Structural weight minimization using necessary and sufficient conditions

This paper considers problems of weight minimization of complex, determinate or indeterminate structures, subject to inequality constraints. Limitations of size of the structural members, allowable stresses, natural frequencies, etc., furnish constraints on the design. We are here principally concerned with the theoretical determination of the necessary and sufficient conditions relating a proposed design to the true constrained minimum-weight design. As an important special case, a study is made of the conditions under which a fully stressed design is a minimum-weight design. Although much attention has been directed toward the fully stressed approach to minimum-weight design, sufficiency conditions and questions relating to global optimality vs local optimality have heretofore not been considered in detail. Example solutions are presented illustrating the application of the present results to design problems. In one such solution, it is demonstrated that, for a broad class of statically determinate structures, sufficiency conditions exist which ensure that the fully stressed design is a globally minimum-weight design.