基于模态扩展和曲率的形变混合重构

文中提出了一种基于模态扩展和曲率的形变混合重构方法，该方法在实物和有限元模型之间存在一定误差的情况下可以适当降低形变重构的误差。首先，通过模态实验在待重构的表面上均匀选取有限个测点来获取实验模态，接着用对应的有限元模态振型列表来平滑扩展这些实验模态，之后用平滑扩展的实验模态来重构大量的应变值，为了防止求取模态坐标时出现过拟合，此处引入了正则项。然后，将应变值转化为曲率，再通过切角递推公式求得相邻点的位移增量，随后耦合单元坐标增量便可获得全场的形变。最后，通过建立有限元模型进行仿真实验验证，并将此方法的重构结果与曲率法的结果进行对比以验证其有效性。

Hybrid Deformation Reconstruction Based on Mode Expansion and Curvature

In this paper, a hybrid deformation reconstruction method based on mode expansion and curvature is proposed. This method can appropriately reduce the error of deformation reconstruction when there is certain error between the real object and the finite element model. Firstly, the experimental modes are obtained by uniformly selecting a limited number of measuring points on the surface to be reconstructed, and then the corresponding finite element mode list is used to smoothly expand the obtained experimental modes. After that, a large number of strain values are reconstructed by the smoothly expanded experimental modes, and a regular term is introduced here to prevent over-fitting when obtaining modal coordinates. Secondly, the strain value is transformed into curvature and the displacement increment of the adjacent points is obtained by the chamfer recurrence formula, and then the deformation of the whole field can be obtained by coupling the coordinate increment of the element. Finally, a finite element model is established to carried out simulation verification. The reconstruction results of this method are compared with those of the curvature method to verify its effectiveness.