On a numerical approach to shakedown analysis of structures

Abstract Two alternative ways of performing the shakedown analysis of structures subjected to variable repeated loads are presented. The first one enables one to check whether the structure shakes down (i.e. responds elastically after a few elastoplastic cycles) or not. Such a check is done by reproducing incrementally a critical cyclic load which corresponds to a cyclic repetition of piecewise-proportional load path that contains all the vertices of the variable load domain. The second approach enables one to find a safety factor for the limit of shakedown capability. The problem is one of convex or linear programming, depending on the kind of yield condition used. Numerical results presented in the paper show that the general purpose software that performs incremental elastoplastic calculations can be successfully used for shakedown analysis.