Optimal structural design and relaxed controls

Abstract

AbstractProblems of optimal design, particularly of the optimal distribution of various materials within the volume of a structure, require consideration of all possible mixtures, i.e. composites, which can be assembled from given components. This paper explains both the mathematical and the physical reasons for such an extended formulation, and it summarizes results which have been obtained concerning effective transport coefficients. Specifically, we describe the set G, U of effective conductivity tensors of composites which may be assembled from components in a given set U taken in prescribed proportions m. By using G, U instead of U as the set of admissible controls, one guarantees the existence of an optimal control for a large class of weakly lower‐semicontinuous functionals of solutions of various boundary‐value problems.