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

Godin, Yuri A.

doi:10.1090/qam/1359503

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