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Sbornik: Mathematics, 2003, Volume 194, Issue 5, Pages 697–732
DOI: https://doi.org/10.1070/SM2003v194n05ABEH000735
(Mi sm735)
 

This article is cited in 45 scientific papers (total in 45 papers)

Homogenization for elasticity problems on periodic networks of critical thickness

V. V. Zhikova, S. E. Pastukhovab

a Vladimir State Pedagogical University
b Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
References:
Abstract: It is a noticeable feature of elasticity problems on periodic structures depending on two geometric parameters that their homogenization has a non-classical nature. The most complicated kind of this non-classical homogenization occurs on structures of so-called critical thickness. Homogenization for periodic networks of this type is presented in the paper.
Received: 03.06.2002
Bibliographic databases:
UDC: 517.9
MSC: 35B27, 74Bxx
Language: English
Original paper language: Russian
Citation: V. V. Zhikov, S. E. Pastukhova, “Homogenization for elasticity problems on periodic networks of critical thickness”, Sb. Math., 194:5 (2003), 697–732
Citation in format AMSBIB
\Bibitem{ZhiPas03}
\by V.~V.~Zhikov, S.~E.~Pastukhova
\paper Homogenization for elasticity problems on periodic networks
of critical thickness
\jour Sb. Math.
\yr 2003
\vol 194
\issue 5
\pages 697--732
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Linking options:
  • https://www.mathnet.ru/eng/sm735
  • https://doi.org/10.1070/SM2003v194n05ABEH000735
  • https://www.mathnet.ru/eng/sm/v194/i5/p61
  • This publication is cited in the following 45 articles:
    1. S. A. Nazarov, A. S. Slutskii, “Homogenization of the Scalar Boundary Value Problem in a Thin Periodically Broken Cylinder”, Sib Math J, 65:2 (2024), 363  crossref
    2. S. A. Nazarov, A. S. Slutskii, “Osrednenie skalyarnoi kraevoi zadachi v tonkom periodicheski izlomannom tsilindre”, Sib. matem. zhurn., 65:2 (2024), 374–394  mathnet  crossref
    3. Grigory Panasenko, Konstantin Pileckas, Advances in Mathematical Fluid Mechanics, Multiscale Analysis of Viscous Flows in Thin Tube Structures, 2024, 473  crossref
    4. S. A. Nazarov, “On the one-dimensional asymptotic models of thin Neumann lattices”, Siberian Math. J., 64:2 (2023), 356–373  mathnet  crossref  crossref  mathscinet
    5. Alexander G. Kolpakov, Sergey I. Rakin, Advanced Structured Materials, 170, Sixty Shades of Generalized Continua, 2023, 401  crossref
    6. Irina V. Fankina, Alexey I. Furtsev, Evgeny M. Rudoy, Sergey A. Sazhenkov, “The homogenized quasi-static model of a thermoelastic composite stitched with reinforcing threads”, Journal of Computational and Applied Mathematics, 434 (2023), 115346  crossref
    7. Georges Griso, Larysa Khilkova, Julia Orlik, “Asymptotic Behavior of 3D Unstable Structures Made of Beams”, J Elast, 150:1 (2022), 7  crossref
    8. Griso G. Khilkova L. Orlik J. Sivak O., “Asymptotic Behavior of Stable Structures Made of Beams”, J. Elast., 143:2 (2021), 239–299  crossref  mathscinet  isi  scopus
    9. Braides A., Piat V.Ch., “Homogenization of Networks in Domains With Oscillating Boundaries”, Appl. Anal., 98:1-2, SI (2019), 45–63  crossref  mathscinet  zmath  isi  scopus
    10. Cherednichenko K.D. Evans J.A., “Homogenisation of Thin Periodic Frameworks With High-Contrast Inclusions”, J. Math. Anal. Appl., 473:2 (2019), 658–679  crossref  mathscinet  zmath  isi  scopus
    11. A. V. Klevtsovs'kyi, “Asymptotic Expansion of the Solution of a Linear Parabolic Boundary-Value Problem in a Thin Starlike Joint”, J Math Sci, 238:3 (2019), 271  crossref
    12. S. A. Nazarov, “Waves in a Plane Rectangular Lattice of Thin Elastic Waveguides”, J Math Sci, 242:2 (2019), 227  crossref
    13. Kolpakov A.G. Andrianov I.V. Rakin S.I. Rogerson G.A., “An Asymptotic Strategy to Couple Homogenized Elastic Structures”, Int. J. Eng. Sci., 131 (2018), 26–39  crossref  mathscinet  zmath  isi  scopus
    14. Abdoul-Anziz H., Seppecher P., “Strain Gradient and Generalized Continua Obtained By Homogenizing Frame Lattices”, Math. Mech. Complex Syst., 6:3 (2018), 213–250  crossref  mathscinet  zmath  isi
    15. Houssam Abdoul-Anziz, Pierre Seppecher, “Homogenization of periodic graph-based elastic structures”, Journal de l'École polytechnique — Mathématiques, 5 (2018), 259  crossref
    16. V. G. Maz'ya, A. B. Movchan, “Meso-Scale Approximations of Fields Around Clusters of Defects”, J Math Sci, 232:4 (2018), 446  crossref
    17. Cherednichenko K.D. Kiselev A.V., “Norm-Resolvent Convergence of One-Dimensional High-Contrast Periodic Problems to a Kronig–Penney Dipole-Type Model”, Commun. Math. Phys., 349:2 (2017), 441–480  crossref  mathscinet  zmath  isi  elib  scopus
    18. Bellieud M., “Homogenization of Stratified Elastic Composites With High Contrast”, SIAM J. Math. Anal., 49:4 (2017), 2615–2665  crossref  mathscinet  zmath  isi  scopus
    19. Mel'nyk T.A., Klevtsovskiy A.V., “Asymptotic Approximation For the Solution to a Semi-Linear Elliptic Problem in a Thin Aneurysm-Type Domain”, Open Math., 15 (2017), 1351–1370  crossref  mathscinet  zmath  isi  scopus
    20. Orlik J. Andra H. Argatov I. Staub S., “Does the Weaving and Knitting Pattern of a Fabric Determine Its Relaxation Time?”, Q. J. Mech. Appl. Math., 70:4 (2017), 337–361  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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