To extend the life of a structure, or a component, which is subjected to cyclic thermomechanical loading history, one has to provide safety margins against excessive inelastic deformations that may lead either to low-cycle fatigue or to ratcheting. Direct methods constitute a convenient tool toward this direction. Two direct methods that have been named residual stress decomposition method (RSDM) and residual stress decomposition method for shakedown (RSDM-S) have recently appeared in the literature. The first method may predict any cyclic elastoplastic state for a given cyclic loading history. The second method RSDM-S that is based upon RSDM is suggested for the shakedown analysis of structures. Both methods may be directly implemented in any finite-element (FE) code. An elastic perfectly plastic material with a von Mises yield surface has been assumed. In this work, through their application to structures that are used as benchmarks in the literature, both methods, applied together, prove their efficiency and capacity to determine shakedown boundaries and reveal unsafe conditions.

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