Generalization of rectangular element stiffness matrix and thermal load vector associated with a0 + a1x + a2y + a3xy type interpolation rule

Explicit expressions for the element stiffness matrix K and element load vector p for the rectangular plane-stress and plane-strain finite elements associated with Ψ(x, y) = a₀ + a₁x + a₂y + a₃xy type interpolation rule are given for the general anisotropic material in xy-planc subjected to non-uniform temperature increases. The expressions are optimized with respect to the numerical operations required for the computation of K and p, and they are valid for special cases of material properties and thermal loading.