 | | 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
|
| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 46, Issue 2 / 2011 | Next article >> |
| V.D. Kubenko, "Wave Processes in an Elastic Half-Plane Impacted by a Blunt-Nosed Rigid Body," Mech. Solids. 46 (2), 256-265 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
2 |
Pages |
256-265 |
| DOI |
10.3103/S0025654411020142 |
| Title |
Wave Processes in an Elastic Half-Plane Impacted by a Blunt-Nosed Rigid Body |
| Author(s) |
V.D. Kubenko (Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Nesterova 3, Kiev, 03057 Ukraine, venkub@ukr.net) |
| Abstract |
The problem of unsteady deformation of an elastic half-plane is considered whose surface is impacted, at an initial instant, by a blunt-nosed rigid body, which generates diverging unsteady elastic waves and deforms the medium. The corresponding initial-boundary-value problem is formulated whose solution is constructed for the early stage of the interaction. The integral Laplace transform in the time variable and the integral Fourier transform in the one of the spatial variables are used. The solution of the problem is obtained in terms of the transforms and a formal solution is constructed in terms of the original functions. For a body with a fixed contact region, an analytical expression of the normal stress at an arbitrary point of the half-plane as a function of time is obtained. For a body shaped as an obtuse-angled wedge, analytical expressions of the normal stress and displacement at an arbitrary point at the symmetry axis of the problem are obtained. Calculations are performed and used to analyze the characteristic features of the wave processes in the medium as functions of time, the surface distance, and the mechanical properties of the material. |
| Keywords |
stress-strain state, unsteady indentation, plane problem, integral transforms, elastic half-plane |
| References |
| 1. | I. I. Vorovich and V. M. Alexandrov (Editors),
Mechanics of Contact Interaction
(Fizmatlit, Moscow, 2001)
[in Russian]. |
| 2. | A. G. Gorshkov and D. V. Tarlakovskii,
Dynamic Contact Problems with Moving Boundaries
(Nauka, Fizmatlit, Moscow, 1995)
[in Russian]. |
| 3. | V. D. Kubenko,
"Impact of Blunted Bodies on a Liquid or Elastic Medium,"
Prikl. Mekh.
40 (11), 3-44 (2004)
[Int. Appl. Mech. (Engl. Transl.)
40 (11), 1185-1225 (2004)]. |
| 4. | V. B. Poruchikov,
Methods of Dynamical Elasticity
(Nauka, Moscow, 1986)
[in Russian]. |
| 5. | V. D. Kubenko and M. V. Ayzenberg-Stepanenko,
"Impact Indentation of a Rigid Body into an Elastic Layer.
Analytical and Numerical Approaches,"
Mat. Met. Fiz.-Mekh. Polya
51 (2), 61-74 (2008)
[J. Math. Sci.
162 (1), 68-84 (2009)]. |
| 6. | I. N. Sneddon and D. S. Berry,
Classical Theory of Elasticity
(Springer, Berling, 1958; Fizmatgiz, Moscow, 1961). |
| 7. | A. N. Guz', V. D. Kubenko, and M. A. Cherevko,
Diffraction of Elastic Waves
(Naukova Dumka, Kiev, 1978)
[in Russian]. |
| 8. | V. D. Kubenko, T. A. Marchenko, and E. I. Starovoitov,
"On the Determination of the Stressed State of a Plane Elastic Layer
at Impact by a Blunt-Nosed Rigid Body on Its Surface,"
Dokl. NAN Ukr.,
No. 8, 111-114 (2006). |
| 9. | V. A. Ditkin and A. P. Prudnikov,
Integral Transforms and Operational Calculus
(Fizmatgiz, Moscow, 1961; Pergamon Press, London, 1965). |
| 10. | H. Bateman and A.Erdélyi,
Tables of Integral Transforms,
Vol. 1: Fourier, Laplace and Mellin Transforms
(McGraw-Hill, New York, 1954; Nauka, Moscow, 1969). |
| 11. | H. Bateman and A. Erdélyi,
Higher Transcendental Functions. Bessel Functions,
Functions of Parabolic Cylinder, Orthogonal Polynomials
(McGraw-Hill, New York-Toronto-London, 1955; Nauka, Moscow, 1966). |
| 12. | L. I. Slepyan,
Unsteady Elastic Waves
(Sudostroenie, Leningrad, 1972)
[in Russian]. |
| 13. | A. Ya. Sagomonyan,
Penetration
(Izd-vo MGU, Moscow, 1974)
[in Russian]. |
| 14. | V. D. Kubenko and T. A. Marchenko,
"Nonstationary Indentation of a Rigid Blunt Indenter into an Elastic Layer: A Plane Problem,"
Prikl. Mekh.
44 (3), 55-65 (2008)
[Int. Appl. Mech. (Engl. Transl.)
44 (3), 286-295 (2008)]. |
|
| Received |
06 December 2010 |
| Link to Fulltext |
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