Non-Linear and Quasi-Linear Models for the Large-Amplitude Static Aeroelastic Response of Very-Flexible Slender Wings in Subsonic Flow at Low Speed

In the framework of lightweight aircraft preliminary design and optimisation, different computational approaches are formulated and assessed for the large-amplitude static aeroelastic response of very-flexible slender thin wings in subsonic incompressible flow at low speed. Starting from either a continuous or a discrete model, either numerical or semi-analytical solutions are derived and compared for several combinations of flow speed and angle of attack. Exploiting the Euler–Bernoulli beam idealisation for the wing structure and its local deformation, non-linear and quasi-linear models are presented where the elastic axis is inextensible and its global displacement is geometrically nonlinear; to this purpose, Hencky’s model is also adopted. Employing modified strip theory for the airload, reduced-order conceptual assessments and parametric evaluations are possible, and the results are shown for the Pazy wing which exhibit excellent agreement with nonlinear higher-fidelity simulations in the literature. Both closed-loop and open-loop solutions are then provided, with the latter being readily resumed from the former in the low-speed limit far away from static aeroelastic divergence. In conclusion, the novel approaches hereby explored demonstrate overall consistency while offering both theoretical insights and practical recommendations for their trust region, especially in terms of the impact and importance of the linear and nonlinear features as well as their effects.