Finite Element Reference Guide Page 1 Finite Element

Finite Element Reference Guide

Preface

Using This Guide Where to Find More Information Conventions

Objects & Characteristics

Elements Linear Triangle Shell Parabolic Triangle Shell Linear Quadrangle Shell Linear Tetrahedron Parabolic Tetrahedron Beam Spring Contact Rod Tightening Beam Periodic Condition Rigid Spider Rigid Beam Smooth Spider Fastened Join Slider Join Contact Join Tightening Join Fitting Join

Physical Properties Shell Property Solid Property Beam Property Spring Property Contact Property Tightening Property Periodic Property Rigid Body Motion Property Smooth Body Motion Property Slider Property Pressure Fitting Property

Index

1Page Finite Element Reference Guide Version 5 Release 13

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

Name of the finite element Type Physical Property Mesh Connectivity

Linear triangle shell

Surface element shell

linear triangle

Parabolic triangle shell parabolic triangle

Linear quadrangle shell linear quadrangle

Linear tetrahedronSolid element solid

linear tetrahedron

Parabolic tetrahedron parabolic tetrahedron

Beam

Lineic element

beam

rod

Spring spring

Contact rod contact

Tightening beam tightening

Periodic condition periodic

Rigid spiderSpider element

rigid body motionspider

Smooth spider smooth body motion

Fastened join

Join element

smooth body motion

join

Slider join slider

Contact join contact

Tightening join tightening

Fitting join pressure fitting

Using This Guide


Where to Find More InformationConventions


Using This GuideThis guide is intended for the user who wants to be familiar with the finite elements and their physical properties used in the Analysis Workbenches.

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

A Glossary has been provided to familiarize you with some of the analysis buzzwords.


Where to Find More InformationPrior to reading this book, we recommend that you read:

● Generative Structural Analysis

● Conventions chapter


ConventionsCertain 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

functionalities that are new or enhanced with this Release.

allows you to switch back 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 the Advanced Tasks

Workbench Description

Customizing

Reference

Methodology

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 thismouse 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

● Right-click (to select contextual menu)


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 shell

Surface element shell

linear triangle

Parabolic triangle shell parabolic triangle

Linear quadrangle shell linear quadrangle

Linear tetrahedronSolid element solid

linear tetrahedron

Parabolic tetrahedron parabolic tetrahedron

Beam

Lineic element

beam

rod

Spring spring

Contact rod contact

Tightening beam tightening

Periodic condition periodic

Rigid spiderSpider element

rigid body motionspider

Smooth spider smooth body motion

Fastened join

Join element

smooth body motion

join

Slider join slider

Contact join contact

Tightening join tightening

Fitting join pressure fitting

Elements

Physical Properties


ElementsThis 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 ShellParabolic Triangle ShellLinear Quadrangle Shell

Linear TetrahedronParabolic Tetrahedron

BeamSpring

Contact RodTightening BeamPeriodic Condition

Rigid SpiderRigid Beam

Smooth SpiderFastened Join

Slider JoinContact Join

Tightening JoinFitting Join


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

Type surface element

Physical property shell

Mesh connectivity linear triangle

Number of nodes 3

Degrees of freedom(per node)

6 (3 translations and 3 rotations)

Type of behavior elastic

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


Parabolic Triangle ShellParabolic Triangle Shell is a six-nodes shell element based on the Degenerate Solid theory.



Mesh connectivity parabolic triangle

Number of nodes 6




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


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



Mesh connectivity parabolic quadrangle

Number of nodes 4




This element has four gauss points:

P1 (- /2 ; - /2) P2 ( /2 ; - /2)

P3 ( /2 ; /2) P4 (- /2 ; /2)


Linear TetrahedronLinear Tetrahedron is a four-nodes isoparametric solid element.

Type solid element

Physical property solid

Mesh connectivity linear tetrahedron

Number of nodes 4


3 (translations)


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

There are only three translations.


Parabolic TetrahedronParabolic Tetrahedron is a ten-nodes isoparametric solid element.

Type solid element

Physical property solid

Mesh connectivity parabolic tetrahedron

Number of nodes 10


3 (translations)


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.


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

Type lineic element

Physical property beam

Mesh connectivity rod

Number of nodes 2





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

Type lineic element

Physical property spring


Number of nodes 2





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

Type lineic element

Physical property contact


Number of nodes 2


3 (translations)

Type of behavior kinematics

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

If during the computation, the minimum clearance is reached, there are two cases:

1. The clearance increases.2. The relative displacement is orthogonal to the direction of the contact

(given either in input or by the element).

