An exact elasto-plastic solution for a thick-walled spherical shell of elastic linear-hardening material with finite deformations

Abstract

An exact elasto-plastic analytical solution for a finitely deformed internal-pressurized thick-walled spherical shell made of elastic linear-hardening material is derived in this paper. This solution is based on the notion of finite strains, the deformation theory of Hencky, the yield criterion of von Mises and the assumption of incompressibility. Being applicable for both the linear-elastic response and the plastic strain-hardening stages of a finitely deformed thick-walled spherical shell, the present solution can uniformly represent the whole expanding process of the shell from its initial yield at the inner surface to its full yield over the wall up to its ultimate bursting with the increase of its operating pressure. It is shown that this exact solution is of general characteristics, from which three specific solutions of practical interest can be obtained. The calculation formulae for the full-yield pressure and the bursting pressure of the finitely deformed spherical shell deduced in this paper are of value for the strength design of a strain-hardening material spherical shell. Being expressed in terms of Lagrangian variables, the explicit expressions of the solution are convenient for engineering use. The present exact solution together with the deduced formulae furnish a new analytical pattern for the elasto-plastic analysis and strength design of a finitely-deformed, internal-pressurized, thick-walled spherical shell made of strain-hardening material.