Error estimation of the analytical method for calculating the elastic-plastic state of thick-walled axisymmetric shells with linear hardening of the material

Abstract

The problem of calculating thick-walled axisymmetric shells under conditions of elastic-plastic strain is considered. Known analytical solutions to such problems do not take into account the physical and geometric nonlinearity, as well as the compressibility of the material. The purpose of the work was to evaluate the errors of the analytical method for calculating the elastic-plastic state of a thick-walled pipe and a sphere loaded with internal pressure, which arise due to the adoption of simplifying hypotheses and assumptions. Solutions of problems on the elastic-plastic state of a thick-walled pipe and sphere are considered by two methods: the analytical method and the numerical-analytical method of variable elasticity parameters. The hypotheses and assumptions adopted by these methods are described and the results obtained are compared. According to the results obtained, the use of analytical formulas under certain conditions can lead to significant errors that depend on the wall thickness and the degree of hardening of the material.