## Finite Element Modeling Approach
### Application of Wind Load on the Whole Model  
A mid-phase jumper oscillates under wind load. According to [PERSON]'s equation, the wind load on the conductor is as shown in Equation (3):  
\[P=\frac{\gamma}{2g}v^{2}\sin\theta. \tag{3}\]  
In Equation (3), \(P\), \(\gamma\), \(g\), \(v\), and \(\theta\) indicate the wind load (N), the air density (kg/m\({}^{3}\)), acceleration of gravity (m/s\({}^{2}\)), wind speed (m/s), and angle between the wind direction and conductor axis, respectively. For a large-span conductor, an aerodynamic coefficient and a nonuniformity coefficient were introduced. According to Equation (3), the main factors influencing the wind load on the conductor are the wind \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Line Strand of** & **Number** & **E (GPa)** & \begin{tabular}{c} **Yield Strength** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Poisson** \\ **Ratio** \\ \end{tabular} & \begin{tabular}{c} **Winding** \\ **Angle (\({}^{\circ}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Pitch** \\ **Ratio** \\ \end{tabular} &
\begin{tabular}{c} **Diameter** \\ **(mm)** \\ \end{tabular} \\ \hline Outermost layer & 24 & 69 & 275 & 0.30 & 74.0 & 11 & 3.07 \\ Layer 3 & 18 & 69 & 275 & 0.30 & 75.3 & 12 & 3.07 \\ Layer 2 & 12 & 69 & 275 & 0.30 & 76.4 & 13 & 3.07 \\ Layer 1 & 6 & 207 & 68 & 0.28 & 81.5 & 21 & 3.07 \\ Central steel wire & 1 & 207 & 68 & 0.28 & 0 & — & 3.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of materials and modeling parameters of the local finite element model. Figure 3: (**a**) Sectional diagram of the local finite element model, (**b**) 3-D local finite element model, and (**c**) the whole microsegment finite element model. speed and angle \(\theta\) between the wind direction and conductor. When \(\theta\) is 90\({}^{\circ}\), the formula for calculating the wind load is shown in Equation (4):  
\[P_{\mathrm{f}}=a_{\mathrm{f}}\cdot K_{\mathrm{a}}\cdot A_{\mathrm{f}}\cdot\frac {v_{\mathrm{f}}{}^{2}}{1600}, \tag{4}\]  
In Equation (4), \(a_{\mathrm{f}}\) indicates the asymmetrical coefficient of the wind pressure. When the wind speed is less than 20 m/s, \(a_{\mathrm{f}}\) is taken to be 1, and when the wind speed is between 20 and 30 m/s, it is taken to be 0.85. In addition, \(K_{\mathrm{a}}\) indicates the aerodynamic coefficient and is taken to be 1, \(A_{\mathrm{f}}\) represents the projected area of the conductor in the direction of the wind load, and \(v_{\mathrm{f}}\) indicates the speed (m/s). Finally, \(P_{\mathrm{f}}\) indicates the wind load (N). The amplitude change of the wind load applied on the mid-phase jumper is shown in Equation (5):  
\[A_{\mathrm{mp}}=\ \sin(\frac{\pi}{2}t) \tag{5}\]  
In Equation (5), \(A_{\mathrm{mp}}\) indicates the amplitude of wind load applied, and \(t\) indicates the time (s). The wind load is converted from the kinetic energy of the wind, and the kinetic energy consumption of the wind perpendicular to the conductor is the largest; therefore, the wind speed component perpendicular to the strand determines the actual wind load, and that parallel to the conductor has little effect. Table 2 shows the applied wind speed level to the whole model, the corresponding wind speed, and the magnitude of the applied wind load when \(\theta\) was 90\({}^{\circ}\). Westerly winds dominate the northwest part of China throughout the year. In this study, the mechanical response of the mid-phase jumper to a westerly wind was mainly considered. As shown in Figure 4, the wind load was applied to the whole model, and the arrow in the figure represents the wind load and wind direction.