Stress Compensation Method for Shakedown Analysis and Its Engineering Applications

This paper introduces a recently proposed direct method, the so-called stress compensation method (SCM), for shakedown analysis of engineering structures under variable repeated mechanical and thermal loads. Instead of establishing the mathematical programming formulation, the SCM performs a two-level iterative procedure based on a series of linear finite element (FE) solutions. By adding an extra stress (named the compensation stress) to the yield regions which may occur at every load vertex of the given loading domain to adjust the total stress to the yield surface and re-solving the equilibrium equations, the residual stress field for static shakedown analysis is constructed. An effective and robust iteration control scheme is presented to check the change of the compensation stress in the inner loop and to update the shakedown load multiplier in the outer loop. The numerical scheme of this method is successfully implemented into the Abaqus platform, which makes it become a general utility tool for shakedown analysis of complex structures. Numerous examples related to pressure vessel and power plant engineering are presented to illustrate the performance of the method for shakedown analysis of large-scale engineering structures under multi-dimensional loading domain.