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Finite Element Reference Guide

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Finite Element Reference Guide Version 5 Release 16

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Special Notices CATIA® is a registered trademark of Dassault Systèmes. Protected by one or more U.S. Patents number 5,615,321; 5,774,111; 5,821,941; 5,844,566; 6,233,351; 6,292,190; 6,360,357; 6,396,522; 6,459,441; 6,499,040; 6,545,680; 6,573,896; 6,597,382; 6,654,011; 6,654,027; 6,717,597; 6,745,100; 6,762,778; 6,828,974; 6,904,392 other patents pending. DELMIA® is a registered trademark of Dassault Systèmes. ENOVIA® is a registered trademark of Dassault Systèmes. SMARTEAM® is a registered trademark of SmarTeam Corporation Ltd.

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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 Index

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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

Linear triangle

Mesh Connectivity

TR3 shell membrane

Parabolic triangle Surface element

shear panel

Linear quadrangle

Parabolic quadrangle

Linear tetrahedron

TR6

QD4

shell membrane

QD8

TE4

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Parabolic tetrahedron

Linear pentahedron

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TE10

Solid element

solid

WE6

Parabolic pentahedron

WE15

Linear hexahedron

HE8

Parabolic hexahedron

HE20

Beam

beam

Linear Bar

bar

Parabolic Bar

bar

Spring

spring

Coincident

Lineic element

rigid body motion

Contact rod

contact

Tightening beam

tightening

Periodic condition

periodic

Rigid Beam

rigid body motion

Rigid spider

rigid body motion Spider element

Smooth spider

BAR

SPIDER smooth body motion

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Fastened join

smooth body motion

Slider join

slider

Contact join

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Join element

contact

Tightening join

tightening

Fitting join

pressure fitting

SPIDER

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...

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Select (menus, commands, geometry in graphics area, ...) Click (icons, dialog box buttons, tabs, selection of a location in the document window, ...)

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Double-click

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Shift-click

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Ctrl-click

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Check (check boxes)

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Drag

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

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Drag

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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

Linear triangle

Mesh Connectivity

TR3 shell membrane

Parabolic triangle Surface element

TR6

shear panel

Linear quadrangle

QD4

shell

Parabolic quadrangle

membrane

QD8

Linear tetrahedron

TE4

Parabolic tetrahedron

TE10

Linear pentahedron

WE6 Solid element

solid

Parabolic pentahedron

WE15

Linear hexahedron

HE8

Parabolic hexahedron

HE20

Beam

beam

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Linear Bar

bar

Parabolic Bar

bar

Spring

Lineic element

spring

Coincident

rigid body motion

Contact rod

contact

Tightening beam

tightening

Periodic condition

periodic

Rigid Beam

rigid body motion

Rigid spider

rigid body motion Spider element smooth body motion

Fastened join

smooth body motion

Slider join

slider Join element

BAR

SPIDER

Smooth spider

Contact join

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contact

Tightening join

tightening

Fitting join

pressure fitting

Elements Physical Properties

SPIDER

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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 Physical property

surface element

shell membrane shear panel

Mesh connectivity

TR3

Number of nodes

3

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

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

Type Physical property

surface element

shell membrane shear panel

Mesh connectivity

TR6

Number of nodes

6

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

elastic

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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.

Type Physical property

surface element

shell membrane shear panel

Mesh connectivity

QD4

Number of nodes

4

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

elastic

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This element has four gauss points: P1 (P3 (

/2 ; /2 ;

/2) /2)

P2 (

/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.

Type Physical property

surface element

shell membrane

Mesh connectivity

QD8

Number of nodes

8

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

elastic

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This element has four gauss points: P1 (P3 (

/2 ; /2 ;

/2) /2)

P2 (

/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

Degrees of freedom

3 (translations)

(per node)

Type of behavior

elastic

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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

Physical property

solid

Mesh connectivity

TE10

Number of nodes

10

Degrees of freedom

3 (translations)

(per node)

Type of behavior

elastic

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This element has four gauss points: 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

Physical property

solid

Mesh connectivity

WE6

Number of nodes

6

Degrees of freedom

3 (translations)

(per node)

Type of behavior

elastic

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This element has four gauss points: 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

Physical property

solid

Mesh connectivity

WE15

Number of nodes

15

Degrees of freedom

3 (translations)

(per node)

Type of behavior

elastic

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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

Physical property

solid

Mesh connectivity

HE8

Number of nodes

8

Degrees of freedom

3 (translations)

(per node)

