Dynamic Shakedown in Elastic-Plastic Bodies

The shakedown problem was first formulated for quasi-static actions, i.e., in absence of inertia forces. In the last 10 yr, with reference to dynamic processes, a more general formulation of the problem has been proposed, introducing the concept of dynamic shakedown. Two basic theorems have been stated: the first corresponds to the Bleich-Melan theorem concerning quasi-static actions; the second is a generalization of Koiter's kinematic theorem. The definition and the methods for determining the safety factor for dynamic shakedown are examined; in the case of periodic actions, linear and nonlinear programming procedures can be formulated. The influence of damping is also considered. The paper is a review of the basic work done in this field, for the most part in Italy, and may form the basis for further analysis.