Efficient Shakedown Solutions in Complex Loading Domains

Abstract

To estimate the life of a structure, or a component, which are subjected to a cyclic loading history, the structural engineer must be able to provide safety margins. This is only possible by performing a shakedown analysis which belongs to the class of direct methods. Most of the existing numerical procedures addressing a shakedown analysis are based on the two theorems of plasticity and are formulated within the framework of mathematical programming. A different approach has recently appeared in the literature. It is rather more physical than mathematical as it exploits the physics of the asymptotic steady state cycle. It has been called RSDM-S and has its roots in a previously published procedure (RSDM) which assumes the decomposition of the residual stresses into Fourier series whose coefficients are found by iterations. RSDM-S is a descending sequence of loading factors which stops when only the constant term of the series remains. The method may be implemented in any existing FE code. It is used herein to establish shakedown boundaries for two-dimensional general loadings consisting of mechanical or thermomechanical loads.