Analysis and Optimal Design of Spherical Shells under Axisymmetric Loads

Abstract

In a companion paper the integral equations for a spherical shell have been developed. This paper is concerned with the engineering applications of the integral equation method. A structure is selected to demonstrate how to apply the method in shell analysis. Two different types of construction are used for the shell: one has constant thickness, the other, piecewise linearly varying thickness. The solutions so obtained are compared with the corresponding ones found by the finite element method. They are also compared against the theoretical solutions whenever possible. A good agreement is attained. The aforementioned shell is also subjected to optimal design. An exterior penalty function method is selected to minimize the weight of the shell with stress and displacement constraints. The integral equation method is used in the analytical phase. Acceptable results are obtained.