Abstract: 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.
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.
Abstract: 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.
Abstract: Analytical seismic response of multi-story building
supported on base isolation system is investigated under real
earthquake motion. The superstructure is idealized as a shear type
flexible building with lateral degree-of-freedom at each floor. The
force-deformation behaviour of the isolation system is modelled by
the bi-linear behaviour which can be effectively used to model all
isolation systems in practice. The governing equations of motion of
the isolated structural system are derived. The response of the system
is obtained numerically by step-by-method under three real recorded
earthquake motions and pulse motions associated in the near-fault
earthquake motion. The variation of the top floor acceleration, interstory
drift, base shear and bearing displacement of the isolated
building is studied under different initial stiffness of the bi-linear
isolation system. It was observed that the high initial stiffness of the
isolation system excites higher modes in base-isolated structure and
generate floor accelerations and story drift. Such behaviour of the
base-isolated building especially supported on sliding type of
isolation systems can be detrimental to sensitive equipment installed
in the building. On the other hand, the bearing displacement and base
shear found to reduce marginally with the increase of the initial
stiffness of the initial stiffness of the isolation system. Further, the
above behaviour of the base-isolated building was observed for
different parameters of the bearing (i.e. post-yield stiffness and
characteristic strength) and earthquake motions (i.e. real time history
as well as pulse type motion).