Nonlinear flexibility effects on flight dynamics of high-aspect-ratio wings

This paper quantifies, in a systematic parametric fashion, the manner in which geometric nonlinearity and structural flexibility alter the flight dynamic characteristics of high-aspect-ratio wings representative of high-altitude long-endurance (HALE) aircraft. A coupled aeroelastic-flight dynamic model is assembled from established constituent formulations-a geometrically-exact beam representation of the structural dynamics, unsteady two-dimensional strip theory for the aerodynamic loading, and quaternion-based rigid-body equations for the flight mechanics-into a monolithic system in which consistent load and motion transfer is enforced at every integration time step. The contribution lies not in new modelling methodology but in the systematic single-parameter investigation this framework enables: the wing stiffness is varied continuously across four orders of magnitude through a non-dimensional flexibility parameter, spanning from effectively rigid to highly flexible configurations, with planform, mass distribution, and flight condition held fixed. The study reveals that increasing flexibility profoundly modifies the trim conditions, flutter boundaries, and the dynamic gust response. In particular, over the flexibility range in which the trimmed state is physically valid, the trim angle of attack is found to vary non-monotonically with flexibility: torsional wash-in initially lowers the required trim angle, whereas increasing static deformation produces an effective dihedral that reorients the local lift vectors and, as the wing bends further, demands higher trim angles to maintain vertical force equilibrium. The degradation of flutter speed with increasing flexibility is quantified through an aeroelastic mode-tracking analysis and is shown to depend on whether the pre-stressed equilibrium state is incorporated, with the pre-stress correction reaching about three per cent at the upper end of the physically valid flexibility range. Consistent with previously published findings, flexibility is found to erode longitudinal flight-dynamic (phugoid) stability so that active control becomes essential; the present framework, constructed and validated for the aeroelastic response, treats this trend qualitatively and does not claim quantitative flight-dynamic eigenvalues, which require a dedicated flight-mechanics model. The framework is validated against established HALE aircraft benchmark cases, demonstrating close agreement in structural natural frequencies, flutter and divergence speeds, and rigid-aircraft trim; the static aeroelastic deflections are conservative (overpredicted) with respect to three-dimensional aerodynamic references, a documented consequence of the two-dimensional strip aerodynamics that is discussed openly in the paper. The results provide quantitative criteria for identifying the conditions under which linear analysis remains adequate and the circumstances under which fully coupled nonlinear computational tools become indispensable.