Mechanics of Shape Optimization in Plate Buckling

Abstract

The paper addresses the problem of finding an optimum thickness distribution for a rectangular, isotropic plate of given volume and plan dimensions (length and width) that would maximize its uniaxial buckling load, loosely referred to as shape optimization. Earlier studies suggest that optimal profiles are not only characterized by a concave thickness distribution with higher values near the edges compared to the center, but also by a convex distribution with very high thickness at the center compared with the edges. This paradox regarding the nature of the optimal thickness distribution is the subject of the present investigation. It is established that the qualitative nature of optimal thickness distribution is dependent on the assumptions made regarding the prebuckling loading state, that is, whether the uniaxial stress or force per unit length remains constant. The paper also highlights the fact that shape optimization is seriously limited by local buckling considerations and illustrates the interactions between thickness variation, the nature of the prebuckling state, and the influence of boundary conditions in the global context of plate instability.