A unified approach to structural weight minimization

Abstract

It is shown that the two classical approaches to structural optimization have now reached a stage where they employ the same basic principles. Indeed, the well-known optimality criteria approach can be viewed as transforming the initial problem in a sequence of simple explicit problems in which the constraints are approximated from virtual work considerations. On the other hand, the mathematical programming approaches have progressively evoluated to a linearization method using the reciprocals of the design variables — this powerful method is proven here to be identical to a generalized optimality criteria approach. Finally, new efficient methods are proposed: (a) a hybrid optimality criterion based on first-order approximations of the most critical stress constraints and zeroth-order approximations of the others and (b) a mixed method which lies between a strict primal mathematical programming method and a pure optimality criteria (or linearization) approach. Simple numerical problems illustrate the concepts established in the paper.