Two efficient methods are presented to detect multiple cracks in 2D elastic bodies, based on the insights from Extended Finite Element. Adetection mesh is assigned to the cracked body and the responses are measured at the nodes. A finite element model with the same mesh is used to represent the uncracked state of the physical body. In the first method which is called Crack Detection based on Residual Error (CDRE), the residual error norm is calculated based on the uncracked body stiffness matrix and the cracked body responses. The contour of the error norm would show the crack pattern; the method is computationally efficient. In the second method that is coined as Crack Detection based on Stiffness Residual (CDSR), the crack locations are found based on the difference between the stiffness matrix of the cracked body and the uncracked body. The stiffness matrix of the cracked body is found by solving a dynamic inverse problem based on a modified Tikhonov regularization. The efficiency and accuracy of the identification method are enhanced by predicting the crack pattern by the CDRE method. Several examples are presented to show the accuracy and robustness of the methods in the presence of high noise levels.

基于扩展有限元的见解，提出了两种有效的方法来检测二维弹性体中的多个裂纹。将检测网格分配给裂纹体，并在节点处测量响应。具有相同网格的有限元模型用于表示物理体的未破裂状态。在第一种方法称为基于残差的裂纹检测（CDRE）中，残差范数基于未破裂的车身刚度矩阵和破裂的车身响应进行计算。误差范数的轮廓将显示裂纹模式。该方法计算效率高。在第二种方法中，该方法被称为基于“残差刚度”（CDSR）的裂纹检测，基于裂纹体和未裂纹体的刚度矩阵之间的差异来找到裂纹位置。通过基于修正的Tikhonov正则化方法解决动态逆问题，可以找到裂纹体的刚度矩阵。通过使用CDRE方法预测裂缝模式，可以提高识别方法的效率和准确性。给出了几个例子来说明在高噪声水平下该方法的准确性和鲁棒性。