# The Effect of Inflatable Pressure on the Strain Deformation of Flexible Wing Skin Film
## 1 Introduction  
Flexible inflatable wings, characterized by their lightweight construction, high folding ratio, and rapid deployment [1, 2, 3], offer significant advantages for unmanned aerial vehicles (UAVs), high-altitude platforms, and cross-domain aircraft. The core structure, composed of flexible membranes (e.g., TPU or fiber-reinforced composites), maintains an aerodynamic shape and bears loads through internal inflation pressure [4, 5]. As a key control parameter, inflation pressure directly governs the biaxial stress state, strain distribution, and structural deformation characteristics of the wing membrane [6, 7]. Research demonstrates that the membrane exhibits a typical biaxial stress state under pressure [1, 7]. Membrane theory and static equilibrium models indicate that increasing inflation pressure significantly elevates spanwise and chord-wise stresses, establishing a defined biaxial stress relationship [1]. Finite element simulations further reveal significant strain non-uniformity; high-curvatureregions (e.g., wing root and tip connections) are prone to stress concentration and warpage, while low-curvature regions experience gentler stress gradients [8; 9; 10]. Inflation pressure modulates overall deformation behavior by altering the membrane's biaxial stiffness. Insufficient pressure can lead to folds on the compressive surface, causing local stiffness degradation and potential bending-torsional instability; conversely, pressure increases linearly enhance wing bending stiffness and critical buckling load [4; 9]. Experimental data confirms this stiffening effect, showing an approximately 250% increase in wing stiffness as pressure rises from 10 kPa to 35 kPa [4]. However, the coupling effects of ambient temperature and aerodynamic loads can exacerbate the nonlinear evolution of strain. Temperature increases alter the membrane's elastic modulus and amplify biaxial stress via thermal expansion, potentially leading to unbalanced Mises stress distributions, particularly between the root and tip regions [7]. Wind tunnel tests indicate that aerodynamic loads interacting with the internal chamber structure can induce a \"wavy\" wing surface, potentially triggering flow separation and further intensifying local strain [10; 11]. Unlike prior studies investigating thermal effects [7], this work establishes a novel pressure-strain framework for flexible inflatable wings, revealing asymmetric biaxial deformation patterns and providing strain-constrained pressure design rules. Therefore, while inflation pressure dominantly controls membrane strain and deformation through biaxial stress adjustment, its coupling mechanisms with material properties, environmental factors, and structural design require further quantitative investigation. Flexible inflatable wings, leveraging their high storage ratio, lightweight nature, and excellent damage tolerance, represent key technology for UAVs and space-deployable structures [11; 12; 13; 14]. The core mechanism relies on using internal pressure to control the membrane's biaxial stress state, thereby influencing strain distribution, dynamic response, and aerodynamic performance. A significant nonlinear relationship exists between inflation pressure and membrane strain. While high-pressure inflation enhances structural stability, it may accelerate material fatigue and increase leakage risk [15]. Conversely, low-pressure environments (e.g., below 25 psi) reduce system mass but can induce membrane wrinkling, local strain concentration, and bending stiffness attenuation [16; 17; 18]. To address this stability-efficiency trade-off, variable inflation rate control strategies have been proposed. Combining instantaneous optimal control (IOC) with extended position dynamics (XPBD) allows for dynamic adjustment of the inflation rate based on real-time strain. Simulations demonstrate that this approach can reduce kinetic energy deployment by 40%, shorten deployment time by 30%, and significantly suppress oscillations in structures like fourfold tubes [13].