Two-dimensional model of an anisotropic plate of the second-order accuracy

Abstract

In a linear approximation a deformation of a thin elastic anisotropic heterogeneous in the thickness direction plate is investigated. By using an asymptotic solution of 3D equations of the theory of elasticity, a 2D model of the second order accuracy with respect to the small thickness parameter is built for a plate with the general anisotropy that is described by 21 elastic modules. The obtained system of equations describes deflections of a middle layer and has the differential order, coinciding with the order of the Timoshenko-Reissner model. The model is acceptable to an investigation of statics, dynamics and stability of multi-layered, and also functionally graded plates. In the previous works, the models of the second-order accuracy were constructed for isotropic plates and for plates with partial kinds of anisotropy. The general anisotropy is studied first.