 | | 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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| S. A. Barsukov, E. V. Glushkov, and N. V. Glushkova, "Stress singularity at corner points of a front of a crack on the interface between two media," Mech. Solids. 37 (2), 63-69 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
2 |
Pages |
63-69 |
| Title |
Stress singularity at corner points of a front of a crack on the interface between two media |
| Author(s) |
S. A. Barsukov (Krasnodar)
E. V. Glushkov (Krasnodar)
N. V. Glushkova (Krasnodar) |
| Abstract |
The method allowing one to separate singular components of the linear
elastic solutions at the corner points of solids was developed earlier for
the wedge-shaped punches [1] and cracks [2] and generalized to arbitrary
polyhedral angles [3]. In the present paper, this method is applied to
study the stress singularities in the neighborhood of corner points of the
front of the crack on the plane interface between two different materials.
The method is based on the reduction of standard three-dimensional boundary
value problems to spectral problems for one-dimensional integral operator by
using the Mellin transform. In the framework of this approach, we derive the
form of this integral operator for the problem under consideration,
implement the method on a computer, and perform the numerical
analysis of singular expansion characteristics as functions of the crack
aperture and the ratio of elastic characteristics of the materials. |
| References |
| 1. | V. A. Babeshko, E. V. Glushkov, and N. V. Glushkova, "On the
singularities at corner points of 3D punches in contact problems,"
Doklady AN SSSR, Vol. 257, No. 2, pp. 289-294, 1981. |
| 2. | E. V. Glushkov and N. V. Glushkova, "On the singularities of the
elastic stress field near the tip of a wedge-shaped spatial crack,"
Isv. AN. MTT [Mechanics of Solids], No. 4, pp. 82-86, 1992. |
| 3. | E. Glushkov, N. Glushkova, and O. Lapina, "3D elastic stress
singularity at polyhedral corner points," Intern. J. Solids and Structures,
Vol. 36, No. 8, pp. 1105-1128, 1999. |
| 4. | V. A. Kondrat'ev, "Boundary value problems for elliptic equations
in domains with conical and corner points," Transactions of Moscow
Mathematical Society, Vol. 16, pp. 209-292, 1967. |
| 5. | V. G. Mazja and B. A. Plamenewski, "On the coefficients of
asymptotic solutions of elliptic boundary value problems near an edge,"
Doklady AN SSSR, Vol. 229, No. 1, pp. 33-36, 1976. |
| 6. | V. M. Alexandrov and V. A. Babeshko, "On the pressure of a
wedge-shaped punch on an elastic half-space," PMM [Applied
Mathematics and Mechanics], Vol. 36, No. 1, pp. 88-93, 1972. |
| 7. | S. G. Mikhlin, Variational Methods in Mathematical Physics
[in Russian], Nauka, Moscow, 1970. |
| 8. | I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko, Nonclassical
Mixed Problems of the Theory of Elasticity [in Russian], Nauka, Moscow,
1974. |
| 9. | M. A. Evgrafov, Analytic Functions [in Russian], Nauka, Moscow,
1968. |
| 10. | H. Bateman and A. Erdélyi, Higher Transcendental Functions.
Volume 2 [Russian translation], Nauka, Moscow, 1974. |
| 11. | V. A. Ditkin and A. P. Prudnikov, Integral Equations and
Operational Calculus [in Russian], Nauka, Moscow, 1974. |
|
| Received |
17 December 1999 |
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