Residual stresses calculation in a thermoelastoplastic torus after cooling

Abstract

The present study deals with the boundary value problems under toroidal symmetry conditions. The residual stresses after cooling (unloading) in an elasto-plastic material are calculated. Throughout the paper the conventional Prandtl-Reuss model is generalised and used. The solution to the problem of hollow torus cooling under a temperature gradient is obtained and discussed. Analytical solutions, as an approximation of complete boundary value problem, describing residual deformations and stresses under conditions of toroidal symmetry are constructed and discussed.