Nonlinear-structural-nonlinear-aerodynamic model for static aeroelastic problems

The study presents the derivation and application of a nonlinear modal-based structural model for static aeroelastic applications. The model, intended for geometrically nonlinear structures, of large deformations, analyzes the deformations of a beam structure by dividing it into a few segment. Large deformations are treated as the sum of large, rigid-body displacements of the segment, plus small, linear, elastic deformation within the segment. The novelty of the approach is that the elastic deformations at each segment are computed using a modal approach, with fictitious masses to facilitate the coupling between segments. The use of the modal approach in a large deformations case introduces difficulties in the application of compatibility equations between segments that are explained and addressed in the paper. The numerical examples include several load cases that validate the implementation of the methodology and demonstrate its use for static aeroelastic applications. The first test case is of a beam subject to a large follower tip forces. Results are in good agreement with those computed by a commercial nonlinear finite element solver, while introducing great improvement in the computational efficiency. The second test case describes a beam subject to aerodynamic loads at various air speeds, and angles of attack. In this case, the nonlinear structural model is coupled with a modified strip model, based on CFD rigid simulations. Comparison with linear-aero linear-structural model shows excellent agreement in the low air speeds, highlighting the shortcomings of the linear-structural-linear-aerodynamic model in representing highly flexible structures under large aerodynamic loads.