Implementation of Discrete Kirchhoff Triangle (DKT) plate element. This element is suitable for thin plates, as the traswerse shear strain energy is neglected. The structure should be defined in x,y plane, nodes should be numbered anticlockwise (positive rotation around zaxis). The element features are summarized in Table 18.
Keyword  dktplate 

Description  2D Discrete Kirchhoff Triangular plate element 

Specific parameters   

Unknowns  Three dofs (wdisplacement, u and v  rotations) are required in each node. 

Approximation  Quadratic approximation of rotations, cubic approximation of displacement along the edges. Note: there is no need to define interpolation for displacement on the element. 

Integration  Default integration of all terms using three point formula. 

Features  Layered cross section support. 

CS properties  Cross section thickness is required. 

Loads  Body loads are supported. Boundary load support is beta. 

Output  On output, the generalized shell strain/force momentum vectors in global coordinate system are printed, with the following meaning:
 
Nlgeo  0. 

Status  Reliable  
Reference  J.L.Batoz, K.J.Bathe, L.W.Ho: A study of threenode triangular plate bending elements, IJNME, 15(12):17711812, 1980 

Implementation of Discrete Kirchhoff Theory plate quad element (QDKT). This element is suitable for thin plates, as the traswerse shear strain energy is neglected. The structure should be defined in x,y plane, nodes should be numbered anticlockwise (positive rotation around zaxis). The element features are summarized in Table 19.
Keyword  qdktplate 

Description  2D Discrete Kirchhoff Quad plate element 

Specific parameters   

Unknowns  Three dofs (wdisplacement, u and v  rotations) are required in each node. 

Approximation  Quadratic approximation of rotations, cubic approximation of displacement along the edges. Note: there is no need to define interpolation for displacement on the element. 

Integration  Default integration of all bending terms using four point formula. 

Features  Layered cross section support. 

CS properties  Cross section thickness is required. 

Loads  Body loads are supported. 

Output  On output, the generalized shell strain/force momentum vectors in global coordinate system are printed, with the following meaning:
 
Nlgeo  0. 

Status  Reliable  
Reference  J.L.Batoz, K.J.Bathe, L.W.Ho: A study of threenode triangular plate bending elements, IJNME, 15(12):17711812, 1980 

Implementation of constant curvature triangular element for plate analysis. Formulation based on Mindlin hypothesis. The structure should be defined in x,y plane. The nodes should be numbered anticlockwise (positive rotation around zaxis). The element features are summarized in Table 20.
Keyword  cctplate 

Description  2D constant curvature triangular plate element 

Specific parameters   

Unknowns  Three dofs (wdisplacement, u and v  rotations) are required in each node. 

Approximation  Linear approximation of rotations, quadratic approximation of displacement. 

Integration  Integration of all terms using one point formula. 

Features  Layered cross section support. 

CS properties  Cross section thickness is required. 

Loads  Body loads are supported. Boundary loads are not supported now. 

Output  On output, the generalized shell strain/force momentum vectors in global coordinate system are printed, with the following meaning:
 
Nlgeo  0. 

Status  Reliable  
Implementation of constant curvature triangular element for plate analysis. Formulation based on Mindlin hypothesis. The element could be arbitrarily oriented in space. The nodes should be numbered anticlockwise (positive rotation around element normal). The element features are summarized in Table 21.
Keyword  cctplate3d 

Description  Constant curvature triangular plate element in arbitray position 

Specific parameters   

Unknowns  Six dofs (u,v,wdisplacements and u,v,w rotations) are in general required in each node. 

Approximation  Linear approximation of ratations, quadratic approximation of displacement. 

Integration  Integration of all terms using one point formula. 

Features  Layered cross section support. 

CS properties  Cross section thickness is required. 

Loads  Body loads are supported. Boundary loads are not supported now. 

Output  On output, the shell force (s_{f}), shell strain (s_{s}), shell momentum (s_{m}), and shell curvature (s_{c}) tensors in global coordinate system are printed as vector form with 6 components, with the following meaning:
 
Nlgeo  0. 

