OPTIMIZATION OF RIGID-PLASTIC SHALLOW CURVED BEAMS

The minimum weight problem of a shallow circular beam is studied in th e case when the beam has a piece-wise constant thickness. The minimum of the weight is sought under the condition that the deflections of th e beam of piece-wise constant thickness do not exceed those of the ref erence beam of constant thickness for given values of the external loa ding. The beam is subjected to uniformly distributed transverse pressu re and to axial dead load. The material of the beam is assumed to be i deally rigid-plastic. Moderately large deflections are taken into acco unt. Necessary optimality conditions are derived and used in order to establish the optimal values of the design parameters.