finite element reference guide

8/12/2019 Finite Element Reference Guide

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Finite Element

Reference Guide

Version 5 Release 16

1Pagenite Element Reference Guide Version 5 Release 16


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ster Imaging Technology copyrighted by Snowbound Software Corporation 1993-2001

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pactXoft, IX Functional Modeling, IX Development, IX, IX Design, IXSPeeD, IX Speed Connector, IX Advndering, IX Interoperability Package, ImpactXoft Solver are trademarks of ImpactXoft. Copyright 200102 ImpactXoft. All rights reserved.

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Copyright 2005, Dassault Systmes. All rights reserved.



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Finite Element Reference Guide

Overview

Conventions

What's New?

Objects & Characteristics

Elements

Linear Triangle

Parabolic Triangle

Linear Quadrangle

Parabolic QuadrangleLinear 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 JoinFitting 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

Index



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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

Smooth spider smooth body motion



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Conventions

Certain conventions are used in CATIA, ENOVIA & DELMIA documentation to help you recognize andunderstand 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

http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


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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



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 mannerthroughout the text.

File-> Newidentifies 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 thismouse button... Whenever you read...

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

Click (icons, dialog box buttons, tabs, selection of a location in the documentwindow, ...)

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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Right-click (to select contextual menu)



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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 quadrangleshell

membraneQD8

Linear tetrahedron

Solid element solid

TE4

Parabolic tetrahedron TE10

Linear pentahedron WE6

Parabolic pentahedron WE15

Linear hexahedron HE8

Parabolic hexahedron HE20

Beam beam



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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


Linear Pentahedron


Linear HexahedronParabolic 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 Triangleis a three-nodes plate finite element with flexing and transverse shear

based on the Reissner/Mindlin theory (thick plates).

Type surface element

Physical propertyshell

membrane

shear panel

Mesh connectivity TR3

Number of nodes 3

Degrees of freedom

(per node)

6 (3 translations and 3 rotations)

Type of behavior elastic



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This element has only one gauss point: the gravity center of the triangle (P1).



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Parabolic Triangle

Parabolic Triangleis 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)


Type of behaviorelastic



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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 Quadrangleis 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)


Type of behaviorelastic



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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 Quadrangleis 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 Tetrahedronis a four-nodes isoparametric solid element.

Type solid element

Physical property solid

Mesh connectivity TE4

Number of nodes 4

Degrees of freedom

(per node)

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 Tetrahedronis a ten-nodes iso-parametric solid element.

Type solid element


Mesh connectivity TE10

Number of nodes 10

Degrees of freedom

(per node)

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)




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Linear Pentahedron

Linear Pentahedronis a six-nodes solid element.

Type solid element


Mesh connectivity WE6

Number of nodes 6

Degrees of freedom

(per node)

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)




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Parabolic Pentahedronis a fifteen-nodes solid element.

Type solid element


Mesh connectivity WE15

Number of nodes 15

Degrees of freedom

(per node)

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)




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Linear Hexahedron

Linear Hexahedronis a eight-nodes solid element.

Type solid element


Mesh connectivity HE8

Number of nodes 8

Degrees of freedom

(per node)

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)




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Parabolic Hexahedron

Parabolic Hexahedronis a twenty-nodes solid element.

Type solid element


Mesh connectivity HE20

Number of nodes 20

Degrees of freedom

(per node)

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)




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Beam

Beamis 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

Degrees of freedom

(per node)





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Linear Bar

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

Type lineic element

Physical property bar


Number of nodes 2 nodes

Degrees of freedom

(per node)

3 translations




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Parabolic Bar

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

Type parabolic element

Physical property bar


Number of nodes 3 nodes

Degrees of freedom

(per node)

3 translations




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Spring

Springrepresents 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

Degrees of freedom

(per node)





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Coincident

Coincidentis 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

Degrees of freedom

(per node)


Type of behavior rigid



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Contact Rod

Contact Rodelement 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

Degrees of freedom

(per node)

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).

If the length of the bar is null, the direction given by the property is used.



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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 Beamelement with two nodes, used to impose a minimum overlap betweentwo nodes.

Type lineic element

Physical property tightening


Number of nodes 2

Degrees of freedom

(per node)



The relations are obtained in the following way:

1. Link the displacement of the two nodes (N1 and N2) according to the rigid bodymotion 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,2. Impose a minimum overlap equal to the overlap obtained in the first step.



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Periodic Condition

Periodic Conditionelement is a two-nodes element.

Type Lineic element

Physical property periodic


Number of nodes 2

Degrees of freedom

(per node)



The displacements of the node N2are 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 N2are equal to the displacement of the node N1.



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Rigid Beam

Rigid Beamconnects a node to a set of nodes in a rigid fashion.

Type beam element



Number of nodes 2 (1 master, 1 slave)

Degrees of freedom

(per node)



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 Spiderconnects 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

Degrees of freedom

(per node)



The degrees of freedom of the master node (N1) are linked to the degrees of freedom of

each slave node (N2to 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 Spiderconnects 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

Degrees of freedom

(per node)





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Fastened Join

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

Type join element

Physical property smooth body motion



Degrees of freedom

(per node)

depend of the dimension


Mesh visualization:

The relations are obtains in the following way:



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

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

3. Link the displacement of the slave node to the displacement of theprojected 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



Degrees of freedom

(per node)

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 theprojection if the property does not contain any direction information).






