Speeding up Nonlinear Time History Analysis of Base-Isolated Structures Using a Nonlinear Exponential Model
The nonlinear time history analysis of seismically base-isolated structures can require a significant computational effort when the behavior of each seismic isolator is predicted by adopting the widely used differential equation Bouc-Wen model. In this paper, a nonlinear exponential model, able to simulate the response of seismic isolation bearings within a relatively large displacements range, is described and adopted in order to reduce the numerical computations and speed up the nonlinear dynamic analysis. Compared to the Bouc-Wen model, the proposed one does not require the numerical solution of a nonlinear differential equation for each time step of the analysis. The seismic response of a 3d base-isolated structure with a lead rubber bearing system subjected to harmonic earthquake excitation is simulated by modeling each isolator using the proposed analytical model. The comparison of the numerical results and computational time with those obtained by modeling the lead rubber bearings using the Bouc-Wen model demonstrates the good accuracy of the proposed model and its capability to reduce significantly the computational effort of the analysis.
 F. Naeim and J. M. Kelly, Design of Seismic Isolated Structures: From Theory to Practice. New York: John Wiley & Sons, 1999.
 M. C. Constantinou, A. S. Whittaker, Y. Kalpakidis, D. M. Fenz and G. P. Warn, “Performance of seismic isolation hardware under service and seismic loading,” Technical Report MCEER-07-0012, State University of New York, Buffalo, 2007.
 S. Nagarajaiah, A. M. Reinhorn and M. C. Constantinou, “Nonlinear dynamic analysis of 3-D base-isolated structures,” Journal of Structural Engineering, vol. 117, no. 7, pp. 2035-2054, 1991.
 R. Bouc, “Modele mathematique d’hysteresis,” Acustica, vol. 24, pp. 16-25, 1971.
 Y. K. Wen, “Method for random vibration of hysteretic systems,” Journal of the Engineering Mechanics Division, vol. 102, no. EM2, pp 249-263, 1976.
 Y. K. Wen, “Equivalent linearization for hysteretic systems under random excitation,” Journal of Applied Mechanics, vol. 47, pp 150-154, 1980.
 M. C. Constantinou, A. Mokha and A. M. Reinhorn, “Teflon bearings in base isolation II: modeling,” Journal of Structural Engineering, vol. 116, no. 2, pp. 455-474, 1990.
 N. Vaiana, F. C. Filippou and G. Serino, “Nonlinear dynamic analysis of base-isolated structures using a partitioned solution approach and an exponential model,” Proceedings of the 19th International Conference on Earthquake and Structural Engineering, London, United Kingdom, 2017.
 M. C. Constantinou and M. A. Adnane, “Dynamics of soil-based-structure systems: evaluation of two models for yielding systems,” Report to the National Science Foundation, Drexel University, Philadelphia, 1987.
 H. Ozdemir, “Nonlinear transient dynamic analysis of yielding structures,” Ph.D. Thesis, University of California, Berkeley, 1976.
 H. H. Rosenbrock, “Some general implicit processes for numerical solution of differential equations,” Computing Journal, vol. 18, no. 1, pp. 50-64, 1964.