Abstract In this paper, a modified scaled boundary finite element method is proposed to deal with the dynamic analysis of a discontinuous layered half-space. In order to describe the geometry of discontinuous layered half-space exactly, splicing lines, rather than a point, are chosen as the scaling center. Based on the modified scaled boundary transformation of the geometry, the Galerkin's weighted residual technique is applied to obtain the corresponding scaled boundary finite element equations in displacement. Then a modified version of dimensionless frequency is defined, and the governing first-order partial differential equations in dynamic stiffness with respect to the excitation frequency are obtained. The global stiffness is obtained by adding the dynamic stiffness of the interior domain calculated by a standard finite element method, and the dynamic stiffness of far field is calculated by the proposed method. The comparison of two existing solutions for a horizontal layered half-space confirms the accuracy and efficiency of the proposed approach. Finally, the dynamic response of a discontinuous layered half-space due to vertical uniform strip loadings is investigated.

中文翻译：

---

不连续分层半空间动态响应的一种修正标度边界有限元方法

摘要 本文提出了一种改进的尺度边界有限元方法来处理不连续分层半空间的动力分析。为了准确描述不连续分层半空间的几何形状，选择拼接线而不是一个点作为缩放中心。基于几何的修正缩放边界变换，应用伽辽金加权残差技术，得到相应的位移缩放边界有限元方程。然后定义了无量纲频率的修改版本，并获得了动态刚度相对于激励频率的控制一阶偏微分方程。全局刚度是通过加入标准有限元方法计算的内部域的动态刚度获得的，远场动刚度由所提出的方法计算。对水平分层半空间的两种现有解决方案的比较证实了所提出方法的准确性和效率。最后，研究了由于垂直均匀带钢载荷引起的不连续分层半空间的动态响应。