Direct determination of limiting cycle during cyclic loading

Abstract

A general framework for the modelling of mechanical behavior of structures has been recently proposed by J. Zarka et al. Its essential feature consists of the introduction of a group of internal parameters which characterize the local inelastic mechanisms of the structure, and a group of transformed internal parameters which are linearly linked to the previous ones through a symmetrical non-negative matrix. With this approach, the treatment of the local plastic yield conditions can be made easily from simple elastic analysis. The problem of the determination of the limit state in the case of cyclic loading is then reduced to the determination of the asymptotic values of the transformed internal parameters. In most cases, this is done by simple geometrical constructions. As an example, we will present a simple structure made of two connected elastoplastic workhardening cylinders of different radius, subjected to cyclic imposed displacement at one end, in order to show the efficiency of the method.