 | | 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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| << Previous article | Volume 37, Issue 3 / 2002 | Next article >> |
| N. D. Vaisfel'd and G. Ya. Popov, "Nonstationary dynamic problems of elastic stress concentration near a spherical imperfection," Mech. Solids. 37 (3), 77-88 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
3 |
Pages |
77-88 |
| Title |
Nonstationary dynamic problems of elastic stress concentration near a spherical imperfection |
| Author(s) |
N. D. Vaisfel'd (Odessa)
G. Ya. Popov (Odessa) |
| Abstract |
By using the method of discontinuous solutions we solve nonstationary
dynamic problems of the elastic stress concentration near a spherical
imperfection which is either a spherical crack or a thin rigid spherical
inclusion. The approach suggested allows one to reduce these problems to
a system of one-dimensional integro-differential or integral equations in
the space of Laplace transforms. The subsequent inversion of these transforms
and using the convolution theorem reduce the equations to two-dimensional
ones which can be solved by using time-discretization or the method of
orthogonal polynomials. As a result, the problem is reduced to the solution
of the sequence of infinite systems of linear algebraic equations. The
detailed development of this approach is given for the problems of
diffraction of nonstationary elastic torsional waves by the spherical
inclusion adhered to an elastic
medium (which is fixed or only adhered to the elastic medium). In the
latter case we apply also the asymptotic method to solve the problem. The
numerical analysis of the applicability area of this method is performed.
Time histories of important mechanical characteristics are calculated. |
| References |
| 1. | G. Ya. Popov, Concentration of Elastic Stresses Near Punches,
Cuts, Thin Inclusions and Reinforcements [in Russian], Nauka,
Moscow, 1982. |
| 2. | A. N. Guz', V. D. Kubenko, and M. A. Cherevko, Diffraction of
Elastic Waves [in Russian], Naukova Dumka, Kiev, 1978. |
| 3. | G. Ya. Popov, "On a new representation of the solution of the
Lamé equations in the spherical coordinate system," Doklady AN, Vol. 356,
No. 1, pp. 47-49, 1997. |
| 4. | D. V. Grilitskii and A. P. Poddubnyak, "Scattering of nonstationary
torsional wave on an immovable sphere in an elastic medium," Izv. AN SSSR.
MTT [Mechanics of Solids], No. 5, pp. 86-92, 1980. |
| 5. | A. P. Prudnikov, Yu. A. Bychkov, and O. I. Marichev, Integrals and
Series. Special Functions [in Russian], Nauka, Moscow, 1983. |
| 6. | M. Abramovitz and I. A. Stegun (Editors), Handbook of Mathematical
Functions with Formulas, Graphs, and Mathematical Tables [Russian
translation], Nauka, Moscow, 1979. |
| 7. | H. Bateman and A. Erdélyi, Tables of Integral Transformations,
Vol. 1 [Russian translation], Nauka, Moscow, 1984. |
| 8. | L. V. Kantorovich and G. P. Akilov, Functional Analysis
[in Russian], Nauka, Moscow, 1984. |
| 9. | G. A. Morar', Method of Discontinuous Solutions in the Mechanics
of Solids [in Russian], Shtiintsa, Kishinev, 1990. |
|
| Received |
27 March 2000 |
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