Integral Equation Method for Spherical Shell under Axisymmetric Loads

Abstract

This paper is concerned with the development of the integral equation method for the analysis of a spherical shell under axisymmetric loads. The governing equations of shell are traditionally described as a set of two ordinary differential equations with two unknown state variables. These equations are normalized by eliminating their first derivatives, then multiplied by a weighting function that is a selected Green's function. Finally they are repeatedly integrated by parts until their differential operator is shifted from acting on the state variables to the weighting function. Consequently, the differential equations are transformed into a set of integral equations. To complete the analysis procedures, efforts are made to insert various boundary conditions of a shell into the kernels of the integral equations, and to express the internal forces, moments, and displacements of a shell in terms of the state variables. Thus, the integral equations are readily available for the analysis as well as the optimum design of a spherical shell.