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
 


IPMech RASWeb hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2010-6pp.778-788

Archive of Issues

Total articles in the database: 9198
In Russian (»Á‚. –ņÕ. Ő““): 6504
In English (Mech. Solids): 2694

<< Previous article | Volume 45, Issue 6 / 2010 | Next article >>
Yu.I. Vikulina, M.A. Grekov, and S.A. Kostyrko, "Model of Film Coating with Weakly Curved Surface," Mech. Solids. 45 (6), 778-788 (2010)
Year 2010 Volume 45 Number 6 Pages 778-788
DOI 10.3103/S0025654410060038
Title Model of Film Coating with Weakly Curved Surface
Author(s) Yu.I. Vikulina (Saint-Petersburg State University, Universitetskiy pr-t 35, Petergof, St.†Petersburg, 198504 Russia, denolia@yandex.ru)
M.A. Grekov (Saint-Petersburg State University, Universitetskiy pr-t 35, Petergof, St.†Petersburg, 198504 Russia, magrekov@mail.ru)
S.A. Kostyrko (Saint-Petersburg State University, Universitetskiy pr-t 35, Petergof, St.†Petersburg, 198504 Russia, sergey.kostyrko@gmail.ru)
Abstract We use the perturbation method to construct a solution of the plane problem of elasticity for a film-foundation composite where the film surface is weakly curved. In the case where the film surface has a periodic shape, the problem solution in each approximation is represented in terms of Fourier series with coefficients expressed in terms of quadrature. In the first approximation, we obtain the stresses on the film surface and on the interphase surface in terms of the surface curvature, the film average thickness, and the film-to-foundation Young's modulus ratio.
Keywords film coating, curved surface, stress concentration
References
1.  P. Kordos and J. Novak (Editors), Heterostructure Epitaxy and Devices - HEAD'97 (Kluwer, Dordrecht, 1998).
2.  L. B. Freund, "Evolution of Waviness on the Surface of a Strained Elastic Solid due to Stressdriven Diffusion," Int. J. Solids Struct. 32 (6/7), 911-923 (1995).
3.  H. Gao and W. D. Nix, "Surface Roughness of Heteroepitaxial Thin Films," Annu. Rev. Mater. Sci. 29, 173-209 (1999).
4.  A. M. Andrews, J. S. Speck, A. E. Romanov, et al., "Modeling Cross-Hatch Surface Morphology in Growing Mismatched Layers," J. Appl. Phys. 91 (4), 1933-1943 (2002).
5.  M. A. Grekov, "Weakly Curved Crack near the Boundary of Junction of Two Different Materials," Vestnik St. Petersburg. Univ. Ser. 1, No. 1, 93-100 (2008).
6.  M. A. Grekov and N. F. Morozov, "Some Modern Methods in Mechanics of Cracks," in Operator Theory: Advances and Applications, Vol. 191: Modern Analysis and Applications. Ed. by V. Adanyan et al. (Birkhäuser, Basel, 2009), pp. 127-142.
7.  H. Gao, "A Boundary Perturbation Analysis for Elastic Inclusions and Interfaces," Int. J. Solids Struct. 28 (6), 703-725 (1991).
8.  M. A. Grekov and S. N. Makarov, "Stress Concentration near a Slightly Curved Part of an Elastic Body Surface," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 53-61 (2004) [Mech. Solids (Engl. Transl.) 39 (6), 40-46 (2004)].
9.  M. A. Grekov, Singular Plane Problem of Elasticity (Izd-vo St. Petersburg Univ., St.Petersburg, 2001) [in Russian].
10.  M. A. Grekov and S. A. Kostyrko, "Stressed State of Thin Coating under the Action of a Periodic System of Surface Concentrated Forces," Vestnik St. Peterburg. Univ. Ser. 10, No. 4, 99-107 (2004).
11.  A. M. Lin'kov, Complex Method of Boundary Integral Equations in Elasticity (Nauka, St. Petersburg, 1999) [in Russian].
12.  J. Dundurs, "Edge-Bonded Dissimilar Orthogonal Elastic Wedges under Normal and Shear Loading," Trans. ASME. J. Appl. Mech. 36 (3), 650-652 (1969).
13.  N. I. Muskhelishvili, Some Fundamental Problems of Mathematical Elasticity Theory (Nauka, Moscow, 1966) [in Russian].
14.  H. Gao, "Stress Concentration at Slightly Undulating Surfaces," J. Mech. Phys. Solids 39 (4), 443-458 (1991).
Received 30 July 2010
Link to Fulltext http://www.springerlink.com/content/31318rv784335151/
<< Previous article | Volume 45, Issue 6 / 2010 | 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, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100