In this paper, a numerical approach based on a three-dimensional (3D) standard coupled boundary element method-finite element method (BEM-FEM) formulation in the frequency domain is presented. The approach allows studying the dynamics response of a structure bonded to the surface of a layered transversely isotropic half-space subjected to time-harmonic loading. The FEM is used to model the structure, and the BEM is employed for the soil, using layered half-space Green's functions, by which the radiation condition is implicitly satisfied. The BEM procedure is improved by implementing exponentially gradient (EG) elements to capture the singular behavior of tractions at the edges and corners of the soil-structure interface. The proposed approach is verified by comparison with existing semi-analytical and numerical results. Afterward, the dynamic response of a building on a layered transversely isotropic half-space subjected to lateral loading is studied, and the effect of soil layering on the response of the structure and interface tractions is demonstrated.

在本文中，提出了一种基于频域中三维 (3D) 标准耦合边界元法 - 有限元法 (BEM-FEM) 公式的数值方法。该方法允许研究粘合到分层横向各向同性半空间表面的结构的动力学响应，该结构受到时谐载荷。有限元法用于结构建模，边界元法用于土壤，使用分层半空间格林函数，隐式满足辐射条件。BEM 过程通过实施指数梯度 (EG) 元素来改进，以捕获土壤-结构界面边缘和拐角处牵引力的奇异行为。通过与现有的半解析和数值结果进行比较，验证了所提出的方法。之后，