Simulation of Dynamic Behavior of Seismic Isolators Using a Parallel Elasto-Plastic Model

In this paper, a one-dimensional (1d) Parallel Elasto-
Plastic Model (PEPM), able to simulate the uniaxial dynamic
behavior of seismic isolators having a continuously decreasing
tangent stiffness with increasing displacement, is presented. The
parallel modeling concept is applied to discretize the continuously
decreasing tangent stiffness function, thus allowing to simulate the
dynamic behavior of seismic isolation bearings by putting linear
elastic and nonlinear elastic-perfectly plastic elements in parallel. The
mathematical model has been validated by comparing the
experimental force-displacement hysteresis loops, obtained testing a
helical wire rope isolator and a recycled rubber-fiber reinforced
bearing, with those predicted numerically. Good agreement between
the simulated and experimental results shows that the proposed
model can be an effective numerical tool to predict the forcedisplacement
relationship of seismic isolators within relatively large
displacements. Compared to the widely used Bouc-Wen model, the
proposed one allows to avoid the numerical solution of a first order
ordinary nonlinear differential equation for each time step of a
nonlinear time history analysis, thus reducing the computation effort,
and requires the evaluation of only three model parameters from
experimental tests, namely the initial tangent stiffness, the asymptotic
tangent stiffness, and a parameter defining the transition from the
initial to the asymptotic tangent stiffness.

Authors:

• Nicolò Vaiana
• Giorgio Serino

Keywords:

• Base isolation
• earthquake engineering
• parallel elasto-plastic model
• seismic isolators
• softening hysteresis loops.

References:

[1] J. M. Kelly, Earthquake-resistant Design with Rubber. London:
Springer-Verlag, 1997.
[2] F. Naeim and J. M. Kelly, Design of Seismic Isolated Structures: From
Theory to Practice. New York: John Wiley & Sons, 1999.
[3] 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.
[4] G. F. Demetriades, M. C. Constantinou and A. M. Reinhorn, “Study of
wire rope systems for seismic protection of equipment in buildings,”
Engineering Structures, vol. 15, no. 5, pp. 321-334, 1993.
[5] M. Spizzuoco, V. Quaglini, A. Calabrese, G. Serino and C. Zambrano,
“Study of wire rope devices for improving the re-centering capability of
base isolated buildings,” Structural Control and Health Monitoring, to
be published.
[6] 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.
[7] A. Mroz, “Non-associated flow rules in plasticity,” Journal de
Mecanique, vol. 2, pp. 21-42, 1963.
[8] D. R. J. Owen, A. Prakash and O. C. Zienkiewicz, “Finite element
analysis of non-linear composite materials by use of overlay systems,”
Computer and Structures, vol. 4, pp. 1251-1267, 1974.
[9] G. N. Pande, D. R. J. Owen and O. C. Zienkiewicz, “Overlay models in
time-dependent nonlinear material analysis,” Computer and Structures,
vol. 7, pp. 435-443, 1977.
[10] R. B. Nelson and A. Dorfmann, “Parallel elastoplastic models of
inelastic material behavior,” Journal of Engineering Mechanics ASCE,
vol. 121, no. 10, pp. 1089-1097, 1995.
[11] 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.
[12] S. Pagano, M. Russo, S. Strano and M. Terzo, “A mixed approach for
the control of a testing equipment employed for earthquake isolation
systems,” Journal of Mechanical Engineering Science, vol. 228, no. 2,
pp. 246-261, 2014. [13] M. Spizzuoco, A. Calabrese and G. Serino, “Innovative low-cost
recycled rubber-fiber reinforced isolator: experimental tests and finite
element analyses,” Engineering Structures, vol. 76, pp. 99-111, 2014.