# Research on the Dynamics of the Space Tubular Expandable Structure Driving Deployment Unit
## 3 Finite Element Analysis
### Simulation Analysis  
After partitioning the hexahedral mesh, Parts \(L_{1}\), \(L_{2}\), and \(L_{3}\) are set as beam structures. Figure 18 shows the displacement contour plots of the triangular configuration with thin-walled flexible beam structures under the parallel configuration at time intervals of 0.25 s, 0.5 s, 0.75 s, and 1.0 s. To provide a clearer view of the driving and stowing units, the simulation contour plots only display the driving and stowing units. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Structural Unit** & **Material** & **Elastic Modulus \(E\)** & **Poisson’s Ratio \(\mu\)** & **Density \(\rho\)** \\ \hline Beam structure & Aluminum Alloy (2A14) & 67.7 GPa & 0.33 & 2800 kg/m\({}^{3}\) \\ Flexible connectors & Spring Steel (40 Cr) & 211 GPa & 0.277 & 7820 kg/m\({}^{3}\) \\ Elastomer & JSR & 0.0078 GPa & 0.47 & 1040 kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameters for the driving-unfolding unit. Figure 17: The finite element model of the variable-radius inner-drive unit. Figure 18 illustrates the maximum deformations in the x and y directions at different time intervals: 0.25 s, 0.50 s, 0.75 s, and 1.00 s. At 0.25 s, the deformations of points \(L_{1}\), \(L_{2}\), and \(L_{3}\) during the initial stage of the inter-level transition under radial load are not significant, with a maximum deformation of 0.3425 mm. At 0.50 s, points \(L_{1}\) and \(L_{2}\) undergo some bending deformation with a maximum deformation of 0.5491 mm, while point \(L_{3}\) is less affected due to symmetric stress distribution. At 0.75 s and 1.00 s, the maximum deformations in the x and y directions are 0.9417 mm and 1.3621 mm, respectively. During these intervals, point \(L_{1}\) experiences bending deformation only at the front end, point \(L_{2}\) undergoes axial deformation with stress concentrated at the contact area with point \(L_{1}\), and point \(L_{3}\) maintains good bending resistance. Additionally, Figure 19 provides a comparative analysis of the centroid displacements in different directions of the thin-walled flexible beam elements during the theoretical stage depicted in Figure 15.  
Figure 19a-c depicts the displacements of the centroid of the drive-unfold unit in the X, Y, and Z directions, respectively. These simulation curves align with the trends observed in the theoretical stage. In the X-direction centroid displacement graph, a series of peaks and valleys appears between 0.2 s and 0.5 s due to radial displacement caused by the transition diameter change during the inter-level transition of the elastic body. The contact between the elastic material and the discontinuous surface rigid body leads to deformation of the elastic material, resulting in a peak-to-peak difference of 1.43 mm in the radial direction. The Y-direction centroid displacement graph shows a phenomenon of axial displacement regression between 0.4 s and 0.6 s, attributed to elastic rebound during the inter-level transition when the elastic body contacts the discontinuous surface rigid body, causing a fluctuation of 0.96 mm. In the Z-direction centroid displacement graph, oscillations occur due to tangential displacement generated by the compression of the elastic body under radial load. During the initial stage of the inter-level transition (between 0.35 s and 0.45 s), the radial load generates stress without adjustment due to the reduction of the transition diameter, leading to increased compression of the elastic body and an associated increase in tangential displacement. However, with timely radial load adjustment, the elastic body undergoes instantaneous radial rebound, resulting in a decrease in tangential displacement. Figure 18: The displacement contour plots at different time intervals.