Status  Reliable  
Combination of CCT plate element (Mindlin hypothesis) with triangular plane stress element for membrane behavior. The element curvature can be specified. Although element requires generally six DOFs per node, no stiffness to local rotation along zaxis (rotation around element normal) is supplied. The element features are summarized in Table 22.
Keyword  rershell 

Description  Simple shell based on combination of CCT plate element (Mindlin hypothesis) with triangular plane stress element. element can be arbitrary positioned in space. 

Specific parameters   

Unknowns  Six dofs (u,v,wdisplacements and u,v,w rotations) are in general required in each node. Note, that although element it requires generally six DOFs per node, no stiffness to local rotation along zaxis (rotation around element normal) is supplied. 

Approximation  Linear approximation of ratations, quadratic approximation of displacement. 

Integration  Integration of all terms using one point formula. 

Features  Layered cross section support. 

CS properties  Cross section thickness is required. 

Loads  Body loads are supported. Boundary loads are not supported now. 

Output  On output, the shell force (s_{f}), shell strain (s_{s}), shell momentum (s_{m}), and shell curvature (s_{c}) tensors in global coordinate system are printed as vector form with 6 components, with the following meaning:
 
Nlgeo  0. 

Status  Reliable  
Combination of CCT3D plate element (Mindlin hypothesis) with triangular plane stress element for membrane behavior. It comes with complete set of 6 DOFs per node. The element features are summarized in Table 23.
Keyword  tr_shell01 

Description  Triangular shell element combining CCT3D plate element (Mindlin hypothesis) with triangular plane stress element with rotational DOFs 

Specific parameters   

Unknowns  Six dofs (u,v,wdisplacements and u,v,w rotations) are in general required in each node. 

Approximation  See description of cct and trplanstrrot elements 

Integration  Integration of all terms using one point formula. 

Features  Layered cross section support. 

CS properties  Cross section thickness is required. 

Loads  Body loads are supported. Boundary loads are supported (only surface loads). 

Output  On output, the shell force (s_{f}), shell strain (s_{s}), shell momentum (s_{m}), and shell curvature (s_{c}) tensors in global coordinate system are printed as vector form with 6 components, with the following meaning:
 
Nlgeo  0. 

Status  Reliable  
Combination of thinplate DKT plate element with plane stress element (TrPlanestressRotAllman). This element comes with complete set of 6 DOFs per node. The element features are summarized in Table 24.
Keyword  tr_shell02 

Description  Triangular shell element combining DKT plate element with triangular plane stress element with rotational DOFs 

Specific parameters   

Unknowns  Six dofs (u,v,wdisplacements and u,v,w rotations) are in general required in each node. 

Approximation  See description of cct and trplanstrrot elements 

Integration  4 integration points necessary, use ”NIP 4” in element record. 

CS properties  Cross section thickness is required. 

Loads  Body loads are supported. Boundary loads are supported (only surface loads). 

Output  On output, the shell force (s_{f}), shell strain (s_{s}), shell momentum (s_{m}), and shell curvature (s_{c}) tensors in global coordinate system are printed as vector form with 6 components, with the following meaning:
 
Nlgeo  0. 

Status    
This class implements an quadrilateral, bilinear, fournode Mindlin plate. This type of element exhibit strong shear locking (thin plates exhibit almost no bending). Implements the lumped mass matrix. The element features are summarized in Table 25.
Keyword  quad1mindlin 

Description  Quadrilateral, bilinear, fournode Mindlin plate 

Specific parameters  [NIP #(in)] 

Unknowns  Three dofs (wdisplacement, u and v  rotation) are required in each node. 

Approximation  Linear for all unknowns. 

Integration  Default uses 4 integration points. No reduced integration is used, as it causes numerical problems. 

Features  Layered cross section support. 

CS properties  Cross section thickness is required. 

Loads  Dead weight loads, and edge loads are supported. 

Output  On output, the generalized shell strain/force momentum vectors in global coordinate system are printed, with the following meaning:
 
Nlgeo  0. 

