基于逆向有限元法的变形机翼鱼骨的变形重构

变形监测技术能够为自适应变形机翼的变形控制系统提供参考信息，是保证结构安全性以及优化结构的运行性能的重要手段。传统的基于光学成像的变形测量方法已经不能满足自适应智能结构的实时变形监测的要求。由于变形机翼表面受气动载荷影响，不便于直接在变形机翼蒙皮表面布置应变传感系统，目前还没有针对鱼骨结构这种真实复杂机翼结构的变形重构研究，大多针对机翼翼型的变形重构研究是将整个机翼简化成简单的翼形板、梁结构。针对上述问题，本文首次以真实复杂变形机翼主承力结构——鱼骨为研究对象，提出了一种基于逆向有限元（iFEM）算法与位移分段叠加思想结合的变形监测方法，根据Mindlin板变形理论建立四节点逆向壳单元，采用应变传感系统测得鱼骨结构表面应变分布作为算法输入，然后基于最小二乘变分方程求解结构应变场和位移场之间的传递函数，重构鱼骨结构的变形形状，为反演机翼翼型的变形形状提供方法。针对真实自适应变形机翼的主要承力构件开展了变形实验，实验结果表明，机翼鱼骨在分别偏转5°、10°、15°的情况下，逆向有限元法能准确重构鱼骨变形形状，验证了基于逆向有限元法的变形重构方法在真实自适应变形机翼结构变形重构研究中的有效性和准确性。

Shape reconstruction of self-adaptive morphing wings' fishbone based on inverse finite element method

Benefiting from the ability of providing reference information for deformation-control system, shape sensing technology is considered as an important way to guarantee the safety and improve the operational performance of self-adaptive morphing structures. However, the conventional optical imaging based shape sensing technologies are unable to meet the need of real-time shape sensing of self-adaptive morphing structures. In this paper, a shape sensing technology based on the inverse Finite Element Method (iFEM) and the idea of superposing segmented displacement is proposed to reconstruct the deformation of morphing wing’s major load-bearing structure of fishbone. Firstly, a four-node quadrilateral inverse-shell element is developed based on Mindlin deformation theory for the major load-bearing structure of the morphing wing. Secondly, strain sensors are used to obtain strain distribution of the structure surface as the input of the proposed method. Then the transfer function between the strain field and the displacement field can be obtained by adopting the least square variational equation. Finally, the corresponding displacement of the major load-bearing structure is reconstructed, based on which the reconstruction of wing deformation can be realized. The proposed method is verified through experiments performed on the major load-bearing structure of a morphing wing. The results show that under the deflection angles of 5°, 10°, and 15° of the morphing wing, the reconstructive displacements have a strong consistency with measured displacements, which verifies the feasibility and accuracy of the proposed method.