 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| O. V. Litvin and V. G. Popov, "Stress concentration near a thin elastic inclusion under interaction with harmonic waves in the case of smooth contact," Mech. Solids. 42 (1), 64-71 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
1 |
Pages |
64-71 |
| Title |
Stress concentration near a thin elastic inclusion under interaction with harmonic waves in the case of smooth contact |
| Author(s) |
O. V. Litvin (Odessa National Maritime Academy, Didrikhsona 8, Odessa, 65029, Ukraine, litvinov@ukr.net)
V. G. Popov (Odessa National Maritime Academy, Didrikhsona 8, Odessa, 65029, Ukraine, dr_popov@te.net.ua) |
| Abstract |
We solve the problem on the interaction of plane harmonic waves with a thin elastic plate-shaped inclusion. The ambient medium is assumed to be in plane strain. The smooth contact conditions are satisfied on both sides of the inclusion. The bending displacements of the inclusion are determined from the corresponding differential equation. In the statement of boundary conditions for this equation, one should take into account the transverse forces and bending moments applied to the lateral edges of the inclusion, while the boundary conditions are posed on the midplane of the inclusion. Using the discontinuous solution method, we reduce the problem to a system of two singular integral equations, which are solved numerically by the mechanical quadrature method. We obtain approximate formulas for the stress intensity coefficients near the ends of the inclusion and for the transverse forces and moments applied to the inclusion. |
| References |
| 1. | V. G. Popov and A. E. Ulanovskii,
"Comparative Analysis of Diffraction Fields
when Elastic Waves Propagate through Defects of Various Nature,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 99-109 (1995)
[Mech. Solids (Engl. Transl.)]. |
| 2. | V. G. Popov,
"Interaction of Plane Elastic Waves with Systems of Radial Defects,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 118-129 (1999)
[Mech. Solids (Engl. Transl.)]. |
| 3. | G. S. Kit, V. V. Mikhas'kiv, and O. M. Khai, "Boundary Element Analysis of
Stationary Oscillations of a Plane Absolutely Rigid Inclusion in a
Three-Dimensional Elastic Body," Prikl. Mat. Mekh. 64 (5), 855-863
(2002) [J. Appl. Math. Mech. (Engl. Transl.)]. |
| 4. | V. V. Mikhas'kiv and O. M. Khai,
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in the Field of Fatigue Dynamic Stresses,"
Mashinoznavstvo,
No. 3, 17-22 (1999). |
| 5. | V. M. Alexandrov and S. M. Mkhitaryan,
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(Nauka, Moscow, 1983)
[in Russian]. |
| 6. | N. T. Stashchuk,
Problems of Mechanics of Elastic Bodies with Crack-Like Defects
(Naukova Dumka, Kiev, 1993)
[in Russian]. |
| 7. | V. G. Popov,
Concentration of Elastic Stresses Near Stamps, Cuts, Thin Inclusions, and Reinforcements
(Nauka, Moscow, 1982)
[in Russian]. |
| 8. | V. T. Grinchenko and V. V. Meleshko, Harmonic Vibrations and Waves in
Elastic Bodies (Naukova Dumka, Kiev, 1981) [in Russian]. |
| 9. | A. K. Pertsev and E. G. Platonov,
Dynamics of Shells and Plates
(Sudostroenie, Leningrad, 1987)
[in Russian]. |
| 10. | O. V. Litvin and V. G. Popov, "Bending Oscillations of a Thin Elastic
Inclusion in an Unbounded Medium under Interaction with Elastic Waves,"
Teoret. i Prikl. Mekhanika, No. 36, 131-140 (2002). |
| 11. | S. M. Belotserkovskii and I. K. Lifanov, Numerical Methods in Singular
Integral Equations and Their Applications in Aerodynamics, Elasticity, and
Electrodynamics (Nauka, Moscow, 1985) [in Russian]. |
| 12. | Z. T. Nazarchuk, Numerical Investigation of Wave Diffraction on
Cylindrical Structures (Naukova Dumka, Kiev, 1989) [in Russian]. |
| 13. | D. V. Grilitskii and G. T. Sulim, "Elastic stresses in a plane with
thin-walled inclutions," Matematicheskie Metody i Fiz.-Mekh. Polya, No. 1,
41-48 (1975). |
|
| Received |
18 May 2004 |
| Link to Fulltext |
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