Simple Direct Method for Shakedown Analysis of Structures

Abstract

This paper presents a simple direct method for the straightforward determination of steady-state solutions in shakedown analysis of structures subjected to sustained and cyclic loadings. The method is based upon the observation that the difficulty with direct determination of the steady-state solution is the existence of the unknown residual-strain field. However, such a residual-strain field does not affect the incremental analysis from one extreme state to the other extreme state, and thus the incremental solution can be found by solving a regular elastic-plastic problem. Then the steady-state solution can be obtained by an analysis of the steady state with the help of the incremental solution. The two-bar structure and the tube and hollow-sphere problems are solved as examples that show the feasibility and efficiency of this approach.