Shakedown limit of elbow pipe under coupled cyclic thermal-mechanical loading based on the LMM

In this paper, the linear matching method (LMM) is used to study the shakedown limit of elbow pipes under coupled cyclic mechanical-thermal load. Firstly, the thermal stress analyses of elbow pipes under constant in-ternal pressure and cyclic temperature load are investigated. Further, the shakedown limits of the elbow pipes are calculated using the LMM. For the verification purposes, step-by-step inelastic analyses are performed, showing different structure responses under different loading conditions. All the obtained results indicate that the LMM is able to simulate large range of coupled cyclic mechanical-thermal loading conditions with high computational efficiency, and provide shakedown limit with high accuracy. In addition, the effects of bend angles, mean radius to wall thickness ratio (r/t) and five load conditions on the shakedown behavior are also presented.