Shakedown analysis of bending plate by a dual algorithm

Abstract

ABSTRACT:

In this paper, the duality between the lower and the upper bound shakedown analyses of bending plate 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 bending plate 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.

Key Words: Numerical method; bending plate; limit analysis; shakedown analysis; duality; non-linear programming