On form invariance of the Kirchhoff-Love plate equation

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.