Reference  [1] 

Status  Experimental 

This class implements a triangular, quadratic, sixnode shell element. The element is a socalled seven parameter shell with seven dofs per node – a displacement field (3 dofs), an extensible director field (3 dofs) and a seventh dof representing inhomogenous thickness strain. This last parameter is included in the model in order to deal with volumetric/Poisson lock effects.
The element features are summarized in Table 25.
Keyword  tr2shell7 
Description  Triangular, quadratic, sixnode shell with 7 dofs/node 
Specific parameters  [NIP #(in)] 
Unknowns  Seven dofs (displacement in u, v and wdirection; change in director field in u, v and wdirection; and inhomgenous thickness stretch) are required in each node. 
Approximation  Quadratic for all unknowns. 
Integration  Default uses 6 integration points in the midsurface plane. Number of integration points in the thickness direction is determined by the Layered cross section. 
Features  Layered cross section support. 
CS properties  This element must be used with a Layered cross section. 
Loads  Edge loads, constant pressure loads and surface loads are supported. 
Nlgeo  Not applicable. The implementation is for large defomrations and hence geometrical nonlinearities will always be present, regardless the value of Nlgeo. 
Reference  [3] 
Status  Experimental 
A fournode quadrilateral shell element formulated using threedimensional continuum mechanics theory degenerated to shell behaviour. The element is applicable to thick and thin shells as the “mixed interpolation of tensorial components” (MITC) approach is used to remove shear locking. The implementation is based on the following paper: Dvorkin, E.N., Bathe, K.J.: A continuum mechanics based fournode shell element for general nonlinear analysis, Eng.Comput., Vol.1, 7788, 1984.
Although element requires generally six DOFs per node, no stiffness to local rotation along zaxis (rotation around director vector) is supplied. The element features are summarized in Table 27.
Keyword  mitc4shell 

Description  Quadrilateral, bilinear, fournode shell element using the MITC technique. 

Specific parameters  [NIP #(in)] [NIPZ #(in)] [directorType #(in)] 

Parameters  NIP: allows to set the number of integration points in local xy plane (default 4). 

NIPZ: allows to set the number of integration points in local zdirection (default 2). 

directorType: allows to set director vectors. Director vectors can be set as normal to the plane (directorType = 0, default), or calculated for each node as an average of neighbouring elements of same crosssection (directorType = 1), or can be specified at crosssection (directorType =2). 

Unknowns  Six dofs (u,v,wdisplacements and u,v,w rotations) are in general required in each node. Note, that although element requires generally six DOFs per node, no stiffness to local rotation along zaxis (rotation around director vector) is supplied. 

Approximation  Linear approximation of displacements and rotations. 

Integration  Integration of all terms using Gauss integration formula in 8 points (default) or specified using NIP and NIPZ parameters. 

Features  Variable cross section support. 

CS properties  Cross section thickness is required (measured along director vector). Director vectors components may be specified [directorx #(in)][directory #(in)][directorz #(in)] in case of directorType 2. 

Loads  Body and boundary loads are supported. 

Output  On output, the shell force (s_{f}), shell momentum (s_{m}), shell strain (s_{s}), shell curvature (s_{c}), strain (ε), and stress (σ) tensors in global coordinate system are printed as vector form with 6 components, with the following meaning:
 
Nlgeo  0. 

Status    
This class implements an quadrilateral, bilinear, fournode plate subsoil element. Typically this element is combined with suitable plate element with quadrilateral geometry to model plate element on (elastic) subsoill foundation, but it can be used alone. The element geometry should be define in xy plane. The element features are summarized in Table 28.
Keyword  quad1plateSubsoil 
Description  Quadrilateral, bilinear, fournode subsoil plate element 
Specific parameters 

Unknowns  One dof (wdisplacement) is required in each node. 
Approximation  Linear for transwersal displacement. 
Integration  4 integration points. 
Loads  Surface load support. 
Note  Requires material model with 2dPlateSubSoil mode support. 
Reference  [2] 
This class implements an quadrilateral, bilinear, fournode plate subsoil element. Typically this element is combined with suitable plate element with quadrilateral geometry to model plate element on (elastic) subsoill foundation, but it can be used alone. The element geometry should be define in xy plane. The element features are summarized in Table 28.
Keyword  tria1platesubsoil 
Description  Tringular, threenode subsoil plate element with linear interpolation 
Specific parameters 

Unknowns  One dof (wdisplacement) is required in each node. 
Approximation  Linear for transwersal displacement. 
Integration  1 integration points. 
Loads  Surface load support. 
Note  Requires material model with 2dPlateSubSoil mode support. 
Reference  [2] 