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

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

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

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topLaurens, 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 -

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