Residual displacement analysis of structures at shakedown

Abstract

The residual displacements developing in the shakedown process of an ideally elastic-plastic beam system under variable repeated loads vary non-monotonically. Therefore, it is important to determine the variation bounds. In this paper, the numerical methods, as well as the extremum energy principles, small displacement assumption and mathematical programming theory are used to develop the mathematical models of the analysis pr oblem. By solving the analysis problem, where the load locus is progr essively expanded, it is pos sible to determine the upper and the lower bounds of the residual displacements. It is assumed that non- monotonically varying residual displacem ents do not exceed these bounds. The application of the proposed load locus expansion met hod is illustrated by a case study of a multisupported beam. The results obtained in this investigation show that, at given repeated variable load, a struct ure can adapt to the changed conditions, but the values of the residual displacements may differ. Using the proposed method, it is possible to determine the bounds of residual displacements wit hout analysing the history of the loading.