科研之友
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摘要
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 principles in 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.
- 出版日期2013-11
- 单位INRIA
