A Variational Principle Useful in Optimizing Rectangular-Base Shallow Shells

Abstract

Thin, elastic, shallow shells with constant thickness and rectangular base are considered. The edges are clamped or simply supported, with no in-plane displacements. Buckling under a uniformly distributed load is analyzed. A variational principle is presented and then utilized to optimize the forms of shells with given surface areas. In some cases, the optimal forms possess significantly higher buckling loads than standard forms.