Optimal Structural Design via Bound Formulation and Mathematical Programming

Abstract

This paper discusses structural optimization based on the concept of integration of modules of structural analysis, sensitivity analysis, and optimization by mathematical programming.

A system of this kind must possess sufficient flexibility to both cope with problems of minimizing cost subject to several behavioral constraints, and problems of multicriteria optimization for given cost. A convenient and simple way of achieving such flexibility is to cast the latter type of problem in scalar form by stating it as minimization of the maximum of a weighted set of the criteria. Such an interpretation of the multicriterion optimization problem can be formulated as a problem of minimizing an upper bound on the weighted criteria, and this bound formulation is very similar to that of the cost minimization problem. The approach has been implemented in connection with a slightly modified version of Fleury and Braibant’s dual mathematical programming method using mixed design variables, and is illustrated via several examples.