Based on Hooke’s Law for orthotropic anisotropic materials including thermal effects, a generalized constitutive matrix is derived from a high-precision rotational shell finite element, formulated on the principle of minimum total potential energy. Optimality of resulting stresses in elements is determined by Hill yield criteria during each iteration, and a new optimized shell section is determined. For multiple load conditions, each element of an optimum shell reaches its allowable stress due to one or more loading conditions.