# Experimental Investigation on the Mechanical Properties of Curved Metallic Plate Dampers
## 3 Mechanical Properties of Curved Plate Damper
### Finite Element Analysis  
#### 3.3.1 Hysteresis Curve Analysis  
The model shown in Figure 11 was built in general FEM software known as ANSYS. The shell unit shell181 was selected for the model. The constitutive relation of the bilinear follow-up reinforcement model was used for steel material. The elastic modulus of Q235 steel was used as \(2.06\times 10^{5}\) Mpa, Poisson's ratio as 0.3, and yield strength was taken according to Table 1. The model was developed according to the size of CSPD-1, CSPD-2, CSPD-3, and CSPD-4 dampers. The flat section of the bottom of the damper was completely fixed, while the flat section of the top was only horizontally displaced.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Specimen** & \begin{tabular}{c} **Yield** \\ **Displacement/mm** \\ \end{tabular} & \begin{tabular}{c} **Limit** \\ **Displacement/mm** \\ \end{tabular} & \
\begin{tabular}{c} **Ductility** \\ **Coefficient \(\mu\)** \\ \end{tabular} &
\begin{tabular}{c} **Energy Dissipation** \\ **Coefficient \(E\)** \\ \end{tabular} \\ \hline CSPD-1 & 4.37 & 40 & 9.15 & 2.90 \\ CSPD-2 & 2.66 & 24 & 9.02 & 2.83 \\ CSPD-3 & 1.86 & 18 & 9.68 & 2.73 \\ CSPD-4 & 4.52 & 42 & 9.29 & 2.96 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mechanical properties of curved plate damper.  
Figure 10: Strain at points 1 (a) and 2 (b).  
In the process of standard loading, the hysteretic loops of the double yield displacement and 10 yield displacements were compared with the results of the finite element method. Two specimens were used in each group at the same time. Therefore, the results of the finite element simulation needed to be magnified twice. Figures 12-15 show the hysteretic curves of the four specimens.  
1. In Figure 12, the hysteretic curve coincides well at 4 mm. The positive and negative values are asymmetric in the hysteretic curve at 40 mm. Because the stiffness of CSPD-1 is small, then the horizontal deformation causes an error in the final load value, when the load displacement is large.
2. In Figure 13, the asymmetry of the hysteretic curve also exists at 2.4 mm. At 24 mm, the maximum load of the test curve and the finite element curve are basically the same, but the envelope area of the finite element curve is slightly larger, and the second stiffness of the damper is smaller.
3. In Figure 14, the hysteretic curve coincides well at 1.8 mm. The maximum load coincides well at 24 mm, and the envelope area of the finite element curve is slightly larger.
4. In Figure 15, the hysteretic curve coincides well at 4.2 mm, and the curve of finite element analysis shows an upward trend at 42 mm, which is different from the shape of the test curve. This is because the boundary condition set in the finite element analysis is complete bonding, and a bolt connection is used in the test, which cannot be precisely achieved.  
Figure 11: Finite element model.  
Figure 12: Hysteresis curve at 4 mm (**a**) and 40 mm (**b**) of CSPD-1.  
Generally speaking, the curve of the finite element analysis is basically the same as that of the test; therefore, the finite element model is reasonable. However, the ideal elastic-plastic model of material in the finite element is different from the actual material. There are many factors affecting the test process, including processing, installation, and other errors. It is impossible to achieve the ideal state in finite element settings, and some errors are acceptable.  
Figure 14: Hysteresis curve at 1.8 mm (**a**) and 18 mm (**b**) of CSPD-3.  
Figure 13: Hysteresis curve at 2.4 mm (**a**) and 24 mm (**b**) of CSPD-2.  
Figure 15: Hysteresis curve at 4.2 mm (**a**) and 42 mm (**b**) of CSPD-4.