Shakedown design of structures under dynamic loading

The optimal (minimum volume) design of elastic plastic structures under static and dynamic loads is studied. The minimum volume design is reached accounting for different resistance limits: it is required that the optimal structure simultaneously satisfies the elastic shakedown limit and the instantaneous collapse limit, or alternatively the elastic and the plastic shakedown limits, adopting for each limit condition a suitably chosen load combination and some appropriate load amplifiers. The load combinations are characterized by the presence of fixed loads, quasi-statical cyclic loads and dynamic (seismic) loads. Reference is made to the Italian Code related to structural analysis and design. The Bree diagrams of the optimal structures are determined and plotted. The numerical applications are related to steel frames.