## 2 Aerodynamic Load and Deformation Analysis of Multi-Stage Telescopic Wings
### Simulation Analysis of Deformation Process of Multi-Stage Telescopic Wing  
To evaluate the deformation characteristics of the multi-stage telescopic wing under the prescribed loading conditions and verify the feasibility of its structural design, a simulation analysis was conducted to investigate its deformation behavior during the deployment process. The simulation model is illustrated in Figure 8, where a fixed constraint is applied at the wing root, and three distinct loading conditions are imposed on the skin surface: (1) aerodynamic loading only, (2) thermal loading only, and (3) combined force-thermal loading. In the simulation setup, the contact interactions between the wing surfaces and moving components are defined as frictional contact, while rigidly connected regions are set as bonded contact. To precisely capture the structural response, a Z-direction deformation probe is placed at the intersection of the wingtip trailing edge and chordwise direction, while a force probe is embedded at the lead screw joint. Additionally, the displacement input of the lead screw is prescribed to simulate the transition of the multi-stage telescopic wing from a fully retracted state to a fully deployed state. The deflection of the wingtip and the driving force are subsequently recorded and analyzed to investigate the deformation behavior and mechanical characteristics of the structure. Under the evaluation load conditions, a simulation analysis of the deformation process of the multi-stage telescopic wing was conducted to assess the feasibility of the structural design based on its deformation performance during deployment. In the simulation, fixed constraints were applied at the root of the wing, and three loading conditions were defined: (1) aerodynamic load only, (2) thermal load only, and (3) combined aerodynamic and thermal loads. Figure 9 illustrates the simulated tip deflection curves of the multi-stage telescopic wing under these three loading conditions during deployment. The results show that the deflection changes are smooth throughout the deployment process, with no sudden transitions, indicating that the structure's response to combined aerodynamic and thermal loads is stable. This preliminary analysis validates the load-bearing capability of the multi-stage telescopic wing. Figure 10 shows the time-dependent curves of the driving force required for the deployment of the telescopic wing under three loading conditions. The driving force under coupled aerodynamic and thermal loads is significantly higher than that under aerodynamic loads alone. The driving force under thermal loads alone is nearly identical to that under coupled aerodynamic and thermal loads. This indicates that the driving force in the coupled condition is primarily influenced by thermal loads, and the impact of aerodynamic loads on the driving force is negligible in the presence of thermal loads. Figure 8: Deformation process simulation model. Table 3 shows the peak values of deformation and driving parameters during the unfolding process of the telescoping wing under three different conditions, based on simulation measurements. Through the analysis of the deformation curve and the driving force variation curve, it is observed that the deformation curve exhibits a smooth and continuous trend, while the driving force variation curve shows no abrupt fluctuations or sudden changes. This indicates that the mechanism can operate stably under the investigated conditions, with no noticeable discontinuities or unexpected transient behaviors during its motion. These findings fully demonstrate the actuation stability of the mechanism under force-thermal coupling effects, further supporting the rationality of its structural design and providing strong validation for its engineering application in complex loading environments. However, to ensure the reliability and practicality of the design, further ground simulation experiments under the assessment load conditions are necessary to complete the full verification of the structural design.