A unified viscoplastic boundary element approach for residual stress analysis of axisymmetric bodies under axisymmetric and non-axisymmetric loads

Abstract

This paper presents a unified viscoplastic boundary element method (BEM) for the residual stress analysis of axisymmetric structures subjected to axisymmetric and non-axisymmetric loads. By using the Fourier expansions of displacements, tractions and viscoplastic stresses including both the symmetric and anti-symmetric terms, the BEM formulations for an axisymmetric body subjected to axisymmetric and non-axisymmetric loads are developed. A unified viscoplastic model including the actual loading and unloading stress-strain material behaviour can be used to generate plasticity solutions in a simple manner when stationary conditions are reached, and at the other extreme, can reproduce standard creep phenomena. Hence, the viscoplastic BEM program developed in this paper for computing residual stresses of axisymmetric structures allows the treatment of a wide range of materially non-linear problems. The solution algorithm employed is relatively simple and possesses many advantages over the conventional computational procedures utilized in elastoplastic material analysis. Several examples of interest to residual stresses of axisymmetric structures due to axisymmetric and non-axisymmetric loads are presented.