An asymptotic analysis of the three-dimensional displacements and stresses in a spherical shell under inward radially opposed concentrated surface loads

Abstract

This paper complements and extends a recent asymptotic treatment of the title problem by Gregory et al. (SIAM J. Appl. Math. 59 (1999) 1080) who considered those solutions of the three-dimensional elasticity equations for an isotropic spherical shell of constant thickness 2 H that can be identified as membrane-like or shell-like. No attempt was made to analyze the solutions of the governing equations in neighborhoods of radius O( H) of the concentrated surface loads, i.e., three-dimensional slab-like solutions. Herein, formal asymptotic solutions are constructed for the shell-like and slab-like solutions. (The membrane-like solutions of Gregory et al. are exact, simple, and explicit and require no asymptotic treatment.) The analysis in the present paper reveals clearly how the three types of solutions blend into one another and allows one to assess the errors in classical (Kirchhoff–Love) shell theory.