\r\nnonlinear dynamic analysis of seismically base-isolated structures, a

\r\nMixed Explicit-Implicit time integration Method (MEIM) has been

\r\nproposed. Adopting the explicit conditionally stable central

\r\ndifference method to compute the nonlinear response of the base

\r\nisolation system, and the implicit unconditionally stable Newmark’s

\r\nconstant average acceleration method to determine the superstructure

\r\nlinear response, the proposed MEIM, which is conditionally stable

\r\ndue to the use of the central difference method, allows to avoid the

\r\niterative procedure generally required by conventional monolithic

\r\nsolution approaches within each time step of the analysis. The main

\r\naim of this paper is to investigate the stability and computational

\r\nefficiency of the MEIM when employed to perform the nonlinear

\r\ntime history analysis of base-isolated structures with sliding bearings.

\r\nIndeed, in this case, the critical time step could become smaller than

\r\nthe one used to define accurately the earthquake excitation due to the

\r\nvery high initial stiffness values of such devices. The numerical

\r\nresults obtained from nonlinear dynamic analyses of a base-isolated

\r\nstructure with a friction pendulum bearing system, performed by

\r\nusing the proposed MEIM, are compared to those obtained adopting a

\r\nconventional monolithic solution approach, i.e. the implicit

\r\nunconditionally stable Newmark’s constant acceleration method

\r\nemployed in conjunction with the iterative pseudo-force procedure.

\r\nAccording to the numerical results, in the presented numerical

\r\napplication, the MEIM does not have stability problems being the

\r\ncritical time step larger than the ground acceleration one despite of

\r\nthe high initial stiffness of the friction pendulum bearings. In

\r\naddition, compared to the conventional monolithic solution approach,

\r\nthe proposed algorithm preserves its computational efficiency even

\r\nwhen it is adopted to perform the nonlinear dynamic analysis using a

\r\nsmaller time step.","references":"[1] C. A. Felippa, K. C. Park and C. Farhat, \u201cPartitioned analysis of coupled\r\nmechanical systems,\u201d Computer Methods in Applied Mechanics and\r\nEngineering, vol. 190, pp. 3247-3270, 2001.\r\n[2] N. Vaiana, F. C. Filippou and G. Serino, \u201cNonlinear dynamic analysis of\r\nbase-isolated structures using a partitioned solution approach and an\r\nexponential model,\u201d Proceedings of the 19th International Conference\r\non Earthquake and Structural Engineering, London, United Kingdom,\r\n2017.\r\n[3] T. J. R. Hughes and W. K. Liu, \u201cImplicit-explicit finite elements in\r\ntransient analysis: implementation and numerical examples,\u201d Journal of\r\nApplied Mechanics, vol. 45, pp. 375-378, 1978.\r\n[4] T. Belytschko, H. J. Yen and R. Mullen, \u201cMixed methods for time\r\nintegration,\u201d Computer Methods in Applied Mechanics and Engineering,\r\nvol. 17, no. 18, pp. 259-275, 1979.\r\n[5] Y. S. Wu and P. Smolinski, \u201cA multi-time step integration algorithm for\r\nstructural dynamics based on the modified trapezoidal rule,\u201d Computer\r\nMethods in Applied Mechanics and Engineering, vol. 187, pp. 641-660,\r\n2000.\r\n[6] A. Combescure and A. Gravouil, \u201cA numerical scheme to couple\r\nsubdomains with different time-steps for predominantly linear transient\r\nanalysis,\u201d Computer Methods in Applied Mechanics and Engineering,\r\nvol. 191, pp. 1129-1157, 2002.\r\n[7] B. Herry, L. Di Valentin and A. Combescure, \u201cAn approach to the\r\nconnection between subdomains with non-matching meshes for transient\r\nmechanical analysis,\u201d International Journal for Numerical Methods in\r\nEngineering, vol. 55, pp. 973-1003, 2002.\r\n[8] S. Nagarajaiah, A. M. Reinhorn and M. C. Constantinou, \u201cNonlinear\r\ndynamic analysis of 3-D base-isolated structures,\u201d Journal of Structural\r\nEngineering, vol. 117, no. 7, pp. 2035-2054, 1991.\r\n[9] K. J. Bathe, Finite Element Procedures. Englewood Cliffs, NJ: Prentice\r\nHall, 1996.\r\n[10] B. D'Acunto, Computational Partial Differential Equations for\r\nEngineering Science. New York: Nova Science Publishers, 2012.\r\n[11] Y. J. Park, Y. K. Wen and A. H. S. Ang, \u201cRandom vibration of\r\nhysteretic systems under bi-directional ground motions,\u201d Earthquake\r\nEngineering and Structural Dynamics, vol. 14, pp. 543-557, 1986.\r\n[12] H. H. Rosenbrock, \u201cSome general implicit processes for numerical\r\nsolution of differential equations,\u201d Computing Journal, vol. 18, no. 1,\r\npp. 50-64, 1964.\r\n[13] E. L. Wilson, Three-Dimensional Static and Dynamic Analysis of\r\nStructures, 3rd ed. Berkeley, CA: Computers and Structures Inc, 2002.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 122, 2017"}