A dual algorithm for shakedown analysis of plate bending

Abstract

Abstract In this paper, the duality between the lower and the upper bound shakedown analyses of plate bending is presented. Based on the duality theory, the shakedown load multiplier formulated by static theorem is proved actually to be the dual form of the shakedown load multiplier formulated by kinematic theorem. A dual algorithm based upon the von Mises yield criterion and a non‐linear optimization procedure is then developed to compute simultaneously both the upper and lower bounds of the plastic collapse limit and the shakedown limit. The DKQ plate bending element is used to discrete the problem field. Numerical examples are presented to show the excellent convergence and accuracy of solutions obtained by the present method. Copyright © 2011 John Wiley & Sons, Ltd.