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Mat. Sb., 2000, Volume 191, Number 2, Pages 149–164 (Mi msb456)  

This article is cited in 3 scientific papers (total in 3 papers)

On homogenization of a variational inequality for an elastic body with periodically distributed fissures

S. E. Pastukhova

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

Abstract: We study the problem of small deformations of an elastic body with periodically distributed fissures, where one-sided constraints are imposed on the sides of the fissures; this problem is equivalent to a variational inequality. We prove that if the linear size of the period of the distribution of the fissures tends to zero, then the solutions of this problem converge in the $L^2$-norm to the solution of the homogenized problem, which is a non-linear boundary-value problem of elasticity theory for a domain without fissures.

DOI: https://doi.org/10.4213/sm456

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English version:
Sbornik: Mathematics, 2000, 191:2, 291–306

Bibliographic databases:

UDC: 517.953
MSC: Primary 35B27; Secondary 35B40, 35C20, 73B27
Received: 06.07.1999

Citation: S. E. Pastukhova, “On homogenization of a variational inequality for an elastic body with periodically distributed fissures”, Mat. Sb., 191:2 (2000), 149–164; Sb. Math., 191:2 (2000), 291–306

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Pastukhova, SE, “The oscillating boundary phenomenon in the homogenization of a climatization problem”, Differential Equations, 37:9 (2001), 1276  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    2. S. E. Pastukhova, “Homogenization of a mixed problem with Signorini condition for an elliptic operator in a perforated domain”, Sb. Math., 192:2 (2001), 245–260  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Pastukhova, SE, “Homogenization for nonlinear elasticity problems on thin periodic structures”, Doklady Mathematics, 65:2 (2002), 257  mathscinet  zmath  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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