Type of behavior

elastic

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This element has eight gauss points: 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

Physical property

solid

Mesh connectivity

HE20

Number of nodes

20

Degrees of freedom

3 (translations)

(per node)

Type of behavior

elastic

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This element has eight gauss points: 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

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

elastic

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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

Mesh connectivity

BAR

Number of nodes

2 nodes

Degrees of freedom

3 translations

(per node)

Type of behavior

elastic

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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

Mesh connectivity

BAR

Number of nodes

3 nodes

Degrees of freedom

3 translations

(per node)

Type of behavior

elastic

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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

Mesh connectivity

BAR

Number of nodes

2

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

elastic

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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

Mesh connectivity

BAR

Number of nodes

2

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

rigid

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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

Mesh connectivity

BAR

Number of nodes

2

Degrees of freedom

3 (translations)

(per node)

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

Type

lineic element

Physical property

tightening

Mesh connectivity

BAR

Number of nodes

2

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

kinematics

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, 2. Impose a minimum overlap equal to the overlap obtained in the first step.

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Periodic Condition Periodic Condition element is a two-nodes element.

Type

Lineic element

Physical property

periodic

Mesh connectivity

BAR

Number of nodes

2

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

kinematics

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

Physical property

rigid body motion

Mesh connectivity

BAR

Number of nodes

2 (1 master, 1 slave)

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

kinematics

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

Physical property

rigid body motion

Mesh connectivity

SPIDER

Number of nodes

1 master, n-1 slaves

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

kinematics

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

Mesh connectivity

SPIDER

Number of nodes

1 slave, n-1 masters

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

kinematics

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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

Mesh connectivity

SPIDER

Number of nodes

1 slave, n-1 masters

Degrees of freedom

depend of the dimension

(per node)

Type of behavior

kinematics

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

Type

join element

Physical property

slider

Mesh connectivity

SPIDER

Number of nodes

1 slave, n-1 masters

Degrees of freedom

3 translations

(per node)

Type of behavior

kinematics

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 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. 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).

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

Type

join element

Physical property

contact

Mesh connectivity

SPIDER

Number of nodes

1 slave, n-1 masters

Degrees of freedom

depend of the dimension

(per node)

Type of behavior

kinematics

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

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

Type

join element

Physical property

tightening

Mesh connectivity

SPIDER

Number of nodes

1 slave, n-1 masters

Degrees of freedom

3 translations

(per node)

Type of behavior

kinematics

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 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 (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).

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.

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

Type

join element

Physical property

pressure fitting

Mesh connectivity

SPIDER

Number of nodes

1 slave, n-1 masters

Degrees of freedom

3 translations

(per node)

Type of behavior

kinematics

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 by n-1 master nodes. 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.

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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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:

Position

Axis System

Finite Element Reference Guide

Characteristics

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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Center of

Nodes of

Gauss

element

element

point

Global Local

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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.

The input and output characteristics are: ●

●

Input: ❍

Material

❍

Thickness

Output: ❍

Stress

❍

Strain

❍

Point force vector

❍

Stress Von Mises

❍

Elastic energy

❍

Elastic energy density

❍

Estimated error

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

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Position

Characteristics

Stress

Strain

Point force vector

Stress Von Mises

Elastic energy

Elastic energy density

Estimated error

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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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.

The input and output characteristics are: ●

●

Input: ❍

Material

❍

Thickness

Output: ❍

Stress

❍

Strain

❍

Point force vector

❍

Elastic energy

❍

Elastic energy density

❍

Estimated error

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

Position

Axis System

Finite Element Reference Guide

Characteristics

Stress

Strain

Point force vector

Elastic energy

Elastic energy density

Estimated error

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Center of

Nodes of

Gauss

element

element

point

Global Local

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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.

The input and output characteristics are: ●

●

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

Characteristics

Stress

Strain

Axis System

Center of

Nodes of

Gauss

Face of

element

element

point

element

Global Local

Finite Element Reference Guide

Estimated error

Stress Von Mises

Elastic energy

Elastic energy density

Point force vector

Pressure

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

The input and output characteristics are: ●

●

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

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

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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

The input and output characteristics are: ●

Input: ❍ Material ❍

●

Cross-sectional Area

Output: ❍

Point force vector

❍

Stress

❍

Strain

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

Position

Characteristics

Point force vector

Stress

Strain

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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

The input and output characteristics are: ●

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:

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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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.

