Direct methods Cyclic loading Fourier series Elastic shakedown Alternating plasticity

e be min adv lati a structure under a given loading is presented. The method exploits the cyclic nature of the expected repea rate be ctures pendent plastic strains, is quite complex. The reason of the com-plexity is the need to perform calculations over the lifetime history of the structure. The computation of the whole loading history, however, leads to lengthy and expensive incremental calculations, especially for structures with a high degree of redun-dancy. Therefore, it is very useful to develop computational approaches for straightforward calculations of the possible stabi-lized state under repeated thermo-mechanical loading. linear Newton-type algorithm [7] or the interior point methods (IPM) (e.g. [8–10]) are employed to estimate the shakedown load factor, with various applications to engineering problems (e.g. [11,12]). Recently Garcea and Leonetti [13], within the MP formulation, arc length techniques have been used instead of the IPMs. Much fewer approaches that are not based on MP also exist in the literature. One such approach uses internal variables each of which correspond to an inelastic mechanism (e.g. [14,15]). A more recent procedure, which has a better physical understanding, i