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Mat. Sb., 2005, Volume 196, Number 7, Pages 101–142 (Mi msb1402)  

This article is cited in 4 scientific papers (total in 4 papers)

Homogenization of elasticity problems on periodic composite structures

S. E. Pastukhova

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)

Abstract: Elasticity problems on a plane plate reinforced with a thin periodic network or in a 3-dimensional body reinforced with a thin periodic box skeleton are considered. The composite medium depends on two parameters approaching zero and responsible for the periodicity cell and the thickness of the reinforcing structure. The parameters can be dependent or independent.
For these problems Zhikov's method of ‘two-scale convergence with variable measure’ is used to derive the homogenization principle: the solution of the original problem reduces in a certain sense to the solution of the homogenized (or limiting) problem. The latter has a classical form. From the operator form of the homogenization principle, on the basis of the compactness principle in the $L^2$-space, which is also established, one obtains for the composite structure the Hausdorff convergence of the spectrum of the original problem to the spectrum of the limiting problem.

DOI: https://doi.org/10.4213/sm1402

Full text: PDF file (478 kB)
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English version:
Sbornik: Mathematics, 2005, 196:7, 1033–1073

Bibliographic databases:

UDC: 517.9
MSC: 35B27, 74Kxx, 74Q05
Received: 07.10.2003 and 13.09.2004

Citation: S. E. Pastukhova, “Homogenization of elasticity problems on periodic composite structures”, Mat. Sb., 196:7 (2005), 101–142; Sb. Math., 196:7 (2005), 1033–1073

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm1402
  • http://mi.mathnet.ru/eng/msb/v196/i7/p101

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Zhikov, S. E. Pastukhova, “On the Trotter–Kato Theorem in a Variable Space”, Funct. Anal. Appl., 41:4 (2007), 264–270  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. S. E. Pastukhova, “Degenerate equations of monotone type: Lavrent'ev phenomenon and attainability problems”, Sb. Math., 198:10 (2007), 1465–1494  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Braides A., Chiadò Piat V., “Non convex homogenization problems for singular structures”, Netw. Heterog. Media, 3:3 (2008), 489–508  crossref  mathscinet  zmath  isi
    4. Cancedda A., “Spectral Homogenization For a Robin-Neumann Problem”, Boll. Unione Mat. Ital., 10:2 (2017), 199–222  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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