Shakedown boundary of limited ductility structures accounting for buckling

A formulation devoted to the determination of the borderline between the elastic/plastic shakedown domains and the incremental/instantaneous collapse zones of the Bree diagram for elastic perfectly plastic structures is proposed. In particular, reference will be made to truss structures and the actions will be given as a combination of mechanical fixed loads and mechanical perfect cyclic loads. The borderline between the above cited domains is determined by solving a search problem consisting into a sequence of maximum fixed load multiplier problems for assigned values of the cyclic load multiplier. In order to take into account suitable limits related to the structure ductility features, suitable bounds on chosen measures of the plastic strains occurring at the end of the transient phase of the structural response, as well as appropriate constraints related to the element buckling, are introduced. For computational purposes an appropriate solution procedure is utilized. A numerical example concludes the paper.