A Non-Cyclic Method for Plastic Shakedown Analysis

Shakedown is a cyclic phenomenon, and for its analysis it seems natural to employ a cyclic analysis method. Two problems are associated when this direct approach is used in finite element analysis. Firstly, the analysis typically needs to be stabilized over several cycles, and the analysis of each individual cycle may need a considerable amount of computing time. Secondly, even in cases where a stable cycle is known to exist, the finite element analysis can show a small continuing amount of strain accumulation. For elastic shakedown, non-cyclic analysis methods that use Melan’s theorem have been proposed. The present paper extends non-cyclic lower bound methods to the analysis of plastic shakedown. The proposed method is demonstrated with several example problems.