An anisotropic rotationally inhomogeneous wedge bent by either a concentrated couple applied at the tip (Carothers problem) or uniform surface loadings (Levy problem) is considered. The existence criteria for homogeneous solutions describing stresses and strains in both problems are established. In the Levy problem there are two types of critical wedge angles, at which homogeneous solutions break down and become infinite. The first type critical wedge angles of Levy’s problem are shown to be critical also for Carothers’problem whatever the rotational inhomogeneity. Particular solutions to both problems are obtained at the critical wedge angle. The form of these solutions is established to depend on two factors: the multiplicity degree of roots of some eigenvalue equation and the number of independent eigenvectors of some real matrix. It is shown also that the eigenvalue equation does not provide an alternative way to calculate the critical angles and in the first-order perturbation theory results in just the same equations for the critical angles.

1.
Barenblatt, G. I., 1979, Similarity, Self-similarity and Intermediate Asymptotics, Consultants Bureau, New York.
2.
Carothers
S. D.
,
1912
, “
Plane Strain in a Wedge
,”
Proceedings of the Royal Society of Edinburgh
, Vol.
23
, pp.
292
306
.
3.
Dempsey
J. P.
,
1981
, “
The Wedge Subjected to Tractions: a Paradox Resolved
,”
Journal of Elasticity
, Vol.
11
, pp.
1
10
.
4.
Dundurs
J.
, and
Markenscoff
X.
,
1989
, “
The Sternberg-Koiter Conclusion and Other Anomalies of the Concentrated Couple
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
56
, pp.
240
245
.
5.
Hwu
Chyanbin
, and
Ting
T. C. T.
,
1990
, “
Solutions for the Anisotropic Elastic Wedge at Critical Wedge Angles
,”
Journal of Elasticity
, Vol.
24
, pp.
1
20
.
6.
Kirchner
H. O. K.
,
1989
, “
Elastically Anisotropic Angularly Inhomogeneous Media. II. A New Formalism
,”
Philosophical Magazine B
, Vol.
60
, pp.
423
432
.
7.
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
.
8.
Leguillon
D.
,
1988
, “
Sur le Moment Punctuel Applique a un Secteur: le Paradox de Sternberg-Koiter
,”
C. R. Acad. Sci. Paris
, Vol.
307
, pp.
1471
1746
.
9.
Levy
M.
,
1898
,
Compt. Rend.
, Vol.
126
, p.
1235
1235
.
10.
Steeds, J. W., 1973, Anisotropic Elasticity Theory of Dislocations, Clarendon Press, Oxford, U.K.
11.
Sternberg
E.
, and
Koiter
W. T.
,
1958
, “
The Wedge under a Concentrated Couple: A Paradox in the Two-Dimensional Theory of Elasticity
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
25
, pp.
575
581
.
12.
Stroh
A. N.
,
1958
, “
Dislocations and Cracks in Anisotropic Elasticity
,”
Philosophical Magazine
, Vol.
7
, pp.
625
646
.
13.
Stroh
A. N.
,
1962
, “
Steady State Problems in Anisotropic Elasticity
,”
Journal of Mathematics and Physics (Cambridge)
, Vol.
41
, pp.
77
103
.
14.
Timoshenko, S. P., and Goodier, J. N., 1970, Theory of Elasticity, 3rd ed., McGraw-Hill, New York.
15.
Ting
T. C. T.
,
1984
, “
The Wedge Subjected to Tractions: a Paradox Reexamined
,”
Journal of Elasticity
, Vol.
14
, pp.
235
247
.
16.
Ting
T. C. T.
,
1985
a, “
A Paradox on the Elastic Wedge Subjected to a Concentrated Couple and on the Jeffrey-Hamel Viscous Flow Problem
,”
Zeitschrift fuer Angewandte Mathematik und Mechanik
, Vol.
65
, pp.
188
190
.
17.
Ting
T. C. T.
,
1985
b, “
Elastic Wedge Subjected to Anti-Plane Shear Tractions—A Paradox Explained
,”
The Quarterly Journal of Mechanics and Applied Mathematics
, Vol.
38
, pp.
245
255
.
18.
Ting
T. C. T.
,
1988
a, “
The Anisotropic Wedge under a Concentrated Couple
,”
Quarterly Journal of Mechanics and Applied Mathematics
, Vol.
20
, pp.
564
578
.
19.
Ting
T. C. T.
,
1988
b, “
The Critical Angle of the Anisotropic Elastic Wedge Subject to Uniform Tractions
,”
Journal of Elasticity
, Vol.
20
, pp.
113
130
.
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