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Homogenization of the Signorini boundary-value problem in a thick junction and boundary integral equations for the homogenized problem

2010; Wiley; Volume: 34; Issue: 7 Linguagem: Inglês

10.1002/mma.1395

1099-1476

Taras Mel’nyk, Iu. A. Nakvasiuk, Wolfgang L. Wendland,

Composite Material Mechanics

Mathematical Methods in the Applied SciencesVolume 34, Issue 7 p. 758-775 Research Article Homogenization of the Signorini boundary-value problem in a thick junction and boundary integral equations for the homogenized problem T. A. Mel'nyk, T. A. Mel'nyk Department of Mathematical Physics, Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, 01033 Kyiv, UkraineSearch for more papers by this authorIu. A. Nakvasiuk, Iu. A. Nakvasiuk Department of Mathematical Physics, Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, 01033 Kyiv, UkraineSearch for more papers by this authorW. L. Wendland, Corresponding Author W. L. Wendland [email protected] Department of Mathematical Physics, Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, 01033 Kyiv, UkraineInstitute for Applied Analysis and Numerical Simulation, University of Stuttgart, 70550 Stuttgart, Germany===Search for more papers by this author T. A. Mel'nyk, T. A. Mel'nyk Department of Mathematical Physics, Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, 01033 Kyiv, UkraineSearch for more papers by this authorIu. A. Nakvasiuk, Iu. A. Nakvasiuk Department of Mathematical Physics, Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, 01033 Kyiv, UkraineSearch for more papers by this authorW. L. Wendland, Corresponding Author W. L. Wendland [email protected] Department of Mathematical Physics, Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, 01033 Kyiv, UkraineInstitute for Applied Analysis and Numerical Simulation, University of Stuttgart, 70550 Stuttgart, Germany===Search for more papers by this author First published: 25 November 2010 https://doi.org/10.1002/mma.1395Citations: 8Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract We consider a mixed boundary-value problem for the Poisson equation in a thick junction Ωε which is the union of a domain Ω0 and a large number of ε—periodically situated thin cylinders. The non-uniform Signorini conditions are given on the lateral surfaces of the cylinders. The asymptotic analysis of this problem is done as ε→0, i.e. when the number of the thin cylinders infinitely increases and their thickness tends to zero. We prove a convergence theorem and show that the non-uniform Signorini boundary conditions are transformed in the limiting variational inequalities in the region that is filled up by the thin cylinders as ε→0. The convergence of the energy integrals is proved as well. The existence and uniqueness of the solution to this non-standard limit problem is established. This solution can be constructed by using a penalty formulation and successive iteration. For some subclass, these problems can be reduced to an obstacle problem in Ω0 and an appropriate postprocessing. The equations in Ω0 finally are also treated with boundary integral equations. Copyright © 2010 John Wiley & Sons, Ltd. Citing Literature Volume34, Issue715 May 2011Pages 758-775 RelatedInformation