| Matrix or Vector | Geometry | Shape Functions | Integration Points |
|---|---|---|---|
| Stiffness and Stress Stiffness Matrices; and Thermal Expansion, Diffusion Expansion, and Electrostatic Force Load Vector | Brick | Equation 11–236, Equation 11–237, and Equation 11–238 |
14 if KEYOPT(6) = 0 2 x 2 x 2 if KEYOPT(6) = 1 |
| Wedge | Equation 11–211, Equation 11–212, and Equation 11–213 | 3 x 3 | |
| Pyramid | Equation 11–195, Equation 11–196, and Equation 11–197 | 2 x 2 x 2 | |
| Tet | Equation 11–187, Equation 11–188, and Equation 11–189 | 4 | |
| Mass Matrix | Same as stiffness matrix. | 14 if brick. If other shapes, same as stiffness matrix | |
| Pressure Load Vector | Quad | Equation 11–82 and Equation 11–83 | 3 x 3 |
| Triangle | Equation 11–58 and Equation 11–59 | 6 | |
| Thermal Conductivity Matrix and Heat Generation Load Vector | Brick | Equation 11–239 | 14 [1] |
| Wedge | Equation 11–214 | 3 x 3 | |
| Pyramid | Equation 11–198 | 2 x 2 x 2 | |
| Tet | Equation 11–190 | 4 | |
| Specific Heat Matrix | Same as thermal conductivity matrix. If KEYOPT(10) = 1 or 2, matrix is diagonalized as described in Lumped Matrices. | ||
| Convection Surface Matrix and Load Vector | Quad | Equation 11–86 | 3 x 3 |
| Triangle | Equation 11–61 | 6 | |
| Dielectric Permittivity and Electrical Conductivity Matrices; Charge Density, Joule Heating, and Peltier Heat Flux Load Vectors | Brick | Equation 11–240 | 14 [1] |
| Wedge | Equation 11–215 | 3 x 3 | |
| Pyramid | Equation 11–199 | 2 x 2 x 2 | |
| Tet | Equation 11–191 | 4 | |
| Magnetic Reluctivity Matrix, Eddy Current Damping Matrices; Source Current and Remnant Magnetization Load Vectors | Brick | Equation 11–289, Equation 11–290, and Equation 11–291 | 14 |
| Wedge | 3 x 3 | ||
| Pyramid |
2 x 2 x 2 or 3 x 3 x 3 [2] | ||
| Tet | Equation 11–283, Equation 11–284, Equation 11–285, Equation 11–286, Equation 11–287, and Equation 11–288, | 4 | |
| Diffusivity Matrix and Diffusing Substance Generation Load Vector | Brick | Equation 11–242 | 14 [1] |
| Wedge | Equation 11–216 | 3 x 3 | |
| Pyramid | Equation 11–200 | 2 x 2 x 2 | |
| Tet | Equation 11–193 | 4 | |
| Diffusion Damping Matrix | Same as diffusivity matrix. If KEYOPT(10)=1, matrix is diagonalized as described in Lumped Matrices | ||
| Diffusion Flux Load Vector | Quad | Equation 11–88 | 3 x 3 |
| Triangle | Equation 11–63 | 6 | |
| Thermoelastic stiffness and Damping Matrices | Same as combination of stiffness and thermal conductivity matrices | ||
| Piezoelectric Coupling Matrix | Same as combination of stiffness matrix and dielectric matrix | ||
| Seebeck Coefficient Coupling Matrix | Same as combination of electrical conductivity and thermal conductivity matrices | ||
| Magneto-Electric and Electromagnetic (velocity current) Coupling Matrices | Same as combination of magnetic reluctivity and electric conductivity matrices | ||
| Magneto-Elastic Stiffness Matrices | Same as combination of stiffness and magnetic reluctivity matrices | ||
| Diffusion-elastic stiffness and damping matrices | Same as combination of stiffness and diffusivity matrices | ||
| Surface Charge Density Load Vector | Quad | Equation 11–199 | 3 x 3 |
| Triangle | Equation 11–62 | 6 | |
When KEYOPT(6) = 1 in a coupled-field analysis with structural DOFs, the unified reduced integration scheme with 2 x 2 x 2 integration points is used to form the thermal, electric, electrostatic matrices and load vectors.
Thermomagnetic and thermo-electromagnetic analyses use 3 x 3 x 3 integration points for all load vector and matrix calculations.
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 element matrices and load vectors as well as electromagnetic 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.