J. Lellep et H. Hein, OPTIMIZATION OF CLAMPED RIGID-PLASTIC SHALLOW SHELLS OF PIECEWISE-CONSTANT THICKNESS, International journal of non-linear mechanics, 29(4), 1994, pp. 625-636
The minimum weight problem is studied under the condition that the con
sidered shell has a piecewise constant thickness. The shell with free
internal edge and clamped outer edge is subjected to uniformly distrib
uted internal pressure. Moderately large deflections are taken into ac
count and a deformation-type theory of plasticity is employed. The opt
imization problem includes the additional restriction, which demands t
hat the maximal deflections of the shell of piecewise constant thickne
ss and of the reference shell, of constant thickness, coincide. Employ
ing the variational methods of the optimal control theory, necessary o
ptimality conditions are established. The results obtained are used to
establish the optimal parameters for the shell of piecewise constant
thickness.