Solid
Solid elements are classified based on stress conditions, such as plane strain, plane stress, axisymmetric, and 3D elements. They can also be categorized by the connected nodes and formulation methods. The currently supported elements are as follows:
- CPS3: 3-node plane stress element (Triangle), standard formulation
- CPS4: 4-node plane stress element (Quadrangle), standard formulation
- CPE3: 3-node plane strain element (Triangle), standard formulation
- CPE4: 4-node plane strain element (Quadrangle), standard formulation
- CAX3: 3-node axisymmetric element (Triangle), standard formulation
- CAX4: 4-node axisymmetric element (Quadrangle), standard formulation
- C3D4: 4-node 3D element (Tetrahedron), standard formulation
- C3D6: 6-node 3D element (Prism), standard formulation
- C3D8: 8-node 3D element (Hexahedron), standard formulation
- C3D8I: 8-node 3D element (Hexahedron), Incompatible mode formulation
- CPE4PMDL: 4-node plane strain PMDL element
- CAX4PMDL: 4-node axisymmetric PMDL element
- C3D8PMDL: 8-node 3D PMDL element
All solid elements are defined using the Solid section type to specify the section properties. The following figure shows the node and integration point numbers:
Fig. 4.6-1. Node and Integration Point Numbers of Solid Elements
For PMDL elements such as C3D8PMDL, it is necessary to specify the formulation method (PMDL or SimplePMDL) and the wave propagation direction in the *Section, TYPE=Solid command. The SimplePMDL formulation uses a midpoint integrated element formulation. This method uses the central integration point in the specified direction in a standard finite element formulation, making it economical for analyzing infinite domains in wave propagation analysis.
- R direction in CPE4PMDL, CAX4PMDL: 1x2 for stiffness matrix calculation, 1x3 for mass matrix calculation.
- S direction in CPE4PMDL, CAX4PMDL: 2x1 for stiffness matrix calculation, 3x1 for mass matrix calculation.
- RS direction in CPE4PMDL, CAX4PMDL: 1x1 for stiffness matrix calculation, 1x1 for mass matrix calculation.
- R direction in C3D8PMDL: 1x2x2 for stiffness matrix calculation, 1x3x3 for mass matrix calculation.
- S direction in C3D8PMDL: 2x1x2 for stiffness matrix calculation, 3x1x3 for mass matrix calculation.
- T direction in C3D8PMDL: 2x2x1 for stiffness matrix calculation, 3x3x1 for mass matrix calculation.
- RS direction in C3D8PMDL: 1x1x2 for stiffness matrix calculation, 1x1x3 for mass matrix calculation.
- TR direction in C3D8PMDL: 1x2x1 for stiffness matrix calculation, 1x3x1 for mass matrix calculation.
- ST direction in C3D8PMDL: 2x1x1 for stiffness matrix calculation, 3x1x1 for mass matrix calculation.
- RST direction in C3D8PMDL: 1x1x1 for stiffness matrix calculation, 1x1x1 for mass matrix calculation.
Example
*Material, Type=IsoElasticity, Name=steel
2E6, 0.2
*Section, Type=Solid, Name=plsec, Mass=Lumped
steel, 0.1
*Element, Type=C3D8
1, 1,2,3,4,5,6,7,8, S=plsec
*Element, TYPE=CPE3
*Element, Type=CPE3, ELSet=elset
id, n1, n2, n3{, S=section}
...
Specifications
- No. of nodes: 3
- No. of integration pts.: 1
- Fields: Material model at each Gauss points
- Compatible section: SolidSection
- Active DOFs: X, Y
*Element, TYPE=CPS3
*Element, Type=CPS4, ELSet=elset
id, n1, n2, n3{, S=section}
...
Specifications
- No. of nodes : 3
- No. of integration pts. : 1
- Fields : Material model at each Gauss points
- Compatible section : SolidSection
- Active DOFs : X, Y
*Element, TYPE=CAX3
*Element, Type=CAX4, ELSet=elset
id, n1, n2, n3{, S=section}
...
Specifications
- No. of nodes : 3
- No. of integration pts. : 1
- Fields : Material model at each Gauss points
- Compatible section : SolidSection
- Active DOFs : X, Y
*Element, TYPE=CPE4
*Element, Type=CPE4, ELSet=elset
id n1 n2 n3 n4{, S=section}
...
Specifications
- No. of nodes: 4
- No. of integration pts.: 2-by-2
- Fields: Material model at each Gauss points
- Compatible section: SolidSection
- Active DOFs: X, Y
*Element, TYPE=CPS4
*Element, Type=CPS4, ELSet=elset
id n1 n2 n3 n4 {, S=section}
...
