Static aeroelasticity analysis of very flexible wings based on physics-informed neural network and modal rotation method

High-altitude low-Reynolds-number solar-powered aircraft are characterized by high aspect ratios, lightweight structures, strong aerodynamic nonlinearities, and large aeroelastic deformations. However, the complex low-Reynolds-number flows, such as laminar separation bubbles, are tightly coupled with large deformations of very flexible structures, making it difficult for conventional aerodynamic models and linear structural analysis methods to accurately and efficiently predict the static aeroelastic responses. To address this challenge, this paper proposes a nonlinear static aeroelastic analysis method for very flexible wings by coupling a physics-informed neural network (PINN) with the modal rotation method. First, considering viscous effects, a PINN-based solver is established to compute the flow field and aerodynamic forces around airfoil sections, providing spanwise aerodynamic loads for high-aspect-ratio wings at low Reynolds numbers. Second, a structural model based on the modal rotation method is developed for the very flexible wing. Through interpolation and bidirectional coupling between aerodynamic loads and structural deformations, the static aeroelastic response characteristics are analyzed. Results show that, compared with experimental data, the flow fields predicted by the PINN yield relative errors within 8%. Under small deformation conditions, the static aeroelastic deformations computed by the proposed method agree with linear theory results within 5%. Furthermore, parametric studies on wings with varying bending stiffnesses reveal that the wingtip deflection increases logarithmically as stiffness decreases, accompanied by a significant redistribution of spanwise twist angles. When the bending stiffness is reduced by one order of magnitude, the effective angle of attack at the wingtip varies by more than 2°, and the mean lift coefficient decreases by over 14%, indicating that low stiffness substantially intensifies geometrical nonlinear effects and induces load redistribution. This study provides a useful reference for aeroelastic analysis and design of high-altitude solar-powered aircraft.