 | | 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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| 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 |
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|
| Received |
11 December 2007 |
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