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Mat. Sb., 2003, Volume 194, Number 5, Pages 61–96 (Mi msb735)  

This article is cited in 24 scientific papers (total in 24 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)

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.


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English version:
Sbornik: Mathematics, 2003, 194:5, 697–732

Bibliographic databases:

UDC: 517.9
MSC: 35B27, 74Bxx
Received: 03.06.2002

Citation: V. V. Zhikov, S. E. Pastukhova, “Homogenization for elasticity problems on periodic networks of critical thickness”, Mat. Sb., 194:5 (2003), 61–96; Sb. Math., 194:5 (2003), 697–732

Citation in format AMSBIB
\by V.~V.~Zhikov, S.~E.~Pastukhova
\paper Homogenization for elasticity problems on periodic networks
of critical thickness
\jour Mat. Sb.
\yr 2003
\vol 194
\issue 5
\pages 61--96
\jour Sb. Math.
\yr 2003
\vol 194
\issue 5
\pages 697--732

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    This publication is cited in the following articles:
    1. S. E. Pastukhova, “On the convergence of hyperbolic semigroups in a variable space”, Dokl. Math., 70:1 (2004), 609–614  mathnet  mathscinet  zmath  isi  elib
    2. S. E. Pastukhova, “Homogenization of elasticity problems on a periodic composite structure”, Dokl. Math., 69:2 (2004), 208–213  mathnet  mathscinet  zmath  isi  elib
    3. S. E. Pastukhova, “Homogenization of elasticity problems on periodic rod frames of critical thickness”, Dokl. Math., 69:1 (2004), 20–25  mathnet  mathscinet  zmath  isi  elib
    4. S. E. Pastukhova, “About homogenization of elasticity problems on combined structures”, J. Math. Sci. (N. Y.), 132:3 (2006), 313–330  mathnet  crossref  mathscinet  zmath  elib  elib
    5. S. E. Pastukhova, “Correctors in the homogenization of elasticity problems on thin structures”, Dokl. Math., 71:2 (2005), 177–182  mathnet  mathscinet  zmath  isi  elib  elib
    6. S. E. Pastukhova, “Homogenization of elasticity problems on periodic composite structures”, Sb. Math., 196:7 (2005), 1033–1073  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. Berlyand L., Cardone G., Gorb Yu., Panasenko G., “Asymptotic analysis of an array of closely spaced absolutely conductive inclusions”, Netw. Heterog. Media, 1:3 (2006), 353–377  crossref  mathscinet  zmath  isi
    8. 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
    9. 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
    10. Cardone G., Corbo Esposito A., Pastukhova S.E., “Homogenization of scalar problems for a combined structure with singular or thin reinforcement”, Z. Anal. Anwend., 26:3 (2007), 277–301  mathscinet  zmath  isi  elib
    11. S. A. Nazarov, “Korn inequalities for elastic junctions of massive bodies, thin plates, and rods”, Russian Math. Surveys, 63:1 (2008), 35–107  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    12. Braides A., Chiadò Piat V., “Non convex homogenization problems for singular structures”, Netw. Heterog. Media, 3:3 (2008), 489–508  crossref  mathscinet  zmath  isi
    13. Pastukhova S.E., “Asymptotic analysis in elasticity problems on thin periodic structures”, Netw. Heterog. Media, 4:3 (2009), 577–604  crossref  mathscinet  zmath  isi  elib
    14. Zhikov V.V., Pastukhova S.E., “Korn inequalities on thin periodic structures”, Netw. Heterog. Media, 4:1 (2009), 153–175  crossref  mathscinet  zmath  isi  elib
    15. Orlik J. Panasenko G. Shiryaev V., “Optimization of Textile-Like Materials via Homogenization and Beam Approximations”, Multiscale Model. Simul., 14:2 (2016), 637–667  crossref  mathscinet  zmath  isi  scopus
    16. Klevtsovskiy A.V. Mel'nyk T.A., “Asymptotic expansion for the solution to a boundary-value problem in a thin cascade domain with a local joint”, Asymptotic Anal., 97:3-4 (2016), 265–290  crossref  mathscinet  zmath  isi  scopus
    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
    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
    21. 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
    22. 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
    23. 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
    24. 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
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