An exact solution to a problem of axisymmetric torsion of an elastic space with a spherical crack

Author:
Yuri A. Godin

Journal:
Quart. Appl. Math. **53** (1995), 679-682

MSC:
Primary 73C99; Secondary 73M25

DOI:
https://doi.org/10.1090/qam/1359503

MathSciNet review:
MR1359503

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Abstract: It is a well-known fact that the three-dimensional axisymmetric dilatation problem for an elastic space containing a spherical crack has an explicit solution, found and analyzed in [1]--[3]. The corresponding torsion problem, however, also of interest, has not apparently been investigated. To remedy this shortage we present here an exact solution to this problem, which incidentally reveals a remarkable effect concerning the stress intensity.

**[1]**V. A. Ziuzin and V. I. Mossakovskii,*Axisymmetric loading of a space with a spherical cut*, Appl. Math. Mech.**34**, 172-177 (1970)**[2]**N. L. Prokhorova and Iu. I. Solov'ev,*Axisymmetric problem for an elastic space with a spherical cut*, Appl. Math. Mech.**40**, 640-646 (1976)**[3]**M. A. Martynenko and A. F. Ulitko,*Stress state near a vertex of a spherical notch in an unbounded elastic medium*, Soviet Appl. Mech.**14**, 911-918 (1978)**[4]**H. Bateman and A. Erdélyi,*Higher Transcendental Functions*, Vol. I, McGraw-Hill, New York, 1955**[5]**Ia. S. Uflyand,*Method of Dual Equations in Mathematical Physics Problems*, Nauka, Leningrad, 1977 (Russian)**[6]**I. N. Sneddon and M. Lowengrub,*Crack Problem in the Classical Theory of Elasticity*, John Wiley and Sons, New York, 1969

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DOI:
https://doi.org/10.1090/qam/1359503

Article copyright:
© Copyright 1995
American Mathematical Society