Thermomechanical shakedown analysis considering temperature-dependent yield stress based on the primal-dual eigenstress-driven method

Many industrial structural components are loaded repeatedly in high-temperature environments. The shakedown limit under variable thermomechanical loads is a critical factor in thermomechanical elastoplastic structure design assessment. The shakedown limit is weakened due to material strength reduction at high-temperature conditions. This paper develops an efficient shakedown analysis Primal-dual Eigenstress-driven Method(PEM) algorithm for temperature-dependent yield condition, which overcomes the obstacle of the original PEM method [1] which can only deal with constant material properties. The developed temperature-dependent PEM algorithm proposes a two-level iteration algorithm to determine the shakedown limit and the time-independent residual stress field. At the inner level the theoretical framework tailored to the temperature dependence problem is derived to solve the Karush-Kuhn-Tucker (KKT) conditions of the extended temperature-dependent shakedown theorem and establish an increment algorithm for forming residual stress fields. Besides, the lower bound safe multipliers are computed to verify the residual stress field obtained by inner-level algorithm. At the outer level an efficient fixedpoint algorithm is applied to search the shakedown multiplier, where the corresponding updating strategy for the yield stress with temperature is nested. For practicability, the proposed algorithm is seamlessly integrated into commercial platform ANSYS, which is applicable to industrial structures. Four numerical examples from multiple perspectives show the effectiveness of developed PEM method.