Optimization of rigid-plastic shallow curved beams

Abstract

The minimum weight problem of a shallow circular beam is studied in the case when the beam has a piece-wise constant thickness. The minimum of the weight is sought under the condition that the deflections of the beam of piece-wise constant thickness do not exceed those of the reference beam of constant thickness for given values of the external loading. The beam is subjected to uniformly distributed transverse pressure and to axial dead load. The material of the beam is assumed to be ideally rigid-plastic. Moderately large deflections are taken into account. Necessary optimality conditions are derived and used in order to establish the optimal values of the design parameters.