Nonlinear Dynamic Analysis of Base-Isolated Structures Using a Partitioned Solution Approach and an Exponential Model
The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can require a significant computational effort. In order to reduce numerical computations, a partitioned solution method and a one dimensional nonlinear analytical model are presented in this paper. A partitioned solution approach can be easily applied to base-isolated structures in which the base isolation system is much more flexible than the superstructure. Thus, in this work, the explicit conditionally stable central difference method is used to evaluate the base isolation system nonlinear response and the implicit unconditionally stable Newmark’s constant average acceleration method is adopted to predict the superstructure linear response with the benefit in avoiding iterations in each time step of a nonlinear dynamic analysis. The proposed mathematical model is able to simulate the dynamic behavior of seismic isolators without requiring the solution of a nonlinear differential equation, as in the case of widely used differential equation model. The proposed mixed explicit-implicit time integration method and nonlinear exponential model are adopted to analyze a three dimensional seismically isolated structure with a lead rubber bearing system subjected to earthquake excitation. The numerical results show the good accuracy and the significant computational efficiency of the proposed solution approach and analytical model compared to the conventional solution method and mathematical model adopted in this work. Furthermore, the low stiffness value of the base isolation system with lead rubber bearings allows to have a critical time step considerably larger than the imposed ground acceleration time step, thus avoiding stability problems in the proposed mixed method.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1128857Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 976
 J. M. Kelly, Earthquake-resistant Design with Rubber. London: Springer-Verlag, 1997.
 F. Naeim and J. M. Kelly, Design of Seismic Isolated Structures: From Theory to Practice. New York: John Wiley & Sons, 1999.
 E. L. Wilson, Three-Dimensional Static and Dynamic Analysis of Structures, 3rd ed. Berkeley, CA: Computers and Structures Inc, 2002.
 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.
 M. Kikuchi and I. D. Aiken, “An analytical hysteresis model for elastomeric seismic isolation bearings,” Earthquake Engineering and Structural Dynamics, vol. 26, pp. 215-231, 1997.
 J. S. Hwang, J. D. Wu, T. C. Pan and G. Yang, “A mathematical hysteretic model for elastomeric isolation bearings,” Earthquake Engineering and Structural Dynamics, vol. 31, pp. 771-789, 2002.
 C. S. Tsai, T. C. Chiang, B. J. Chen and S. B. Lin, “An advanced analytical model for high damping rubber bearings,” Earthquake Engineering and Structural Dynamics, vol. 32, pp. 1373-1387, 2003.
 D. Way and V. Jeng, “N-Pad, A three-dimensional program for the analysis of base isolated structures,” Proceedings of American Society of Civil Engineers Structures Congress, San Francisco, 1989.
 W. H. Huang, G. L. Fenves, A. S. Whittaker and S. A. Mahin, “Characterization of seismic isolation bearings from bidirectional testing,” Proceedings of the 12th World Conference on Earthquake Engineering, Auckland, New Zealand, 2000.
 W. H. Huang, “Bi-directional testing, modeling, and system response of seismically isolated bridges,” Ph.D. Thesis, University of California, Berkeley, 2002.
 P. C. Tsopelas, P. C. Roussis, M. C. Constantinou, R. Buchanan and A. M. Reinhorn, “3D-BASIS-ME-MB: Computer program for nonlinear dynamic analysis of seismically isolated structures,” Technical Report MCEER-05-0009, State University of New York, Buffalo, 2005.
 Y. J. Park, Y. K. Wen and A. H. S. Ang, “Random vibration of hysteretic systems under bi-directional ground motions,” Earthquake Engineering and Structural Dynamics, vol. 14, pp. 543-557, 1986.
 C. A. Felippa, K. C. Park and C. Farhat, “Partitioned analysis of coupled mechanical systems,” Computer Methods in Applied Mechanics and Engineering, vol. 190, pp. 3247-3270, 2001.
 T. J. R. Hughes and W. K. Liu, “Implicit-explicit finite elements in transient analysis: implementation and numerical examples,” Journal of Applied Mechanics, vol. 45, pp. 375-378, 1978.
 T. Belytschko, H. J. Yen and R. Mullen, “Mixed methods for time integration,” Computer Methods in Applied Mechanics and Engineering, vol. 17, no. 18, pp. 259-275, 1979.
 Y. S. Wu and P. Smolinski, “A multi-time step integration algorithm for structural dynamics based on the modified trapezoidal rule,” Computer Methods in Applied Mechanics and Engineering, vol. 187, pp. 641-660, 2000.
 A. Combescure and A. Gravouil, “A numerical scheme to couple subdomains with different time-steps for predominantly linear transient analysis,” Computer Methods in Applied Mechanics and Engineering, vol. 191, pp. 1129-1157, 2002.
 B. Herry, L. Di Valentin and A. Combescure, “An approach to the connection between subdomains with non-matching meshes for transient mechanical analysis,” International Journal for Numerical Methods in Engineering, vol. 55, pp. 973-1003, 2002.
 F. Naeim, The Seismic Design Handbook, 2nd ed. New York: Springer Science+Business Media, 2001.
 H. H. Rosenbrock, “Some general implicit processes for numerical solution of differential equations,” Computing Journal, vol. 18, no. 1, pp. 50-64, 1964.