Three-dimensional time-harmonic Green's functions of saturated soil under buried loading

2007 ◽  
Vol 27 (5) ◽  
pp. 448-462 ◽  
Author(s):  
S.L. Chen ◽  
L.Z. Chen ◽  
E. Pan
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Saturated Soil ◽  
Time Harmonic

A Method to Evaluate Three-Dimensional Time-Harmonic Elastodynamic Green’s Functions in Transversely Isotropic Media

1992 ◽  
Vol 59 (2S) ◽  
pp. S96-S101 ◽  
Author(s):  
H. Zhu
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Isotropic Case ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Transversely Isotropic Media ◽  
Time Harmonic ◽  
Isotropic Media

The three-dimensional time-harmonic elastodynamic Green’s functions in infinite transversely isotropic media have been derived explicitly. The Green’s functions consist of the corresponding static Green’s functions and double integral representations over a finite domain with the integrands being continuous. The Green’s functions will reduce to those for the isotropic case when the isotropic elastic constants are substituted. The singular parts of the Green’s functions have been shown to be the same as those of the static ones. The far-field approximations have been obtained by using the stationary phase method. In addition, a simpler method to construct wave front curves has been presented.

Three-Dimensional Green’s Functions in Anisotropic Elastic Bimaterials With Imperfect Interfaces

2003 ◽  
Vol 70 (2) ◽  
pp. 180-190 ◽  
Author(s):  
E. Pan
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Imperfect Interface ◽  
Boundary Integral ◽  
Stress Fields ◽  
Superposition Method ◽  
Interface Conditions ◽  
Complementary Part ◽  
Anisotropic Elastic

In this paper, three-dimensional Green’s functions in anisotropic elastic bimaterials with imperfect interface conditions are derived based on the extended Stroh formalism and the Mindlin’s superposition method. Four different interface models are considered: perfect-bond, smooth-bond, dislocation-like, and force-like. While the first one is for a perfect interface, other three models are for imperfect ones. By introducing certain modified eigenmatrices, it is shown that the bimaterial Green’s functions for the three imperfect interface conditions have mathematically similar concise expressions as those for the perfect-bond interface. That is, the physical-domain bimaterial Green’s functions can be obtained as a sum of a homogeneous full-space Green’s function in an explicit form and a complementary part in terms of simple line-integrals over [0,π] suitable for standard numerical integration. Furthermore, the corresponding two-dimensional bimaterial Green’s functions have been also derived analytically for the three imperfect interface conditions. Based on the bimaterial Green’s functions, the effects of different interface conditions on the displacement and stress fields are discussed. It is shown that only the complementary part of the solution contributes to the difference of the displacement and stress fields due to different interface conditions. Numerical examples are given for the Green’s functions in the bimaterials made of two anisotropic half-spaces. It is observed that different interface conditions can produce substantially different results for some Green’s stress components in the vicinity of the interface, which should be of great interest to the design of interface. Finally, we remark that these bimaterial Green’s functions can be implemented into the boundary integral formulation for the analysis of layered structures where imperfect bond may exist.

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