The input and output characteristics are: ●

●

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:

Position

Characteristics

Point force vector

Final clearance

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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

The input and output characteristics are: ●

●

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 in different axis system:

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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

The input and output characteristics are: ●

●

Input: ❍ 3D Transformation Output: ❍ Point force vector ❍

Point moment vector

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

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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

The input and output characteristics are: ●

Input: ❍ Degrees of freedom: relaxation of some relations (optional) ❍

●

Local Axis (optional)

Output: ❍ Point force vector ❍

Point moment vector

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

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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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.

The input and output characteristics are: ●

Input: ❍ Degrees of freedom: relaxation of some relations (optional) ❍

●

Local Axis (optional)

Output: ❍ Point force vector ❍

Point moment vector

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

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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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.

The input and output characteristics are: ●

Input: ❍ Direction (optional) ❍

●

Local Axis (optional)

Output: ❍ Point force vector

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

Position

Characteristics

Point force vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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

The input and output characteristics are: ●

Input: ❍ Direction (optional) ❍

●

Local Axis (optional)

Output: ❍ Point force vector ❍

Point moment vector

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

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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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

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View more...
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Special Notices CATIA® is a registered trademark of Dassault Systèmes. Protected by one or more U.S. Patents number 5,615,321; 5,774,111; 5,821,941; 5,844,566; 6,233,351; 6,292,190; 6,360,357; 6,396,522; 6,459,441; 6,499,040; 6,545,680; 6,573,896; 6,597,382; 6,654,011; 6,654,027; 6,717,597; 6,745,100; 6,762,778; 6,828,974; 6,904,392 other patents pending. DELMIA® is a registered trademark of Dassault Systèmes. ENOVIA® is a registered trademark of Dassault Systèmes. SMARTEAM® is a registered trademark of SmarTeam Corporation Ltd.

Any of the following terms may be used in this publication. These terms are trademarks of: Java

Sun Microsystems Computer Company

OLE, VBScript for Windows, Visual Basic

Microsoft Corporation

IMSpost

Intelligent Manufacturing Software, Inc.

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 Copyright © Dassault Systemes of America Copyright © D-Cubed Ltd., 1997-2000 Copyright © ITI 1997-2000 Copyright © Cenit 1997-2000 Copyright © Mental Images Gmbh & Co KG, Berlin/Germany 1986-2000 Copyright © Distrim2 Lda, 2000 Copyright © Institut National de Recherche en Informatique et en Automatique (INRIA Copyright © Compaq Computer Corporation Copyright © Boeing Company Copyright © IONA Technologies PLC Copyright © Intelligent Manufacturing Software, Inc., 2000 Copyright © SmarTeam Corporation Ltd Copyright © Xerox Engineering Systems Copyright © Bitstream Inc. Copyright © IBM Corp. Copyright © Silicon Graphics Inc. Copyright © Installshield Software Corp., 1990-2000 Copyright © Microsoft Corporation Copyright © Spatial Corp. Copyright © LightWork Design Limited 1995-2000 Copyright © Mainsoft Corp. Copyright © NCCS 1997-2000 Copyright © Weber-Moewius, D-Siegen Copyright © Geometric Software Solutions Company Limited, 2001 Copyright © Cogito Inc. Copyright © Tech Soft America Copyright © LMS International 2000, 2001

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Raster Imaging Technology copyrighted by Snowbound Software Corporation 1993-2001 CAM-POST ® Version 2001/14.0 © ICAM Technologies Corporation 1984-2001. All rights reserved 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 ImpactXoft, IX Functional Modeling, IX Development, IX, IX Design, IXSPeeD, IX Speed Connector, IX Advanced Rendering, IX Interoperability Package, ImpactXoft Solver are trademarks of ImpactXoft. Copyright ©20012002 ImpactXoft. All rights reserved. This software contains portions of Lattice Technology, Inc. software. Copyright © 1997-2004 Lattice Technology, Inc. All Rights Reserved. Copyright © 2005, Dassault Systèmes. All rights reserved.

