0
TECHNICAL PAPERS

Anisotropic Elastic Materials With a Parabolic or Hyperbolic Boundary: A Classical Problem Revisited

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

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

Y. Hu

Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China

H. O. K. Kirchner

Institut de Science des Materiaux, bat. 413 Universite Paris Sud, F91405 Orsay Cedex, France

J. Appl. Mech 68(4), 537-542 (Jan 02, 2001) (6 pages) doi:10.1115/1.1381393 History: Received August 29, 2000; Revised January 02, 2001
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.

References

Muskhelishvili, N. I., 1953, Some Basic Problems of the Mathematical Theory of Elasticity, transl. 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.
Ting,  T. C. T., 2000, “Common Errors on Mapping of Non-Elliptic Curves in Anisotropic Elasticity,” ASME J. Appl. Mech., 67, pp. 655–657.
Lekhnitskii, S. G., 1957, Anisotropic Plates, 2nd Ed., Gostekhizdat, Moscow (in Russian); transl. by S. W. Tsai and T. Cheron, Gordon and Breach, New York (1968, 1984, 1987).
Barnett,  D. M., and Lothe,  J., 1973, “Synthesis of the Sextic and the Integral Formalism for Dislocations, Greens Function and Surface Waves in Anisotropic Elastic Solids,” Phys. Norv., 7, pp. 13–19.
Chadwick,  P., and Smith,  G. D., 1977, “Foundations of the Theory of Surface Waves in Anisotropic Elastic Materials,” Adv. Appl. Mech., 17, pp. 303–376.
Ting, T. C. T., 1996, Anisotropic Elasticity: Theory and Applications, Oxford University Press, Oxford, UK.
Hu,  Y. T., and Zhao,  X. H., 1996, “Green’s Functions of Two-Dimensional Anisotropic Body With a Parabolic Boundary,” Appl. Math. Mech., 17, pp. 393–402.
Neuber, H., 1958, Kerbspannungslehre, Springer-Verlag, Berlin, Chapter 4.
Smith,  C. B., 1949, “Effect of Hyperbolic Notches on the Stress Distribution in a Wood Plate,” Q. Appl. Math., 6, No. 4, pp. 452–456.
Okubo, H., 1949, “On the Problem of a Notched Plate of an Aeolotropic Material,” Philos. Mag., 40 , Ser. 7, No. 308.
Dongye,  Changsong, and Ting,  T. C. T., 1989, “Explicit Expressions of Barnett-Lothe Tensors and Their Associated Tensors for Orthotropic Materials,” Q. Appl. Math., 47, pp. 723–734.
Ting,  T. C. T., 1997, “New Explicit Expression of Barnett-Lothe Tensors for Anisotropic Linear Elastic Materials,” J. Elast., 47, pp. 23–50.
Ingebrigtsen,  K. A., and Tonning,  A., 1969, “Elastic Surface Waves in Crystal,” Phys. Rev., 184, pp. 942–951.
Kirchner,  H. O. K., and Lothe,  J., 1986, “On the Redundancy of the N̄ Matrix of Anisotropic Elasticity,” Philos. Mag., A53, pp. L7–L10.

Figures

Grahic Jump Location
Mapping of a parabola (drawn for Re p > 0); (a) the (x1,x2)-plane, (b) the ζ-plane
Grahic Jump Location
Mapping of a hyperbola (drawn for Re p > 0); (a) the (x1,x2)-plane, (b) the ζ-plane

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In