Abstract A new semi-analytical method is developed for solving the dynamic response of an embedded flexible foundation of general shape in a transversely isotropic and multilayered half-space. It is based on the hybrid Green's functions (GFs) and finite-element method (FEM) via the modified subtraction method. The GFs in the multilayered half-space are derived by virtue of the dual variable and position (DVP) method whilst the FEM is utilized to discretize the domain of the embedded foundation. Making use of the modified subtraction method, the GFs and FEM formulations are combined to derive the dynamic impedance matrix of the embedded foundation. After verifying the accuracy and stability of the proposed algorithm, numerical studies are carried out to investigate the effect of the foundation modulus, half-space anisotropy, and layering on the dynamic impedance matrix of the embedded foundation. Results show that these factors could significantly affect the dynamic impedance matrix of the foundation, which could provide reference for practical engineering design.

中文翻译：

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横向各向同性多层半空间中一般形状嵌入式柔性基础的动力响应

摘要 开发了一种新的半解析方法，用于求解横向各向同性多层半空间中一般形状的嵌入式柔性基础的动力响应。它基于混合格林函数 (GFs) 和有限元法 (FEM)，通过改进的减法方法。多层半空间中的 GF 是通过双变量和位置 (DVP) 方法导出的，而 FEM 用于离散嵌入式基础的域。利用修正减法方法，结合GFs和FEM公式，推导出嵌入式地基的动态阻抗矩阵。在验证了所提出算法的准确性和稳定性后，进行数值研究以研究基础模量、半空间各向异性、并在嵌入式基础的动态阻抗矩阵上分层。结果表明，这些因素对地基的动态阻抗矩阵有显着影响，可为实际工程设计提供参考。