Shakedown limits for a general yield condition: implementation and application for a Von Mises yield condition

Abstract

The paper describes the generalisation of the programming method for the determination of optimal upper bound shakedown limits for an elastic/perfectly plastic solid given by Ponter and Carter (1997). The method is based on similar principles to the `Elastic Compensation' method which has been used in design calculations for a number of years. A convergence proof for a general yield surface is given based upon the convexity conditions derived in the accompanying paper on limit analysis (Ponter and Engelhardt, 2000). The method has been implemented in the commercial code, ABAQUS, using the user defined procedures. A sequence of examples for a Von Mises yield condition demonstates the ability of the method to produce stable converged solutions for problems involving both cyclic load and temperature. Two unconventional shakedown problems are then solved. The first involves the determination of a minimum high temperature creep rupture stress, defined as a temperature varying yield stress, for a problem with a defined load and temperature history and low temperature yield stress. Such problems occur in high temperature structural life assessment methods. The second involves the evaluation of the loads corresponding to a prescribed average maximum creep rate for the creep rapid cycle solution for the Bailey-Orowan creep constitutive relationship. These examples demonstrate the flexibility of the method in producing a range of performance indicators for structures subjected to complex cyclic loading