On Variational Formulations for Structures Design Problems

It has been shown in a number of problems that necessary and sufficient conditions for optimal design of a single purpose structure may be obtained directly through a simple procedure, in cases where the mode of response being considered is covered by an extremum principle. The conditions relate to global optimality whenever the cost function is linear in the design variable, as well as in some cases where the relation is nonlinear. The proof of sufficiency is facilitated in particular by the association with an extremum principle. This association has also proved to be useful in the construction of certain techniques for the numerical treatment of structures optimization problems.