一种针对局部结构的有限元模型修正方法

针对实际结构有限元模型（FEM）的建模误差通常仅存在于局部区域，提出了一种对局部结构单独进行模型修正的方法。首先，根据频响函数（FRF）解耦理论得到由残余结构频响函数与包含待修正参数的局部结构动刚度所重构的整体结构频响函数的拟合值，然后通过迭代优化使其与测量值的残差最小化，从而得到参数的极大似然估计。在此基础上，将残差关于参数的灵敏度以局部结构动力学矩阵表示，建立了模型修正的基本方程，利用整体结构的测试数据即可直接对分离出来的局部结构进行模型修正。最后，对喷气式飞机和三角机翼飞机分别进行了数值模拟和实验研究，验证了所提方法的可行性和有效性。结果表明，所提方法可以成功地用于仅局部区域含有建模误差的实际结构有限元模型的修正，修正后的有限元模型的动态特性与实际结构有较好的一致性。

A finite element model updating method for local structures

For an actual structure, the modeling errors of the Finite Element Model(FEM) often only exist in some local area. A model updating method is presented to update the local structures. Firstly, according to the Frequency Response Function (FRF) decoupling method, the fitting FRF of the global structure is reconstructed from the residual structure FRF and the local structure dynamic stiffness including the parameters to be updated. Then, the iterative optimization process of maximum likelihood estimation is carried out to get the parameters minimizing the residual error between the fit value and the measured value. On this basis, the sensitivity of the residual error to the parameters is represented by the dynamic matrix of the local structure, and the fundamental equation for model updating is constructed. The measured FRF of the global structure is utilized to update the FEM of the separated local structure directly. Finally, numerical simulation of a jet plane and experimental investigation of the delta-winged aircraft are performed to validate the feasibility and efficiency of the present method. The obtained results show that the proposed method can be successfully used to update the model of the actual structure with modeling errors only in the local area, achieving a good agreement between the dynamic properties of the updated FEM and the actual structure.