 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
|
| << Previous article | Volume 44, Issue 5 / 2009 | Next article >> |
| S.M. Mkhitaryan, A.L. Shekyan, and L.A. Shekyan, "Indentation of a Round Punch into a Rough Elastic Half-Space," Mech. Solids. 44 (5), 729-736 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
5 |
Pages |
729-736 |
| DOI |
10.3103/S0025654409050094 |
| Title |
Indentation of a Round Punch into a Rough Elastic Half-Space |
| Author(s) |
S.M. Mkhitaryan (Institute of Mechanics, National Academy of Sciences of Republic of Armenia, 24b Marshal Baghramian ave., Erevan, 0019, Republic of Armenia, Lilit_Dashtoyan@mechins.sci.am)
A.L. Shekyan (Institute of Mechanics, National Academy of Sciences of Republic of Armenia, Marshal Baghramian ave. 24b, Yerevan, 0019, Republic of Armenia, MrTiko@mail.ru)
L.A. Shekyan (State Engineering University of Armenia, Teryan 105, Yerevan, 0009, Republic of Armenia, MrTiko@mail.ru) |
| Abstract |
We consider the axisymmetric contact problem on the indentation of a round punch with plane base into an elastic half-space. Roughness is taken into account in the framework of the well-known model in which the local surface displacements are proportional to some power of the contact pressures at the same point. To study the problem, we use the theory of nonlinear integral equations of Hammerstein type together with the mathematical technique of orthogonal Legendre polynomials and the contraction mapping principle. We obtain an approximate analytic solution of the problem, numerically analyze the results, and reveal typical laws of variation of the main mechanical variables. |
| Keywords |
contact problem, punch, integral equation, roughness |
| References |
| 1. | I. Ya. Shtaerman,
Contact Problem of the Theory of Elasticity
(Gostekhizdat, Moscow-Leningrad, 1949)
[in Russian]. |
| 2. | G. Ya. Popov and V. V. Savchuk,
"Contact Problem of Elasticity for a Circle Contact Region
Taking into Account a Surface Structure of Contacting Bodies,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 3, 80-87 (1971)
[Mech. Solids (Engl. Transl.)]. |
| 3. | V. M. Alexandrov and I. I. Kudish,
"Asymptotic Analysis of Plane and Axially Symmetric Contact Problems with the Surface Structure of Interacting Bodies Taken into Account,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 1, 58-70 (1979)
[Mech. Solids (Engl. Transl.)]. |
| 4. | A. S. Rabinovich,
"On Solving the Contact Problems for Rough Bodies,"
Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela,
No. 1, 52-57 (1979)
[Mech. Solids (Engl. Transl.)]. |
| 5. | V. M. Alexandrov,
"Contact Problems in Tribology,"
in Mechanics and Scientific and Technological Progress.
Vol. 3: Mechanics of Solids
(Nauka, Moscow, 1988),
pp. 170-180
[in Russian]. |
| 6. | I. G. Goryacheva,
Mechanics of Friction Interaction
(Nauka, Moscow, 2001)
[in Russian]. |
| 7. | G. Ya. Popov,
"Some Properties of Classical Polynomials and Their Application to Contact Problems,"
Prikl. Mat. Mekh.
27 (5), 821-832 (1963)
[J. Appl. Math. Mech. (Engl. Transl.)
27 (5), 1255-1271 (1963)]. |
| 8. | S. M. Mkhitaryan
"A Special Relationship in Spheroidal Wave Functions and Its Application to Contact Problems,"
Prikl. Mat. Mekh.
48 (5), 105-113 (1984)
[J. Appl. Math. Mech. (Engl. Transl.)
48 (5), 611-618 (1984)]. |
| 9. | L. A. Lyusternik and V. I. Sobolev,
Elements of Functional Analysis
(Nauka, Moscow, 1965; Hindustan Publishing Corp., Delhi, 1974; Halsted Press, New York, 1974). |
| 10. | V. M. Alexandrov and S. M. Mkhitaryan,
Contact Problems for Bodies with Thin Coatings and Interlayers
(Nauka, Moscow, 1983)
[in Russian]. |
| 11. | E. V. Kovalenko,
"On an Efficient Method for Solving Contact Problems for
a Linearly Deformable Basement with a Thin Reinforcing Coating,"
Izv. Akad. Nauk Armyan. SSR. Ser. Mekh.
32 (2), 76-82 (1979)
[Soviet J. Contemporary Math. Anal. (Engl. Transl.)]. |
| 12. | N. B. Demkin,
Contacting of Rough Surfaces
(Nauka, Moscow, 1970)
[in Russian]. |
| 13. | H. Bateman and A. Erdelyi,
Tables of Integral Transforms, Vol. 2
(McGraw-Hill, New York, 1954; Nauka, Moscow, 1974). |
| 14. | F. G. Tricomi,
Integral Equations
(Dover, New York, 1985; Izd-vo Inostr. Lit., Moscow, 1960). |
| 15. | S. M. Mkhitaryan and L. A. Shekyan,
"Plane Contact Problem for Two Rough Rigid Bodies Made of
Power-Law Strengthening Materials,"
Izv. Akad. Nauk Armyan. SSR. Ser. Mekh.
30 (3), 15-32 (1977)
[Soviet J. Contemporary Math. Anal. (Engl. Transl.)]. |
| 16. | I. P. Natanson,
Theory of Functions of a Real Variable
(Ungar, New York, 1961; Nauka, Moscow, 1974). |
|
| Received |
24 September 2007 |
| Link to Fulltext |
|
| << Previous article | Volume 44, Issue 5 / 2009 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English