Abstract:
A methodology is proposed for averaging in boundary value problems with plane bondary, and also problems on the contact of several microstructures with plane contact surface. Boundary layers are taken into account in this methodology. The author considers both direct contact of two structures and contact of two media separated by a thin inhomogeneous layer having periodic structure. Formal asymptotic solutions of some problems on the contact of two media are constructed, and estimates of how close the asymptotic solution is to the exact solution are derived.
Bibliography: 34 titles.
Citation:
G. P. Panasenko, “Higher order asymptotics of solutions of problems on the contact of periodic structures”, Math. USSR-Sb., 38:4 (1981), 465–494
\Bibitem{Pan79}
\by G.~P.~Panasenko
\paper Higher order asymptotics of solutions of problems on the contact of periodic structures
\jour Math. USSR-Sb.
\yr 1981
\vol 38
\issue 4
\pages 465--494
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\crossref{https://doi.org/10.1070/SM1981v038n04ABEH001453}
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Linking options:
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https://doi.org/10.1070/SM1981v038n04ABEH001453
https://www.mathnet.ru/eng/sm/v152/i4/p505
This publication is cited in the following 33 articles:
Alexander G. Kolpakov, Sergey I. Rakin, Igor V. Andrianov, Advanced Structured Materials, 170, Sixty Shades of Generalized Continua, 2023, 419
Alexander G. Kolpakov, Igor V. Andrianov, Sergey I. Rakin, Advanced Structured Materials, 195, Mechanics of Heterogeneous Materials, 2023, 341
Alexander G. Kolpakov, Sergey I. Rakin, Igor V. Andrianov, “Boundary layers in the vicinity of the prepreg interface in layered composites and the homogenized delamination criterion”, International Journal of Solids and Structures, 267 (2023), 112166
Markus Gahn, Willi Jäger, Maria Neuss-Radu, “Correctors and error estimates for reaction–diffusion processes through thin heterogeneous layers in case of homogenized equations with interface diffusion”, Journal of Computational and Applied Mathematics, 383 (2021), 113126
S. A. Nazarov, “Homogenization of Kirchhoff plates joined by rivets which are modeled by the Sobolev point conditions”, St. Petersburg Math. J., 32:2 (2021), 307–348
MARÍA ANGUIANO, “Homogenization of a non-stationary non-Newtonian flow in a porous medium containing a thin fissure”, Eur. J. Appl. Math, 30:2 (2019), 248
S. Koley, P.M. Mohite, C.S. Upadhyay, “Boundary layer effect at the edge of fibrous composites using homogenization theory”, Composites Part B: Engineering, 173 (2019), 106815
Alexander G Kolpakov, Igor V Andrianov, Danila A Prikazchikov, “Asymptotic strategy for matching homogenized structures. Conductivity problem”, The Quarterly Journal of Mechanics and Applied Mathematics, 2018
María Anguiano, Francisco Javier Suárez-Grau, “Derivation of a coupled Darcy–Reynolds equation for a fluid flow in a thin porous medium including a fissure”, Z. Angew. Math. Phys., 68:2 (2017)
Holloway Ch.L., Kuester E.F., “Corrections to the Classical Continuity Boundary Conditions at the Interface of a Composite Medium”, Photonics Nanostruct., 11:4 (2013), 397–422
A.G. Kolpakov, “Influence of non degenerated joint on the global and local behavior of joined plates”, International Journal of Engineering Science, 2011
Panasenko G., “The Partial Homogenization: Continuous and Semi-Discretized Versions”, Math. Models Meth. Appl. Sci., 17:8 (2007), 1183–1209
Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S161–S167
Teplinskii A., “Asymptotic Expansions for the Eigenvalues and the Eigenfunctions of Boundary Value Problems with Rapidly Oscillating Coefficients in a Layer”, Differ. Equ., 36:6 (2000), 911–917
Demidov A., “Some Applications of the Helmholtz-Kirchhoff Method (Equilibrium Plasma in Tokamaks, Hele-Shaw Flow, and High-Frequency Asymptotics”, Russ. J. Math. Phys., 7:2 (2000), 166–186
S. Gnélécoumbaga, G. P. Panasenko, “Asymptotic analysis of the problem of contact of a highly conducting and a perforated domain”, Comput. Math. Math. Phys., 39:1 (1999), 65–80
S. A. Nazarov, A. S. Slutskij, “Asymptotic behaviour of solutions of boundary-value problems for equations with rapidly oscillating coefficients in a domain with a small cavity”, Sb. Math., 189:9 (1998), 1385–1422
Panasenko G., “Method of Asymptotic Partial Decomposition of Domain”, Math. Models Meth. Appl. Sci., 8:1 (1998), 139–156
Panasenko G., “Asymptotic Analysis of Bar Systems .2.”, Russ. J. Math. Phys., 4:1 (1996), 87–116
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