Two-dimensional problems of anisotropic piezoelectric composite wedges and spaces are studied. The Stroh formalism is employed to obtain the basic real-form solution in terms of two arbitrary constant vectors for a particular wedge. Explicit real-form solutions are then obtained for (i) a composite wedge subjected to a line force and a line charge at the apex of the wedge and (ii) a composite space subjected to a line force, line charge, line dislocation, and an electric dipole at the center of the composite space. For the composite wedge the surface traction on any radial plane θ = constant and the electric displacement Dθ normal to the radial plane θ = constant vanish everywhere. For the composite space these quantities may not vanish but they are invariant with the choice of the radial plane.

1.
Barnett
D. M.
, and
Lothe
J.
,
1973
, “
Synthesis of the Sextic and the Integral Formalism for Dislocations, Greens Functions and Surface Waves in Anisotropic Elastic Solids
,”
Physica Norvegica
, Vol.
7
, pp.
13
19
.
2.
Barnett
D. M.
, and
Lothe
J.
,
1975
, “
Dislocations and Line Charges in Anisotropic Piezoelectric Insulators
,”
Physica Status Solidi B
, Vol.
67
, pp.
105
111
.
3.
Cady, W. G., 1946, Piezoelectricity, McGraw-Hill, New York.
4.
Chadwick
P.
, and
Smith
G. D.
,
1977
, “
Foundations of the Theory of Surface Waves in Anisotropic Elastic Materials
,”
Advances in Applied Mechanics
, Vol.
17
, pp.
303
376
.
5.
Eshelby
J. D.
,
Read
W. T.
, and
Shockley
W.
,
1953
, “
Anisotropic Elasticity with Applications to Dislocation Theory
,”
Acta Metallurgica
, Vol.
1
, pp.
251
259
.
6.
Horn, R. A., and Johnson, C. R., 1990, Matrix Analysis, Cambridge University Press, New York, pp. 21–22.
7.
Hwu
Chyanbin
, and
Ting
T. C. T.
,
1990
, “
Solutions for the Anisotropic Elastic Wedges at Critical Wedge Angles
,”
Journal of Elasticity
, Vol.
24
, pp.
1
20
.
8.
Kirchner
H. O. K.
, and
Lothe
J.
,
1986
, “
On the Redundancy of the N¯ Matrix of Anisotropic Elasticity
,”
Philosophical Magazine A
, Vol.
53
, pp.
L7–L10
L7–L10
.
9.
Kuo, C. M., and Barnett, D. M., 1991, “Stress Singularities of Interface Cracks in Bonded Piezoelectric Half-Spaces,” Modern Theory of Anisotropic Elasticity and Applications, J. J. Wu, T. C. T. Ting, and D. M. Barnett, eds., SIAM Proceedings Series, SIAM, Philadelphia, PA, pp. 33–51.
10.
Lothe
J.
, and
Barnett
D. M.
,
1976
, “
Integral Formalism for Surface Waves in Piezoelectric Crystals. Existence Considerations
,”
Journal of Applied Physics
, Vol.
47
, pp.
1799
1807
.
11.
Pak
Y. Eugene
,
1992
, “
Circular Inclusion Problem in Antiplane Piezoelectricity
,”
International Journal of Solids and Structures
, Vol.
29
, pp.
2403
2419
.
12.
Reitz, J. R., Milford, F. J., and Christy, R. W., 1980, Foundations of Electromagnetic Theory, Addison-Wesley, MA.
13.
Sosa
Horacio
,
1991
, “
Plane Problems in Piezoelectric Media with Defects
,”
International Journal of Solids and Structures
, Vol.
28
, pp.
491
505
.
14.
Stroh
A. N.
,
1958
, “
Dislocations and Cracks in Anisotropic Elasticity
,”
Philosophical Magazine
, Vol.
3
, pp.
625
646
.
15.
Stroh
A. N.
,
1962
, “
Steady State Problems in Anisotropic Elasticity
,”
Journal of Mathematics and Physics
, Vol.
41
, pp.
77
103
.
16.
Suo
Z.
,
Kuo
C. M.
,
Barnett
D. M.
, and
Willis
J. R.
,
1992
, “
Fracture Mechanics for Piezoelectric Ceramics
,”
Journal of Mechanics and Physics of Solids
, Vol.
40
, pp.
739
765
.
17.
Tiersten, H. F., 1969, Linear Piezoelectric Plate Vibrations, Plenum Press, New York.
18.
Ting
T. C. T.
,
1986
, “
Explicit Solution and Invariance of the Singularities at an Interface Crack in Anisotropic Composites
,”
International Journal of Solids and Structures
, Vol.
22
, pp.
965
983
.
19.
Ting
T. C. T.
,
1988
a, “
Line Forces and Dislocations in Anisotropic Elastic Composite Wedges and Spaces
,”
Physica Status Solidi B
, Vol.
145
, pp.
81
90
.
20.
Ting
T. C. T.
,
1988
b, “
The Anisotropic Elastic Wedge Under a Concentrated Couple
,”
Quarterly Journal of Mechanics and Applied Mathematics
, Vol.
41
, pp.
563
578
.
21.
Ting
T. C. T.
,
1988
c, “
Some Identities and the Structure of Ni in the Stroh Formalism of Anisotropic Elasticity
,”
Quarterly of Applied Mathematics
, Vol.
46
, pp.
109
120
.
22.
Ting
T. C. T.
, and
Yan
Gongpu
,
1991
, “
The Anisotropic Elastic Solid with an Elliptic Hole or Rigid Inclusion
,”
International Journal of Solids and Structures
, Vol.
27
, pp.
1879
1894
.
This content is only available via PDF.
You do not currently have access to this content.