Finite Element Reference Guide

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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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Finite Element Reference Guide

Contact Property Tightening Property Periodic Property Rigid Body Motion Property Smooth Body Motion Property Slider Property Pressure Fitting Property Index

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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

Linear triangle

Mesh Connectivity

TR3 shell membrane

Parabolic triangle Surface element

shear panel

Linear quadrangle

Parabolic quadrangle

Linear tetrahedron

TR6

QD4

shell membrane

QD8

TE4

Finite Element Reference Guide

Parabolic tetrahedron

Linear pentahedron

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TE10

Solid element

solid

WE6

Parabolic pentahedron

WE15

Linear hexahedron

HE8

Parabolic hexahedron

HE20

Beam

beam

Linear Bar

bar

Parabolic Bar

bar

Spring

spring

Coincident

Lineic element

rigid body motion

Contact rod

contact

Tightening beam

tightening

Periodic condition

periodic

Rigid Beam

rigid body motion

Rigid spider

rigid body motion Spider element

Smooth spider

BAR

SPIDER smooth body motion

Finite Element Reference Guide

Fastened join

smooth body motion

Slider join

slider

Contact join

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Join element

contact

Tightening join

tightening

Fitting join

pressure fitting

SPIDER

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

Finite Element Reference Guide

Version 5 Release 16

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

Page 10

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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

Finite Element Reference Guide ●

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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

Linear triangle

Mesh Connectivity

TR3 shell membrane

Parabolic triangle Surface element

TR6

shear panel

Linear quadrangle

QD4

shell

Parabolic quadrangle

membrane

QD8

Linear tetrahedron

TE4

Parabolic tetrahedron

TE10

Linear pentahedron

WE6 Solid element

solid

Parabolic pentahedron

WE15

Linear hexahedron

HE8

Parabolic hexahedron

HE20

Beam

beam

Finite Element Reference Guide

Linear Bar

bar

Parabolic Bar

bar

Spring

Lineic element

spring

Coincident

rigid body motion

Contact rod

contact

Tightening beam

tightening

Periodic condition

periodic

Rigid Beam

rigid body motion

Rigid spider

rigid body motion Spider element smooth body motion

Fastened join

smooth body motion

Slider join

slider Join element

BAR

SPIDER

Smooth spider

Contact join

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contact

Tightening join

tightening

Fitting join

pressure fitting

Elements Physical Properties

SPIDER

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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 Physical property

surface element

shell membrane shear panel

Mesh connectivity

TR3

Number of nodes

3

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

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

Type Physical property

surface element

shell membrane shear panel

Mesh connectivity

TR6

Number of nodes

6

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

elastic

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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.

Type Physical property

surface element

shell membrane shear panel

Mesh connectivity

QD4

Number of nodes

4

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

elastic

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This element has four gauss points: P1 (P3 (

/2 ; /2 ;

/2) /2)

P2 (

/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.

Type Physical property

surface element

shell membrane

Mesh connectivity

QD8

Number of nodes

8

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

elastic

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This element has four gauss points: P1 (P3 (

/2 ; /2 ;

/2) /2)

P2 (

/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

Degrees of freedom

3 (translations)

(per node)

Type of behavior

elastic

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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

Physical property

solid

Mesh connectivity

TE10

Number of nodes

10

Degrees of freedom

3 (translations)

(per node)

Type of behavior

elastic

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This element has four gauss points: 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

Physical property

solid

Mesh connectivity

WE6

Number of nodes

6

Degrees of freedom

3 (translations)

(per node)

Type of behavior

elastic

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This element has four gauss points: 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

Physical property

solid

Mesh connectivity

WE15

Number of nodes

15

Degrees of freedom

3 (translations)

(per node)

Type of behavior

elastic

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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

Physical property

solid

Mesh connectivity

HE8

Number of nodes

8

Degrees of freedom

3 (translations)

(per node)

Type of behavior

elastic

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This element has eight gauss points: 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

Physical property

solid

Mesh connectivity

HE20

Number of nodes

20

Degrees of freedom

3 (translations)

(per node)

Type of behavior

elastic

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This element has eight gauss points: 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

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

elastic

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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

Mesh connectivity

BAR

Number of nodes

2 nodes

Degrees of freedom

3 translations

(per node)

Type of behavior

elastic

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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

Mesh connectivity

BAR

Number of nodes

3 nodes

Degrees of freedom

3 translations

(per node)

Type of behavior

elastic

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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

Mesh connectivity

BAR

Number of nodes

2

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

elastic

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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

Mesh connectivity

BAR

Number of nodes

2

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

rigid

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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

Mesh connectivity

BAR

Number of nodes

2

Degrees of freedom

3 (translations)

(per node)

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

Type

lineic element

Physical property

tightening

Mesh connectivity

BAR

Number of nodes

2

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

kinematics

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, 2. Impose a minimum overlap equal to the overlap obtained in the first step.

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Periodic Condition Periodic Condition element is a two-nodes element.

