| Matrix or Vector | Shape Functions | Integration Points |
|---|---|---|
| Magnetic Potential Coefficient Matrix | Equation 11–232 | 2 x 2 x 2 |
| Electrical Conductivity Matrix | Equation 11–231 | 2 x 2 x 2 |
| Thermal Conductivity Matrix | Equation 11–229 | 2 x 2 x 2 |
| Stiffness Matrix and Thermal Expansion Load Vector | Equation 11–217, Equation 11–218, and Equation 11–219 or, if modified extra shapes are included (KEYOPT(3) = 0), Equation 11–233, Equation 11–234, and Equation 11–235 | 2 x 2 x 2 |
| Piezoelectric Coupling Matrix | Same as combination of stiffness matrix and conductivity matrix. | 2 x 2 x 2 |
| Specific Heat Matrix | Same as conductivity matrix. Matrix is diagonalized as described in 3D Lines | 2 x 2 x 2 |
| Mass and Stress Stiffening Matrices | Equation 11–217, Equation 11–218, and Equation 11–219 | 2 x 2 x 2 |
| Load Vector due to Imposed Thermal and Electric Gradients, Heat Generation, Joule Heating, Magnetic Forces, Magnetism due to Source Currents and Permanent Magnets | Same as coefficient or conductivity matrix | 2 x 2 x 2 |
| Load Vector due to Convection Surfaces and Pressures | Same as stiffness or conductivity matrix specialized to the surface. | 2 x 2 x 2 |
References: Wilson([39]), Taylor([50]), Coulomb([77]), Mayergoyz([120]), Gyimesi([142],[150])
Structures describes the derivation of structural element matrices and load vectors as well as stress evaluations. Heat Flow describes the derivation of thermal element matrices and load vectors as well as heat flux evaluations. Derivation of Electromagnetic Matrices discusses the scalar potential method, which is used by this element. Piezoelectrics discusses the piezoelectric capability used by the element.