| | 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
|
In English (Mech. Solids): | | 4810 |
|
<< Previous article | Volume 45, Issue 1 / 2010 | Next article >> |
A.P. Moiseenok and V.G. Popov, "Interaction of Plane Elastic Nonstationary Waves with an Elastic Inclusion under Complete Adhesion," Mech. Solids. 45 (1), 74-84 (2010) |
Year |
2010 |
Volume |
45 |
Number |
1 |
Pages |
74-84 |
DOI |
10.3103/S0025654410010115 |
Title |
Interaction of Plane Elastic Nonstationary Waves with an Elastic Inclusion under Complete Adhesion |
Author(s) |
A.P. Moiseenok (Mechnikov Odessa National University, Dvoryanskaya 2, Odessa, 65023 Ukraine, yogan@ua.fm)
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 elastic
nonstationary waves with a thin elastic strip-shaped inclusion. The inclusion is contained in an unbounded body (matrix) which in under conditions of plane strain. It is assumed that the condition of perfect adhesion between the inclusion and the matrix is satisfied. Because of the small thickness of the inclusion we assume that the bending and shear displacements at any inclusion point coincide with the displacements of the corresponding points of its midplane. The displacements on the midplane itself are found from the corresponding equations of the theory of plates. The statement of the boundary conditions for these equations takes into account the forces and moments acting on the inclusion edges from the matrix. The solution method is based on representing the displacements in the space of Laplace transforms as a discontinuous solution of the Lamé equations for the plane strain with subsequent determining the transforms of the unknown jumps from integral equations. The passage to the original functions is performed numerically by methods based on replacement of the Mellin integral by the Fourier series. As a result, we obtain approximate formulas for calculating the stress intensity factors for the inclusion. These formulas are used to study the time dependence of the stress intensity factors and the influence of the inclusion rigidity on their values. We also study the possibility of treating inclusions of high rigidity as absolutely rigid inclusions. |
Keywords |
thin inclusion, nonstationary elastic wave, stress intensity factor |
References |
1. | H. S. Kit, V. V. Mikhas'skiv, and O. M. Khaj,
"Analysis of the Steady Oscillations of a Plane Absolutely
Rigid Inclusion in a Three-Dimensional Elastic Body by the Boundary Element Method,"
Prikl. Mat. Mekh.
66 (5), 855-863 (2002)
[J. Appl. Math. Mech. (Engl. Transl.)
66 (5), 817-824 (2002)] |
2. | V. V. Mikhas'kiv and O. M. Khai,
"On the Theory of Hardness of Elastic Solids with Plane Rigid Inclusions in the Field of Fatigue Dynamic Stresses,"
Mashinoznavstvo,
No. 3, 17-22 (1999). |
3. | A. P. Moiseenok,
"Study of Stressed State near a Thin Rigid Inclusion under Interaction with Waves under Complete Adhesion,"
in Theory and Practice of Processes of Crushing, Separation, Mixing, and Compression: the Book of Articles,
Vol. 12
(ONMA, Odessa, 2006),
pp. 88-95. |
4. | V. V. Mikhas'kiv,
"Transient Response of a Plane Rigid Inclusion to an Incident Wave in an Elastic Solid,"
Wave Motion
41 (2), 133-144 (2005). |
5. | A. Tadeu, P. Mendes, and J. Antonio,
"The Simulation of 3D Elastic Scattering Produced by Thin Rigid Inclusions Using the Traction Boundary Element Method,"
Comput. Struct.
84 (31-32), 2244-2253 (2006). |
6. | V. G. Popov and A. E. Ulanovskii,
"Comparative Study of Diffraction Fields Generated by Elastic Waves Passing Through Imperfections
of Various Nature,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 99-109 (1995)
[Mech. Solids (Engl. Transl.)
30 (4), 93-102 (1995)]. |
7. | H. S. Kit, Ya. I. Kunets, and V. V. Mikhas'kiv,
"Interaction of a Stationary Wave with a Thin Low Stiffness Penny-Shaped Inclusion in an Elastic Body,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 82-89 (2004)
[Mech. Solids (Engl. Transl.)
39 (5), 64-70 (2004)]. |
8. | H. S. Kit, Ya. I. Kunets, and V. F. Yemets,
"Elastodynamic Scattering from a Thin-Walled Inclusion of Low Rigidity,"
Int. J. Engng Sci.
37 (3), 331-345 (1999). |
9. | V. F. Yemets,
"Plane Inverse Problem of Elastic Wave Scattering at a Thin-Walled Inclusion of High Rigidity,"
Akust. Zh.
41 (3), 432-438 (1995)
[Acoust. Phys. (Engl. Transl.)]. |
10. | O. V. Litvin and V. G. Popov,
"Bending Oscillations of a Thin Elastic Inclusion in an Unbounded Medium under Interaction with Elastic Waves,"
Teor. Prikl. Mekh.,
No. 36, 131-140 (2002). |
11. | O. V. Litvin and V. G. Popov,
"Interaction of Plane Harmonic Waves with Inclusions in the Elastic Space,"
Fiz.-Khim. Mekh. Mat.,
No. 3, 58-64 (2007)
[Mat. Sci. (Engl. Transl.)
43 (3), 361-369 (2007)]. |
12. | G. Ya. Popov,
Concentration of Elastic Stresses Near Punches, Cuts, Rigid Inclusions, and Stiffeners
(Nauka, Moscow, 1982)
[in Russian]. |
13. | A. K. Pertsev and E. G. Platonov,
Dynamics of Shells and Plates
(Sudostroenie, Leningrad, 1987)
[in Russian]. |
14. | 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]. |
15. | Z. T. Nazarchuk,
Numerical Investigation of Wave Diffraction on Cylindrical Structures
(Naukova Dumka, Kiev, 1989)
[in Russian]. |
16. | L. T. Berezhnitskii, V. V. Panasyuk, and N. T. Stashchuk,
Interaction of Rigid Linear Inclusions and Cracks
in Deformable Body
(Naukova Dumka, Kiev, 1983)
[in Russian]. |
17. | D. V. Grilitskii and G. T. Sulim,
"Elastic Stresses in a Plane with Thin-Walled Inclusions,"
Mat. Met. Fiz.-Mekh. Polya
No. 1, 41-48 (1975). |
18. | B. Davies and B. Martin,
"Numerical Inversion of the Laplace Transform:
A Survey and Comparison of Methods,"
J. Comput. Phys.
33 (1), 1-32 (1979). |
19. | A. Jaemin, K. Sungkwon, and K. YongHoon,
"A Flexible Inverse Laplace Transform Algorithm and Its Application,"
Computing
71 (2), 115-131 (2003). |
|
Received |
11 December 2007 |
Link to Fulltext |
|
<< Previous article | Volume 45, Issue 1 / 2010 | Next article >> |
|
If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|