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Sbornik: Mathematics, 2005, Volume 196, Issue 7, Pages 1033–1073
DOI: https://doi.org/10.1070/SM2005v196n07ABEH000947
(Mi sm1402)
 

This article is cited in 5 scientific papers (total in 5 papers)

Homogenization of elasticity problems on periodic composite structures

S. E. Pastukhova

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
References:
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.
Received: 07.10.2003 and 13.09.2004
Bibliographic databases:
UDC: 517.9
MSC: 35B27, 74Kxx, 74Q05
Language: English
Original paper language: Russian
Citation: S. E. Pastukhova, “Homogenization of elasticity problems on periodic composite structures”, Sb. Math., 196:7 (2005), 1033–1073
Citation in format AMSBIB
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\by S.~E.~Pastukhova
\paper Homogenization of elasticity problems on periodic composite structures
\jour Sb. Math.
\yr 2005
\vol 196
\issue 7
\pages 1033--1073
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Linking options:
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  • https://doi.org/10.1070/SM2005v196n07ABEH000947
  • https://www.mathnet.ru/eng/sm/v196/i7/p101
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:595
    Russian version PDF:223
    English version PDF:20
    References:74
    First page:1
     
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