 | | 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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| << Previous article | Volume 41, Issue 2 / 2006 | Next article >> |
| A. P. Moiseenok and V. G. Popov, "Interaction of a transient longitudinal shear wave with a thin rigid partially debonded inclusion," Mech. Solids. 41 (2), 19-25 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
2 |
Pages |
19-25 |
| Title |
Interaction of a transient longitudinal shear wave with a thin rigid partially debonded inclusion |
| Author(s) |
A. P. Moiseenok (Odessa)
V. G. Popov (Odessa) |
| Abstract |
A nonstationary problem is considered for the elastic stress
concentration near a thin rigid partially debonded inclusion in a
medium in an antiplane strain state. It is assumed that at the
initial instant the inclusion is subjected to a transient
longitudinal shear wave. The proposed approach involves the
application of the integral Laplace transform with respect to time
and the representation of the displacement in the transform space by
a discontinuous solution of the corresponding differential equation.
This enables one to reduce the initial problem to a system of two
singular integral equations with respect to unknown displacement and
stress jumps. The inverse transforms are restored from the resulting
transforms numerically by using the Papulis method combined with
Tikhonov regularization, as well as by the methods based on the
replacement of the Mellin integral by the Fourier series. |
| References |
| 1. | G. Ya. Popov, Elastic Stress Concentration Near Punches,
Cuts, Thin Inclusions, and Stiffeners [in Russian], Nauka, Moscow,
1982. |
| 2. | V. G. Popov, "Study of the vibrational stresses in the case of
diffraction of elastic shear waves on a thin debonded inclusion,"
Izv. AN. MTT [Mechanics of Solids], No. 3, pp. 139-146, 1992. |
| 3. | I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums,
Series, and Products [in Russian], Nauka, Moscow, 1971. |
| 4. | W. Kecs and P. Teodoresku, Applications of the Theory of Distributions
in Mechanics [Russian translation], Mir, Moscow, 1978. |
| 5. | S. M. Belotserkovskii and I. K. Lifanov, Numerical Methods for
Singular Integral Equations and their Applications in Aerodynamics,
Elasticity, and Electrodynamics [in Russian], Nauka, Moscow, 1985. |
| 6. | V. I. Krylov, Approximate Calculation of Integrals [in Russian],
Nauka, Moscow, 1967. |
| 7. | V. M. Alexandrov, B. I. Smetanin, and B. V. Sobol', Thin
Stress Concentrators in Elastic Solids [in Russian], Nauka, Moscow, 1993. |
| 8. | Sh. M. Aitaliev, L. A. Alekseev, Sh. A. Dil'dabaev, and N. B. Zhandarbaev,
Boundary Integral Equation Method in the Problems of Dynamics of
Elastic Multiply Connected Solids [in Russian],
Gylym, Alma-Ata, 1992. |
| 9. | V. A. Ditkin and A. P. Prudnikov, Operational Calculus [in Russian],
Vysshaya Shkola, Moscow, 1975. |
| 10. | V. Davies and B. Martin, "Numerical inversion of the
Laplace transform: a survey and comparison of methods,"
J. Comput. Phys., Vol. 33, No. 1, pp. 1-32, 1979. |
|
| Received |
02 July 2004 |
| << Previous article | Volume 41, Issue 2 / 2006 | Next article >> |
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