OPTIMIZATION OF RIGID-PLASTIC SHALLOW SPHERICAL-SHELLS OF PIECE-WISE CONSTANT THICKNESS

An approximate method developed earlier for the investigation of large plastic deflections of circular and annular plates is accommodated fo r shallow spherical shells. The material of the shells is assumed to o bey Tresca's yield condition and the associated deformation law. The m inimum weight problem concerning shells operating in the post-yield ra nge is posed under the conditions that (i) the thickness of the struct ure is piece-wise constant and (ii) the maximal deflections of the opt imized shell and a reference shell of constant thickness, respectively , coincide. Necessary optimality conditions are derived with the aid o f the variational methods of the optimal control theory. The set of eq uations obtained is solved numerically.