For a cyclically loaded structure made of elastic-plastic material it is considered elastic shakedown if plastic straining occurs in the first few cycles and the sequent response is wholly elastic. In this paper the finite element method is used to develop upper and lower bounds limits for the elastic shakedown of structures under periodic loading conditions. Linear methods using elastic compensation approach and the residual stress method derived from Melan’s theorem are used to generate the lower bound limit for the shakedown load while the upper bound is found through a method derived from Koiter’s theorem. Furthermore the results are compared with cycle-by-cycle method based on nonlinear material properties.

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