Design Optimization of Flexible Airfoil Rib Structures for the Specified Deformation Based on Normalized Fourier Descriptors

doi:10.3901/JME.2025.09.123

Abstract

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

CLC Number:

V224

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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