Optimal Elastic Design for Prescribed Maximum Deflection

ABSTRACT For the problems of the optimal elastic design with prescribed maximum deflection, a variational formulation is proposed, with reference to the one-or two-dimensional bending structures. Necessary optimum conditions are found, and the physical features of the optimal solutions are discussed for the “absolute” minimum cost problems, and, when dealing with beams, for the solutions with piece-wise constant design function. Some examples are solved by using numerical methods that are directly derived from the variational formulation.