 | | 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
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| In English (Mech. Solids): | | 3212 |
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| A.A. Amirjanyan and A.V. Sahakyan, "On Indentation of a Pair of Rigid Punches Connected by an Elastic Beam into an Elastic Half-Plane with Regard to the Friction and Adhesion Forces in the Contact Region," Mech. Solids. 52 (2), 161-171 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
2 |
Pages |
161-171 |
| DOI |
10.3103/S0025654417020066 |
| Title |
On Indentation of a Pair of Rigid Punches Connected by an Elastic Beam into an Elastic Half-Plane with Regard to the Friction and Adhesion Forces in the Contact Region |
| Author(s) |
A.A. Amirjanyan (Institute of Mechanics of the National Academy of Sciences of the Republic of Armenia, pr. Marshala Bagramyana 24B, Erevan, 375019 Republic of Armenia)
A.V. Sahakyan (Institute of Mechanics of the National Academy of Sciences of the Republic of Armenia, pr. Marshala Bagramyana 24B, Erevan, 375019 Republic of Armenia, avsah@mechins.sci.am) |
| Abstract |
The contact problem of indentation of a pair of rigid punches with plane bases connected by an elastic beam into the boundary of an elastic half-plane is considered under the conditions of plane strain state. The external load is generated by lumped forces applied to the punches and a uniformly distributed normal load acting on the beam.
It is assumed that the contact between the punch and the elastic half-plane can be described by L. A. Galin's statement, i.e., it is assumed that the adhesion acts in the interior part of each of the contact regions and the tangential stresses obeying the Coulomb law act on their boundaries.
With the symmetry taken into account, the problem is stated only for a single punch, and solving this problem is reduced to a system of four singular integral equations for the tangential and normal stresses in the adhesion region and the contact pressure in the sliding zones. The solution of the constitutive system together with three conditions of equilibrium of the system of punches connected by a beam is constructed by direct numerical integration by the method of mechanical quadratures.
As a result of the numerical analysis, the contact stress distribution functions were constructed and the values of the sliding zones and the punch rotation angle were determined for various values of the geometric, elastic, and force
characteristics. |
| Keywords |
singular integral equation, contact problem, elastic beam, friction, adhesion, numerical method, method of mechanical quadratures |
| References |
| 1. | 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.)]. |
| 2. | 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)]. |
| 3. | 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)]. |
| 4. | V. I. Ostrik and A. F. Ulitko,
Wiener-Hopf Method in Contact Problems of Elasticity
(Naukova Dumka, Kiev, 1006). |
| 5. | A. V. Sahakyan, "Solution of a Contact Problem with Contact and
Adhesion Regions (Galin's Problem) by the Method of Discrete
Singularities," in Development of L. A. Galin's Ideas in Mechanics, Collection of Research Papers (Moscow-Izhevsk, 2013),
pp. 103-120 [in Russian]. |
| 6. | A. A. Amirjanyan and A. V. Sahakyan,
"On Indentation of a Π-Shaped Rigid Punch into an Elastic Half-Plane
with Regard to Forces of Sliding Friction and Adhesion,"
Izv. NAN RA. Ser. Mekh.
66 (3), 3-11 (2013). |
| 7. | N. I. Muskhelishvili,
Singular Integral Equations
(Nauka, Moscow, 1968)
[in Russian]. |
| 8. | A. V. Sahakyan,
"The Method of Discrete Singularities for Solutions of Singular Integral
and Integro-Differential Equations,"
Proc. A. Razmadze Math. Inst. Georgia
156, 101-111 (2011). |
| 9. | A. V. Sahakyan,
"Quadrature Formulas of Maximum Algebraic Accuracy
for Cauchy-Type Integrals with Complex Exponents
of the Jacobi Weight Function,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 116-121 (2012)
[Mech. Solids (Engl. Transl.)
47 (6), 695-699 (2012)]. |
| 10. | A. A. Amirjanyan and L. V. Hakobyan,
"Uniform Motion of Absolutely Rigid Punch on the Inner Surface
of an Infinite Hollow Cylinder,"
in Proc. Intern. Conf. "Actual Problems of Continuum Mechanics, Vol. 1
(EGUAS, Erevan, 2010),
pp. 81-85
[in Russian]. |
|
| Received |
20 October 2014 |
| Link to Fulltext |
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