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IssuesArchive of Issues2007-5pp.710-722

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S. A. Nazarov, "Thin elastic coatings and surface enthalpy," Mech. Solids. 42 (5), 710-722 (2007)
Year 2007 Volume 42 Number 5 Pages 710-722
Title Thin elastic coatings and surface enthalpy
Author(s) S. A. Nazarov (Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Bol’shoy pr-t 61, St. Petersburg, 199178, Russia, serna@snark.ipme.ru)
Abstract We obtain explicit formulas for the first few terms in the asymptotics of the solution of the problem on the deformation of a body with a thin elastic coating and propose several methods, based on these formulas, for modeling the problem with the use of the Wentzel boundary conditions or a regular perturbation of the boundary. We present estimates of the asymptotic remainders, including those in formulas obtained by modeling.
References
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5.  S. A. Nazarov, "Two-Term Asymptotics of Solutions of Spectral Problems with Singular Perturbations," Mat. Sb. 181 (3), 291-320 (1990) [Russian Acad. Sci. Sb. Math. (Engl. transl.)].
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11.  S. A. Nazarov, "Boundary Layers and Hinge Support Conditions for Thin Plates," Zap. Nauchn. Sem. POMI 257, 228-287 (1999) [J. Math. Sci. (Engl. transl.)].
12.  N. F. Morozov, S. A. Nazarov, and A. V. Proskura, "Boundary Value Problems of the Elasticity Theory for Plane Domains with Thin Borderings," in Mechanics of Deformable Bodies (Nauka, Moscow, 1986), pp. 82-93 [in Russian].
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17.  S. A. Nazarov, "Asymptotic Conditions at a Point, Selfadjoint Extensions of Operators and the Method of Matched Asymptotic Expansions," Trudy St.-Petersburg Mat. Obshch. 5, 112-183 (1996).
18.  S. A. Nazarov and J. Sokolowski, "Asymptotic Analysis of Shape Functionals," J. Math. Pures Appl. 82 (2), 125-196 (2003).
19.  V. G. Maz'ya, S. A. Nazarov, and B. A. Plamenevskii, Asymptotics of Solutions to Elliptic Boundary-Value Problems under a Singular Perturbation of the Domain (Izd-vo TGU, Tbilisi, 1981) [in Russian].
20.  A. B. Movchan and S. A. Nazarov, "Cracks in Composite Materials. I. Half-Infinite Crack in Elastic Plane with Orthotropic Composite Strip," Mekh. Komposit. Mater., No. 5, 842-851 (1990).
21.  S. A. Nazarov, "The Spatial Structure of the Stress Field in the Neighbourhood of the Corner Point of a Thin Plate," Prikl. Mat. Mekh. 55 (4), 653-661 (1991) [J. Appl. Math. Mech. (Engl. transl.)].
Received 14 December 2006
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