Dynamic Green’s function for a three-dimensional concentrated load in the interior of a poroelastic layered half-space using a modified stiffness matrix method.

*(English)*Zbl 1403.74315Summary: This paper presents a new modified stiffness matrix method for the dynamic response analysis of a three-dimensional poroelastic layered half space subject to internal concentrated loads. This three-dimensional problem can be simplified as two two-dimensional problems consisting of the in-plane response and the anti-plane response. Similar to the principle of displacement method in structural mechanics, firstly, the top and bottom surfaces of a loaded layer are fixed, and the reaction forces at two “fixed ends” can be obtained using the superposition of the particular and homogeneous solution. Secondly, the displacement at the layer interface can be obtained using a direct stiffness method. In the loaded layer, the Greens function is decomposed into the particular solution, the homogeneous solution and the reaction solution, and the particular solution can be replaced by the analytical solution for the poroelastic full space. With this technique, the convergence problem due to the improper integral can be addressed with sources and receivers at similar or at the same depth, and a fictitious surface does not need to be introduced as in the traditional method. Finally, the results of the dynamic response of a poroelastic layered half space are presented both in the frequency and time domain.

##### MSC:

74S30 | Other numerical methods in solid mechanics (MSC2010) |

65N80 | Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

##### Keywords:

Green’s function; poroelastic layered half-space; dynamic concentrated load; modified stiffness matrix method
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\textit{Z. Liu} et al., Eng. Anal. Bound. Elem. 60, 51--66 (2015; Zbl 1403.74315)

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