Optimization of structures with unrestricted dynamic shakedown constraints

The unrestricted dynamic shakedown theory is here utilized with the aim to formulate different optimal design problems for structures mainly subjected to seismic loads. In particular, reference is made to plane frame structures constituted by elastic perfectly plastic material subjected to load combinations characterized by the presence of simultaneous fixed and seismic actions. The design problems, formulated on the ground of a statical approach, are devoted to structures with and without seismic protection devices, with special emphasis to seismic isolators. For the proposed design problem formulations different constraints are utilized; actually, for structures without protection devices the design problem must impose that the optimal structure remains elastic for fixed loads, shakes down for serviceability seismic conditions and prevents the instantaneous collapse for high seismic loads; while for structures provided with a given base isolation system, it is imposed that they remain elastic for fixed loads and shakes down for full seismic conditions. Appropriate modal analyses are utilized in order to take into account for both classically and non-classically damped structures. The seismic load history to be considered for shakedown and collapse limit admissibility conditions is a repeated seismic load one according with the unrestricted shakedown theory. The effected applications are related to plane steel frames.