Optimization of the shape of axisymmetric shells

summary:Axisymmetric thin elastic shells of constant thickness are considered and the meridian curves of their middle surfaces taken for the design variable. Admissible functions are smooth curves of a given length, which are uniformly bounded together with their first and second derivatives, and such that the shell contains a given volume. The loading consists of the hydrostatic pressure of a liquid, the shell's own weight and the internal or external pressure. As the cost functional, the integral of the second invariant of the stress deviator on both surfaces of the shell is chosen. Existence of an optimal design is proved on an abstract level. Approximate optimal design problems are defined and convergence of their solutions studied in detail