相关论文: Transformation Cloaking in Elastic Plates

We develop a very general theory on the regularized approximate invisibility cloaking for the wave scattering governed by the Helmholtz equation in any space dimensions via the approach of transformation optics.

Steering waves in elastic solids is more demanding than steering waves in electromagnetism or acoustics. As a result, designing material distributions which are the counterpart of optical invisibility cloaks in elasticity poses a major…

The coordinate transformation offers a remarkable way to design cloaks that can steer electromagnetic fields so as to prevent waves from penetrating into the {\em cloaked region} (denoted by $\Omega_0$, where the objects inside are…

This paper studies the electrostatic responses of a polarly radially anisotropic cylinder and a spherically radially anisotropic sphere. For both geometries, the permittivity components differ from each other in the radial and tangential…

This paper is devoted to the mathematical modelling of a vibrating orthotropic plate equipped with a laminated piezosensor, under the influence of a lumped force actuation. We employ the Kirchhoff plate theory to derive the corresponding…

The onset of transformation optics has opened avenues for designing of a plenitude of applications related to propagation of electromagnetic waves in anisotropic media. In this paper, an algorithm is proposed using a coordinate…

This paper focuses on the simultaneous homogenization and dimension reduction of periodic composite plates within the framework of non-linear elasticity. The composite plate in its reference (undeformed) configuration consists of a periodic…

Coordinate-transformation approaches to invisibility cloaking rely on the design of an anisotropic, spatially inhomogeneous "transformation medium" capable of suitably re-routing the energy flux around the region to conceal without causing…

In transformation optics, the space transformation is viewed as the deformation of a material. The permittivity and permeability tensors in the transformed space are found to correlate with the deformation field of the material. By solving…

This work presents a generalized Kirchhoff-Love shell theory that can explicitly capture fiber-induced anisotropy not only in stretching and out-of-plane bending, but also in in-plane bending. This setup is particularly suitable for…

The invariance under co-ordinate transformations of a set of partial differential equations can lead to the possibility of invisibility cloaking, whereby an anomaly in the interior of a body is shielded from an external observer. The form…

Beginning with a straightforward formulation of electromagnetic cloaking that reduces to a boundary value problem involving a single Maxwell first-order differential equation, explicit formulae for the relative permittivity-permeability…

The purpose of this work is to develop a model for a rectangular plate made of an orthotropic material. If compared with the classical model of the isotropic plate, the relaxed condition of orthotropy increases the degrees of freedom as a…

The approximate cloaking is investigated for time-harmonic Maxwell's equations via the approach of transformation optics. The problem is reduced to certain boundary effect estimates due to an inhomogeneous electromagnetic inclusion with an…

The nearly cloaking via transformation optics approach for the isotropic elastic wave fields is considered. This work extends the study of the nearly cloaking scheme to the elasticity system with residual stress in \mathbb{R}^{N} for N=2,3,…

In this work, we develop a general mathematical framework on regularized approximate cloaking of elastic waves governed by the Lam\'e system via the approach of transformation elastodynamics. Our study is rather comprehensive. We first…

A plate is rigid if its admissible displacement fields inducing vanishing two-dimensional strain tensors must vanish. We prove that the nonlinear model of Kirchhoff-Love for such a plate has a solution for any applied forces and boundary…

Recently, researchers have proposed several carpet cloaking designs that are able to hide a real object under a bump in a way that it is perceived as a flat ground plane. Here, we present a method to design two-dimensional isotropic carpet…

We investigate two-dimensional invisibility cloaking via transformation optics approach. The cloaking media possess much more singular parameters than those having been considered for three-dimensional cloaking in literature. Finite energy…

This paper investigates the optimal distribution of hard and soft material on elastic plates. In the class of isometric deformations stationary points of a Kirchhoff plate functional with incorporated material hardness function are…