Specifications
- No. of nodes : 4
- No. of integration pts. : 2-by-2
- Fields : Material model at each Gauss points
- Compatible section : SolidSection
- Active DOFs : X, Y
*Element, TYPE=CAX4
*Element, Type=CAX4, ELSet=elset
id n1 n2 n3 n4 {, S=section}
...
Specifications
- No. of nodes : 4
- No. of integration pts. : 2-by-2
- Fields : Material model at each Gauss points
- Compatible section : SolidSection
- Active DOFs : X, Y
*Element, TYPE=C3D4
*Element, Type=C3D4, ELSet=elset
id n1 n2 n3 n4 {, S=section}
...
Specifications
- No. of nodes : 4
- No. of integration pts. : 1
- Fields : Material model at each Gauss points
- Compatible section : SolidSection
- Active DOFs : X, Y, Z
*Element, TYPE=C3D6
*Element, Type=C3D6, ELSet=elset
id n1 n2 n3 n4 n5 n6 {, S=section}
...
Specifications
- No. of nodes : 6
- No. of integration pts. : 2
- Fields : Material model at each Gauss points
- Compatible section : SolidSection
- Active DOFs : X, Y, Z
*Element, TYPE=C3D8
*Element, Type=C3D8, ELSet=elset
id n1 n2 n3 n4 n5 n6 n7 n8{, S=section}
...
Specifications
- No. of nodes : 8
- No. of integration pts. : 2-by-2-by-2
- Fields : Material model at each Gauss points
- Compatible section : SolidSection
- Active DOFs : X, Y, Z
*Element, TYPE=C3D8I
*Element, Type=C3D8I, ELSet=elset
id n1 n2 n3 n4 n5 n6 n7 n8{, S=section}
...
Specifications
- No. of nodes : 8
- No. of integration pts. : 2-by-2-by-2
- Fields : Material model at each Gauss points
- Compatible section : SolidSection
- Active DOFs : X, Y, Z
*Element, TYPE=CPE4PMDL
*Element, Type=CPE4PMDL, ELSet=elset
id n1 n2 n3 n4{, S=section}
...
Specifications
- No. of nodes: 4
- No. of integration pts.: formulation depependent*
- Fields: Material model at each Gauss points
- Compatible section: SolidSection
- Active DOFs: X, Y
2-by-2 integration is used for PMDL formuation, but 1-by-2 or 2-by-1 integration is used for SimplePMDL formuation
*Element, TYPE=CAX4PMDL
*Element, Type=CAX4PMDL, ELSet=elset
id n1 n2 n3 n4 {, S=section}
...
Specifications
- No. of nodes : 4
- No. of integration pts.: formulation depependent*
- Fields : Material model at each Gauss points
- Compatible section : SolidSection
- Active DOFs : X, Y
2-by-2 integration is used for PMDL formuation, but 1-by-2 or 2-by-1 integration is used for SimplePMDL formuation
*Element, TYPE=C3D8PMDL
*Element, Type=C3D8PMDL, ELSet=elset
id n1 n2 n3 n4 n5 n6 n7 n8{, S=section}
...
Specifications
- No. of nodes : 8
- No. of integration pts.: formulation depependent*
- Fields : Material model at each Gauss points
- Compatible section : SolidSection
- Active DOFs : X, Y, Z
2-by-2-by-2 integration is used for PMDL formuation, but 1-by-2-by-2, 2-by-1-by-2, or 2-by-2-by-1 integration is used for SimplePMDL formuation
*Section, TYPE=Solid
Defines properties of solid element
*Section, Type=Solid, Name=name, Mass={Consistent|Lumped}
mat, thickness
formulation, direction
Keyword line
- Name=name: Section name (required). Section names must be unique.
- Mass={Consistent|Lumped}: Consistent or Lumped, which specifies whether the mass is consistent or lumped, respectively. (Optional, default is Consistent)
First dataline
- material: Material (required)
- thickness: Thickness (required), only used for plane stress or plane strain elements.
Second dataline (optional, used only for PMDL elements)
- formulation: PMDL or SimplePMDL
- direction: R, S, T, RS, RT, TR, RST
The second dataline is used for PMDL elements such as CPE4PMDL, CAX4PMDL, C3D8PMDL, AC2D4PMDL, AC3D8PMDL, etc. For PMDL element formulations, either PMDL or SimplePMDL can be specified. SimplePMDL refers to the Mid-Point Integrated Element Formulation, which integrates at the midpoint in the specified direction. When using SimplePMDL, it must be combined with elements like ViscousBoundary to effectively dissipate wave propagation.