Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Singular asymptotics analysis for the singularity at a hole near a boundary


Authors: Constantine J. Callias and Xanthippi Markenscoff
Journal: Quart. Appl. Math. 47 (1989), 233-245
MSC: Primary 73C45
DOI: https://doi.org/10.1090/qam/998098
MathSciNet review: 998098
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Abstract | References | Similar Articles | Additional Information

Abstract: The hoop stress at a hole near the edge of a plate loaded in tension is analyzed as the hole approaches the boundary. The solution given by Mindlin in terms of a series is converted to an integral to which singular asymptotics are applied to obtain the singularity in the limit.


References [Enhancements On Off] (What's this?)

  • [1] G. B. Jeffery, Plane stress and plane strain in bipolar coordinates, Trans. Roy. Soc. London Ser. A 221, 265-293 (1920)
  • [2] R. D. Mindlin, Stress distribution around a hole near the edge of a plate under tension, Proc. Soc. Exptl. Stress Anal. 5, 56-67 (1948)
  • [3] Z. P. Duan, R. Kienzler, and G. Herrmann, An integral equation method and its application to defect mechanics, J. Mech. Phys. Solids 34 (1986), no. 6, 539–561. MR 868582, https://doi.org/10.1016/0022-5096(86)90036-0
  • [4] C. J. Callias and X. Markenscoff, Singular asymptotics of integrals and the near field of a non-uniformly moving dislocation, Arch. Rat. Mech. Anal., 102, 273-285 (1988)
  • [5] C. J. Callias and G. A. Uhlmann, Singular asymptotics approach to partial differential equations with singular coefficients, Bull. Amer. Math. Soc. Res. Announcement (July 1984)
  • [6] C. J. Callias and G. A. Uhlmann, Asymptotics of the scattering amplitude for singular potentials, to appear

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DOI: https://doi.org/10.1090/qam/998098
Article copyright: © Copyright 1989 American Mathematical Society


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