Influence of protecting devices on the optimal design of elastic plastic structures

The paper concerns the minimum volume design of structures constituted by elastic perfectly plastic material. The relevant optimal design problem is formulated on the grounds of a statical approach and two different resistance limits are considered: in particular, it is required that the optimal structure satisfies the elastic shakedown limit and the instantaneous collapse limit, imposing for each different condition a suitably chosen safety factor. For sake of generality, the structure is thought as discretized into compatible finite elements and subjected to loads quasi-statically acting as well as to dynamic (seismic) loads. The effects of the dynamic actions are studied on the grounds of the dynamic features of the relevant structure and, with the aim of reducing such response, special base isolation systems or alternatively the presence of suitably disposed cross bracing elements are taken into account. The proposed treatment is referred to the most recent Italian Codes related to the structural analysis and design: all the actions are considered quasi static and suitably given as a combination of fixed loads and perfect cyclic loads, the latter depending on the dynamic properties of the given structure. Following the referenced Italian rules, two different formulations of the minimum volume design are developed: the first one is related to the search for the optimal structure without any seismic protecting device with simultaneous constraints on the elastic shakedown behaviour and on the instantaneous collapse, the second one is related to the search for the optimal elastic shakedown design of the structure equipped, alternatively, with two different protecting devices. The obtained optimal structures are compared in order to evaluate the effect of the different seismic protecting devices with regard to the computational effort, to the safety features of the structure and to the cost of the structure and of its maintenance. In order to verify the validity of the obtained optimal designs dynamic elastoplastic Monte Carlo simulations have been performed for the structure without any seismic protecting device subjected to simulated ground motions. The numerical applications are related to steel frames.