Volume 5, Issue 4
The Hole-Filling Method and the Uniform Multiscale Computation of the Elastic Equations in Perforated Domains

Int. J. Numer. Anal. Mod., 5 (2008), pp. 612-634.

Published online: 2008-05

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• 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.

• Keywords

homogenization, multiscale analysis, elastic equations, perforated domain, hole-filling method.

35R35, 49J40, 60G40

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@Article{IJNAM-5-612, author = {X. and Wang and and 21157 and and X. Wang and L.-Q. and Cao and and 21158 and and L.-Q. Cao}, title = {The Hole-Filling Method and the Uniform Multiscale Computation of the Elastic Equations in Perforated Domains}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/829.html} }
TY - JOUR T1 - The Hole-Filling Method and the Uniform Multiscale Computation of the Elastic Equations in Perforated Domains AU - Wang , X. AU - Cao , L.-Q. JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 612 EP - 634 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/829.html KW - homogenization, multiscale analysis, elastic equations, perforated domain, hole-filling method. AB -

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.

X. Wang & L.-Q. Cao. (1970). The Hole-Filling Method and the Uniform Multiscale Computation of the Elastic Equations in Perforated Domains. International Journal of Numerical Analysis and Modeling. 5 (4). 612-634. doi:
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