NECESSARY CONDITIONS FOR OPTIMAL-DESIGN OF STRUCTURES WITH A NONSMOOTH EIGENVALUE BASED CRITERION

Necessary conditions of optimality for maximizing the buckling load fo r single or multimodal structures are derived using generalized gradie nts. The possible design dependence of the pre-buckling displacement i s taken into account and implies the appearance of a number of adjoint problems not normally present in, for example, standard vibration pro blems. The relation to other equivalent forms of the necessary conditi ons are pointed out and the formulae are demonstrated on simple exampl e problems.