Computer-aided design of optimal structures with uncertainty

Uncertainties in applied loads are introduced into the theory of optimization by use of ellipsoidal convex models. Mathematical derivations for quantifying uncertainty with the convex model are presented and are incorporated into an optimization computer algorithm. The algorithm is used in two design examples—a continuous two-span reinforced concrete beam and a steel ten-bar truss—with varying levels of uncertainty. Beam and truss designs are obtained under nominal loading, under uncertain loading while employing the convex model, and under uncertain loading using the maximum load condition. The overall cost of the optimal structures is minimized and the resulting designs are compared. The comparisons show that the design costs of the optimal designs produced under the convex model compare favorably to the design costs under nominal loading. However, the design costs associated with the maximum load condition are shown to significantly exceed both the costs associated with nominal loading and the costs associated with the convex model.