 | | 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
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| In English (Mech. Solids): | | 4810 |
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| V. B. Zelentsov, "Transient dynamic contact problem of elasticity for an impact of a parabolic punch against an elastic half-plane," Mech. Solids. 41 (1), 20-34 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
1 |
Pages |
20-34 |
| Title |
Transient dynamic contact problem of elasticity for an impact of a parabolic punch against an elastic half-plane |
| Author(s) |
V. B. Zelentsov (Rostov-on-Don) |
| Abstract |
The transient dynamic contact problem for an impact of a rigid parabolic punch
against an elastic half-plane is reduced to the initial value (Cauchy) problem
for the integro-differential equation of motion of the punch combined with an
additional nonlinear equation governing the relative motion of the punch and
the contact region half-width. At each step of the numerical solution of the
initial value problem, one utilizes an approximate analytical solution of an
auxiliary transient dynamic contact problem of the indentation of a rigid
parabolic punch, the width of the contact region of which is temporarily fixed.
The solution of the auxiliary problem is constructed on the basis of [1-3].
Transient contact problems with variable width of the contact region have been
considered previously in [3-5]. |
| References |
| 1. | V. B. Zelentsov, "On an asymptotic method for solving transient
dynamic contact problems," PMM [Applied Mathematics and Mechanics], Vol. 63,
No. 2, pp. 303-311, 1999. |
| 2. | V. B. Zelentsov, "A transient contact problem of indentation of a
rigid punch into an elastic half-plane," Izv. RAN. MTT [Mechanics of Solids],
No. 3, pp. 34-44, 1999. |
| 3. | V. B. Zelentsov, "On the transient dynamic contact problems of
elasticity with variable width of the contact region," PMM [Applied Mathematics
and Mechanics], Vol. 68, No. 1, pp. 199-134, 2004. |
| 4. | V. B. Poruchikov, Methods of Dynamic Theory of Elastcity [in Russian],
Nauka, Moscow, 1986. |
| 5. | A. G. Gorshkov and D. V. Tarlakovskii, Dynamic Contact Problems with
Moving Boundaries [in Russian], Nauka, Fizmatlit, Moscow, 1995. |
| 6. | A. I. Lur'e, Theory of Elasticity [in Russian], Nauka, Moscow, 1970. |
| 7. | V. Z. Parton and P. I. Perlin, Methods of Mathematical Theory of
Elasticity [in Russian], Nauka, Moscow, 1891. |
| 8. | H. Bateman and A. Erdélyi, Tables of Integral Transforms
[Russian translation], Nauka, Moscow, 1969. |
| 9. | V. M. Alexandrov, "Asymptotic methods in mechanics of contact
interactions," in I. I. Vorovich and V. M. Alexandrov (Editors), Mechanics
of Contact Interactions [in Russian], pp. 10-19, Fizmatlit, Moscow, 2001. |
| 10. | B. Noble, Methods based on the Wiener-Hopf Technique for the
Solution of Partial Differential Equations [Russian translation], Izd-vo
Inostr. Lit-ry, Moscow, 1962. |
| 11. | P. P. Zabreiko, A. I. Koshelev, M. A. Krasnosel'skii, et al., Integral
Equations [in Russian], Nauka, Moscow, 1968. |
| 12. | I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko, Nonclassical
Mixed Problems of Elasticity [in Russian], Nauka, Moscow, 1974. |
| 13. | D. Gaier, Lectures on Complex Approximation
[Russian translation], Mir, Moscow, 1986. |
| 14. | G. Doetsch, Guide to the Applications of the Laplace and
Z-transforms [Russian translation], Nauka, Moscow, 1971. |
| 15. | K. S. Kunts, Numerical Analysis [in Russian], Tekhnika, Kiev, 1964. |
| 16. | I. Babuska, M. Prager, and E. Vitasek, Numerical
Processes in Differential Equations [Russian translation], Mir,
Moscow, 1969. |
|
| Received |
15 December 2004 |
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