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Lower and upper bounds for the Rayleigh conductivity of a perforated plate

Published online by Cambridge University Press:  11 October 2013

S. Laurens ,
S. Tordeux ,
A. Bendali ,
M. Fares  and
P.R. Kotiuga
S. Laurens
Affiliation:
CERFACS – EMA, 42 avenue Gaspar Coriolis,31100 Toulouse, France. sophie.laurens@insa-toulouse.fr
S. Tordeux
Affiliation:
INRIA Bordeaux Sud-Ouest – Magique 3D  Université de Pau, LMA (UMR-CNRS 5142), avenue de l’Université,64013 Pau, France; sebastien.tordeux@inria.fr
A. Bendali
Affiliation:
INSA-Mathematical Institute of Toulouse (UMR-CNRS 5219),135 avenue de Rangueil, 31077 Toulouse, France; abderrahmane.bendali@insa-toulouse.fr
M. Fares
Affiliation:
CERFACS - EMA, 42 avenue Gaspar Coriolis, 31100 Toulouse, France; fares@cerfacs.fr
P.R. Kotiuga
Affiliation:
Boston University, Department of Electrical and Computer Engineering, 8 Saint Mary’s Street, Boston MA, 02215, USA; prk@bu.edu
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Abstract

Lower and upper bounds for the Rayleigh conductivity of a perforation in a thick plate are usually derived from intuitive approximations and by physical reasoning. This paper addresses a mathematical justification of these approaches. As a byproduct of the rigorous handling of these issues, some improvements to previous bounds for axisymmetric holes are given as well as new estimates for tilted perforations. The main techniques are a proper use of the Dirichlet and Kelvin variational principlesin the context of Beppo-Levi spaces. The derivations are validated by numerical experiments in 2D for the axisymmetric case as well as for the full three-dimensional problem.

Keywords

Rayleigh conductivityperforated plateKelvin principleDirichlet principle
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 6 , November 2013 , pp. 1691 - 1712
Copyright
© EDP Sciences, SMAI, 2013

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