## 4 Results and Discussion
### Two-Dimensional Topology Optimization  
The optimized layout using both aerothermal heat and aerodynamic pressure loads is displayed in Figure 9. Compared to the origin design, the angles between the webs and the inner surfaces of the optimized design decreased in order to have a longer heat transfer path. In this way, more of the heat flux could be absorbed by the insulation materials before reaching BFSs. In contrast to improving thermal performance, the decline of angles is likely to weaken the support of webs to the TFSs. As a result of balancing thermal and mechanical performance of the ITPS, a horizontal web emerged to suppress the deformation. It should be noted that materials of intermediate density occur in the optimized design. Even though the existence of materials with medium thermal conductivity and modulus might be a method for resolving the conflict between thermal and mechanical performance, as supported by [45], these results are not favorable to topology optimization. Nonetheless, a clear morphology was obtained. According to this morphology, two configurations were presented and analyzed in this study. OPT-T was exactly the same as in Figure 9a, and OPT-P was slightly modified to reduce deformation based on OPT-T. Parameters are listed in Table 5. Thermal and mechanical responses, including maximum temperatures at each component of the ITPSs (\(T_{t,\text{max}}\) for TFSs, \(T_{b,\text{max}}\) for BFSs and \(T_{w,\text{max}}\) for mid-point on webs) and maximum deformation at TFSs (\(d_{t,\text{max}}\)), are plotted in Figure 10. Temperature and  
The maximum temperature of the BTS, \(T_{b,\max}\), reveals the severity of the thermal short effect. Webs with high conductivity are the main path for heat transfer and are the reason for thermal short effect. In the optimized design, the web material is redistributed, and more heat can be absorbed by the surrounding insulation materials. Consequently, the thermal short effect was alleviated as shown in Figure 11. Although \(T_{w,\max}\) of OPT-P is similar to the original design, \(T_{b,\max}\) is still lower than that in the initial concept. The \(T_{b,\max}\) of the original model is 439 K and of OPT-T and OPT-P is 345 K and 361 K, with the reduction of 21.4% and 11.8%, respectively.  
Deformations were controlled by the coupled thermal and mechanical loads before the time of 2100 s. After 2100 s, pressure load on the outer surface of TFS gradually elevated and counterbalanced the pressure on the inner surface. Thus, along with the temperature decrease of the TFS, \(D_{t,\max}\) declines rapidly during the period around 2100 s to 2500 s. The main difference between the initial design and optimized designs lies in the interaction between TFSs and BFSs. The lower webs were connected to the end of BFSs, which is the fixed point in this problem, in the optimized design. In this case, deformations of TFSs would not lead to the deformation of BFSs, and vice versa. After time 2500 s, deformations were mainly controlled by thermal expansion. Deflections of the BFSs increased since \(T_{b,\max}\) kept increasing. Through the webs between the TFS and BFS, the TFS was pushed to deform during this period for the initial design. The \(d_{t,\max}\) of the initial model is 7.54 mm and of OPT-T and OPT-P is 6.92 mm and 2.26 mm, with the reduction of 8.2% and 70.0%, respectively.  
Compared to the initial design, both optimized designs show better load carrying and insulating performance. The mass of OPT-T slightly increases by 3.8%, while OPT-P is lightened by 0.3%. Taken all factors into account, OPT-P was believed to be the optimal result for this problem.