Maximum Strength Elastic Structural Design

An energy formulation is presented for the problem of optimal design of one and two-dimensional elastic sandwich structures. The object in design is to determine the distribution of material associated with the stiffest/strongest structure. The limit on local material strength is expressed through a prescribed upper bound on the unit strain energy, when the stiffest structure has the maximum load-carrying capacity among equal volume structures of similar style. Analytical solutions are obtained for the optimal simply-supported and clamped circular sandwich plates. The counterpart designs for maximum safety (according to the von Mises yield condition) are determined along with these solutions for elastic design. The carrying capacity of the optimal plate is found to exceed that of the equal volume plate of constant thickness by 67% and 92% respectively for the simply-supported and clamped boundaries.