An exact elasto-plastic solution for a closed-end thick-walled cylinder of elastic linear-hardening material with large strains

Abstract

An exact elasto-plastic analytical solution for a large-strained internal-pressurized thick-walled cylinder 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 and the yield criterion of von Mises. Being applicable for both the linear-elastic response and the plastic strain-hardening stages of a large-strained closed-end thick-walled cylinder, the present solution can uniformly represent the whole expanding process of the cylinder from its initial yield at the inner surface to its full yield over the wall up to its ultimate bursting with an 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 large-strained cylinder deduced in this paper are of value for the strength design of a strain-hardening material cylinder. The present exact solution together with the deduced formulae furnish a new analytical pattern for the elasto-plastic analysis and strength design of a large-strained, internal-pressurized, closed-end, thick-walled cylinder made of strain-hardening material.