For an isotropic elastic material under a two-dimensional plane-stress or plane-strain deformation that involves a closed boundary of a given geometry Γ, it is a common practice to use a conformal mapping to map Γ to a circle of unit radius. For an anisotropic elastic material, the mapping produces the correct solution to the physical problem when Γ is an ellipse. There are published (and unpublished) papers that report solutions to anisotropic elasticity problems with a nonelliptic curve Γ. They all fail to solve the physical problem correctly. The purpose of this paper is to show the common errors made by many researchers, and to alert newcomers on the subject so that they do not fall into the same trap. [S0021-8936(00)02403-X]
Common Errors on Mapping of Nonelliptic Curves in Anisotropic Elasticity
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Sept. 10, 1999; final revision, Dec. 15, 1999. Associate Technical Editor: W. J. Drugan. Discussion on the paper should be addressed to the Technical Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Ting, T. C. T. (December 15, 1999). "Common Errors on Mapping of Nonelliptic Curves in Anisotropic Elasticity ." ASME. J. Appl. Mech. December 2000; 67(4): 655–657. https://doi.org/10.1115/1.1311961
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