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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
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Preface 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 shell Parabolic triangle shell
linear triangle Surface element
shell
Linear quadrangle shell
Solid element
solid
beam
Spring
spring Lineic element
contact
Tightening beam
tightening
Periodic condition
periodic
Rigid spider
rigid body motion
Smooth spider
Spider element
smooth body motion
Fastened join
smooth body motion
Slider join
slider
Contact join
Join element
linear tetrahedron parabolic tetrahedron
Beam
Contact rod
parabolic triangle linear quadrangle
Linear tetrahedron Parabolic tetrahedron
Mesh Connectivity
contact
Tightening join
tightening
Fitting join
pressure fitting
Using This Guide
rod
spider
join
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Where to Find More Information Conventions
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Using This Guide This 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.
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Where to Find More Information Prior to reading this book, we recommend that you read: ●
Generative Structural Analysis
●
Conventions chapter
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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
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Graphic conventions used in the table of contents
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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:
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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.
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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 shell Parabolic triangle shell
linear triangle Surface element
shell
Linear quadrangle shell
Solid element
solid
beam
Spring
spring Lineic element
contact
Tightening beam
tightening
Periodic condition
periodic
Rigid spider Smooth spider
rod
rigid body motion Spider element
smooth body motion
Fastened join
smooth body motion
Slider join
slider
Contact join
linear tetrahedron parabolic tetrahedron
Beam
Contact rod
parabolic triangle linear quadrangle
Linear tetrahedron Parabolic tetrahedron
Mesh Connectivity
Join element
contact
Tightening join
tightening
Fitting join
pressure fitting
Elements Physical Properties
spider
join
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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 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
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Linear Triangle Shell Linear 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).
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Parabolic Triangle Shell Parabolic Triangle Shell is a six-nodes shell element based on the Degenerate Solid theory.
Type
surface element
Physical property
shell
Mesh connectivity
parabolic triangle
Number of nodes
6
Degrees of freedom (per node)
6 (3 translations and 3 rotations)
Type of behavior
elastic
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 Shell Linear Quadrangle Shell is a four-nodes shell element based on the Reissner/Mindlin theory.
Type
surface element
Physical property
shell
Mesh connectivity
parabolic quadrangle
Number of nodes
4
Degrees of freedom (per node)
6 (3 translations and 3 rotations)
Type of behavior
elastic
This element has four gauss points: P1 (P3 (
/2 ; - /2) /2 ; /2)
P2 ( P4 (-
/2 ; /2 ;
/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
linear tetrahedron
Number of nodes
4
Degrees of freedom (per node)
3 (translations)
Type of behavior
elastic
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 isoparametric solid element.
Type
solid element
Physical property
solid
Mesh connectivity
parabolic tetrahedron
Number of nodes
10
Degrees of freedom (per node)
3 (translations)
Type of behavior
elastic
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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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
rod
Number of nodes
2
Degrees of freedom (per node)
6 (3 translations and 3 rotations)
Type of behavior
elastic
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Spring Spring element represents three translation and three rotational springs of stiffness, coupling two coincident points of a structure.
Type
lineic element
Physical property
spring
Mesh connectivity
rod
Number of nodes
2
Degrees of freedom (per node)
6 (3 translations and 3 rotations)
Type of behavior
elastic
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Contact Rod Contact 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
Mesh connectivity
rod
Number of nodes
2
Degrees of freedom (per node)
3 (translations)
Type of behavior
kinematics
The nodes of this element can support rotation but only the three translations at each node are used. If during the computation, the minimum clearance is reached, there are two cases: 1. The clearance increases. 2. The relative displacement is orthogonal to the direction of the contact (given either in input or by the element). If the length of the bar is null, the direction given by the property is used.
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
rod
Number of nodes
2
Degrees of freedom (per node)
6 (3 translations and 3 rotations)
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
rod
Number of nodes
2
Degrees of freedom (per node)
6 (3 translations and 3 rotations)
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 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 (per node)
6 (3 translations and 3 rotations)
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. 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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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
beam
Number of nodes
2 : 1 master, n-1 slaves
Degrees of freedom (per node) Type of behavior
6
kinematics
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.
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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 (per node)
6 (3 translations and 3 rotations)
Type of behavior
kinematics
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
mean
Number of nodes
1 slave, n-1 masters
Degrees of freedom (per node)
depend of the dimension
Type of behavior
kinematics
Mesh visualization:
The relations are obtains in the following way: 1. Compute the projection of the slave node (N1) on the surface defined by n1 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.
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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
mean slider
Number of nodes
1 slave, n-1 masters
Degrees of freedom (per node)
3 translations
Type of behavior
kinematics
Mesh visualization
The relations are obtains in the following way: 1. Compute the projection of the slave node (N1) on the surface defined by n1 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).
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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
join
Number of nodes
1 slave, n-1 masters
Degrees of freedom (per node)
depend of the dimension
Type of behavior
kinematics
Mesh visualization
The relations are obtains in the following way: 1. Compute the projection of the slave node (N1) on the surface defined by n1 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.
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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
join
Number of nodes
1 slave, n-1 masters
Degrees of freedom (per node)
3 translations
Type of behavior
kinematics
Mesh visualization
The relations are obtains in the following way: 1. Compute the projection of the slave node (N1) on the surface defined by n1 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).
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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
join
Number of nodes
1 slave, n-1 masters
Degrees of freedom (per node)
3 translations
Type of behavior
kinematics
Mesh visualization
The relations are obtains in the following way: 1. Compute the projection of the slave node (N1) on the surface defined by n1 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 (or ....).
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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 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
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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 Characteristics Stress Strain Point force vector
Center of element
Nodes of element
Axis System Gauss point
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Point moment vector Stress Von Mises Elastic energy Elastic energy density Estimated error Curvature Transverse shear strain Transverse shear stress
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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 Estimated error Stress Von Mises Elastic energy Elastic energy density Point force vector Pressure
Center of element
Nodes of element
Gauss point
Axis System Face of element
Global Local
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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)
❍
Shear Factor (two values)
❍
Shear Center (two values)
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
Center of element
Nodes of element
Axis System Gauss 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
Center of element
Nodes of element
Axis System Gauss 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
Position Characteristics Point force vector Final clearance
Center of element
Axis System
Nodes of element Gauss 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
Center of element
Nodes of element
Axis System Gauss 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
Center of element
Nodes of element
Axis System Gauss 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
Center of element
Nodes of element
Axis System Gauss 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
Center of element
Nodes of element
Axis System Gauss 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
Center of element
Axis System
Nodes of element Gauss 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
Center of element
Nodes of element
Axis System Gauss point
Global Local
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Index B beam beam property
C contact property rod
F fastened join fitting join
J join fastened fitting slider tightening
L linear
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quadrangle shell linear tetrahedron linear triangle shell
P parabolic 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
R rigid beam rigid body motion property rigid spider rod
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contact
S shell property slider join property smooth body motion property smooth spider solid property spring property spring
T tightening beam join property
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