## 3 Numerical Simulations
### Simulation Results and Analysis of the Proposed System
The rear legs had a maximum stress approximately 7% greater than the front legs because of the differences in interaction forces by front and rear floats. Table 4 lists the statistics of the dynamic responses and stresses of the platform. Owing to the influence of WECs, the positive maximum x-displacement at the top of the structure was larger than the negative maximum. This means that the structure tends to move more in the incident wave direction. In this study, simulation results were analyzed using Root Mean Square (RMS), one of the statistical parameters as a measure of dynamic fluctuation. The RMS values of the stress were approximately 20% increased because of the influence of the floats. On the other hand, the maximum value differed by approximately 2.2 times. Hence, fully coupled analysis is essential for the reliable design of the structure. Figure 15 and Table 5 show the time histories of the constraint forces acting on the hinge points and their statistics considering the influence of the floats. As shown in Figure 15a, the \(x\)-axis constraint force at Hinge 1 (front) has large positive values, and that at Hinge 2 (rear) has similar negative values. This is because the movement of each float is constrained by the hinge point, so the constraint force acts in the opposite direction to the movement of the float to satisfy the constraint condition. The \(z\)-axis constraint forces acting on the two hinge points are similar in magnitude, as shown in Figure 15b. The RMS value of the constraint force is larger in the \(z\)-axis, but the maximum value occurred on the \(x\)-axis. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Case** & **Maximum** & **Minimum** & **RMS** & **Standard Deviation** \\ \hline \multirow{2}{*}{\(x\)-axis displacement at the top [m]} & 2 floats & 0.635 & \(-\)0.546 & 0.122 & 0.121 \\  & No floats & 0.059 & \(-\)0.060 & 0.014 & 0.014 \\ \hline \multirow{4}{*}{Stress at the bottom [MPa]} & 2 floats—Leg 1,2 & \(-\)40.31 & \(-\)102.11 & 50.99 & 8.02 \\  & 2 floats—Leg 3,4 & \(-\)39.54 & \(-\)110.74 & 51.17 & 8.23 \\ \cline{1-1}  & No floats—Leg 1,2 & \(-\)40.61 & \(-\)46.39 & 41.85 & 0.78 \\ \cline{1-1}  & No floats—Leg 3,4 & \(-\)40.53 & \(-\)46.23 & 41.82 & 0.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistics of the dynamic responses of the platform. Figure 14: Maximum responses along the height of the platform: (**a**) Displacements; (**b**) Stresses. Figure 16 and Table 6 show the differences in the float rotational motions with or without considering platform elastic responses, i.e., elastic platform vs. fixed platform. The rotational motions of both floats are slightly increased after including the elastic response of the platform. Because the foundation structure is not as flexible, their differences are expected to be small, as in Figure 16 and Table 6.  
Figure 17 and Table 7 show the time histories of the produced wave power and their statistics for both fixed and elastic foundation structures. Similar to the previous results, the RMS values of the produced power from Floats 1 and 2 are affected slightly by the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **Float** & **Maximum** & **Minimum** & **RMS** & **Standard Deviation** \\ \hline \multirow{2}{*}{Coupled analysis} & Float 1 & \(0.528\) & \(-0.525\) & \(0.126\) & \(0.126\) \\  & Float 2 & \(0.673\) & \(-0.574\) & \(0.134\) & \(0.134\) \\ \hline \multirow{2}{*}{Fixed platform analysis} & Float 1 & \(0.460\) & \(-0.515\) & \(0.106\) & \(0.106\) \\  & Float 2 & \(0.679\) & \(-0.365\) & \(0.118\) & \(0.118\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Statistics of the rotational displacement of the floats (unit: rad). Figure 16: Time histories of rotational displacements of the floats: (**a**) Float 1; (**b**) Float 2. Figure 15: Time histories of the constraint forces acting on the hinge points: (**a**) \(x\)-axis; (**b**) \(z\)-axis. elastic responses of the platform.