2D, Quasi 3D and 3D Exact Solutions for Bending of Thick and Thin Sandwich Plates

Abstract

A previous author's work related to the exact solution of a single layer isotropic plate is extended to the case of multilayered plate structures composed of isotropic layers. The method solves a first order linear system of differential equations in the unknown amplitudes of the displacements and stresses. An eigenvalue problem, in which analytical expressions for the basis of eigenvectors and generalized eigenvectors are available, is then formulated. This makes the coding of exact solution of multilayered structures very simple and effective compared with other exact methods present in the literature. The paper is mainly concerned about the analysis of sandwich structures made of isotropic layers. Challenging cases of thick and moderately thick plates (a/h = 1, 4, 10) and thin plates (a/h = 100) are analyzed in detail and the displacements and stresses are found and plotted through the thickness of the plate. An extensive study of the ratio between the elastic modulus of the skins and the elastic modulus of the core, as well as the change in the displacements and stresses with that parameter, is conducted. The exact three-dimensional results are also validated with quasi-3D results obtained by adopting a mixed assiomatic theory of order 9 presented here for the first time. Twenty three two-dimensional theories are assessed, five of which are presented here for the first time. The use of Murakami's zig—zag function and the consequent improvement of the ESL theories is also analyzed and discussed. All the results of this work are an useful tool to test and compare approximated methods, such as Finite Element Method.