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 Issues2007-1pp.64-71

Archive of Issues

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

<< Previous article | Volume 42, Issue 1 / 2007 | Next article >>
O. V. Litvin and V. G. Popov, "Stress concentration near a thin elastic inclusion under interaction with harmonic waves in the case of smooth contact," Mech. Solids. 42 (1), 64-71 (2007)
Year 2007 Volume 42 Number 1 Pages 64-71
Title Stress concentration near a thin elastic inclusion under interaction with harmonic waves in the case of smooth contact
Author(s) O. V. Litvin (Odessa National Maritime Academy, Didrikhsona 8, Odessa, 65029, Ukraine, litvinov@ukr.net)
V. G. Popov (Odessa National Maritime Academy, Didrikhsona 8, Odessa, 65029, Ukraine, dr_popov@te.net.ua)
Abstract We solve the problem on the interaction of plane harmonic waves with a thin elastic plate-shaped inclusion. The ambient medium is assumed to be in plane strain. The smooth contact conditions are satisfied on both sides of the inclusion. The bending displacements of the inclusion are determined from the corresponding differential equation. In the statement of boundary conditions for this equation, one should take into account the transverse forces and bending moments applied to the lateral edges of the inclusion, while the boundary conditions are posed on the midplane of the inclusion. Using the discontinuous solution method, we reduce the problem to a system of two singular integral equations, which are solved numerically by the mechanical quadrature method. We obtain approximate formulas for the stress intensity coefficients near the ends of the inclusion and for the transverse forces and moments applied to the inclusion.
References
1.  V. G. Popov and A. E. Ulanovskii, "Comparative Analysis of Diffraction Fields when Elastic Waves Propagate through Defects of Various Nature," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 99-109 (1995) [Mech. Solids (Engl. Transl.)].
2.  V. G. Popov, "Interaction of Plane Elastic Waves with Systems of Radial Defects," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 118-129 (1999) [Mech. Solids (Engl. Transl.)].
3.  G. S. Kit, V. V. Mikhas'kiv, and O. M. Khai, "Boundary Element Analysis of Stationary Oscillations of a Plane Absolutely Rigid Inclusion in a Three-Dimensional Elastic Body," Prikl. Mat. Mekh. 64 (5), 855-863 (2002) [J. Appl. Math. Mech. (Engl. Transl.)].
4.  V. V. Mikhas'kiv and O. M. Khai, "On the Theory of Hardness of Elastic Solids with Plane Rigid Inclusions in the Field of Fatigue Dynamic Stresses," Mashinoznavstvo, No. 3, 17-22 (1999).
5.  V. M. Alexandrov and S. M. Mkhitaryan, Contact Problems for Bodies with Thin Coatings and Interlayers (Nauka, Moscow, 1983) [in Russian].
6.  N. T. Stashchuk, Problems of Mechanics of Elastic Bodies with Crack-Like Defects (Naukova Dumka, Kiev, 1993) [in Russian].
7.  V. G. Popov, Concentration of Elastic Stresses Near Stamps, Cuts, Thin Inclusions, and Reinforcements (Nauka, Moscow, 1982) [in Russian].
8.  V. T. Grinchenko and V. V. Meleshko, Harmonic Vibrations and Waves in Elastic Bodies (Naukova Dumka, Kiev, 1981) [in Russian].
9.  A. K. Pertsev and E. G. Platonov, Dynamics of Shells and Plates (Sudostroenie, Leningrad, 1987) [in Russian].
10.  O. V. Litvin and V. G. Popov, "Bending Oscillations of a Thin Elastic Inclusion in an Unbounded Medium under Interaction with Elastic Waves," Teoret. i Prikl. Mekhanika, No. 36, 131-140 (2002).
11.  S. M. Belotserkovskii and I. K. Lifanov, Numerical Methods in Singular Integral Equations and Their Applications in Aerodynamics, Elasticity, and Electrodynamics (Nauka, Moscow, 1985) [in Russian].
12.  Z. T. Nazarchuk, Numerical Investigation of Wave Diffraction on Cylindrical Structures (Naukova Dumka, Kiev, 1989) [in Russian].
13.  D. V. Grilitskii and G. T. Sulim, "Elastic stresses in a plane with thin-walled inclutions," Matematicheskie Metody i Fiz.-Mekh. Polya, No. 1, 41-48 (1975).
Received 18 May 2004
Link to Fulltext
<< Previous article | Volume 42, Issue 1 / 2007 | 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