In this study, a directional interpolation infinite element suited to a saturated porous medium is presented to account for dynamic problems with semi-infinite or infinite domain. By employing the Galerkin method, the element property matrixes for a two-dimensional space are given. Using the governing differential equations for wave propagation in the saturated porous media, the analytical solutions for one-dimensional wave propagation are derived in detail. Then the shape functions for the infinite element based on the analytical solutions are formulated and the dynamic stiffness matrix is presented in analytical form is presented. As a result, a fully coupled 2D infinite element for the analysis of dynamic problems in unbounded saturated porous media is presented. The effectiveness and accuracy of the proposed element is well demonstrated by a comparison of the numerical results with known analytical solutions for 1D and 2D wave propagation problems. The results highlight that the proposed directional interpolation infinite element is useful and effective for addressing the dynamic problems with semi-infinite or infinite domain, with consideration of both compression and shear waves.

中文翻译：

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饱和多孔介质动力问题的方向插值无限元

在这项研究中，提出了一种适用于饱和多孔介质的方向插值无限元，以解决半无限或无限域的动力学问题。通过采用Galerkin方法，给出了二维空间的元素属性矩阵。利用控制波在饱和多孔介质中的传播微分方程，详细推导了一维波传播的解析解。在此基础上，建立了基于解析解的无限元形状函数，并以解析形式给出了动态刚度矩阵。结果，提出了用于分析无界饱和多孔介质中动力问题的全耦合二维无限元。通过将数值结果与一维和二维波传播问题的已知解析解进行比较，可以很好地证明所提出元件的有效性和准确性。结果表明，所提出的方向插值无限元对于解决半无限或无限域的动力学问题，既考虑压缩波又考虑剪切波，是有用且有效的。