PSI - Issue 44

1478 Gaspar Auad et al. / Procedia Structural Integrity 44 (2023) 1474–1481 Gaspar Auad / Structural Integrity Procedia 00 (2022) 000–000 5 The impact force (+) is developed if the lateral displacement of the isolator exceeds the lateral capacity of the bearing (i.e., ‖ (1: 2)‖ ≥ - ). Assuming that the components of the impact force are normal to the contact plane, this force can be computed as: (+) = + [ (9:.);E] ‖ (9:.)‖ (11) In this study, the impact magnitude + is estimated employing a Kelvin-Voigt model (i.e., spring dashpot element) (Anagnostopoulos, 2004) as follows: + = m + (‖ (1: 2)‖ − - ) + + o ̇(1: 2)o, (‖ (1: 2)‖ − - ) ≥ 0 0, ℎ t (12) 2.4. Action-deformation The projection of the restoring force into the global coordinate system ℑ 9 , solidary with the ground, is calculated as: = W 2 2 X / = D O E = (13) in which = ? ( 0) ; (1) A is the vector containing the forces transmitted by the bearing projected into the global coordinate system. 3. Validation of the physical model using a Finite Element Model In this section, a Finite Element Model (FEM) of a variable curvature frictional isolator is developed in the Finite Element Analysis (FEA) ANSYS software (Lee (2018)) to validate the constitutive equations presented in Section 2. The studied isolator has the following geometric parameters: = 0.56 m, = 0.14 m, and - = 0.40 m. Note that the radius of curvature of the device at undeformed configuration is equal to E = . / = 2.25 m (i.e., the initial period of the isolator during the sliding phase is equal to ) = 3 sec). The dimensions of the isolator are presented in Fig. 3(a) and the deformed configuration of the FEM is shown in Fig. 3(b). A friction coefficient of 5 = 0.07 characterized the contact between the articulated slider and the sliding surface; all the other contacts were defined with a friction coefficient of 5 = 0.10 . In the analyses of the FEM, a constant vertical load of 853 kN (or a mass of 86,952 kg) was applied to the articulated slider.

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Fig. 3. (a) Geometry of the FEM; (b) FEM deformed configuration; (c) Static hysteretic loop.