Shakedown analysis of elastic-plastic structures considering the effect of temperature on yield strength: theory, method and applications

According to the extended Melan's static theorem, theoretical and numerical aspects of the stress compensation method (SCM) are presented to perform shakedown analysis of elastic-plastic structures considering the effect of temperature on yield strength. Instead of constructing a mathematical programming formulation, this developed method consists of the two-level iterative scheme. The inner loop constructs the statically admissible self-equilibrating stress field, while the outer loop evaluates a sequence of decreasing load factors to approach to the shakedown limit multiplier. The yield strength considering temperature effect is updated based on the current temperature at each outer iteration, and the yield conditions are checked at all Gauss points. The numerical procedure is well incorporated into ABAQUS finite element code and used for calculating the shakedown limits of structures considering yield strengths as different functions of temperature under complex thermomechanical loading system. The method is validated by some plane stress and axisymmetric numerical examples with theoretical and numerical solutions, and subsequently applied to solve the practical shakedown problem of a pipe with oblique nozzle. The results demonstrate that the developed method is stable, accurate and efficient, and can effectively evaluate the shakedown limit of an elastic-plastic structure where the yield strength of material varies with temperature.