High-fidelity Aerostructural Optimization of Flexible Wings with Flutter Constraints

Abstract

High-fidelity optimization of aircraft has the potential to produce more efficient designs and to further reduce the risk of late design changes. For the optimization to generate a useful design, all the relevant constraints must be considered, including flutter. This is especially important in the high-fidelity aerostructural optimization of commercial aircraft, which is likely to result in high-aspect-ratio wing designs that are prone to flutter. To address this issue, we develop a flutter constraint formulation suitable for gradient-based aerostructural optimization with accurate and efficient adjoint derivatives. This approach scales well with the number of design variables and considers both structural sizing and aerodynamic planform variables. An effective bounding curve defines the flutter-free flight envelope, prevents discontinuities in the flutter constraint, and allows for minimum flutter speed to be specified implicitly. The flutter constraint formulation utilizes an efficient non-iterative p-k method, an effective bounding curve, and an aggregation technique that results in a single constraint in the optimization problem. Accurate and efficient derivatives of the flutter constraint value with respect to structural sizing variables and aerodynamic planform variables are computed. Furthermore, to enable changes in planform, derivatives of the mode shapes are also computed efficiently. The derivatives are computed using a combination of analytic and automatic differentiation methods in reverse mode (adjoint) and rigorously validated using the complex-step method. We perform a multipoint, high-fidelity aerostructural optimization of a wing and full configuration aircraft with and without the flutter constraint, subject to stress and buckling constraints. With the flutter constraint, we obtain a stiffer, lower aspect ratio wing with stark differences in structural sizing, but without a significant reduction in objective. These results demonstrate the importance of including flutter constraints in wing design optimization. The proposed approach can be used to enforce such constraints in other applications and could be adapted to constrain other types of phenomena with the same form.