Static condensation procedure of finite element models for fast non-linear time history analyses of base-isolated structures

Non-linear time history analysis represents the most realistic simulation of the effects of selected seismic events on a structural system. Especially when natural recorded signals are applied, it is possible to evaluate maximum values of internal forces for all elements, as well as if the studied structure had been subjected to the considered earthquakes. On the other hand, Finite Element Models of building structures in real application may have a large number of elements, and consequently higher and higher computational times can be reached. In addition, when seismically base-isolated structures are implemented, the isolation system is generally characterized by non-linear constitutive behaviors, so that convergence failure can occur. In this work a static condensation procedure is proposed for building structures, in order to define a Multi Degree of Freedom system, with same dynamic properties of the Finite Element Model of the considered base-isolated structural system. Through the fast direct integration of the lumped-mass model, it is possible to define a number of time instants, which corresponds to the worst cases for the overall structure; thus, static deformed shapes can be applied to the Finite Element Model, in order to evaluate internal forces for all elements. Results have shown a fairly good agreement between the outcomes of the proposed procedure and the envelope of internal forces returned by the non-linear time history analysis of the full Finite Element Model.