3.2.3. Strain Analysis

The longitudinal coordinate of the strain analysis curve represents the strain value at the measuring point. As shown in Figure 5, strain gauges were attached at three locations on the curved surface steel plate damper. Because the locations of measuring points 1 and 3 were the same, the average values of positive strain extremum at measuring points 1 and 3 were taken. The transverse coordinates were unified as the loading displacement (n × Δ), where Δ is the prediction of the yield displacement.

From Figure 10, it can be seen that the strain at point 1 is much larger than that at point 2, which shows that the plastic deformation at the end of the semi-circular arc was large, and that the stress was also large for curved plate dampers. It is not di fficult to see from Figure 10a that when the loading displacement was greater than 3 Δ, the strain values of the specimens began to di ffer significantly. The strains of specimens CSPD-1 and CSPD-4 increased rapidly. At 6 Δ, the strain increment of the CSPD-2 specimens slowed down, while the strain of the CSPD-3 specimens increased rapidly from 7 Δ.

Figure 10b demonstrates the strain curve at point 2. It can be seen that the strain increment trend of the four groups of specimens was approximately the same. When loaded to 10 Δ, the strain values of the other specimens were similar except for the small strain values of CSPD-2 specimens.

**Figure 10.** Strain at points 1 (**a**) and 2 (**b**).

#### *3.3. 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 × 10<sup>5</sup> 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.

**Figure 11.** Finite element model.

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.


**Figure 12.** Hysteresis curve at 4 mm (**a**) and 40 mm (**b**) of CSPD-1.

**Figure 13.** Hysteresis curve at 2.4 mm (**a**) and 24 mm (**b**) of CSPD-2.

**Figure 14.** Hysteresis curve at 1.8 mm (**a**) and 18 mm (**b**) of CSPD-3.

**Figure 15.** Hysteresis curve at 4.2 mm (**a**) and 42 mm (**b**) of CSPD-4.

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.

#### 3.3.2. Analysis of Mechanical Property Parameters

According to the theoretical formula of the curved plate damper, combined with the experimental and numerical data presented in this paper, a comparison of mechanical properties of curved plate dampers is provided in Table 4. The coefficient beta (β)in the calculation formula can be determined according to the test value and the finite element value. The yield displacement and yield bearing capacity in the test and the finite element simulation were averaged, and then, correspondingly, the theoretical values were determined to be equal. The error was smaller when the calculation yields a β factor value of 1.78. The maximum error of the mechanical properties is listed in Table 4. Except for some errors of elastic stiffness greater than 10%, the other errors were smaller. This shows that the finite element calculations in conjunction with theoretical formulae can reasonably reflect the performance of the damper.


**Table 4.** Comparison of mechanical properties of curved plate dampers.
