## 3 Results and Analysis
### Nonlinear Finite Element Analysis  
#### 3.4.1 Establishment of Finite Element Model  
The grid diagram of model is shown in Figure 15.The force damage simulation of the test process was carried out by the finite element software ANSYS15.0 and compared and analyzed with the test results to check and optimize the test results to some extent. Based on the characteristics of the test components and the need to simplify the model and improve operational efficiency, the following basic assumptions were followed in the course of this analysis: (1) The deformation of the member cross-section after the test frame has been stressed still satisfies the flat section assumption; (2) good bonding between reinforcement  
Figure 14: The restoring force model of the framework. and concrete without relative slippage; (3) disregarding the axial tensile strength of the concrete and ignoring the mechanical bite between the aggregates after its cracking; (4) the reinforcement had no transverse shear effect, ignoring the transverse shear deformation of the frame or the torsional effect generated during the test. A combined model was selected for the reinforced concrete structure. The Solid65 element provided by ANSYS was adopted in concrete. This model can consider many nonlinear properties of concrete and other nonlinear materials, such as cracking, crushing, plastic deformation, and creep of concrete in three orthogonal directions. Beam188 element provided by ANSYS was used for longitudinal and circumferential reinforcement. This element can be applied to plastic, spiral, linear, large rotation, nonlinear large strain, and other problems. Formula (9) was adopted for the stress-strain relationship of concrete under uniaxial compression. A bilinear follow-up hardening steel bar model was adopted in the model, with the same direction of tension and compression. Since the material composition of the test frame members had a strong nonlinear intrinsic relationship between ordinary or low yield point reinforcement and concrete, the ultimate load of the entire frame member was not determined by whether the ultimate load was reached in a single part of the material. In the process of increasing load, the material would inevitably enter the elastic-plastic stage, and the stress-strain relationship for some of the materials may also enter a decreasing segment after the peak. Therefore, when performing finite element analysis, the Multilinear Isotropic Hardening model was used for the concrete principal structure relationship. The steel intrinsic structure relationship is based on the Bilinear Kinematic Hardening model. This test analysis uses the five-parameter [PERSON] strength criterion, which basically reflects the damage characteristics of concrete. The reinforced concrete frame model was built in a bottom-up manner from points to lines to surfaces. In order to prevent the influence of secondary parts on the computational convergence, the main body of the test member was taken for the simulation. In order to prevent localized damage of concrete, a 150 mm thick steel mat was added at each end of the frame column, and various restraints and loads were added to the steel mat. The completed concrete and steel skeleton models are shown in Figure 16. During the loading process, the loading step simulated the loading regime in the test as much as possible, including the load control phase and the displacement control phase. The simulation convergence error was controlled to be within 2% to 3%, not exceeding 5%. \[ \begin{cases}y=\alpha_{\mathrm{a}}x+(3-2\alpha_{\mathrm{a}})x^{2}+(\alpha_{ \mathrm{a}}-x)x^{3}&x\leq 1\\ y=x/[\alpha_{\mathrm{d}}(x-1)+x]&x>1\end{cases}