Three-dimensional Green’s function for an anisotropic multi-layered half-space

2015 ◽  
Vol 56 (5) ◽  
pp. 795-814 ◽  
Author(s):  
Lin Chen
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Three Dimensional ◽  
Layered Half Space

The Method of Generalized Ray-Revisited

2000 ◽  
Vol 16 (1) ◽  
pp. 37-44
Author(s):  
Franz Ziegler ◽  
Piotr Borejko
Keyword(s):  
Wave Propagation ◽  
Parallel Computing ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Plane Waves ◽  
Solution Technique ◽  
New Developments ◽  
Infinite Space ◽  
Layered Half Space

ABSTRACTBased on a landmark paper by Pao and Gajewski, some novel developments of the method of generalized ray integrals are discussed. The expansion of the dynamic Green's function of the infinite space into plane waves allows benchmark 3-D solutions in the layered half-space and even enters the background formulation of elastic-viscoplastic wave propagation. New developments of software of combined symbolic-numerical manipulation and parallel computing make the method a competitive solution technique.

Three-dimensional static Green's function for a half space over mixed PEC and dielectric wedges

2014 ◽  
Vol 72 (3) ◽  
pp. 203-209
Author(s):  
Ehsan Zareian-Jahromi ◽  
Seyed Hossein H. Sadeghi ◽  
Reza Sarraf-Shirazi ◽  
Rouzbeh Moini ◽  
Fabio Napolitano
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Three Dimensional

The Three-Dimensional Infinite Space and Half-Space Green's Functions for Orthotropic Materials

2014 ◽  
Vol 31 (1) ◽  
pp. 21-28
Author(s):  
V.-G. Lee
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Mathematical Concept ◽  
Orthotropic Materials ◽  
Superposition Method ◽  
Infinite Domain

ABSTRACTCommon materials, ranging from natural wood to modern composites, have been recognized as ortho-tropic materials. The elastic properties of such materials are governed by nine elastic constants. In this paper the complete set of Green's functions for an infinite medium and a half space is given, which were not reported completely before. Analytic expressions for the infinite Green's functions are derived through the explicit form of the sextic equation given explicitly. For an orthotopic half space, the Green's function is derived by a superposition method. The mathematical concept is based on the addition of a complementary term to the Green's function in an orthotropic infinite domain to fulfill the boundary condition on the free surface. Both solutions are illustrated in certain directions to demonstrate the nature of orthotropy.

Three-Dimensional Green's Function for a Layered Isotropic Half-space

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 713-714
Author(s):  
Lin Chen ◽  
Christoph Butenweg ◽  
Sven Klinkel
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Three Dimensional

Three-Dimensional Green’s Functions in an Anisotropic Half-Space With General Boundary Conditions

2003 ◽  
Vol 70 (1) ◽  
pp. 101-110 ◽  
Author(s):  
E. Pan
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Different Boundary Conditions

This paper derives, for the first time, the complete set of three-dimensional Green’s functions (displacements, stresses, and derivatives of displacements and stresses with respect to the source point), or the generalized Mindlin solutions, in an anisotropic half-space z>0 with general boundary conditions on the flat surface z=0. Applying the Mindlin’s superposition method, the half-space Green’s function is obtained as a sum of the generalized Kelvin solution (Green’s function in an anisotropic infinite space) and a Mindlin’s complementary solution. While the generalized Kelvin solution is in an explicit form, the Mindlin’s complementary part is expressed in terms of a simple line-integral over [0,π]. By introducing a new matrix K, which is a suitable combination of the eigenmatrices A and B, Green’s functions corresponding to different boundary conditions are concisely expressed in a unified form, including the existing traction-free and rigid boundaries as special cases. The corresponding generalized Boussinesq solutions are investigated in details. In particular, it is proved that under the general boundary conditions studied in this paper, the generalized Boussinesq solution is still well-defined. A physical explanation for this solution is also offered in terms of the equivalent concept of the Green’s functions due to a point force and an infinitesimal dislocation loop. Finally, a new numerical example for the Green’s functions in an orthotropic half-space with different boundary conditions is presented to illustrate the effect of different boundary conditions, as well as material anisotropy, on the half-space Green’s functions.

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