 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| V. A. Babeshko, S. V. Ratner, and P. V. Syromyatnikov, "Anisotropic bodies with inhomogeneities: The case of a set of cracks," Mech. Solids. 42 (5), 700-709 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
5 |
Pages |
700-709 |
| Title |
Anisotropic bodies with inhomogeneities: The case of a set of cracks |
| Author(s) |
V. A. Babeshko (Kuban State University, Stavropol’skaya 149, Krasnodar, 350040, Russia, rector@kubsu.ru)
S. V. Ratner (South Scientific Centre, Russian Academy of Sciences, Chekhova 41, Rostov-on-Don, 344006, Russia, lanarat@mail.ru)
P. V. Syromyatnikov (South Scientific Centre, Russian Academy of Sciences, Chekhova 41, Rostov-on-Don, 344006, Russia, syromyatnikov@math.kubsu.ru) |
| Abstract |
We use the Betti theorem to obtain the integral equations of the dynamic theory of elasticity for a multilayer convex body with an arbitrary elastic anisotropy of layers containing plane infinitely thin cracks. The systems of integral equations relate the displacement jumps to the stresses on the crack lips and are stated numerically in terms of Fourier transforms. For the case of plane-parallel layers with a set of plane cracks on the interfaces between the layers, we propose a simple numerical-analytic method for constructing the Fourier symbol, i.e., the matrix of the kernel of the system of integral equations. The method is stable for an arbitrary combination of continuous and discontinuous conditions on the layer boundaries. Numerical examples are given for a packet of four heterogeneous anisotropic layers. |
| References |
| 1. | V. A. Babeshko,
"Bodies with Inhomogeneities; the Case of Sets of Cracks,"
Dokl. Ross. Akad. Nauk
373 (2), 191-193 (2000)
[Russian Acad. Sci. Dokl. Math. (Engl. transl.)]. |
| 2. | V. A. Babeshko, A. V. Pavlova, S. V. Ratner, and R. Williams,
"Solution to the Problem on Vibration of an Elastic Solid with Inner Cavities,"
Dokl. Ross. Akad. Nauk
382 (5), 625-628 (2002)
[Russian Acad. Sci. Dokl. Math. (Engl. Transl.)]. |
| 3. | V. A. Babeshko and O. M. Babeshko,
"Factorization Method in the
Theory of Vibration Strength Viruses,"
Dokl. Ross. Akad. Nauk 393 (4), 473-477 (2003) [Russian Acad. Sci. Dokl. Math. (Engl.
Transl.)]. |
| 4. | V. A. Babeshko and O. M. Babeshko,
"Study of Boundary Value Problems by Double Factorization,"
Dokl. Ross. Akad. Nauk
403 (1), 20-24 (2005)
[Russian Acad. Sci. Dokl. Math. (Engl. Transl.)]. |
| 5. | V. A. Babeshko and O. M. Babeshko,
"Integral Transforms and Factorization Method for Boundary Problems,"
Dokl. Ross. Akad. Nauk
403 (6), 748-751 (2005)
[Russian Acad. Sci. Dokl. Math. (Engl. Transl.)]. |
| 6. | W. Nowacki,
Electromagnetic Effects in Solids
(PWN, Warsaw, 1983; Mir, Moscow, 1986). |
| 7. | O. D. Pryakhina and A. V. Smirnova,
"An Efficient Method for Solving Dynamic
Problems for Laminated Media
with Discontinuous Boundary Conditions,"
Prikl. Mat. Mekh.
68 (3), 500-507 (2004)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 8. | V. M. Alexandrov, B. I. Smetanin, and B. V. Sobol',
Thin Stress Concentrators in Elastic Bodies
(Nauka, Moscow, 1993)
[in Russian]. |
| 9. | V. A. Babeshko, E. V. Glushkov, and Zh. F. Zinchenko,
Dynamics of Inhomogeneous Linearly Elastic Media
(Nauka, Moscow, 1989)
[in Russian]. |
| 10. | V. A. Babeshko and P. V. Syromyatnikov,
"A Method for the Construction of the Fourier Symbol of
the Green Matrix for Multi-Layered Electroelastic Half-Space,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 35-47 (2002)
[Mech. Solids (Engl. Transl.)]. |
| 11. | M. P. Shaskol'skaya (Editor),
Acoustic Crystals: Handbook
(Nauka, Moscow, 1982)
[in Russian]. |
| 12. | I. Zelenka,
Piezoelectric Resonators on Volume and Surface Acoustic Waves
(Mir, Moscow, 1990)
[in Russian]. |
|
| Received |
26 May 2005 |
| Link to Fulltext |
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