 | | 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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| S. A. Dokuchaev, V. B. Zelentsov, and R. V. Sakhabudinov, "Impact of a plane die on an elastic orthotropic half-plane," Mech. Solids. 44 (1), 45-56 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
1 |
Pages |
45-56 |
| DOI |
10.3103/S002565440901004X |
| Title |
Impact of a plane die on an elastic orthotropic half-plane |
| Author(s) |
S. A. Dokuchaev (North Caucasus Branch of Moscow Technical University of Communications and Informatics, Serafimovicha 62, Rostov-on-Don, 344002, Russia, fathill@donpac.ru)
V. B. Zelentsov (Rostov Military Institute of Missile Troops, pr-t Oktyabrya 24/50, Rostov-on-Don, 344027, Russia, zelentsov47@mail.ru)
R. V. Sakhabudinov (Rostov Military Institute of Missile Troops, pr-t Oktyabrya 24/50, Rostov-on-Don, 344027, Russia, sahabudinov@mail.ru) |
| Abstract |
To study the process of impact of a rigid body on the surface of an elastic body made of a composite material, we consider a nonstationary dynamic contact problem about the impact of a plane rigid die on an elastic orthotropic half-plane. The problem is reduced to solving an integral equation of the first kind for the Laplace transform of the contact stresses under the die base. An approximate solution of the integral equation is constructed with the use of a special approximation to the symbol of the kernel of the integral equation in the complex plane. The inverse Laplace transform of the solution results in determining the scalar contact stress field on the die base, the force exerted by the die on the elastic medium, and the vertical displacement field of the free surface of the orthotropic medium out side the die. The solutions thus obtained permit studying specific features of the process of die penetration into an orthotropic medium and the strain properties of the medium. |
| References |
| 1. | S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body (Nauka, Moscow, 1977; Mir Publishers, Moscow, 1981). |
| 2. | A. G. Gorshkov and D. V. Tarlakovskii, Dynamic Contact Problems with Moving Boundaries (Nauka, Fizmatlit, Moscow, 1995) [in Russian]. |
| 3. | R. M. Christensen, Mechanics of Composite Materials (Wiley, New York, 1979; Mir, Moscow, 1982). |
| 4. | V. B. Zelentsov, "An Asymptotic Method of Solving Transient Dynamic Contact Problems," Prikl. Mat. Mekh. 63(2), 303-311 (1999) [J. Appl. Math. Mech. (Engl. Transl.) 63 (2), 291-298 (1999)]. |
| 5. | P. P. Zabreiko, A. I. Koshelev, M. A. Kransnosel’skii, et al., Integral Equations (Nauka, Moscow, 1968) [in Russian]. |
| 6. | B. Noble, Methods Based on Wiener-Hopf Technique for the Solution of Partial Differential Equations (Pergamon Press, London, 1958; Izd-vo Inostr. Lit., Moscow, 1962). |
| 7. | V. B. Poruchikov, Methods of Dynamical Elasticity (Nauka, Moscow, 1986) [in Russian]. |
|
| Received |
13 February 2006 |
| Link to Fulltext |
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