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Contact Join


Type join element

Physical property contact



Degrees of freedom

(per node)

depend of the dimension


Mesh visualization:




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






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Tightening Join


Type join element

Physical property tightening



Degrees of freedom

(per node)

3 translations


Mesh visualization:




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3. Link the displacement of the slave node (N1) to the displacement of theprojected point (P) using rigid-body equations, except for the translationin 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,2. Impose a minimum overlap equal to the overlap obtained in the first step.



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Fitting Join


Type join element

Physical property pressure fitting



Degrees of freedom

(per node)

3 translations


Mesh visualization:




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

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

4. Impose a minimum clearance between the slave node (N1) and theprojected 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


Solid Property

Beam Property

Bar Property

Spring Property

Contact Property

Tightening Property

Periodic Property



Slider Property




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Shell Property

Shell propertyis 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:

Position Axis System



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CharacteristicsCenter of

element

Nodes of

element

Gauss

pointGlobal Local

Stress

Strain

Point force vector

Point moment vector

Stress Von Mises

Elastic energy


Estimated error

Curvature

Transverse shear

strain

Transverse shear

stress



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Membrane Property

Membrane propertyis 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.


Input:

Material

Thickness

Output:

Stress

Strain

Point force vector

Stress Von Mises

Elastic energy


Estimated error





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element

Nodes of

element

Gauss

pointGlobal Local

Stress

Strain

Point force vector

Stress Von Mises

Elastic energy


Estimated error



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Shear Panel propertyis 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.


Input:

Material

Thickness

Output:

Stress

Strain

Point force vector

Elastic energy


Estimated error






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element

Nodes of

element

Gauss

pointGlobal Local

Stress

Strain

Point force vector

Elastic energy


Estimated error



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Solid Property

Solid propertyis 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


Point force vector

Pressure (optional)

The output characteristics can be expressed at the given positions in the element and in




element

Nodes of

element

Gauss

point

Face of

elementGlobal Local

Stress

Strain



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Estimated error

Stress Von Mises

Elastic energy

Elastic energy

density

Point force vector

Pressure



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Beam Property

Beam propertyis 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





element

Nodes of

element

Gauss

pointGlobal Local

Point force vector

Point moment vector



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Bar Property

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


Input:

Material

Cross-sectional Area

Output:

Point force vector

Stress

Strain





element

Nodes of

element

Gauss

pointGlobal Local

Point force vector

Stress

Strain



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Spring Property

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


Input:

Translational stiffness

Rotational stiffness

Output:

Point force vector

Point moment vector

The output characteristics can be expressed at the given positions of the element and in

different axis system:



element

Nodes of

element

Gauss

pointGlobal Local

Point force vector

Point moment vector



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Contact Property

Contact propertyis 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)


Initial clearance (optional)

Output: Point force vector

Final clearance

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



element

Nodes of

element

Gauss

pointGlobal Local

Point force vector

Final clearance



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Tightening Property

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


Input:

Orientation vector (optional)

Local axis (optional)

Tightening force

Output:

Point force vector

Point moment vector

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


Characteristics

Center of

element

Nodes of

element

Gauss

pointGlobal Local

Point force vector

Point moment vector



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Periodic Property

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


Input:

3D Transformation

Output:

Point force vector

Point moment vector





element

Nodes of

element

Gauss

pointGlobal Local

Point force vector

Point moment vector



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Rigid Body Motion propertyis a physical property assigned to a connection.

Rigid Body motion behavior.


Input:

Degrees of freedom: relaxation of some relations (optional)


Output:

Point force vector

Point moment vector




Characteristics Center ofelement

Nodes ofelement

Gausspoint

Global Local

Point force vector

Point moment vector



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Smooth Body Motion propertyis 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)


Output:

Point force vector

Point moment vector





element

Nodes of

element

Gauss

pointGlobal Local

Point force vector

Point moment vector



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Slider Property

Slider propertyis 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:



Output:

Point force vector




Characteristics Center of

element

Nodes of

element

Gauss

pointGlobal Local

Point force vector



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


Input:



Output:

Point force vector

Point moment vector





element

Nodes of

element

Gauss

pointGlobal Local

Point force vector

Point moment vector



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Index

Bbar

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 beamrigid spider

slider join

smooth spider

spring

tightening beam

tightening join

F

fastened join

fitting join

Hhexahedron

linear

parabolic

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Jjoin

contact

fastened

fitting

slider

tightening

Llinear

hexahedron

pentahedron

quadrangle

tetrahedron

triangle

linear bar

element

M

membrane property

Pparabolic

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

Qquadrangle

linear

parabolic

http://-/?-http://-/?-http://-/?-


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Rrigid

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

Ttetrahedron

linear

parabolic

tightening

beam

join

http://-/?-


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property

triangle

linear

parabolic


finite element reference guide

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