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TECHNICAL PAPERS

Common Errors on Mapping of Nonelliptic Curves in Anisotropic Elasticity

[+] Author and Article Information
T. C. T. Ting

Department of Civil and Materials Engineering, University of Illinois at Chicago, 842 W. Taylor Street, M/C 246, Chicago, IL 60607-7023

J. Appl. Mech 67(4), 655-657 (Dec 15, 1999) (3 pages) doi:10.1115/1.1311961 History: Received September 10, 1999; Revised December 15, 1999
Copyright © 2000 by ASME
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References

Muskhelishvili, N. I., 1953, Some Basic Problems of the Mathematical Theory of Elasticity (translation by J. R. M. Radok, Noordhoff, Groningen).
Lekhnitskii, S. G., 1950, Theory of Elasticity of an Anisotropic Body, Gostekhizdat, Moscow (in Russian), Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day, San Francisco (in English, 1963), and Mir Pub. Moscow (in English, 1981).
Stroh,  A. N., 1958, “Dislocations and Cracks in Anisotropic Elasticity,” Philos. Mag., 3, pp. 625–646.
Savin, G. N., 1961, Stress Concentration Around Holes, Pergamon Press, London.
Ting, T. C. T., 1996, Anisotropic Elasticity: Theory and Applications, Oxford University Press, New York.
Lekhnitskii, S. G., 1957, Anisotropic Plates, 2nd Ed., Gostekhizdat, Moscow (in Russian), (translation by S. W. Tsai and T. Cheron, Gordon and Breach, New York (1968, 1984, 1987).
Churchill, R. V., 1948, Introduction to Complex Variables and Applications, McGraw-Hill, New York.
Ting,  T. C. T., 1994, “On Anisotropic Elastic Materials That Possess Three Identical Stroh Eigenvalues as do Isotropic Materials,” Q. Appl. Math., 52, pp. 363–375.
Ting,  T. C. T., 1996, “Existence of an Extraordinary Degenerate Matrix N for Anisotropic Elastic Materials,” Q. J. Mech. Appl. Math., 49, pp. 405–417.
Yin,  W.-L., 2000, “Deconstructing Plane Anisotropic Elasticity, Part I: The Latent Structure of Lekhnitskii’s Formalism,” Int. J. Solids Struct., 37, pp. 5257–5276.
Yin,  W.-L., 2000, “Deconstructing Plane Anisotropic Elasticity, Part II: Stroh’s Formalism Sans Frills,” Int. J. Solids Struct., 37, pp. 5277–5296.
Ting,  T. C. T., 2000, “Anisotropic Elastic Materials That Uncouple Antiplane and Inplane Displacements but Not Antiplane and Inplane Stresses, and Vice Versa,” Math. Mech. Solids, 5, pp. 139–156.

Figures

Grahic Jump Location
A triangle in the (x1,x2)-plane is mapped to a circle in the ζα-plane through Eq. (21)

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