The majority of shakedown prediction methods available, amenable to practical engineering application, are based on Melan’s lower bound theorem and are capable only of predicting elastic shakedown. Structural discontinuities and the severe thermal transients typical of nuclear power plant operating scenarios may lead to local, elastically bounded, alternating plasticity. Consequently, Melan’s theorem is not satisfied, often leading to cycle-by-cycle finite element analysis which for large problems may be impractical. In contrast, direct methods lead to reduced data storage and analysis time. Direct methods capable of predicting alternating plasticity are now available, developed to a level applicable to the complex thermo-mechanical loading experienced in real structures. This paper compares the stress-strain response and solution times obtained from the Fourier based direct cyclic approach formulated within the finite element code Abaqus with the cycle-by-cycle method and a superposition implementation of Melan’s theorem. The approaches are applied to the Bree problem and a more complex case representative of a real plant load scenario. Automated application of the direct cyclic approach has resulted in the rapid generation of interaction diagrams, providing the pressure vessel designer with a tool to assess the shakedown sensitivity of structures to changes in the design domain.

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