❍ Direction (optional) ❍ Local Axis (optional) ● Output:

Gauss

Point force vector

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Index

B

bar property beam property rigid tightening

C

coincident contact join property rod

E

element beam coincident contact join contact rod fastened join fitting join linear bar linear hexahedron

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linear pentahedron linear quadrangle linear tetrahedron linear triangle parabolic bar parabolic hexahedron parabolic pentahedron parabolic quadrangle parabolic tetrahedron parabolic triangle periodic condition rigid beam rigid spider slider join smooth spider spring tightening beam tightening join

F

fastened join fitting join

H

hexahedron linear parabolic

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J

join contact fastened fitting slider tightening

L

linear hexahedron pentahedron quadrangle tetrahedron triangle linear bar element

M

membrane property

P

parabolic hexahedron pentahedron quadrangle tetrahedron triangle

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parabolic bar element pentahedron linear parabolic periodic condition periodic property physical property

pressure fitting property property bar beam contact membrane periodic pressure fitting rigid body motion shear panel shell

slider

smooth body motion solid spring tightening

Q

quadrangle linear parabolic

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R

rigid

beam spider

rigid body motion property rod, contact

S

shear panel property shell property slider join property smooth spider

smooth body motion property solid property spider rigid smooth spring spring property

T

tetrahedron linear parabolic tightening beam join

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property triangle

linear parabolic