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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.
DOI:
https://doi.org/10.4213/sm735
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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
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http://mi.mathnet.ru/eng/msb735https://doi.org/10.4213/sm735 http://mi.mathnet.ru/eng/msb/v194/i5/p61
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S. E. Pastukhova, “On the convergence of hyperbolic semigroups in a variable space”, Dokl. Math., 70:1 (2004), 609–614
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S. E. Pastukhova, “Homogenization of elasticity problems on a periodic composite structure”, Dokl. Math., 69:2 (2004), 208–213
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S. E. Pastukhova, “Homogenization of elasticity problems on periodic rod frames of critical thickness”, Dokl. Math., 69:1 (2004), 20–25
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S. E. Pastukhova, “About homogenization of elasticity problems on combined structures”, J. Math. Sci. (N. Y.), 132:3 (2006), 313–330
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S. E. Pastukhova, “Correctors in the homogenization of elasticity problems on thin structures”, Dokl. Math., 71:2 (2005), 177–182
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S. E. Pastukhova, “Homogenization of elasticity problems on periodic composite structures”, Sb. Math., 196:7 (2005), 1033–1073
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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
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S. E. Pastukhova, “Degenerate equations of monotone type: Lavrent'ev phenomenon and attainability problems”, Sb. Math., 198:10 (2007), 1465–1494
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V. V. Zhikov, S. E. Pastukhova, “On the Trotter–Kato Theorem in a Variable Space”, Funct. Anal. Appl., 41:4 (2007), 264–270
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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
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S. A. Nazarov, “Korn inequalities for elastic junctions of massive bodies, thin plates, and rods”, Russian Math. Surveys, 63:1 (2008), 35–107
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Braides A., Chiadò Piat V., “Non convex homogenization problems for singular structures”, Netw. Heterog. Media, 3:3 (2008), 489–508
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Pastukhova S.E., “Asymptotic analysis in elasticity problems on thin periodic structures”, Netw. Heterog. Media, 4:3 (2009), 577–604
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Zhikov V.V., Pastukhova S.E., “Korn inequalities on thin periodic structures”, Netw. Heterog. Media, 4:1 (2009), 153–175
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Orlik J. Panasenko G. Shiryaev V., “Optimization of Textile-Like Materials via Homogenization and Beam Approximations”, Multiscale Model. Simul., 14:2 (2016), 637–667
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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
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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
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Bellieud M., “Homogenization of Stratified Elastic Composites With High Contrast”, SIAM J. Math. Anal., 49:4 (2017), 2615–2665
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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
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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
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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
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Abdoul-Anziz H., Seppecher P., “Strain Gradient and Generalized Continua Obtained By Homogenizing Frame Lattices”, Math. Mech. Complex Syst., 6:3 (2018), 213–250
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Braides A., Piat V.Ch., “Homogenization of Networks in Domains With Oscillating Boundaries”, Appl. Anal., 98:1-2, SI (2019), 45–63
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Cherednichenko K.D. Evans J.A., “Homogenisation of Thin Periodic Frameworks With High-Contrast Inclusions”, J. Math. Anal. Appl., 473:2 (2019), 658–679
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