The Hole-Filling Method and the Uniform Multiscale Computation of the Elastic Equations in Perforated Domains
Year: 2008
International Journal of Numerical Analysis and Modeling, Vol. 5 (2008), Iss. 4 : pp. 612–634
Abstract
In this paper, we discuss the boundary value problem for the linear elastic equations in a perforated domain $\Omega^{\varepsilon}$. We fill all holes with a very compliant material, then we study the homogenization method and the multiscale analysis for the associated multiphase problem in a domain $\Omega$ without holes. We are interested in the asymptotic behavior of the solution for the multiphase problem as the material properties of one weak phase go to zero, which has a wide range of applications in shape optimization and in 3-D mesh generation. The main contribution obtained in this paper is to give a full mathematical justification for this limiting process in general senses. Finally, some numerical results are presented, which support strongly the theoretical results of this paper.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-IJNAM-829
International Journal of Numerical Analysis and Modeling, Vol. 5 (2008), Iss. 4 : pp. 612–634
Published online: 2008-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: homogenization multiscale analysis elastic equations perforated domain hole-filling method.