Optimal Design for Plate Buckling

Abstract

This paper extends Keller's classic solution for the optimal design of columns to the case of plates. After the introduction of nondimensional variables, a calculus of variations technique is used to derive an optimality condition, which states that “the strain‐energy density is proportional to the thickness of an optimal plate design.” The case of a simply supported plate is then discussed, using a truncated Fourier series solution. For a square, isotropic plate, the buckling load of the optimal design is larger than that of the uniform plate by a factor of