Computational Methods , Seismic Protection , Hybrid Testing and Resilience in Earthquake Engineering

Origins and development of 3D-BASIS (3-Dimensional BASe Isolated Structures) was initially envisioned by the need for an efficient tool for nonlinear dynamic analysis of three-dimensional base isolated structures, particularly in solving the highly nonlinear bidirectional stick-slip hysteretic response of a collection of sliding isolation bearings and the resulting response of the superstructure, as this was not available at that time. The primary challenge was to solve the stick-slip behavior of friction bearings—modeled using a differential equation (Bouc-Wen Model) due to its efficiency in representing constant Coulomb friction or variable velocity depended friction by using a very small yield displacement during the stick phase resulting in very high tangential stiffness followed by a very small tangential stiffness during the sliding phase—and the resulting stiff differential equations. A challenge that is compounded when biaxial-friction is modeled, wherein even the traditional method of using Gear’s method to solve stiff differential equations breaks down—a problem that was vexing the research team at University at Buffalo trying to solve the problem at that time. The answer was the development of the novel pseudo-force solution algorithm along with a semi-implicit Runge-Kutta method to solve the difficult problem. The efficient solution procedure is needed primarily for the nonlinear isolation system consisting of (1) sliding and/or elastomeric bearings, (2) fluid dampers, (3) other energy dissipation devices, while the superstructure is represented by three dimensional superstructure model appropriately condensed (where only master nodes at the center of mass of the floor are retained). This chapter describes the origins, development of 3D-BASIS and its impact.