## 3 Topology Optimization and Parametric Analysis
### Parametric Analysis  
Once the layout of the reinforced ribs had been determined, the selection of the dimensions of the reinforced ribs also determined their effectiveness in reducing the RMS of the reflector surface. In existing designs, the choice of the height and thickness of  
Figure 16: Topology optimization result. Figure 17: Layout of reconstructed reinforcing ribs. the reinforced ribs largely relied on the designer's experience. Moreover, there has been a scarcity of research on the impact patterns of these two parameters on the RMS of the reflector surface. If the influence patterns of the height and thickness of reinforced ribs, which are made of composite materials, on the RMS of the reflector surface can be determined, this would not only provide suitable design parameters for the reinforced ribs but also offer a valuable reference for future engineering designs. Due to the distance constraints between the antenna and the entire satellite, along with the weight requirements, the height of the reinforced ribs needed to be controlled within the range of 30 mm to 120 mm. The thickness had to be constrained within the range of 20 mm to 35 mm. First, the effect of varying the reinforced rib height on the RMS of the reflector surface was simulated. The variation in the reinforced ribs' height at thicknesses of 20 mm, 25 mm, 30 mm, and 35 mm was simulated. Simulation calculations for the reflector RMS of the reflector surface at intervals of 5 mm were performed, ranging from a height of 30 mm to 120 mm. The characteristic curves were obtained, as shown in Figure 18, depicting the change in the RMS of the reflector surface with varying back reinforced rib heights for specific rib thickness conditions. From Figure 18, it can be observed that, under the four thickness conditions, the RMS of the reflector surface did not linearly decrease with the increase in reinforced rib height. In the height range of 40 mm to 55 mm for reinforced ribs, the RMS of the reflector surface decreased with the increase in height for all four thicknesses. This range is referred to as the reduction interval of RMS for the reflector surface. In the height range of 55 mm to 65 mm for reinforced ribs, under the 20 mm thickness condition, the RMS of the reflector surface showed a relatively flat trend within this interval, while for the other three thicknesses, the RMS increased with the height of the reinforced ribs. Additionally, the slope relationships changed, with the 35 mm curve having the steepest slope, followed by 30 mm, and lastly, 25 mm. This range was identified as the turning point interval of the RMS of the reflector surface. In the height range of 65 mm to 120 mm for reinforced ribs, the RMS of the reflector surface linearly increased with the increase in back reinforced rib height. This range was identified as the growth interval of the RMS for the reflector surface. Next, simulations were conducted to investigate the influence of the reinforced rib thickness on the RMS of the reflector surface. Heights were selected from the reduction interval, turning point interval, and growth interval: 40 mm, 45 mm, 50 mm, 65 mm, 80 mm, 100 mm, and 120 mm. The influence of thickness on the RMS of the reflector surface was simulated at different reinforced rib heights. Thickness varied from 20 mm to 35 mm, with  
Figure 18: RMS of the reflector surface at thicknesses of 20, 25, 30, and 35 mm. calculations conducted at 1 mm intervals. The obtained patterns of the RMS of the reflector surface variation with reinforced rib thickness are illustrated in Figures 19-21. It can be observed that the RMS of the reflector surface effectively decreased with the increase in reinforced rib thickness at different heights within the reduction interval (40 mm, 45 mm, and 50 mm). For the turning point interval, specifically at a back reinforced rib height of 65 mm, the RMS of the reflector surface showed no significant increase or decrease with the increase in the thickness of the reinforced rib.