Study On Refined Theory Of A Transversely Isotropic Plate With Anisotropic Plane

The plane which its all directions have the same elastic properties is called isotropic plane. If every point of the material has a parallel isotropic plane, it is called the transverse isotropic material. The transversely isotropic material with anisotropic plane is a very common engineering material, but there is relatively little study on this material. In this paper, by using of the research ideas about the refined theory of elastic mechanics, the refined theory of transversely isotropic plate with anisotropic plane is studied.First, from the 3D theory of elasticity, using the Elliott–Lodge general solution and trigonometric operator method, the stress and displacement expressions of transversely isotropic plate are derived without any assumptions. In the case of homogeneous boundary conditions, using Lur’e method, the exact solution of the plate is obtained. Then, the decomposed form of the transversely isotropic stretching plate is studied, the decomposed theory of the transversely isotropic stretching plate is obtained and is proven strictly, and it consists of three parts: the generalized plane-stress state, the shear state, and the Papkovich–Fadle state. At last, in the case of non-homogeneous boundary conditions, the approximate control differential equation of the plate is obtained.For transversely isotropic plate with anisotropic plane, according to the Elliott– Lodge solution and Lur’e method, the stress and displacement expressions of transversely isotropic bending and stretching plate with anisotropic plane are derived without any assumptions, respectively. In the case of non-homogeneous boundary conditions, the refined theory of transversely isotropic bending and stretching plate with anisotropic plane are derived, respectively. Using the non-homogeneous boundary conditions of Winkler foundation, the refined theory of transversely isotropic bending and stretching plate with anisotropic plane posting inside Winkler foundation are obtained, respectively.