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arXiv · 1901.00067

On form invariance of the Kirchhoff-Love plate equation

Lucas Pomot·Stephane Bourgeois·Cedric Payan·Marcel Remillieux·Sebastien Guenneau
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Abstract

We propose an alternative approach called backward transformation for the design of platonic cloaks, without resorting to in-plane body forces and pre-stresses, which can lead to unphysical features. It is shown that the Kirchhoff-Love equation for an anisotropic heterogeneous plate is actually form invariant for a class of transformations with a vanishing Hessian. This formalism is detailed and numerically validated with three-dimensional simulations in the time domain. Results published in the literature fall in the class of transformations proposed here.

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Lucas Pomot, Stephane Bourgeois, Cedric Payan, Marcel Remillieux, Sebastien Guenneau. 2019-01-01. On form invariance of the Kirchhoff-Love plate equation. https://arxiv.org/abs/1901.00067

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