基于归一化傅里叶描述子的柔性翼肋结构指定变形设计

doi:10.3901/JME.2025.09.123

摘要/Abstract

摘要： 弦向变弯度机翼可以通过结构的变形，使机翼外形适用于不同的工况。柔性机构是实现机翼弦向变弯度的一种重要方式，通过指定变形柔性机构设计，能够实现翼肋结构由初始外形向目标外形的转变。结构指定变形设计问题中，需要描述变形后外形与目标外形的接近程度。区别于基于节点坐标的外形接近程度描述方法，引入傅里叶描述子的概念，消除了两个外形轮廓点一一对应的限制，验证了傅里叶描述子低频分量对轮廓的描述精度，讨论了基于归一化傅里叶描述子进行指定变形设计的优点。进而，采用拓扑优化中的各向同性材料惩罚模型，建立了基于归一化傅里叶描述子的指定变形优化列式，推导了目标函数的灵敏度，通过移动渐近线方法进行优化求解，得到指定变形的柔性机构拓扑。通过将归一化傅里叶描述子描述的外形扩大，消除非设计轮廓对优化结果的影响，得出了该方法的适用条件，验证了该方法在柔性翼肋结构指定变形优化上的可行性。

关键词: 拓扑优化, 指定变形, 柔性机构, 傅里叶描述子, 变体机翼

Abstract: The chordwise morphing wing can adapt its shape to different working conditions through structural deformation. The compliant mechanism is an important way to design chordwise morphing wing. Through specific deformation design, the rib structure can be transformed from the initial shape to the target shape. In the structure design problem of specified deformation, it is necessary to formulate a metric for shape-comparison between the deformed contour and the target contour. Different from the node coordinate-based shape-matching description method, the concept of Fourier descriptor is introduced, which removes the limitation of the one-to-one correspondence between two contours, verifies the accuracy of the low-frequency component of Fourier descriptors in describing the contour, and discusses advantages of the least quadratic square difference of normalized Fourier descriptors as the objective function for the design of specified deformation. Further, the isotropic material penalty model in topology optimization is used to establish the optimization formulation of specified deformation based on the normalized Fourier descriptors, the sensitivity of the objective function is deduced, and the optimization problem is solved using the method of moving asymptotes (MMA). Finally, the topology of the flexible mechanism with specified deformation is obtained. By expanding the contour described by the normalized Fourier descriptors and eliminating the influence of non-designed contours on the optimization results, the applicability conditions of the method are derived, and the feasibility of the method is verified for the optimization of specified deformation of flexible airfoil rib structures.

Key words: topology optimization, specified deformation, flexible mechanism, Fourier descriptors, morphing wing

中图分类号:

V224

牛斌, 于浩俣. 基于归一化傅里叶描述子的柔性翼肋结构指定变形设计[J]. 机械工程学报, 2025, 61(9): 123-131.

NIU Bin, YU Haoyu. Design Optimization of Flexible Airfoil Rib Structures for the Specified Deformation Based on Normalized Fourier Descriptors[J]. Journal of Mechanical Engineering, 2025, 61(9): 123-131.

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