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

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 inclined perforations. The main techniques are a proper use of the variational principles of Dirichlet and Kelvin in the context of Beppo-Levi spaces. The derivations are validated by numerical experiments in the two-dimensional axisymmetric case and the full three-dimensional one.
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ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2013, 47 (6), pp.1691-1712. 〈10.1051/m2an/2013082〉
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Sophie Laurens, Sébastien Tordeux, Abderrahmane Bendali, M'Barek Fares, P. Robert Kotiuga. Lower and upper bounds for the Rayleigh conductivity of a perforated plate. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2013, 47 (6), pp.1691-1712. 〈10.1051/m2an/2013082〉. 〈hal-00686438〉

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