Keywords: base isolation, geometric nonlinearity.

Line elements such as viscous dampers and springs are used to control the displacements at the isolation interface of a base isolation system. These elements are designed to accommodate displacements, which are comparable to their length (typically 30% to 50% of the initial length). For such large displacements the resulting variation in the direction of the element is significant and introduces an additional geometrical nonlinearity to the already nonlinear behaviour of the isolation system. Moreover, the locus of the movement of the axis of these elements is of particular importance during a dynamic excitation as it imposes constructional constraints for the infrastructure of the isolation system.

The well-known base isolation code 3D-BASIS [1] and its extensions 3D-BASIS-ME [2] and 3D-BASIS-TABS [3] use geometrically linear spring and dash-pot elements, which in general are inadequate to treat the above mentioned conditions. The force of these elements depends only on the displacement and the velocity of the node that is connected to the superstructure (1-node elements). In this work the geometrically nonlinear spring and dash-pot elements are formulated and incorporated into the 3D-BASIS-ME code as 2-node elements. When the superstructure is displaced, in the event of the earthquake, the length and the direction of the elements are modified in accordance with the locus of the superstructure node (base node) and the infrastructure node (ground node). The dynamic equilibrium of the isolation system is established in the deformed configuration of the elements. In addition the critical geometrical parameters related to the feasibility of the design are monitored and displayed appropriately. The proposed modifications more accurately establish the nonlinear response of base isolation systems using spring and dash-pot elements, while the corresponding geometrical and constructional constraints are checked in a systematic way. A concentrated mass connected to two node spring and dash-pot elements that moves along the two horizontal directions due to a specific earthquake accelerogram is used for the verification of the introduced modifications. The response of this model that is established using the modified 3D-BASIS-ME program is verified by solving the non-linear differential equations of motion numerically using a stiff integration algorithm [4].

As a case study, a realistic model of the isolation system of a statue is presented that includes four flat sliders combined with two viscoelastic dampers. The isolated structure is subjected to the ground acceleration of 1.5 times the Kocaeli 1999 earthquake Two different configurations of the isolation system are examined, the first includes unlubricated PTFE sliders while the second includes lubricated PTFE sliders with a significantly smaller coefficient of friction. The examined case studies indicate that the geometrically nonlinear behaviour of the springs and dash-pot elements (2-node elements) that are used in seismic isolation systems modifies the dynamic response of the system. This modification is more drastic when these elements undertake a significant part of the total seismic force. For the case of the realistic model of an isolated statue both the displacements and the accelerations increased for decreasing length of the supplemental viscoelastic dampers. Thus, if the analysis was based on the geometrically linear elements that are commonly used in base isolation codes such as 3D-BASIS-ME the design of the isolation system would be unconservative. Moreover, monitoring the movement of the body of the dampers defines a region at the isolation interface that should be free from obstacles, which constitutes an additional constructional constraint for the design of the infrastructure.

1

S. Nagarajaiah, A.M. Reinhorn, M.C. Constantinou, "Nonlinear Dynamic Analysis of Three Dimensional Base-Isolated Structures (3D-BASIS)", Report No. NCEER 91-0005, National Center for Earthquake Engineering Research, State University of New York, Buffalo, NY, 1991.

2

P. Tsopelas, M.C. Constantinou, A.M. Reinhorn, "3D-BASIS-ME: Computer Program for Nonlinear Dynamic Analysis of Seismically Isolated Single and Multiple Structures and Liquid Storage Tanks", Report No. NCEER 94-0010, National Center for Earthquake Engineering Research, State University of New York, Buffalo, NY, 1994.

3

A.M. Reinhorn, S. Nagarajaiah, M.C. Constantinou, P. Tsopelas, Li Renfen, "3D-BASIS-TABS: Version 2.0 Computer Program for Nonlinear Dynamic Analysis of Three Dimensional Base Isolated Structures", Report No. NCEER 94-0018, National Center for Earthquake Engineering Research, State University of New York, Buffalo, NY, 1994.

4

K. Radhakrishnan, A.C. Hindmarsh, "Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations", LLNL report UCRL-ID-113855, December 1993.

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