An optimal design technique is suggested for axisymmetric shallow shel
ls exhibiting nonstable behaviour in the post-yield point range. The m
aterial of the shells is ideally rigid-plastic obeying the von Mises y
ield condition, which is satisfied in the average and the associated d
eformation law. Spherical shells pierced with a hole and subjected to
uniformly distributed transverse pressure are studied. Different cases
of the support conditions are considered. Making use of the methods o
f the optimal control theory the problem is transformed into a boundar
y value problem which is solved numerically.