Lower and upper bounds for the Rayleigh conductivity of a perforated plate
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 6, p. 1691-1712

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.

DOI : https://doi.org/10.1051/m2an/2013082
Classification:  35Q35,  35J05,  35J25
Keywords: Rayleigh conductivity, perforated plate, Kelvin principle, Dirichlet principle
@article{M2AN_2013__47_6_1691_0,
     author = {Laurens, S. and Tordeux, S. and Bendali, A. and Fares, M. and Kotiuga, P. R.},
     title = {Lower and upper bounds for the Rayleigh conductivity of a perforated plate},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {6},
     year = {2013},
     pages = {1691-1712},
     doi = {10.1051/m2an/2013082},
     zbl = {1283.35088},
     mrnumber = {3123372},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2013__47_6_1691_0}
}
Laurens, S.; Tordeux, S.; Bendali, A.; Fares, M.; Kotiuga, P. R. Lower and upper bounds for the Rayleigh conductivity of a perforated plate. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 6, pp. 1691-1712. doi : 10.1051/m2an/2013082. http://www.numdam.org/item/M2AN_2013__47_6_1691_0/

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