Commenced in January 2007
Paper Count: 31107
Nonlinear Dynamic Analysis of Base-Isolated Structures Using a Mixed Integration Method: Stability Aspects and Computational Efficiency
Abstract:In order to reduce numerical computations in the nonlinear dynamic analysis of seismically base-isolated structures, a Mixed Explicit-Implicit time integration Method (MEIM) has been proposed. Adopting the explicit conditionally stable central difference method to compute the nonlinear response of the base isolation system, and the implicit unconditionally stable Newmark’s constant average acceleration method to determine the superstructure linear response, the proposed MEIM, which is conditionally stable due to the use of the central difference method, allows to avoid the iterative procedure generally required by conventional monolithic solution approaches within each time step of the analysis. The main aim of this paper is to investigate the stability and computational efficiency of the MEIM when employed to perform the nonlinear time history analysis of base-isolated structures with sliding bearings. Indeed, in this case, the critical time step could become smaller than the one used to define accurately the earthquake excitation due to the very high initial stiffness values of such devices. The numerical results obtained from nonlinear dynamic analyses of a base-isolated structure with a friction pendulum bearing system, performed by using the proposed MEIM, are compared to those obtained adopting a conventional monolithic solution approach, i.e. the implicit unconditionally stable Newmark’s constant acceleration method employed in conjunction with the iterative pseudo-force procedure. According to the numerical results, in the presented numerical application, the MEIM does not have stability problems being the critical time step larger than the ground acceleration one despite of the high initial stiffness of the friction pendulum bearings. In addition, compared to the conventional monolithic solution approach, the proposed algorithm preserves its computational efficiency even when it is adopted to perform the nonlinear dynamic analysis using a smaller time step.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1128865Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 670
 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.
 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.
 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.
 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.
 K. J. Bathe, Finite Element Procedures. Englewood Cliffs, NJ: Prentice Hall, 1996.
 B. D'Acunto, Computational Partial Differential Equations for Engineering Science. New York: Nova Science Publishers, 2012.
 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.
 H. H. Rosenbrock, “Some general implicit processes for numerical solution of differential equations,” Computing Journal, vol. 18, no. 1, pp. 50-64, 1964.
 E. L. Wilson, Three-Dimensional Static and Dynamic Analysis of Structures, 3rd ed. Berkeley, CA: Computers and Structures Inc, 2002.