Type

Lineic element

Physical property

periodic

Mesh connectivity

BAR

Number of nodes

2

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

kinematics

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

Physical property

rigid body motion

Mesh connectivity

BAR

Number of nodes

2 (1 master, 1 slave)

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

kinematics

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

Physical property

rigid body motion

Mesh connectivity

SPIDER

Number of nodes

1 master, n-1 slaves

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

kinematics

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

Mesh connectivity

SPIDER

Number of nodes

1 slave, n-1 masters

Degrees of freedom

6 (3 translations and 3 rotations)

(per node)

Type of behavior

kinematics

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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

Mesh connectivity

SPIDER

Number of nodes

1 slave, n-1 masters

Degrees of freedom

depend of the dimension

(per node)

Type of behavior

kinematics

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

Type

join element

Physical property

slider

Mesh connectivity

SPIDER

Number of nodes

1 slave, n-1 masters

Degrees of freedom

3 translations

(per node)

Type of behavior

kinematics

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 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. 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).

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

Type

join element

Physical property

contact

Mesh connectivity

SPIDER

Number of nodes

1 slave, n-1 masters

Degrees of freedom

depend of the dimension

(per node)

Type of behavior

kinematics

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

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

Type

join element

Physical property

tightening

Mesh connectivity

SPIDER

Number of nodes

1 slave, n-1 masters

Degrees of freedom

3 translations

(per node)

Type of behavior

kinematics

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 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 (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).

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.

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

Type

join element

Physical property

pressure fitting

Mesh connectivity

SPIDER

Number of nodes

1 slave, n-1 masters

Degrees of freedom

3 translations

(per node)

Type of behavior

kinematics

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 by n-1 master nodes. 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.

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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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:

Position

Axis System

Finite Element Reference Guide

Characteristics

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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Center of

Nodes of

Gauss

element

element

point

Global Local

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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.

The input and output characteristics are: ●

●

Input: ❍

Material

❍

Thickness

Output: ❍

Stress

❍

Strain

❍

Point force vector

❍

Stress Von Mises

❍

Elastic energy

❍

Elastic energy density

❍

Estimated error

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

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Position

Characteristics

Stress

Strain

Point force vector

Stress Von Mises

Elastic energy

Elastic energy density

Estimated error

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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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.

The input and output characteristics are: ●

●

Input: ❍

Material

❍

Thickness

Output: ❍

Stress

❍

Strain

❍

Point force vector

❍

Elastic energy

❍

Elastic energy density

❍

Estimated error

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

Position

Axis System

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Characteristics

Stress

Strain

Point force vector

Elastic energy

Elastic energy density

Estimated error

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Nodes of

Gauss

element

element

point

Global Local

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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.

The input and output characteristics are: ●

●

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

Characteristics

Stress

Strain

Axis System

Center of

Nodes of

Gauss

Face of

element

element

point

element

Global Local

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Stress Von Mises

Elastic energy

Elastic energy density

Point force vector

Pressure

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

The input and output characteristics are: ●

●

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

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

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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

The input and output characteristics are: ●

Input: ❍ Material ❍

●

Cross-sectional Area

Output: ❍

Point force vector

❍

Stress

❍

Strain

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

Position

Characteristics

Point force vector

Stress

Strain

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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

The input and output characteristics are: ●

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:

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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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.

The input and output characteristics are: ●

●

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:

Position

Characteristics

Point force vector

Final clearance

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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

The input and output characteristics are: ●

●

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 in different axis system:

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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

The input and output characteristics are: ●

●

Input: ❍ 3D Transformation Output: ❍ Point force vector ❍

Point moment vector

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

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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

The input and output characteristics are: ●

Input: ❍ Degrees of freedom: relaxation of some relations (optional) ❍

●

Local Axis (optional)

Output: ❍ Point force vector ❍

Point moment vector

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

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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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.

The input and output characteristics are: ●

Input: ❍ Degrees of freedom: relaxation of some relations (optional) ❍

●

Local Axis (optional)

Output: ❍ Point force vector ❍

Point moment vector

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

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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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.

The input and output characteristics are: ●

Input: ❍ Direction (optional) ❍

●

Local Axis (optional)

Output: ❍ Point force vector

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

Position

Characteristics

Point force vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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

The input and output characteristics are: ●

Input: ❍ Direction (optional) ❍

●

Local Axis (optional)

Output: ❍ Point force vector ❍

Point moment vector

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

Position

Characteristics

Point force vector

Point moment vector

Axis System

Center of

Nodes of

Gauss

element

element

point

Global Local

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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

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