Shakedown analysis using the pp-adaptive finite element method and linear programming

In this paper, we investigate the use of an adaptive pp-version of the finite element method to perform shakedown analyses of 2D plane strain problems within the static approach. Moreover, efficient piecewise linearizations of the yield surfaces are carried out in a semi-adaptive fashion so that we need to solve the more tractable linear, rather than nonlinear, programming problems. State-of-the-art linear programming solvers, based on the very efficient interior point methodology, are used for solving the optimization problems. Various numerical examples are provided to compare the efficiency of the proposed approach with those of uniform and nonuniform pp-mesh models and nonlinear programming.