Professor Ting’s paper (1) clearly clarifies several simple but important concepts on conformal mapping techniques applied to anisotropic plane elasticity. Here, I would like to add my own comments on these interesting issues.

(1) First, it should be stated that conformal mapping techniques, combined with the Stroh’s method, have been successfully applied in some important cases to anisotropic elasticity with nonelliptical curves. An example is the Eshelby’s problem for an inclusion of arbitrary shape in an anisotropic medium (2), or in a piezoelectric medium 3, of the same material constants. As stated by Prof. Ting in 1, and also by some other authors elsewhere, because a point z on Γ will be transformed, under three different mappings wαξα=1,2,3, to three different points ξα on the unit circle...

1.
Ting
,
T. C. T.
,
2000
, “
Common Errors on Mapping of Nonelliptic Curves in Anisotropic Elasticity
,”
ASME J. Appl. Mech.
,
67
, pp.
655
657
.
2.
Ru, C. Q., 2001, “Analytic Solution for an Inclusion of Arbitrary Shape in an Anisotropic Plane or Half-Plane” (submitted for publication).
3.
Ru
,
C. Q.
,
2000
, “
Eshelby’s Problem for Two-Dimensional Piezoelectric Inclusions of Arbitrary Shape
,”
Proc. R. Soc. London, Ser. A
,
A456
, pp.
1051
1068
.
4.
Ru
,
C. Q.
,
1999
, “
Analytic Solution for Eshelby’s Problem of an Inclusion of Arbitrary Shape in a Plane or Half-Plane
,”
ASME J. Appl. Mech.
,
66
, pp.
315
322
.
5.
Ivanov, V. I., and Trubetakov, M. K., 1995, Handbook of Conformal Mapping With Computer-Aided Visualization, CRC Press, Boca Raton, FL.
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