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

This paper complements and extends a recent asymptotic treatment of the tit le problem by Gregory et al. (SIAM J. Appl. Math. 59 (1999) 1080) who consi dered those solutions of the three-dimensional elasticity equations for an isotropic spherical shell of constant thickness 2H that can be identified a s 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 concentr ated surface loads, i.e., three-dimensional slab-like solutions. Herein, fo rmal 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 pr esent 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. (C) 2001 Elsevier Science Ltd. All rights reserved.