Semi-analytical FEM for modelling 3D guided waves scattering in an infinite plate

Reconstructing true flaw shapes in three-dimensional (3D) structures using ultrasonic guided waves is still a challenging problem nowadays. Therefore, a thorough and visual analysis of 3D guided waves scattering interacting with defects is urgently needed. The 3D semi-analytical finite element method (FEM) proposed in this paper can not only have advantages on mesh reduction and need no absorption medium or perfectly matched layer to suppress the reflected waves compared to traditional FEM, but also can directly obtain the scattering coefficients of each guided wave to visualize the scattering phenomena and mechanism. Moreover, the virtual non-reflecting boundary is processed perfectly, thus eliminating all spurious reflected waves. A three-step strategy of this method is performed as follows: Firstly, the 3D scattered waves at the virtual boundary are represented by a series of Lamb and SH cylindrical guided waves of Bessel function form with unknown scattering coefficients; Secondly, utilizing the mode orthogonality, the unknown tractions at the virtual boundary are expressed in terms of the unknown scattering displacements at the virtual boundary via scattering coefficients; Thirdly, this linear relationship at the virtual boundary can be assembled into the global FEM matrix to solve the problem. This method is implemented to analyze the scattering phenomena due to symmetric defects in a 3D infinite plate. The correctness and effectiveness of the proposed method is finally validated compared with existing methods, and the scattering mechanisms of different defect types, shapes and sizes are discussed in detail.