Optimal shakedown design of base isolated structures

The optimal design problem of finite element discretized elastic perfectly plastic structures is studied. In particular, a minimum volume formulation is developed, based on a statical approach, and two different resistance limits are considered: the elastic shakedown limit and the instantaneous collapse limit, imposing for each a suitably chosen safety factor. The structure is thought as subjected to quasi-static loads as well as to dynamic actions. The dynamic features of the relevant structure are determined taking also into account an appropriate base isolation system in order to reduce the seismic effects. According with the Italian code related to the structural analysis and design, the actions are all considered quasi static and given as a combination of fixed loads and perfect cyclic loads, the latter depending on the dynamic properties of the given structure. Two different formulations of the minimum volume design are proposed: the first one is related to the optimal design of the structure without any base isolation system with constraints on the elastic shakedown behaviour and on the instantaneous collapse, the second one is related to the optimal elastic shakedown design of the isolated structure. The two obtained optimal structures are compared in order to evaluate the effect of the base isolation system with regard to the safety features of the structure and to the cost of the structure and of its maintenance. The numerical applications are related to a steel frame