In this paper, a two-dimensional Dirichlet-to-Neumann (DtN) finite element method (FEM) is developed to analyze the scattering of SH guided waves due to an interface delamination in a bi-material plate. During the finite element analysis, it is necessary to determine the far-field DtN conditions at virtual boundaries where both displacements and tractions are unknown. In this study, firstly, the scattered waves at the virtual boundaries are represented by a superposition of guided waves with unknown scattered coefficients. Secondly, utilizing the mode orthogonality, the unknown tractions at virtual boundaries are expressed in terms of the unknown scattered displacements at virtual boundaries via scattered coefficients. Thirdly, this relationship at virtual boundaries can be finally assembled into the global DtN-FEM matrix to solve the problem. This method is simple and elegant, which has advantages on dimension reduction and needs no absorption medium or perfectly matched layer to suppress the reflected waves compared to traditional FEM. Furthermore, the reflection and transmission coefficients of each guided mode can be directly obtained without post-processing. This proposed DtN-FEM will be compared with boundary element method (BEM), and finally validated for several benchmark problems.

翻译：本文发展了一种二维Dirichlet-to-Neumann（DtN）有限元法（FEM），用于分析双材料板中界面分层引起的SH导波散射问题。在有限元分析过程中，需确定虚拟边界处的远场DtN条件，该边界上的位移与面力均为未知。本研究首先将虚拟边界处的散射波表示为具有未知散射系数的导波叠加形式。其次，利用模态正交性，通过散射系数将虚拟边界处的未知面力用该处的未知散射位移表示。再次，虚拟边界处的这一关系最终可组装到全局DtN-FEM矩阵中以求解该问题。该方法简洁而优美，与传统FEM相比，在降维方面具有优势，且无需吸波介质或完美匹配层来抑制反射波。此外，各导波模式的反射与透射系数可直接获取，无需后处理。所提出的DtN-FEM将与边界元法（BEM）进行比较，并最终通过若干基准算例进行验证。