Analysis of Spherical Shells of Variable Wall Thickness

This article presents a solution to the problem of finding the forces and moments which occur in a spherical shell which is axisymmetrically loaded, when the variation in wall thickness is taken as a quadratic function of the coordinate of latitude. The so-called Love-Meissner differential equations for the case of nonuniform wall thickness are derived herein. By appropriate substitutions these are reduced to one linear equation of the fourth order having constant coefficients. The solution to this equation when taken in the homogeneous form is first given. This homogeneous solution will be the general solution for all problems where the shell surface is free from external force, and the only loads on the shell consist of forces and moments applied at the boundaries. When, however, the shell surface itself is loaded, a particular integral, which will depend upon the type of loading, must also be obtained for the nonhomogeneous equations. The solution contained herein is illustrated by a numerical example for a shell of one boundary when acted upon by dead-load forces, and the results are plotted.