Ensuring sufficient safety against shakedown or ratchet is a fundamental requirement of pressure vessel design. Determining the shakedown or ratchet boundary can however prove difficult when using a full elastic plastic finite element analysis and a number of direct methods have been proposed that overcome the difficulties associated with shakedown or ratchet boundary evaluation. Here a new direct lower bound shakedown method, which can be extended to a ratchet method, is proposed. The method maintains a constitutively accurate description of the assumed material response through the use of non-smooth multi yield surface plasticity models. The proposed shakedown method can consider arbitrary load cases and may be solved in a single analysis step in a standard finite element analysis with a user-programed non-smooth multi yield surface plasticity model. It is demonstrated that by maintaining a constitutively accurate description of the plastic strains the method is able to calculate strict lower bound shakedown boundaries. The resulting boundary is shown to give excellent agreement with the upper and lower bound linear matching method.

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