Load and resistance convex models for optimum design

This paper is concerned with the optimal design of structures that are affected by uncertainties present in the loads applied to the structure, and by uncertainties affecting the internal resistance of the structural members. The magnitude of the applied loads and the modulus of elasticity of the structural members are assumed to vary within deterministic bounds. These uncertainties are idealized using a nonprobabilistic method, the convex model. The two types of uncertainties are considered simultaneously by employing the Cartesian product of convex sets. Two different convex models are examined to account for the uncertainties: the ellipsoidal convex model, and the uniform bound convex model. The optimum designs of a truss using the two convex models are compared to a worst case scenario optimum design in order to evaluate their performance. It is shown that it is not possible to identify a single worst case scenario that would be able to account for all possible combinations of uncertainties. However, both the ellipsoidal and the uniform bound convex model designs are found to be superior to the worst case scenario design in terms of constraint violations.