A numerical procedure for the shakedown analysis of structures under cyclic thermomechanical loading

Determining safety margins for a structure or a component against excessive inelastic deformations is an important issue for engineering design. Direct methods and particularly shakedown analysis constitute a convenient tool towards this direction. Most of the developed approaches in shakedown analysis are based on optimization algorithms. In this paper, a procedure for the shakedown analysis of structures under thermo-mechanical loads is presented. The approach makes use of the recently published Residual Stress Decomposition Method (RSDM) which assumes the decomposition of the residual stress field into Fourier series with respect to time. Starting from a high loading factor, the shakedown limit is estimated through an iterative procedure that updates the Fourier coefficients, reducing at the same time this loading factor until the only remaining term of the Fourier series is the constant term. The method is formulated within the finite element method and is applied to two-dimensional structures under thermal and mechanical cyclic loading.