## 2 Numerical Analysis
### Modelling of Structures  
The FEA software PERFORM-3D (2018, ACE-Hellas, Athens, Greece) was used to simulate the testing models (the isolation one and the non-isolated one) considering the elasto-plastic mechanics [28]. The structural model was first established with boundary conditions, followed by the employment of elasto-plastic concrete and steel material model. Subsequently, the seismic waves were inputted into the model for analyzing the mechanical performance of both isolation structure and non-isolated one. The details of each part are described as follows. Figure 5 shows the structural model of the simulated isolation structure and a non-isolated one. The dimensions of the buildings are the same to those shown in Figure 3. The bar elements are selected in the FEA model. The fiber model (column, inelastic fiber section) and plastic hinge model (moment hinge, curvature type) are respectively used as the material model for simulating the plastic area in the columns and beams. The plastic hinge adopts the moment-curvature model to calculate the component yield stress, moment and curvature when the component reaches its maximum bearing \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Length** & **Elastic Modulus** & **Stiffness** & **Acceleration** & **Time** & **Displacement** & **Mass** \\ \hline (mm) & MPa & N/mm & gal & s & (mm) & Kg \\ \(1/5\) & 1 & 1/5 & 2 & 1/3 & 1/5 & 1/98 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Similarity ratios of the model structure. Figure 4: Cross-section and reinforcements of columns and beams of the isolation and non-isolated models (unit: mm): (**a**) Bottom column of isolation model; (**b**) bottom column of non-isolated model; (**c**) columns in the 2–7 layers; (**d**) The frame beam of the isolation layer and coupled beam; (**e**) beams in the 2–7 layers. capacity. The 3D fiber elements with eight steel fiber elements and 36 concrete fiber elements are used in the columns; this meshing is sufficient to cause the stable stress-strain analysis results. Only the elastic deformation of the isolation rubber bearing without considering its plastic deformation in the vertical direction is considered. This is reasonable as the earthquake excitations inputted to the model in this study only have the horizontal component. The strength loss and stiffness hardening caused by the shear deformation in the horizontal direction are ignored. The horizontal stress-strain property is not influenced by the stress and strain in the vertical direction. The LNR adopts a linear elastic model with an equivalent stiffness as the horizontal control parameter. This equivalent stiffness was calculated from Table 1. The LRB uses a bilinear restoring force model with stiffnesses before yielding and after yielding as well as yield force as the horizontal control parameters. Both LNR and LRB adopt the same tension and compression stiffness in the vertical direction. The above assumption is made to properly simulate the stress-strain relationship of the isolation rubber bearing. The theoretical mechanical property values of LNR and LRB were obtained according to the specifications and model type, as shown in Table 4. These parameters were then calibrated by experimental work, and then the updated values were inputted into the numerical model for FEA. Note that the tested shearing force vs. horizontal deformation of LNR and LRB are shown in Figure 16. It should be mentioned that studies [29; 30; 31] show that the constitutive law of seismic devices is sensitive to static or dynamic loading conditions. Thus, we strictly follow the seismic standard [18] to ensure the constitutive law of our isolators is reasonable. Under the static condition (i.e., the shear strain of isolator equals 0), the stiffness before yielding is used; under the dynamic condition (i.e., the shear strain of isolator equals 100% and 250%, corresponding to design earthquake and rare earthquake), the horizontal equivalent stiffness, equivalent damping ratio, and post-yield stiffness were applied in the material model.