Adjoint-Based Sensitivity Formulation for Fully Coupled Unsteady Aeroelasticity Problems

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 to demonstrate the proof of concept.

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