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

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.


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

Type lineic element

Physical property tightening


Number of nodes 2




The relations are obtained in the following way:

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

2. Impose a minimal overlap between the two nodes in the direction N1N2

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

Tightening elements generate a two-steps computation:

1. Submit a tightening force,2. Impose a minimum overlap equal to the overlap obtained in the first step.


Periodic ConditionPeriodic Condition element is a two-nodes element.

Type Lineic element

Physical property periodic


Number of nodes 2




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

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

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


Rigid SpiderRigid 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




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.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.


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

Type beam element

Physical property rigid body motion

Mesh connectivity beam

Number of nodes 2 : 1 master, n-1 slaves


6


The degrees of freedom of the master node (N1) are linked to the degrees of freedom of the slave node (N2 to Nn) 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.


Smooth SpiderSmooth 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




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.


Fastened JoinJoin element allows connecting a node and a face of an element.

Type join element

Physical property smooth body motion

Mesh connectivity mean



depend of the dimension


Mesh visualization:

The relations are obtains in the following way:

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.


Slider JoinJoin element allows connecting a node and a face of an element.

Type join element

Physical property slider

Mesh connectivity mean slider



3 translations


Mesh visualization




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).




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

Type join element

Physical property contact

Mesh connectivity join



depend of the dimension


Mesh visualization




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




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

Type join element

Physical property tightening




3 translations


Mesh visualization




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

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



Tightening elements generate a two-steps computation:

1. Submit a tightening force,2. Impose a minimum overlap equal to the overlap obtained in the first step.


Fitting JoinJoin element allows connecting a node and a face of an element.

Type join element

Physical property pressure fitting




3 translations


Mesh visualization



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 (or ....).




Physical Properties

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

Shell PropertySolid PropertyBeam PropertySpring PropertyContact Property

Tightening PropertyPeriodic Property

Rigid Body Motion PropertySmooth Body Motion Property

Slider PropertyPressure Fitting Property


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

Characteristics Center of element

Nodes of element

Gauss point Global Local

Stress

Strain

Point force vector


Point moment vector

Stress Von Mises

Elastic energy

Elastic energy density

Estimated error

Curvature

Transverse shear strain

Transverse shear stress


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:



Nodes of element

Gauss point

Face of element Global Local

Stress

Strain

Estimated error

Stress Von Mises

Elastic energy

Elastic energy density

Point force vector

Pressure


Beam Property

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


❍ Material

❍ Local Axis (optional)

❍ Cross-sectional Area

❍ Moment of inertia (tree values)

❍ Shear Factor (two values)

❍ Shear Center (two values)

● Output:❍ Point force vector


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



Nodes of element


Point force vector

Point moment vector


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

The input and output characteristics are:

● Input:❍ Translational stiffness

❍ Rotational stiffness



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



Nodes of element


Point force vector

Point moment vector


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.


❍ Direction (optional)


❍ Initial clearance (optional)

● Output: ❍ Point force vector

❍ Final clearance


Characteristics Center of element Nodes of element Gauss point Global Local

Point force vector

Final clearance


Tightening Property

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


❍ Orientation vector (optional)

❍ Local axis (optional)

❍ Tightening force



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



Nodes of element


Point force vector

Point moment vector


Periodic Property

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


❍ 3D Transformation






Nodes of element


Point force vector

Point moment vector


Rigid Body Motion Property

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

Rigid Body motion behavior.


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







Nodes of element


Point force vector

Point moment vector


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.


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







Nodes of element


Point force vector

Point moment vector


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.







Characteristics Center of element Nodes of element Gauss point Global Local

Point force vector


Pressure Fitting Property

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









Nodes of element


Point force vector

Point moment vector


Index

Bbeam

beam property

Ccontact

property

rod

Ffastened

join fitting

join

Jjoin

fastened

fitting

slider

tightening

Llinear


quadrangle shell

linear tetrahedron

linear triangle shell

Pparabolic tetrahedron

parabolic triangle shell periodic

property

periodic condition pressure fitting

property property

beam

contact

periodic

pressure fitting

rigid body motion

shell

slider

smooth body motion

solid

spring

tightening

Rrigid beam rigid body motion

property

rigid spider rod


contact

Sshell

property slider

join

property smooth body motion

property

smooth spider solid

property spring

property

spring

Ttightening

beam

join

property


Documents

Finite Element Reference Guide Page 1 Finite Element