# The Effect of Inflatable Pressure on the Strain Deformation of Flexible Wing Skin Film
## 3 Inflation Deformation Modeling and Bearing Deformation Simulation  
### Inflatable Flexible Deformation Modeling  
This study employs the theory of flexible mechanical films and the principle of pneumatic expansion deformation of flexible wing skin materials, based on a flat straight flexible inflatable wing model [7, 8]. The flexible wing skin maintains a three-dimensional deformation state under pressure-stabilized inflation. However, since the skin film is a foldable and stretchable flexible structural material, local deformation of the skin film unit primarily induces biaxial tensile deformation within the film surface, allowing the flexible skin film to be approximated as undergoing in-plane, two-dimensional stress deformation. According to the references [7, 8], when we want to study the local deformation analysis of the skin film, only the representative volume element (RVE) deformation needs to be selected for research, and the selected rectangular curved meso-component structural RVE is shown in Figure 2. The flexible skin thin film RVE is subjected to the tension along the biaxial directions of the \(x\)-axis and the \(y\)-axis to cause biaxial deformation, and the deformation in the \(z\)-axis direction has little effect on the load performance and deformation of the flexible skin film; therefore, it could be almost negligible. A similar matrix is composed of a fiber bundle matrix and various isotropic functional films. Since the fiber bundle matrix and various isotropic functional films are all isotropic materials, the fiber bundle matrix and various isotropic functional films could all be simplified as the similar matrix and marked as the matrix during modeling. In a plane stress state, the similar matrix stress in the \(x\) and \(y\) directions are \(\sigma_{xm}\) and \(\sigma_{ym}\), respectively. Since the biaxial RVE is subjected to tensile loads in two directions, it forms a curved structure within the _xoz_ and _yoz_ planes. The skin film exhibits an arc-shaped profile in each plane, and the corresponding arc radius is \(R_{x}\) in the _xoz_ plane, the corresponding radius of curvature is \(K_{x}\), and the central angle is \(\alpha\). Similarly, the arc radius is \(R_{z}\) in the _yoz_ plane (orthogonal to the _xoz_ plane), the corresponding radius of curvature is \(K_{y}\), and the central angle is \(\beta\)[7, 8]. The skin film is subjected to biaxial stress and produces tensile deformation. The tensile stresses in both the \(x\)-axis and the \(y\)-axis are the combined stresses between the fiber bundle and the matrix. Meanwhile, the skin film is also subjected to external/outside atmospheric environmental pressure \(P_{E}\), the aerodynamic pressure load \(P_{a}\), the internal/inside inflation pressure \(P_{int}\), and the self-gravity effect. Considering these factors, the equilibrium relationship for the skin film RVE, including self-gravity, can be expressed as follows: \begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **Symbol** & **Parameter** & **Value** \\ \hline
1 & \(E_{x}=E_{y}\) & Elastic modulus & 7.001 GPa \\ \hline
2 & \(\rho\) & Area density & 155 g/m\({}^{2}\) \\ \hline
3 & \(t\) & Thickness & 0.135 mm \\ \hline
4 & \(\mu\) & Poisson’s ratio & 0.3 \\ \hline
5 & \(l\) & Wing span & 1200 mm \\ \hline
6 & \(b\) & Wing chord length & 300 mm \\ \hline
7 & \(\rho_{d}\) & Body density & 962.963 kg/m\({}^{3}\) \\ \hline \end{tabular}
\end{table} 
Table 1: The material parameters of the flexible inflatable wing skin film. Here, \(\sigma_{x}\) and \(\sigma_{y}\) denote the internal film stresses in the \(x\)- and \(y\)-directions, respectively, and \(t\) represents the film thickness.