# Design Method of Primary Structures of a Cost-Effective Cable-Supported Photovoltaic System
## 2 Numerical Simulation  
### Finite Element Model  
Finite-element simulation is an effective and efficient method for structural analysis. In this study, the finite element method was adopted to investigate the failure models and bearing capacity of the primary structures of the new CSPS. Different element types are used to simulate each component of the structure: (1) the columns and lateral beams are simulated with \"Beam\" elements; (2) the cables (load-bearing cables and anchor cables), triangle brackets, and lateral connectors are simulated using the \"Link\" element; and (3) the PV modules use \"Shell\" elements.  
The boundary conditions are described as follows:  
1. The PV modules are mounted on cables 1 and 2, and they are connected by nodes.
2. Both ends of cables 1, 2, and 3 were fixed on the beams.
3. The lower end of the anchor cable was fixed to the ground, and the upper end was fixed to the beam.
4. Triangular brackets are interconnected with cables 1, 2, and 3 by the nodes.
5. Beams were fixed at the top of the columns.
6. The bottom end of the column was fixed to the ground, and the upper ends were connected to the beam.  
The prototype of the finite element modeling (FEM) model of the present study is a real CSPS solar farm built by the Tong Wei Group in Tianjin, China. The structural parameters and material properties of the CSPS are listed in Table 2. Figure 4 shows a comparison of the prototype and FEM models.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Component** & **Material** & **Equivalent Area (m\({}^{2}\))** & **Equivalent Elastic Modulus (Pa)** & **Poisson’s Ratio** & **Density (kg/m\({}^{3}\))** & **Design Parameters** \\ \hline Beam & Reinforced concrete & 6.61 \(\times\) 10\({}^{-3}\) & 2.06 \(\times\) 10\({}^{11}\) & 0.3 & 7850 & / \\ Column & Steel I-beams & 1.11 \(\times\) 10\({}^{-3}\) & 2.06 \(\times\) 10\({}^{11}\) & 0.3 & 7850 & / \\ Triangle brackets & Steel bar & 2.39 \(\times\) 10\({}^{-4}\) & 2.06 \(\times\) 10\({}^{11}\) & 0.3 & 7850 & \(h_{1}\)= 1.5 m, \(h_{2}\)= 1.05 m \\ PV module & Composite material & 2.08 & 5.50 \(\times\) 10\({}^{10}\) & 0.2 & 1927 & m = 24 kg \\ Cables 1 and 2 & Steel strand & 0.97 \(\times\) 10\({}^{-4}\) & 1.85 \(\times\) 10\({}^{11}\) & 0.3 & 8100 & \(H_{1}\)= \(H_{2}\)= 30 kN \\ Cable 3 & Steel strand & 1.36 \(\times\) 10\({}^{-4}\) & 1.69 \(\times\) 10\({}^{11}\) & 0.3 & 8100 & \(H_{3}\)= 18 kN \\ Anchor cable & Steel strand & 4.90 \(\times\) 10\({}^{-4}\) & 2.06 \(\times\) 10\({}^{11}\) & 0.3 & 7850 & \(H_{A}\)= 18 kN \\ \hline \hline \end{tabular} Note: Height \(h\) of the triangle brackets is defined as the length of the line connecting the midpoint of the base of the inverted triangle to its apex, as shown in Figure 7. \(D\) and \(d\) represent the outer and inner diameters of the rods, respectively.  
\end{table}
Table 2: Example of a new CSPS [31].  
Static analyses were conducted, and the structural nonlinearity of large deformation was considered. The structure response is solved using the Newton-Raphson method, and the load substep is set as 20.