| Matrix or Vector | Geometry | Shape Functions | Integration Points |
|---|---|---|---|
| Stiffness and Stress Stiffness Matrices; and Thermal Expansion, Diffusion Expansion, and Electrostatic Force Load Vector | Equation 11–217, Equation 11–218, and Equation 11–219 | 2 x 2 x 2 1 if element shape is tetrahedral | |
| Mass Matrix | Same as stiffness matrix. | 2 x 2 x 2 | |
| Pressure Load Vector | Quad | Equation 11–70 and Equation 11–71 | 2 x 2 |
| Triangle | Equation 11–50 and Equation 11–51 | 3 | |
| Thermal Conductivity Matrix and Heat Generation Load Vector | Equation 11–227 | 2 x 2 x 2 | |
| Specific Heat Matrix | Equation 11–227. | 2 x 2 x 2 | |
| Convection Surface Matrix and Load Vector | Equation 11–227 specialized to the face | 2 x 2 | |
| Dielectric Permittivity and Electrical Conductivity Matrices; Charge Density, Joule Heating, and Peltier Heat Flux Load Vectors | Equation 11–228 | 2 x 2 x 2 | |
| Surface Charge Density Load Vector | Equation 11–228 specialized to the face | 2 x 2 | |
| Diffusivity Matrix and Diffusing Substance Generation Load Vector | Equation 11–230 | 2 x 2 x 2 | |
| Diffusion Damping Matrix | Equation 11–230. If KEYOPT(10) = 1, matrix is diagonalized as described in Lumped Matrices. | 2 x 2 x 2 | |
| Diffusion Flux Load Vector | Equation 11–230 specialized to the face | 2 x 2 | |
| 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 | ||
| Diffusion-elastic stiffness and damping matrices | Same as combination of stiffness and diffusivity matrices | ||
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 electric element matrices and load vectors as well as electric 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. Diffusion describes the derivation of diffusion matrices and load vectors. Structural-Diffusion Coupling discusses diffusion strain coupling.
This element uses the 
method (selective reduced integration technique for volumetric terms)
(Hughes([221]), Nagtegaal et al. ([222]))
If KEYOPT(6) = 2 or 3, the enhanced strain formulation from the works of Simo and Rifai([318]), Simo and Armero([319]), Simo et al.([320]), Andelfinger and Ramm([321]), and Nagtegaal and Fox([322]) is used. It introduces additional internal (user-inaccessible) structural degrees of freedom (DOFs) to prevent shear and volumetric locking (KEYOPT(6) = 2) or shear locking only (KEYOPT(6) = 3). These internal DOFs are created and condensed out at the element level.