J. Lellep et H. Hein, OPTIMIZATION OF RIGID-PLASTIC SHALLOW SPHERICAL-SHELLS OF PIECE-WISE CONSTANT THICKNESS, Structural optimization, 6(2), 1993, pp. 134-141
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.