A CR theory-based approach for solving nonlinear aeroelasticity of very flexible wings

Very flexible wings under aerodynamic loads tend to produce larger deformation, it results in significant changes in inertial and stiffness characteristics, and dynamic aeroelastic features, the linear aeroelastic analysis method is no longer applicable. Here, based on the co-rotational (CR) theory, the tangent stiffness matrix and mass matrix of a wing after deformation were derived, the structural dynamic model of very flexible wings considering geometric nonlinearity was then established. Coupled with ONERA dynamic stall model, an efficient method to solve nonlinear aeroelasticity of very flexible wings was proposed. Using Newmark direct integration method and loose coupled algorithms, a numerical procedure for solving nonlinear aeroelastic dynamic equations was presented, and the efficiency and precision of the method were verified through tests. The results showed that structural and aerodynamic nonlinearities should be considered for complete nonlinear dynamic aeroelastic simulations of very flexible wings; the wing's critical limit cycle oscillation speed decreases 15% or more due to its bending deformation, but it increases through shifting forward the wing's elastic axis; the proposed method has a good precision and efficiency, and meets requirements of nonlinear aeroelastic analysis of very flexible wings.