Multimodal optimal design of a compressed column with respect to buckling in two planes (Q1087052)

The aim of this paper is to present the optimal design of a compressed column with respect to buckling in two planes. The cross-section of the column is a rectangle and the ends of the column are elastically clamped. The optimization problem is to determine the two independent dimensions of the cross-section that minimize the total volume of the column under given external load and geometrical constraints. The necessity of the multi(uni-, bi-, tri-, quadri-)modal formulation of optimization is pointed out. The problem is solved using the Pontryagin maximum principle.