Nonlinear slender beam-wise schemes for structural behavior of flexible UAS wings

The innovative highly flexible wings made of extremely light structures, yet still capable of carrying a considerable amount of non- structural weights, requires significant effort in structural simulations. The complexity involved in such design demands for simplified mathematical tools based on appropriate nonlinear structural schemes combined with reduced order models capable of predicting accurately their aero-structural behaviour. The model presented in this paper is based on a consistent nonlinear beam-wise scheme, capable of simulating the unconventional aeroelastic behaviour of flexible composite wings. The partial differential equations describing the wing dynamics are expanded up to the third order and can be used to explore the effect of static deflection imposed by external trim, the effect of gust loads and the one of nonlinear aerodynamic stall. As to provide a rationale evaluation of the important nonlinear contributions in aeroelastic wing simulations, the aeroelastic governing equations in linear, quadratic, and cubic forms, are considered and compared. Critical conditions will be investigated. The governing equations will be solved based on a discretization technique, along with Galerkin's method starting with a reduced order procedure and passing through a multi-modal approach. Three degrees of freedom in edgewise, flapwise, and torsion, are needed to describe efficiently the dynamics of the wing. Interesting design indicators will be highlighted.