An efficient optimality criteria approach to the minimum weight design of elastic structures

Abstract This paper is concerned with the optimality criteria approach to the minimum weight design of elastic structures analyzed by finite elements. It is first shown that the classical methods apply the lagrangian multiplier technique to an explicit problem. This one results from high quality, first order approximations of the displacement constraints and cruder, zero order approximations of the stress constraints. A generalized optimality criterion is then proposed as the explicit Kuhn-Tucker conditions of a first order approximate problem. Hence a hybrid optimality criterion is developed by using both zero and first order approximations of the stress constraints, according to their criticality. Efficient solution algorithms of the explicit approximate problem are suggested. Its dual statement generalizes the classical lagrangian approaches. Its primal statement leads to a rigorous definition of the optimality criteria approach, which appears to be closely related to the linearization methods of mathematical programming. Finally some numerical applications clearly illustrate the efficiency of the generalized and hybrid optimality criteria.