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
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
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.
V. A. Ziuzin and V. I. Mossakovskii, Axisymmetric loading of a space with a spherical cut, Appl. Math. Mech. 34, 172–177 (1970)
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)
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)
H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. I, McGraw-Hill, New York, 1955
Ia. S. Uflyand, Method of Dual Equations in Mathematical Physics Problems, Nauka, Leningrad, 1977 (Russian)
I. N. Sneddon and M. Lowengrub, Crack Problem in the Classical Theory of Elasticity, John Wiley and Sons, New York, 1969
V. A. Ziuzin and V. I. Mossakovskii, Axisymmetric loading of a space with a spherical cut, Appl. Math. Mech. 34, 172–177 (1970)
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)
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)
H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. I, McGraw-Hill, New York, 1955
Ia. S. Uflyand, Method of Dual Equations in Mathematical Physics Problems, Nauka, Leningrad, 1977 (Russian)
I. N. Sneddon and M. Lowengrub, Crack Problem in the Classical Theory of Elasticity, John Wiley and Sons, New York, 1969
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73C99,
73M25
Retrieve articles in all journals
with MSC:
73C99,
73M25
Additional Information
Article copyright:
© Copyright 1995
American Mathematical Society
