It is difficult to obtain explicit expressions of Green’s function for elastic medium with general anisotropy. The difficulty is associated with an integration of functions with high degrees of singularity. In this paper, we propose a method employing extend functions. This method avoids the difficulty of singularities and renders an explicit series expression of Green’s function for general anisotropic conditions. Analytical expression of the coefficients in the series are provided. Numerical examples are given to evaluate the applicability of this method.

Issue Section:
Technical Papers
Topics:
Anisotropy
1.
Brebbia, C. A., Telles, J. C. F., and Wrobel, L C., 1984, Boundary Element Techniques, Springer-Verlag, Berlin.
2.
Elliott
H. A.
,
1948
, “
Three-dimensional stress distribution in hexagonal aeolo-tropic crystals
,”
Proceedings, Cambridge Philosophical Society
, Vol.
44
, pp.
522
–
533
.
3.
Eshelby
J. D.
,
1959
, “
The elastic field outside an ellipsoidal inclusion
,”
Proceedings of Royal Society, London
, Vol.
A252
,
561
–
569
.
4.
Friedman, B., 1956, Principles and Techniques of Applied Mathematics, John Wiley and Sons, New York.
5.
Hill
R.
,
1962
, “
Acceleration waves in Solids
,”
Journal of Mechanics and Physics of Solids
, Vol.
10
, pp.
1
–
16
.
6.
Hill
R.
, and
Hutchinson
J. W.
,
1975
, “
Bifurcation phenomena in the plane tension test
,”
Journal of Mechanics and Physics of Solids
, Vol.
23
, pp.
239
–
264
.
7.
Kinoshita
N.
, and
Mura
T.
,
1971
, “
Elastic Fields of inclusions in anisotropic media
,”
Physica Status Solidi (a)
, Vol.
5
, pp.
759
–
768
.
8.
Kroner
E.
,
1953
, “
Das fundamentalintegral der anisotropen elastischen differentialgleichungene
,”
Zeitschrift fur Physik
, Vol.
136
, pp.
402
–
410
.
9.
Lejcek
L.
,
1969
, “
The Green function of the theory of elasticity in an anisotropic hexagonal medium
,”
Czech. Journal of Physics, Series B
, Vol.
19
, pp.
799
–
803
.
10.
Mura
T.
,
1971
, “
Displacement and Plastic Distortion Fields Produced by Dislocations in Anisotropic Media
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
38
, pp.
865
–
868
.
11.
Mura
T.
, and
Kinoshita
N.
,
1971
, “
Green’s functions for anisotropic elasticity
,”
Physica status solidi (b)
, Vol.
47
, pp.
607
–
618
.
12.
Mura, T., 1987, Micromechanics of Defects in solids, Martinus Nijhoff Publishers, Dordrecht, The Netherlands.
13.
Pan
Y. C.
, and
Chou
T. W.
,
1976
, “
Point Force Solution for an Infinite Transversely Isotropic Solid
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
43
, pp.
608
–
612
.
14.
Sveklo
V. A.
,
1969
, “
Concentrated force in a transversely isotropic half-space and in a composite space
,”
Journal of Applied Mathematics and Mechanics
, Vol.
33
, pp.
517
–
523
.
15.
Thompson, Sir W. (Lord Kelvin), 1848, “Note on the integration of the equation of equilibrium of an elastic solid,” Cambridge and Dublin Mathematical Journal, pp. 76–99.
16.
Vogel, S. M., and Rizzo, F. J., 1973, “An integral equation formulation of three dimensional anisotropic elastostatic boundary value problems,” Journal of Elasticity, Vol. 3, Sept.
17.
Walpole
L. J.
,
1967
, “
The elastic field of an inclusion in an anisotropic medium
,”
Proceedings of Royal Society, London
, Vol.
A300
, pp.
270
–
289
.
18.
Woo
T. C.
, and
Shield
R. T.
,
1962
, “
Fundamental solutions for small deformations superposed on finite biaxial extension of an elastic body
,”
Archive for Rational Mechanics and Analysis
, Vol.
9
, pp.
196
–
224
.
19.
Willis
J. R.
,
1965
, “
The elastic interaction energy of dislocation loops in anisotropic media
,”
Quarterly Journal of Mechanics and Applied Mathematics
, Vol.
18
, pp.
419
–
433
.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.