13.223. PLANE223 - 2D 8-Node Coupled-Field Solid

Matrix or VectorGeometryShape FunctionsIntegration Points
Stiffness and Stress Stiffness Matrices; Thermal Expansion, Diffusion ExpansionQuadEquation 11–137 and Equation 11–1382 x 2[a]
TriangleEquation 11–114 and Equation 11–1153
Mass MatrixQuadSame as stiffness matrix3 x 3
Triangle3
Pressure Load VectorSame as stiffness matrix, specialized to the face2
Thermal Conductivity Matrix and Heat Generation Load VectorQuadEquation 11–141 2 x 2
TriangleEquation 11–119 3
Specific Heat MatrixSame as thermal conductivity matrix. If KEYOPT(10) = 1 or 2, matrix is diagonalized as described in Lumped Matrices.
Convection Surface Matrix and Load VectorSame as thermal conductivity matrix, specialized to the face2
Dielectric Permittivity and Electrical Conductivity Matrices; Charge Density, Joule Heating, and Peltier Heat Flux Load VectorsQuadEquation 11–142 2 x 2
TriangleEquation 11–1203
Magnetic Reluctivity Matrix, Eddy Current Damping Matrices; Source Current and Remnant Magnetization Load Vectors QuadEquation 11–140

2 x 2

or

3 x 3

TriangleEquation 11–1173
Diffusivity Matrix and Diffusing Substance Generation Load VectorQuadEquation 11–1432 x 2
TriangleEquation 11–1213
Diffusion Damping MatrixSame as diffusivity matrix. If KEYOPT(10)=1, matrix is diagonalized as described in Lumped Matrices
Diffusion Flux Load VectorSame as diffusivity matrix, specialized to the face2
Thermoelastic stiffness and Damping MatricesSame as combination of stiffness and thermal conductivity matrices
Piezoelectric and Electroelastic Coupling MatrixSame as combination of stiffness matrix and dielectric matrix
Seebeck Coefficient Coupling MatrixSame as combination of electrical conductivity and thermal conductivity matrices
Magneto-Electric and Electromagnetic (velocity current) Coupling MatricesSame as combination of magnetic reluctivity and electric conductivity matrices
Magneto-Elastic Stiffness MatricesSame as combination of stiffness and magnetic reluctivity matrices
Diffusion-Elastic Stiffness MatrixSame as combination of stiffness and diffusivity matrices
Surface Charge Density Load VectorSame as dielectric matrix, specialized to the face2

[a] For coupled-field analyses with structural DOFs, the element uses 2 x 2- and 3-point integration rules to calculate the element matrices and load vectors for the quad and triangle geometries, respectively. All other analyses use 3x3- and 6-point integration rules for the quad and triangle geometries, respectively.

13.223.1. Other Applicable Sections

Structures describes the derivation of structural element matrices and load vectors as well as stress evaluations. General Element Formulations gives the general element formulations used by this element. Electromagnetics describes the derivation of the electric and magnetic element matrices and load vectors, as well as electric and magnetic field evaluations. Piezoelectrics discusses the piezoelectric capability used by the element. Piezoresistivity discusses the piezoresistive effect. Thermoelectrics discusses the thermoelectric effects. Thermoelasticity discusses the thermoelastic effects. Electroelasticity discusses the Maxwell stress electroelastic coupling. Thermoplasticity discusses the thermoplastic effect. Structural-Diffusion Coupling discusses diffusion strain coupling. Magnetoelasticity discusses magneto-elastic coupling matrices derived from magnetic Maxwell and Lorentz forces.