## 2 Finite Element Analysis of the Original Structure
### Finite Element Thermal Analysis of the Original Structure  
This model is subject to three constraint conditions: the connection between the left and right reflector surfaces and the central reflector surface through the side hinge mechanisms, and the bolt fixation between the base and the feed source compartment. The central position of the side hinge mechanism is located at the midpoint of the \(x\)-axis projection of the reflector surfaces, with lengths extending 100 mm along both the \(+\)x and \(-\)x directions. Therefore, RBE2 was used to equivalent the side hinge mechanisms and the bolt fixation. Fixed constraints conditions were set at the center of the bolts. Shell elements were used to model the reflector surfaces and the original reinforced ribs, as illustrated in Figures 9 and 10. The equation for thermal expansion of the antenna in orbit is as follows:  
\[\Delta V=V_{0}\times\alpha\times\Delta T \tag{8}\]  
where \(\Delta V\) is the volume increase due to thermal expansion. \(V_{0}\) is the original volume of the antenna. \(\alpha\) is the volume expansion coefficient with units of \({}^{\circ}\)C\({}^{-1}\). \(\Delta T\) represents the change in temperature. Figure 8: Temperature variation curve of the measuring points over time. The reflector and base of the antenna both adopt a honeycomb sandwich panel structure. The core of the honeycomb sandwich panel is made of aluminum honeycomb. The skin is symmetrically layered with 4 layers of M40 JB/cyanate ester carbon fiber, with a single layer thickness of 0.1 mm. To ensure polarization of electrical performance, the surface layer has a layering pattern of \(-45^{\circ}/90^{\circ}/45^{\circ}/0^{\circ}\). The specific parameters are detailed in Table 2, and a sample of the honeycomb sandwich structure is shown as Figure 11:  
Figure 10: Finite element model of the antenna reflector (back view). Figure 9: Finite element model of the antenna reflector (front view). Based on the simulation calculations in Section 2.2, it was determined that during the in-orbit operation of the antenna, the lowest temperature experienced would be \(-113.65\)\({}^{\circ}\)C. Therefore, applying a temperature excitation of \(-113.65\)\({}^{\circ}\)C to the reflector surfaces with the original reinforced ribs layout (height of 80 mm, thickness of 20 mm) and the surfaces without reinforced ribs, a deformation contour map of the reflector was obtained, as shown in Figures 12 and 13. From Figure 12, it can be observed that the deformations were relatively small near the fixed constraints. As the distance from the constraint points increased, the deformations gradually became larger. The maximum deformation occurred at the upper end of the central reflector plate, with a maximum deformation value of 1.013 mm. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Young’s** & **Poisson’s Ratio** & **Density** & **Thermal** & **Thermal** & **Heat** \\  & **Modulus** & & & **Coefficient** & **Conductivity** & **Capacity** \\ \hline Honeycomb & 1927.85 MPa & 0.33 & 2530 kg/m\({}^{3}\) & \(1.8\times 10^{-6}\)/\({}^{\circ}\)C & 3.2 W/m\(\cdot\)K & 678.9 J/kg\(\cdot\)K \\ \hline \end{tabular}
\end{table} 
Table 2: Relevant parameters of composite materials. Figure 11: Sample of honeycomb sandwich structure. Figure 12: Thermal deformation contour plot of the antenna with the original layout of reinforced ribs. Compared to the reflector surface with reinforced ribs in Figure 12, the deformation trend of the reflector surface without reinforced ribs shows differences. For the left reflector surface, the lower-left corner region experienced a larger deformation compared to the upper-left corner region. Similarly, for the right reflector surface, the lower-right corner region exhibited a larger deformation compared to the upper-right corner region. This trend differed from that observed in Figure 12. The maximum deformation still occurred at the upper end of the central reflector surface, with a maximum deformation value of 1.247 mm.