Limit analysis of viscoplastic flows using an extended general algorithm sequentially: convergence analysis and validation

Abstract

 The paper presents the extension of a general algorithm to limit analysis of viscoplastic flow problems. Based on the concept of sequential limit analysis, the paper treats viscoplastic flow problems as a sequence of limit analysis problems. In the formulation, a general plane-strain problem involving incompressible rigid-viscoplastic materials was stated in the upper bound formulation. The von Mises yield criterion was employed to model the yield behavior. In each step of a deformation sequence, limit load was computed by using a combined smoothing and successive approximation (CSSA) algorithm. Especially, the extended CSSA algorithm was shown to be unconditionally convergent by utilizing the Hölder inequality. Finally, numerical and analytical studies of a thick-walled cylinder under internal pressure were performed to demonstrate the applicability and accuracy of the computational procedure presented here. It is found that the computed limit loads are rigorous upper bounds and agree very well with the analytical solutions.