 | | 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 |
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| In English (Mech. Solids): | | 4811 |
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| V.I. Ostrik, "Indentation of a Punch into an Elastic Strip with Friction and Adhesion," Mech. Solids. 46 (5), 755-765 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
5 |
Pages |
755-765 |
| DOI |
10.3103/S0025654411050098 |
| Title |
Indentation of a Punch into an Elastic Strip with Friction and Adhesion |
| Author(s) |
V.I. Ostrik (Institute of Applied Physics, National Academy of Sciences of Ukraine, Petropavlovskaya St., 58, Sumy, 40030 Ukraine, ostrik_v@rambler.ru) |
| Abstract |
In the contact interaction between elastic bodies with friction taken into account, the contact region splits, as a rule, into adhesion and sliding regions [1]. Contact with adhesion and sliding was first considered by L. A. Galin [2] in the problem of indentation of a punch with a rectilinear foundation into an elastic half-plane, who obtained an approximate solution of this problem [2, 3]. Galin's problem was further studied in [4-9].
The paper considers an analogue of Galin's problem for a strip, namely, the problem of contact with adhesion and sliding between a punch with a rectilinear foundation and a strip one of whose sides is fixed. The Wiener-Hopf method is used to reduce the system of integral equations of the problem to an infinite system of algebraic equations. The case of a half-infinite punch was considered earlier [10]. An asymptotic solution was obtained in [11-13]. |
| Keywords |
contact with adhesion and sliding, elastic strip, stresses, factorization |
| References |
| 1. | K. L. Johnson,
Contact Mechanics
(Cambridge University Press, Cambridge, 1987; Mir, Moscow, 1989). |
| 2. | L. A. Galin,
"Indentation of a Punch in the Presence of Friction and Adhesion,"
Prikl. Mat. Mekh.
9 (5), 413-424 (1945)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 3. | L. A. Galin,
Contact Problems in Elasticity
(Gostekhizdat, Moscow, 1953)
[in Russian]. |
| 4. | V. I. Mossakovskii and A. G. Biskup,
"Impression of a Stamp with Friction and Adhesion Present,"
Dokl. Akad. Nauk SSSR
206 (5), 1068-1070 (1972)
[Sov. Phys. Dokl. (Engl. Transl.)
17, 984-986 (1973)]. |
| 5. | D. A. Spence,
"An Eigenvalue Problem for Elastic Contact with Finite Friction,"
Proc. Cambridge Phil. Soc.
73, 249-268 (1973). |
| 6. | V. I. Mossakovskii, A. G. Biskup, and L. V. Mossakovskaya,
"Further Development of the Galin Problem with Friction and Adhesion,"
Dokl. Akad. Nauk SSSR
271 (51), 60-64 (1983)
[Sov. Phys. Dokl. (Engl. Transl.)
28, 557-559 (1983)]. |
| 7. | I. I. Mishishin,
"On a Mixed Problem,"
in Hydroaeromechanics and Elasticity, Vol. 32
(Izd-vo DGU, Dnepropetrovsk, 1984),
pp. 93-100
[in Russian]. |
| 8. | Yu. A. Antipov and N. Kh. Arutyunyan,
"Contact Problems of the Theory of Elasticity with Friction and Adhesion,"
Prikl. Mat. Mekh.
55 (6), 1005-1017 (1991)
[J. Appl. Math. Mech. (Engl. Transl.)
55 (6), 887-901 (1991)]. |
| 9. | V. I. Ostrik,
"Contact Interaction between a Punch and an Elastic Half-Plane
with Friction and Adhesion,"
Teor. Prikl. Mekh.,
No. 39, 94-101 (2004). |
| 10. | V. I. Ostrik,
"Impression of a Semiinfinite Stamp in an Elastic Strip with
Regard for Friction and Adhesion,"
Mat. Met. Fiz.-Mekh. Polya
51 (1), 138-149 (2008)
[J. Math. Sci. (Engl. Transl.)
160 (4), 453-469 (2009)]. |
| 11. | L. I. Manevich and A. V. Pavlenko,
"To the Solution of Contact Problems of Elasticity
for an Orthotropic Strip with Friction Forces Taken into Account,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 6, 72-80 (1974)
[Mech. Solids (Engl. Transl.)]. |
| 12. | S. G. Koblik and L. I. Manevich,
"Contact Problem for an Orthotropic Strip with Adhesion and Sliding Areas
in the Contact Region,"
in Hydroaeromechanics and Elasticity, Vol. 20
(Izd-vo DGU, Dnepropetrovsk, 1976),
pp. 106-110
[in Russian]. |
| 13. | L. I. Manevich, A. V. Pavlenko, and S. G. Koblik,
Asymptotic Methods in Theory of Elasticity of Orthotropic Solids
(Vishch. Shk., Kiev-Donetsk, 1982)
[in Russian]. |
| 14. | A. F. Ulitko and V. I. Ostrik,
"Mixed Problem of Elasticity for a Strip on a Rigid Foundation,"
in Proc. Third All-Russia Conf. on Elasticity
with International Participation
(Novaya kniga, Rostov-on-Don, 2004),
pp. 372-375
[in Russian]. |
| 15. | V. I. Ostrik,
"Sliding and Smooth Contacts of Punches of Different Cross-Sections
with an Elastic Strip,"
Mat. Met. Fiz.-Mekh. Polya
49 (4), 133-146 (2006). |
| 16. | M. P. Ganin,
"On the Fredholm Integral Equation with an Argument Difference Dependent Kernel,"
Izv. Vyssh. Uchebn. Zaved. Mat.,
No. 2, 31-43 (1963)
[Sov. Math. (Izv. VUZ)]. |
| 17. | M. M. Ignatenko and V. Kh. Kirillov,
"On the Solution of Some Problems of Mathematical Physics,"
Differents. Uravn.
5 (7), 1296-1302 (1969)
[Differ. Equations (Engl. Transl.)]. |
| 18. | Yu. A. Antipov,
"Exact Solution of the Problem on the Indentation of an Annular Punch into a Half-Space,"
Dokl. Akad. Nauk Ukr. SSR. Ser. A. Fiz. Mat. Tekhn. Nauki,
No. 7, 29-33 (1987). |
| 19. | V. I. Ostrik,
"Contact of Elastic and Rigid Wedges with Friction and Adhesion Taken into Account,"
Mat. Met. Fiz.-Mekh. Polya
48 (3), 88-100 (2005). |
| 20. | B. Noble,
Methods Based on the Wiener-Hopf Technique
for the Solution of Partial Differential Equations
(Pergamon Press, London etc., 1958; Izd-vo Inostr. Lit., Moscow, 1962). |
| 21. | G. M. Zrazhevskii and V. I. Ostrik,
"Asymptotics of Canonical Solutions,"
Mat. Met. Fiz.-Mekh. Polya
47 (3), 69-77 (2004). |
| 22. | M. V. Fedoryuk,
Asymptotics: Integrals and Series
(Nauka, Moscow, 1987)
[in Russian]. |
|
| Received |
27 April 2009 |
| Link to Fulltext |
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