Optimization of clamped rigid-plastic shallow shells of piecewise constant thickness

Abstract

The minimum weight problem is studied under the condition that the considered shell has a piecewise constant thickness. The shell with free internal edge and clamped outer edge is subjected to uniformly distributed internal pressure. Moderately large deflections are taken into account and a deformation-type theory of plasticity is employed. The optimization problem includes the additional restriction, which demands that the maximal deflections of the shell of piecewise constant thickness and of the reference shell, of constant thickness, coincide. Employing the variational methods of the optimal control theory, necessary optimality conditions are established. The results obtained are used to establish the optimal parameters for the shell of piecewise constant thickness.