The determination of shakedown load or shakedown domain is an important task in structural design and integrity assessment. In this paper, a novel numerical procedure based on the Stress Compensation Method (SCM) is developed to perform shakedown analysis of engineering structures under multiple variable mechanical and thermal loads. By applying the compensation stress on the yield regions that occur at every load vertex of the prescribed loading domain to adjust the total stress to the yield surface and re-solving the equilibrium equations, the statically admissible residual stress field for static shakedown analysis is constructed. A robust and effective iteration control technique with some convergence parameters is used to check the change of the compensation stress in the inner loop and to update the shakedown load multiplier in the outer loop. For the purpose of general use, the method is implemented into ABAQUS platform. The shakedown problems for the Bree plate, a square plate with a central circular hole and a practical thick vessel with nozzles under some two-dimensional and three-dimensional loading domains are effectively solved and analyzed. Both alternating plasticity mechanism and ratcheting mechanism to determine the shakedown boundary of these structures are revealed. Numerical applications show that the proposed method has good numerical stability, high accuracy and efficiency, and is well suited for shakedown analysis of large-scale practical engineering structures.
- shakedown analysis
- stress compensation method
- cyclic loading
- multi-dimensional loading domain