In this paper we formulate the problem of elastodynamic transformation cloaking for Kirchhoff-Love plates and elastic plates with both the in-plane and out-of-plane displacements. A cloaking transformation maps the boundary-value problem of an isotropic and homogeneous elastic plate (virtual problem) to that of an anisotropic and inhomogeneous elastic plate with a hole surrounded by a cloak that is to be designed (physical problem). For Kirchhoff-Love plates, the (out-of-plane) governing equations of the virtual plate is transformed to those of the physical plate up to an unknown scalar field. In doing so, one finds the initial stress and the initial tangential body force for the physical plate, along with a set of constraints that we call cloaking compatibility equations. These constraints involve the cloaking transformation, the unknown scalar field, and the elastic constants of the virtual plate. It is noted that the cloaking map needs to satisfy certain conditions on the outer boundary of the cloak and the surface of the hole. In particular, the cloaking map needs to fix the outer boundary of the cloak up to the third order. Assuming a generic radial cloaking map, we show that cloaking a circular hole in Kirchoff-Love plates is not possible; the cloaking compatibility equations and the boundary conditions that the cloaking map needs to satisfy are the obstruction to cloaking. Next, relaxing the pure bending assumption, the transformation cloaking problem of an elastic plate in the presence of in-plane and out-of-plane displacements is formulated. In this case, there are two sets of governing equations that need to be simultaneously transformed under the cloaking map. We show that cloaking a circular hole is not possible for a general radial cloaking map; the cloaking compatibility equations and the boundary conditions that the cloaking map needs to satisfy obstruct cloaking.
Stretching and bending of (really) thick elastic plates
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）
Coarse-Grained Methods for Heterogeneous Vesicles with Phase-Separated Domains: Elastic Mechanics of Shape Fluctuations, Plate Compression, and Channel Insertion
