Abstract: Regarding the contradiction between computational efficiency, precision and robustness of design and analysis of unsteady fluid-structure coupling problems, a time spectral method which can couple with adjoint to solve the unsteady fluid-structure coupling optimization design problems of high-aspect-ratio wings is established in this paper. The time spectral method is built by directly coupling the Chebyshev spectral method with a fluid-structure interaction analysis method based on the unsteady panel method and the geometrically-nonlinear beam finite element model. The Chebyshev spectral method uses Chebyshev operators to replace the state parameters of the whole system, and then transforms the unsteady problems into steady problems. In this way, the built fluid-structure time spectral method has a high computational precision, high calculation efficiency and enough robustness. Validation cases and calculation of the flutter speed of Goland wings indicate that the calculation precision of the Chebyshev spectral method is improved continuously with the increase of the number of Chebyshev collocation points. With very few collocation points, the Chebyshev spectral method can obtain the calculation results of required accuracy. The time spectral method proposed is suitable for both periodic and non-periodic unsteady problems.

Key words: time spectral method, Chebyshev, optimization design, aeroelasticity, unsteady, non-periodic, geometrically-nonlinear