Application of h-adaptive FEM and Zarkaʹs approach to analysis of shakedown problems

The Zarka shakedown approach and the h-adaptive finite element method are applied to evaluate residual stresses resulting from arbitrary cyclic loading. Two error indicators are used to refine the mesh: the explicit residual one which controls accuracy of the momentum balance and the interpolation error indicator which controls approximation of the modified back stresses. Validation tests performed for the Zarka method of simplified shakedown analysis suggest that such an approach may be used to obtain a quick estimate of residual states with the error acceptable for engineering purposes. Thus, it has been applied to compute residual stresses arising from service load in railroad rails