Optimization of Connecting Shell

Abstract

A procedure based on a direct variational method is presented for the determination of an optimum shape of a shell of revolution connecting a cylinder to a sphere under internal pressure. The optimized configuration of variable thickness has the same strength as that of an unpierced sphere subjected to internal pressure. The design is set up with respect to volume restriction, weight constraint and governing yield criterion. Geometric discontinuity is avoided by representing the midsurface of the shell of revolution by a function differentiable at least twice, up to and including boundaries. Required integrations and iterations are carried out numerically by a digital computer.