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 - <p style="text-align: justify;">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.</p>