针对非定常流固耦合设计、分析问题所面临的计算效率与精度、鲁棒性之间的矛盾，采取将Chebyshev谱方法与基于非定常面元和几何非线性梁有限元模型的流固耦合分析方法相结合的方式，建立了针对大展弦比机翼非定常流固耦合优化设计问题的，可与伴随方法相结合的时间谱方法。Chebyshev谱方法直接对流固耦合的控制方程进行处理，利用Chebyshev算子替换系统状态变量，将非定常问题转化为Chebyshev控制点处耦合的定常问题。通过这种方式建立的流固耦合时间谱方法具有较高的计算精度、效率和足够的鲁棒性。验证算例及Goland机翼颤振速度计算实例表明，Chebyshev谱方法的计算精度随着Chebyshev控制点个数的增加而不断增大。只需选取较少的控制点，Chebyshev谱方法便可以达到满足精度要求的计算结果。与此同时，建立的流固耦合时间谱方法不仅适用于周期性非定常问题还适用于非周期性非定常问题。
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.
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