# 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
For the isotropic material \(E_{x}=E_{y}=E\), the strain-deformation relationship under the pressure-holding condition of the above biaxial flexible skin film could be further simplified as follows:  
\[\left\{ \begin{array}{l}\varepsilon_{x}=\frac{(p_{in}-p_{E}-p_{a}-\rho g)}{Et/R _{y}}\frac{n-\mu^{2}n}{1+2\mu\mu^{2}}\\ \varepsilon_{y}=\frac{(p_{in}-p_{E}-p_{a}-\rho g)}{Et/R_{y}}\frac{1-\mu^{2}}{1+ 2\mu\mu+n^{2}}\end{array} \right. \tag{7}\]  
Because the excessive deformation of the flexible film (inducing the severe stiffness deformation) seriously affects the aerodynamic performance of the flexible inflated wing and the required load bearing function, it is necessary to study the local deformation stiffness of the flexible skin film, meanwhile, due to the excessive aerodynamic load, which would make the inflatable wing susceptible to wrinkle deformation failure and even cracking. The whole stiffness design needs to comprehensively consider the biaxial deformation limit of the skin film around the inflatable wing, including the flexible film material selection, structural configuration design, connection method, etc. And the strain deformation state and the excessive deformation of the flexible film skin could be verified with the method of the finite element simulation. In order to make the inflatable wing meet the stiffness requirement, according to the strain deformation criterion, the biaxial strain value of the wing skin at any position under the pressure holding state should be required to be smaller than the allowable value [\(\varepsilon\)] of the skin flexible film material; [\(\varepsilon\)] is the smaller value of the allowable strain of the fiber yarn bundle [\(\varepsilon_{f}\)] and the allowable strain of the fiber yarn bundle [\(\varepsilon_{m}\)], and the \(\varepsilon_{b}\) limit strain is the smaller value of the ultimate strain of the fiber yarn bundle \(\varepsilon_{mb}\) and the ultimate strain of the fiber yarn bundle \(\varepsilon_{mb}\). That is,  
\[ \begin{array}{l}\varepsilon_{x}\leq[\varepsilon]=\frac{\varepsilon_{b}}{n_{ f}},\ \ \ \varepsilon_{y}\leq[\varepsilon]=\frac{\varepsilon_{b}}{n_{f}}\\ \left[\varepsilon\right]=\min(\left[\varepsilon_{f}\right],\left[\varepsilon_ {m}\right]),\varepsilon=\min(\varepsilon_{fb},\varepsilon_{mb})\end{array}  \tag{8}\]  
In the relational formula, \(\varepsilon_{b}\) is the corresponding tensile deformation limit value when the flexible skin film material fails, which could be determined by the biaxial-uniaxialtensile elongation deformation test, and a smaller value could be taken. Here, \(n_{f}\) represents the safety factor for the selected film materials. Considering the comprehensive influencing factors of internal inflation pressure, environmental pressure and aerodynamic load, and the properties of flexible skin film, the strain deformation analysis model and deformation stiffness condition are proposed for the flexible inflatable wing skin film material under biaxial load-bearing conditions. When the strain deformation at a certain position of the inflatable wing skin film material is greater than the allowable strain value of the material, the wing skin film might locally deform excessively to damage or seriously affect the aerodynamic shape so that the flexible inflatable wing would be twisted as a whole. The failure eventually leads to large deformation of the entire wing and thus loses the original aerodynamic performance. A strain-deformation model is proposed for biaxial loading, considering internal pressure, external loads, and material properties. If local strain exceeds \([\varepsilon]\), the wing may become distorted, losing aerodynamic function. Thus, inflation pressure must be optimized to maintain deformation within permissible limits.