An algorithm for shakedown analysis with nonlinear yield functions

Abstract This paper is devoted to propose an algorithm to solve the discrete form of the shakedown analysis problem with a nonlinear yield function. Firstly, variational formulations for shakedown analysis of structures under variable loads are considered. Secondly, the corresponding discrete forms are briefly recalled. Then, the algorithm is derived by combining a Newton formula based on the discrete equality conditions with a return mapping procedure focusing plastic admissibility. The proposed numerical procedure can be applied to finite element models with large number of degrees of freedom because the algorithm is specially designed to take advantage of the structure of such models. The numerical procedure is applied to a square plate with a circular hole under variable traction in two directions, and the obtained approximations are compared with available results. Finally, a rectangular plate with two small holes is considered in both plane strain and plane stress conditions. All application use the Mises condition without linearization.

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