A Review of  Elasto-Plastic Shakedown Analysis with Limited Plastic Deformations and Displacements

In classical plasticity the shakedown analysis is among the most important basic problems. The principles of shakedown analysis are counterparts to those of limit analysis in the sense that they provide static and kinematic approaches to the question of whether or not shakedown will occur for a body under multiple variable loading conditions. The principles of limit analysis provide static and kinematic approaches to the question of whether or not the plastic limit state will be reached by a body under proportional loading. The principles of shakedown analysis are, however, considerably more difficult to apply than those of limit analysis. In spite of these difficulties, shakedown analysis is a vital and developing topic in plasticity and a great number of applications have been made. At the application of the plastic analysis and design methods the control of the plastic behaviour of the structures is an important requirement. Since the shakedown analysis provide no information about the magnitude of the plastic deformations and residual displacements accumulated before the adaptation of the structure, therefore for their determination bounding theorems and approximate methods have been proposed.