Buckling of Complete Spherical Shells under Slightly Nonuniform Loads

Abstract

This chapter discusses buckling of complete spherical shells under slightly nonuniform load. It presents the study of the axisymmetric deformations of a complete thin spherical shell subject to external loads, of the form p(θ) = p0 + τ d(θ); θ is the latitude and τ measures the deviation of the load from a uniform pressure, p0. The techniques for solving this and a broad class of related problems are quite new and particularly relevant in elasticity theory. Estimates of the error in any iterate can be given and the results also show that some specific perturbation schemes actually yield asymptotic results. The problem is formulated in the chapter based on a modification of the equations. The chapter presents the analysis that is applied to this finite case is elementary and easily shows how these methods yield a rigorous treatment using only the first two variations of the energy functional.