|
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
Full text:
PDF file (447 kB)
References:
PDF file
HTML file
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
\Bibitem{ZhiPas03}
\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
\mathnet{http://mi.mathnet.ru/msb735}
\crossref{https://doi.org/10.4213/sm735}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1992110}
\zmath{https://zbmath.org/?q=an:1077.35023}
\elib{https://elibrary.ru/item.asp?id=13435608}
\transl
\jour Sb. Math.
\yr 2003
\vol 194
\issue 5
\pages 697--732
\crossref{https://doi.org/10.1070/SM2003v194n05ABEH000735}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000185858900003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0142086985}
Linking options:
http://mi.mathnet.ru/eng/msb735https://doi.org/10.4213/sm735 http://mi.mathnet.ru/eng/msb/v194/i5/p61
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:
-
S. E. Pastukhova, “On the convergence of hyperbolic semigroups in a variable space”, Dokl. Math., 70:1 (2004), 609–614
-
S. E. Pastukhova, “Homogenization of elasticity problems on a periodic composite structure”, Dokl. Math., 69:2 (2004), 208–213
-
S. E. Pastukhova, “Homogenization of elasticity problems on periodic rod frames of critical thickness”, Dokl. Math., 69:1 (2004), 20–25
-
S. E. Pastukhova, “About homogenization of elasticity problems on combined structures”, J. Math. Sci. (N. Y.), 132:3 (2006), 313–330
-
S. E. Pastukhova, “Correctors in the homogenization of elasticity problems on thin structures”, Dokl. Math., 71:2 (2005), 177–182
-
S. E. Pastukhova, “Homogenization of elasticity problems on periodic composite structures”, Sb. Math., 196:7 (2005), 1033–1073
-
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
-
S. E. Pastukhova, “Degenerate equations of monotone type: Lavrent'ev phenomenon and attainability problems”, Sb. Math., 198:10 (2007), 1465–1494
-
V. V. Zhikov, S. E. Pastukhova, “On the Trotter–Kato Theorem in a Variable Space”, Funct. Anal. Appl., 41:4 (2007), 264–270
-
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
-
S. A. Nazarov, “Korn inequalities for elastic junctions of massive bodies, thin plates, and rods”, Russian Math. Surveys, 63:1 (2008), 35–107
-
Braides A., Chiadò Piat V., “Non convex homogenization problems for singular structures”, Netw. Heterog. Media, 3:3 (2008), 489–508
-
Pastukhova S.E., “Asymptotic analysis in elasticity problems on thin periodic structures”, Netw. Heterog. Media, 4:3 (2009), 577–604
-
Zhikov V.V., Pastukhova S.E., “Korn inequalities on thin periodic structures”, Netw. Heterog. Media, 4:1 (2009), 153–175
-
Orlik J. Panasenko G. Shiryaev V., “Optimization of Textile-Like Materials via Homogenization and Beam Approximations”, Multiscale Model. Simul., 14:2 (2016), 637–667
-
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
-
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
-
Bellieud M., “Homogenization of Stratified Elastic Composites With High Contrast”, SIAM J. Math. Anal., 49:4 (2017), 2615–2665
-
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
-
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
-
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
-
Abdoul-Anziz H., Seppecher P., “Strain Gradient and Generalized Continua Obtained By Homogenizing Frame Lattices”, Math. Mech. Complex Syst., 6:3 (2018), 213–250
-
Braides A., Piat V.Ch., “Homogenization of Networks in Domains With Oscillating Boundaries”, Appl. Anal., 98:1-2, SI (2019), 45–63
-
Cherednichenko K.D. Evans J.A., “Homogenisation of Thin Periodic Frameworks With High-Contrast Inclusions”, J. Math. Anal. Appl., 473:2 (2019), 658–679
|
Number of views: |
This page: | 480 | Full text: | 181 | References: | 43 | First page: | 1 |
|