 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| A. V. Loveikin and A. F. Ulitko, "Stress-strain state analysis for an incompressible half-space with a near-surface wedge-shaped crack," Mech. Solids. 41 (1), 104-113 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
1 |
Pages |
104-113 |
| Title |
Stress-strain state analysis for an incompressible half-space with a near-surface wedge-shaped crack |
| Author(s) |
A. V. Loveikin (Kiev)
A. F. Ulitko (Kiev) |
| Abstract |
Equilibrium of an elastic incompressible half-space weakened by a near-surface
wedge-shaped crack with surfaces subjected to an internal pressure is
considered. By using the Papkovich-Neuber representation, the problem is
reduced to the determination of two harmonic functions which satisfy mixed
boundary conditions. The construction of these functions is carried out in the
spherical coordinates using the Mellin and Mehler-Fock type integral
transforms. The analytical solution obtained enabled the stress distribution to
be obtained, and the stress-strain field in the vicinity of the point where the
crack edge intersects the free surface of the half-space to be analyzed. |
| References |
| 1. | E. S. Folias,
"On the 3-dimensional theory of cracked plates,"
Trans. ASME. Ser. E. J. Appl. Mech.,
Vol. 42, No. 3, pp. 663-674, 1975. |
| 2. | M. Shmuely and Z. Alterman, "A three-dimensional numerical analysis
of stress distribution in the vicinity of a crack tip," Isr. J. Technol.,
Vol. 9, No. 5, pp. 523-530, 1971. |
| 3. | J. P. Bentem,
"State of stress at the vertex of a quarter-infinite crack in a half-space,"
Int. J. Solids Structures,
Vol. 13, No. 5, pp. 479-492, 1977. |
| 4. | Z. P. Bazant and L. F. Estenssoro, "Surface singularity and crack
propagation," Int. J. Solids Structures, Vol. 15, No. 4, pp. 405-426, 1979. |
| 5. | F. Ghahremani and C. F. Shih, "Corner singularities of 3-dimensional
planar interface crack," Trans. ASME. Ser. E. J. Appl. Mech., Vol. 59, No. 1,
pp. 61-68, 1992. |
| 6. | E. V. Glushkov, N. V. Glushkova, and O. N. Lapina,
"Singularity exponents of elastic stresses
at the point where the crack reaches the surface," Izv. AN. MTT [Mechanics of Solids],
No. 5, pp. 146-153, 1998. |
| 7. | Ya. S. Uflyand, Integral Transforms in Elasticity [in Russian], Nauka, Leningrad, 1967. |
| 8. | N. N. Lebedev, Special Functions and Their Applications [in Russian],
Fizmatgiz, Moscow, Leningrad, 1963. |
| 9. | D. N. Parfenenko and F. A. Ulitko, "On a new integral transform and its application in
contact problems of elasticity," Doklady AN UkrSSR, Ser. A, No. 11, pp. 53-58, 1988. |
| 10. | N. N. Lebedev and I. P. Skal'skaya, "Integral expansions related to
the Mehler-Fock transformations," Diff. Uravnenia, Vol. 22, No. 9,
pp. 1515-1523, 1986. |
| 11. | H. Bateman and A. Erdélyi, Higher Transcendental Functions.
Volume 1, McGraw-Hill Book Co., New York, 1953. |
| 12. | V. F. Fedoryuk, Asymptotics: Integrals and Series, Nauka, Moscow, 1987. |
| 13. | B. Noble, Methods Based on the Wiener-Hopf Technique for the
Solution of Partial Differential Equations, Pergamon Press, London, 1958. |
| 14. | R. Mittra, and S. W. Lee, Analytical Techniques in the Theory of
Guided Waves, Macmillan, New York, 1971. |
|
| Received |
19 October 2004 |
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