RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2004, Volume 75, Issue 6, Pages 818–833 (Mi mz73)

Homogenization of Elasticity Problems with Boundary Conditions of Signorini type

G. A. Iosif'yan

A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Abstract: In a perforated domain $\Omega^\varepsilon =\Omega\cap\varepsilon \omega$ formed of a fixed domain $\Omega$ and an $\varepsilon$-compression of a 1-periodic domain $omega$, we consider problems of elasticity for variational inequalities with boundary conditions of Signorini type on a part of the surface $S^\varepsilon _0$ of perforation. We study the asymptotic behavior of solutions as $\varepsilon\to0$ depending on the structure of the set $S^\varepsilon _0$. In the general case, the limit (homogenized) problem has the two distinguishing properties: (i) the limit set of admissible displacements is determined by nonlinear restrictions almost everywhere in the domain $\Omega$, i.e., in the limit, the Signorini conditions on the surface $S^\varepsilon _0$ can turn into conditions posed at interior points of $\Omega$ (ii) the limit problem is stated for an homogenized Lagrangian which need not coincide with the quadratic form usually determining the homogenized elasticity tensor. Theorems concerning the homogenization of such problems were obtained by the two-scale convergence method. We describe how the limit set of admissible displacements and the homogenized Lagrangian depend on the geometry of the set $S^\varepsilon _0$ on which the Signorini conditions are posed.

DOI: https://doi.org/10.4213/mzm73

Full text: PDF file (293 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2004, 75:6, 765–779

Bibliographic databases:

UDC: 517.958

Citation: G. A. Iosif'yan, “Homogenization of Elasticity Problems with Boundary Conditions of Signorini type”, Mat. Zametki, 75:6 (2004), 818–833; Math. Notes, 75:6 (2004), 765–779

Citation in format AMSBIB
\Bibitem{Ios04} \by G.~A.~Iosif'yan \paper Homogenization of Elasticity Problems with Boundary Conditions of Signorini type \jour Mat. Zametki \yr 2004 \vol 75 \issue 6 \pages 818--833 \mathnet{http://mi.mathnet.ru/mz73} \crossref{https://doi.org/10.4213/mzm73} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2085809} \zmath{https://zbmath.org/?q=an:02121423} \elib{http://elibrary.ru/item.asp?id=13446315} \transl \jour Math. Notes \yr 2004 \vol 75 \issue 6 \pages 765--779 \crossref{https://doi.org/10.1023/B:MATN.0000030986.37555.f1} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000222492400020} 

• http://mi.mathnet.ru/eng/mz73
• https://doi.org/10.4213/mzm73
• http://mi.mathnet.ru/eng/mz/v75/i6/p818

 SHARE:

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. Stelzig Ph.E., “Homogenization of Many-Body Structures Subject to Large Deformations”, ESAIM-Control OPtim. Calc. Var., 18:1 (2012), 91–123
2. Jaeger W., Neuss-Radu M., Shaposhnikova T.A., “Homogenization of a Variational Inequality for the Laplace Operator with Nonlinear Restriction for the Flux on the Interior Boundary of a Perforated Domain”, Nonlinear Anal.-Real World Appl., 15 (2014), 367–380
3. Capatina A., Timofte C., “Homogenization results for micro-contact elasticity problems”, J. Math. Anal. Appl., 441:1 (2016), 462–474
4. Ptashnyk M., “Homogenization of Some Degenerate Pseudoparabolic Variational Inequalities”, J. Math. Anal. Appl., 469:1 (2019), 44–75
•  Number of views: This page: 207 Full text: 69 References: 35 First page: 1