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

S. Laurens; S. Tordeux; A. Bendali; M. Fares; P. R. Kotiuga

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 6, page 1691-1712
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Laurens, S., et al. "Lower and upper bounds for the Rayleigh conductivity of a perforated plate." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.6 (2013): 1691-1712. <http://eudml.org/doc/273224>.

@article{Laurens2013,
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.},
author = {Laurens, S., Tordeux, S., Bendali, A., Fares, M., Kotiuga, P. R.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Rayleigh conductivity; perforated plate; Kelvin principle; Dirichlet principle; boundary element code CESC of CERFACS},
language = {eng},
number = {6},
pages = {1691-1712},
publisher = {EDP-Sciences},
title = {Lower and upper bounds for the Rayleigh conductivity of a perforated plate},
url = {http://eudml.org/doc/273224},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Laurens, S.
AU - Tordeux, S.
AU - Bendali, A.
AU - Fares, M.
AU - Kotiuga, P. R.
TI - Lower and upper bounds for the Rayleigh conductivity of a perforated plate
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 6
SP - 1691
EP - 1712
AB - 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.
LA - eng
KW - Rayleigh conductivity; perforated plate; Kelvin principle; Dirichlet principle; boundary element code CESC of CERFACS
UR - http://eudml.org/doc/273224
ER -

References

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