Linearization of the Coupled Unsteady Fluid-Structure Equations: Application to Flutter Control

A method to compute sensitivities for use in gradient-based shape optimization applied to unsteady aeroelasticity problems is presented. The method takes into account the coupling between all three fundamental aspects of computational aeroelasticity, namely, unsteady flow equations, time varying structural response to aerodynamic loads, and dynamic meshes that accommodate geometric deformations. The devised method provides discretely exact sensitivities of time-integrated and non-time-integrated objective functions with respect to design variables that control the shape of geometry. The algorithm is formulated in a general manner and can be readily extended to coupled multidisciplinary problems involving any number of disciplines. The algorithm is applied to a simple two-dimensional flutter model in order to demonstrate the proof-of-concept.