Mechanics of Solids (about journal) 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

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2002-2pp.47-55

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 37, Issue 2 / 2002 | Next article >>
I. I. Argatov, "The pressure of a slender rectangular punch on an elastic half-space," Mech. Solids. 37 (2), 47-55 (2002)
Year 2002 Volume 37 Number 2 Pages 47-55
Title The pressure of a slender rectangular punch on an elastic half-space
Author(s) I. I. Argatov (St. Petersburg)
Abstract The method of matching asymptotic expansions is applied to study the contact problem for a slender rectangular punch on an elastic half-space. A consistent integral equation for the pressure per unit length is derived by using a modified procedure of matching. The results of numerical calculations are compared with the known data. The solution obtained is generalized to the case of a slender curved punch, elastic layer, and unilateral contact.
References
1.  L. A. Galin, "On the Zimmerman-Winkler hypothesis for beams," PMM [Applied Mathematics and Mechanics], Vol. 7, No. 4, pp. 293-300, 1943.
2.  N. M. Borodachev, "An indentation of a punch with a slender rectangular base into an elastic half-space," Izv. AN SSSR. MTT [Mechanics of Solids], No. 4, pp. 135-141, 1970.
3.  N. M. Borodachev and L. A. Galin, "A contact problem for a punch with slender rectangular base," PMM [Applied Mathematics and Mechanics], Vol. 38, No. 1, pp. 125-130, 1974.
4.  L. A. Galin, Contact Problems in the Theory of Elasticity and Viscoelasticity [in Russian], Nauka, Moscow, 1980.
5.  V. M. Alexandrov and M. A. Sumbatyan, "Asymptotic solution of integral equations of convolution type with logarithmic singularity of the kernel transform and its application in mechanics," Izv. AN SSSR. MTT [Mechanics of Solids], No. 2, pp. 80-88, 1980.
6.  V. M. Alexandrov and D. A. Pozharskii, Nonclassical Three-dimensional Problems of Mechanics of Contact Interactions of Elastic Solids [in Russian], Factorial, Moscow, 1998.
7.  J. Vrbik, B. M.Singh, and H. T. Danyluk, "Contact problem of a pair of flat rectangular stamps resting on an elastic half-plane," Acta Mech., Vol. 112, No. 1-4, pp. 77-82, 1995.
8.  M. D. Van-Dyke, Perturbation Methods in Fluid Mechanics [Russian translation], Mir, Moscow, 1967.
9.  A. M. Il'in, Matching of Asymptotic Expansions in Solving Boundary Value Problems [in Russian], Nauka, Moscow, 1987.
10.  W. G. Mazja, S. A. Nazarow, and B. A. Plamenewski, Asymptotische Theorie Elliptischer Randwertaufgaben in singulär gestörten Gebieten. Bd. 1, Akadem. Verlag, Berlin, 1991.
11.  J. J. Kalker, "On elastic line contact," Trans. ASME, Ser. E, J. Appl. Mech., Vol. 39, No. 4, pp. 1125-1132, 1972.
12.  G. I. Sivashinsky, "The problem of a slender die," J. Elasticity, Vol. 5, No. 2, pp. 161-166, 1975.
13.  C. Panek and J. J. Kalker, "A solution for the narrow rectangular punch," J. Elasticity, Vol. 7, No. 2, pp. 213-218, 1977.
14.  E. O.Tuck and C. C. Mei, "Contact of one more slender bodies with an elastic half-space," Int. I. Solids and Structures, Vol. 19, No. 1, pp. 1-23, 1983.
15.  A. N. Burmistrov, "Contact problem of theory of elasticity for slender regions," Zh. Prikl. Mekhaniki i Tekhn. Fiziki, No. 5, pp. 149-157, 1988.
16.  I. I. Argatov and S. A. Nazarov, "Pressure of a slender annular punch on an elastic half-space," PMM [Applied Mathematics and Mechanics], Vol. 60, No. 5, pp. 810-825, 1996.
17.  M. V. Fedoryuk, "Dirichlet problem for Laplace operator in the external region of a slender body of revolution," in Theory of Cubature Formulas and Applications of Functional Analysis to Problems of Mathematical Physics. Proceedings of S. L. Sobolev Seminar. Volume 1 [in Russian], pp. 113-131, 1980.
18.  V. G. Mazja, S. A. Nazarov, and B. A. Plamenewski, "On the asymptotics of solutions of Dirichlet problem in a three-dimensional domain with a slender body cut out," Doklady AN SSSR, Vol. 256, No. 1, pp. 37-39, 1981.
19.  W. Nowacki, Theory of Elasticity [Russian translation], Mir, Moscow, 1975.
20.  J. J. Kalker, "The surface displacement of an elastic half-space loaded in a slender, bounded, curved surface region with application to the calculation of the contact pressure under a roller," J. Inst. Math. Appl., Vol. 19, No. 2, pp. 127-144, 1977.
21.  N. I. Muskhelishvili, Some Basic Problems of the Theory of Elasticity [in Russian], Nauka, Moscow, 1966.
22.  I. S. Gradshtein and I. M. Ryzik, Tables of Integrals, Sums, Series, and Products [in Russian], Fizmatgiz, Moscow, 1963.
23.  S. G. Mikhlin, Variational Methods in Mathematical Physics [in Russian], Nauka, Moscow, 1970.
24.  V. I. Smirnov, A Course in Higher Mathematics. Volume 4 [in Russian], Gostekhizdat, Moscow, 1953.
25.  A. F. Verlan' and V. S. Sizikov, Methods for Solving Integral Equations with Computer Codes [in Russian], Naukova Dumka, Kiev, 1978.
26.  G. Fichera, Existence Theorems in the Theory of Elasticity [Russian translation], Mir, Moscow, 1974.
27.  G. Duvaut and J.-L. Lions, Inequalities in Mechanics and Physics [Russian translation], Nauka, Moscow, 1980.
28.  A. S. Kravchuk, Variational and Quasivariational Inequalities in Mechanics [in Russian], Izd-vo MGAPI, Moscow, 1997.
29.  I. I. Argatov and S. A. Nazarov, "Asymptotic solution of Signorini's problem with an obstacle in a thin elongated set," Matem. Sbornik, Vol. 187, No. 10, pp. 3-32, 1996.
30.  R. Glowinski, J.-L. Lions, and R. Trémoliéres, Numerical Study of Variational Inequalities [Russian translation], Mir, Moscow, 1979.
31.  I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko, Nonclassical Mixed Problems of the Theory of Elasticity [in Russian], Nauka, Moscow, 1974.
Received 10 November 1999
<< Previous article | Volume 37, Issue 2 / 2002 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100