## 3 Design of the Unit Structure of the Main Reflector in the Deployable Reflector Antenna
### Performance Evaluation According to Honeycomb Core of Reflector Antenna  
In the previous subsection, the structural performance of the unit structure of the main reflector was investigated with respect to the laminated pattern of the facesheet. The stacking angle of a facesheet wrapped around the honeycomb core was selected as Case 1.1 of [0/45]. As shown in Figure 2, the honeycomb core can be divided into four parts to determine the distribution of the honeycomb core. Because the maximum stress during the operating condition is generated at the root part of the main reflector of the deployed main reflector, the honeycomb core in Part 1 is wrapped with eight plies on the top and bottom. Part 4 is the outer part of the main reflector covered with two plies on the top and bottom. The thickness of the honeycomb core is 16 mm. Figure 2 show four different designs; (Case 2.1) applying a relatively high-density core uniformly to the main reflector; (Case 2.2) applying a relatively low-density core uniformly to the main reflector; (Case 2.3) \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Laminate Sequence**} & \multicolumn{5}{c}{**Effective Properties (Pa)**} \\  & & \(E_{1}\) & \(E_{2}\) & \(G_{12}\) & \(\
u_{12}\) & \(E_{fk}\) & \(E_{fy}\) \\ \hline
1.1 & \(\left[0/45/\overline{Core}\right]_{s}\) & \(2.09\times 10^{9}\) & \(2.09\times 10^{9}\) & \(5.28\times 10^{8}\) & \(0.315\) & \(4.85\times 10^{8}\) & \(4.85\times 10^{8}\) \\
1.2 & \(\left[0/90/\overline{Core}\right]_{s}\) & \(2.93\times 10^{9}\) & \(2.93\times 10^{9}\) & \(1.01\times 10^{8}\) & \(0.040\) & \(6.91\times 10^{8}\) & \(6.91\times 10^{8}\) \\
1.3 & \(\left[/-45/\overline{Core}\right]_{s}\) & \(6.20\times 10^{8}\) & \(6.42\times 10^{8}\) & \(9.55\times 10^{8}\) & \(0.789\) & \(1.13\times 10^{8}\) & \(1.13\times 10^{8}\) \\
1.4 & \(\left[0/30/\overline{Core}\right]_{s}\) & \(2.34\times 10^{9}\) & \(2.34\times 10^{9}\) & \(3.22\times 10^{8}\) & \(0.233\) & \(5.46\times 10^{8}\) & \(5.46\times 10^{8}\) \\
1.5 & \(\left[-30/30/\overline{Core}\right]_{s}\) & \(1.48\times 10^{9}\) & \(1.48\times 10^{9}\) & \(6.43\times 10^{7}\) & \(0.516\) & \(3.28\times 10^{8}\) & \(3.28\times 10^{8}\) \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**\(E_{1}\), \(E_{2}\), \(G_{12}\) and \(\
u_{12}\) mean 1- and 2-directional, shear stiffness and Poisson’s ratio, and \(E_{fk}\), \(E_{fk}\) mean the bending stiffness. As shown in Table 2, the Case 1.2 model with the [0/90] stacking pattern shows high stiffness in Directions 1 and 2, but relatively low shear stiffness. The Case 1.3 model with the [45/\(-\)45] stacking pattern was applied and had a higher calculated shear stiffness compared to the stacking pattern, but the 1- and 2-directional stiffness were 50% lower than those of other stacking patterns. As a result of comparing the stiffness calculated through CLT formulation, Case 1.1 with the [0/45] stacking pattern and Case 1.4 with the [0/30] stacking pattern have high axial stiffness and shear stiffness on average.**  
\end{table} 
Table 2: Lamination Sequence and Effective Modulus. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Laminated Pattern**} & \multicolumn{3}{c}{**Effective Properties (Pa)**} \\  & & **First Bending Mode** & **Second Bending Mode** & **Third Twisting Mode** \\ \hline
1.1 & \(\left[0/45/\overline{Core}\right]_{s}\) & 27.93 Hz & 78.09 Hz & 94.81 Hz \\
1.2 & \(\left[0/90/\overline{Core}\right]_{s}\) & 30.75 Hz & 70.22 Hz & 41.73 Hz \\
1.3 & \(\left[/-45/\overline{Core}\right]_{s}\) & 16.15 Hz & 48.75 Hz & 57.97 Hz \\
1.4 & \(\left[0/30/\overline{Core}\right]_{s}\) & 28.28 Hz & 76.39 Hz & 80.03 Hz \\
1.5 & \(\left[-30/30/\overline{Core}\right]_{s}\) & 24.37 Hz & 71.94 Hz & 116.95 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of Modal Analysis for Laminate Sequence.