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: 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.
G. B. Jeffery, Plane stress and plane strain in bipolar coordinates, Trans. Roy. Soc. London Ser. A 221, 265–293 (1920)
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)
- 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, DOI https://doi.org/10.1016/0022-5096%2886%2990036-0
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)
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)
C. J. Callias and G. A. Uhlmann, Asymptotics of the scattering amplitude for singular potentials, to appear
G. B. Jeffery, Plane stress and plane strain in bipolar coordinates, Trans. Roy. Soc. London Ser. A 221, 265–293 (1920)
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)
Z.-P. Duan, R. Kienzler, and G. Herrmann, An integral equation method and its application to defect mechanics, J. Mech. Phys. Solids, 36, 539–562 (1986)
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)
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)
C. J. Callias and G. A. Uhlmann, Asymptotics of the scattering amplitude for singular potentials, to appear
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Article copyright:
© Copyright 1989
American Mathematical Society
