## 5 Structural Analysis of the Full Model of Deployable Reflector Antenna  
In this section, the finite element analysis of the DR-A assembly consisting of a total of 24 petals is performed using the material properties and stacking sequence. The unit structure applied to the antenna assembly is assumed to be two cases, Case 2.1 and Case 2.2. Both antenna models satisfy the weight requirement of the primary payload (less than 110 kg) including the other antenna components. Modal and quasi-static analyses are performed for the antenna assembly composed of 24 main reflectors under the deployed condition. In order to evaluate the effect of the attitude control during the mission operation, the transient analysis of the deployed antenna assembly is implemented. The modal analyses of satellite assembly under the stowed and deployed conditions are conducted for the launch and on-orbit environments, respectively. The finite element model and boundary conditions are shown in Figure 7a,b. In the case of the deployed condition, the local vibrating modes are individually generated at all unit structures. Thus, the first and second mode of the deployed antenna assembly in Figure 7d,f are the same as those of the unit structure shown in Figure 6d,f, whereas the mode frequencies of the antenna assembly under the stowed mode in Figure 7c,e are lower than those of the unit structure. This is because the vibrating mode is determined by the strut assembly as well as the dynamic stiffness of the main reflector. Although the vibrating mode is partially different from the unit structure, the fundamental mode of both cases satisfies the stiffness requirements for the stowed (\(\geq\)33 Hz) and deployed conditions (\(\geq\)3 Hz) [16]. Also, the mode frequency with the main reflector applied with the stacking sequence of Case 2.2 has a relatively high natural frequency, because the model with the low-density core material has a higher weight reduction rate than stiffness reduction, leading to higher natural frequency. As mentioned above, the satellite is exposed to various dynamic loads during the launch process and the structural safety for sinusoidal vibration in the low-frequency band (below 100 Hz) can be evaluated by quasi-static analysis. In this paper, the dynamic load during the launch process can be simulated as quasi-static loads (\(\times\), \(y\), z Combination Load (=15 g)). The results of the quasi-structural analysis are shown in Table 6 and Figure 8. As shown in Table 6, the antenna assembly applied with the main reflector consisting of the low-density core (Case 2.2) has relatively high MOS for the quasi-static loading condition. Compared with the MOS for each direction of the carbon fiber and the honeycomb, the MOS for the one-directional compression load of the carbon fiber composite facesheet is the lowest, indicating that if the actual quasi-static load is applied heavily, failure is likely to occur due to the behavior of the carbon fiber composite facesheet in one-directional compression. The margin of safety (MOS) is shown as follows:  
\[\text{MOS}=\frac{\sigma_{a}}{\sigma_{a}\times SF}-1,\quad\quad\text{where }SF=2, \tag{1}\]  
where \(\sigma_{a}\) and \(SF\) are the allowable stress and safety factor, respectively. Figure 9 shows the results of the maneuver analysis of the deployed antenna assembly. During the orbit operation in which the satellite may require spotlight shooting for a specific area [19], the high performance for the attitude control is required. For satellite imaging, right after the satellite's beam angle changes, the satellite rapidly stops and the antenna assembly exhibits a transient response called the pre-image maneuver. With the pre-image maneuver, the transient vibrational response is shown in the main reflector of the antenna assembly. In this regards, the transient analyses to evaluate the effect of micro-vibration for the stacking sequences of Case 2.1 and Case 2.2 of the antenna assembly with each stacking sequence are implemented.