Optimization of plastic spherical shells with a central hole

Abstract

An optimization method for plastic spherical shells is presented. The shells under consideration are clamped at the outer edge and contain a central hole. The material of the shells obeys the generalized square yield condition and the associated flow rule. The problem of maximization of the load carrying capacity under the condition that the weight (material volume) of the shell is fixed is transformed into a problem of nonlinear programming. The latter is solved with the aid of Lagrangian multipliers. The solution obtained is compared with the optimal solution of the minimum weight problem for given load carrying capacity.