AN EXACT ELASTOPLASTIC SOLUTION FOR A THICK-WALLED SPHERICAL-SHELL OFELASTIC LINEAR-HARDENING MATERIAL WITH FINITE DEFORMATIONS

An exact elasto-plastic analytical solution for a finitely deformed in ternal-pressurized thick-walled spherical shell made of elastic linear -hardening material is derived in this paper. This solution is based o n 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 expandin g 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 incr ease of its operating pressure. It is shown that this exact solution i s of general characteristics, from which three specific solutions of p ractical interest can be obtained. The calculation formulae for the fu ll-yield pressure and the bursting pressure of the finitely deformed s pherical shell deduced in this paper are of value for the strength des ign of a strain-hardening material spherical shell. Being expressed in terms of Lagrangian variables, the explicit expressions of the soluti on are convenient for engineering use. The present exact solution toge ther with the deduced formulae furnish a new analytical pattern for th e elasto-plastic analysis and strength design of a finitely-deformed, internal-pressurized, thick-walled spherical shell made of strain-hard ening material.