## 3 Dynamic Force-Thermal Follow-Up Loading Method for Multi-Stage Telescopic Wings
### Dynamic Multi-Point Distribution Equivalence Method for Aerodynamic Loads
In this study, the Courant-Euler-Lagrange (CEL) stability condition is applied, as follows:  
\[\Delta t=\frac{L_{\text{min}}}{c_{\text{max}}} \tag{8}\]  
This condition ensures the numerical computation remains stable and accurate, allowing for the precise capture of dynamic physical phenomena. To guarantee that the simulation results accurately reflect the real-world physical process, the time step \(\Delta t\) in numerical simulations should be consistent with the characteristic timescale of the physical process. During the deformation process of the multi-stage telescopic wing, the spanwise length dynamically changes with the deployment state, necessitating an investigation into the influence of mesh size on computational convergence. To address this issue, this study proposes a mesh update strategy based on a fixed total number of mesh elements, ensuring uniformity in mesh distribution throughout the simulation and preventing errors caused by uneven mesh sizes. Since planar meshing is employed in this study, maintaining a constant mesh size across different deployment states would result in varying mesh densities in different regions, potentially affecting computational accuracy. Therefore, instead of fixing the mesh size directly, a strategy of maintaining a constant total number of mesh elements along a specific direction is adopted. This allows the mesh size to adapt dynamically to changes in the spanwise dimension, ensuring consistent meshing across different deformation states. By analyzing the error variations in aerodynamic load calculations under different mesh element counts, the minimum required mesh number for achieving computational convergence is determined. This approach not only guarantees mesh consistency under varying deformation states but also enhances computational efficiency by avoiding unnecessary over-refinement, thereby improving the overall stability and reliability of the numerical simulation. The sensitivity analysis is performed at the state of t\({}_{1}\), with a total of 12 loading points acting on the wing surface. Sensitivity to grid quantity is analyzed separately for chordwise and spanwise directions. The first analysis examines the influence of chordwise grid quantity, and the second analysis examines the influence of spanwise grid quantity. (1) Sensitivity Analysis of Chordwise Grid Quantity  
The initial value of the spanwise grid quantity is set to 100, and the chordwise grid quantity is increased from 5 to 300 in increments of 5 to analyze the changes in the load  
Figure 17: Discretization of the dynamic multi-point distribution method. equivalence at the 12 loading points, as shown in Figure 18. The results indicate that the loading force at each unit becomes nearly unaffected by further increases in the grid quantity once it exceeds 50. (2) Sensitivity Analysis of Spanwise Grid Number  
The number of spanwise grids is initially set to 50, and the spanwise grid number is increased from 50 to 3000 in increments of 50. The variations in the load equivalence at 12 loading points are analyzed, as shown in Figure 19. The loads with significant variations, after the number increases to 1500 or more, show an absolute error of less than 0.2 N when compared to the final convergent value. The force load distribution is almost no longer affected by the change in the number of grids. Based on the grid sensitivity analysis, the increase in grid number has a certain impact on the load equivalence results. However, once the grid number reaches a certain threshold, the change in grid number has minimal effect on the load equivalence results. Therefore, the grid update method for each moment is to keep the grid unchanged based on a certain number. The chordwise grid length remains unchanged as the wing does not deform in the chordwise direction, while the spanwise grid length gradually increases. In subsequent analyses, the grid reconstruction number is determined to be 50 for the chordwise direction and 1500 for the spanwise direction.