A unified formulation to assess theories of multilayered plates for various bending problems

Abstract

This work uses a unified formulation to compare about 40 theories for multilayered, composites and sandwich plates which are loaded by transverse pressure with various in-plane distributions (harmonic, constant, triangular and tent-like). So-called equivalent single layer models (ESLMs), which preserve the number of the unknown variables to be independent by the number of layers, as well as layer-wise models (LWMs) are considered in both framework of principle of virtual displacement (PVD) and Reissner Mixed Variational Theorem (RMVT). Murakami’s Zig-Zag Function is used to introduce zig-zag (ZZ) effects while independent assumptions for transverse stresses (both shear and normal components) are used to enforce interlaminar continuity (IC) between two adjacent layers. Linear and higher order expansions (fourth-order) are introduced for displacements and stresses in the thickness plate directions. The fundamental effects of transverse strain is evaluated for most of the considered analyses. The whole modeling has been herein written by employing a unified formulation recently proposed by the first author. As a results a large number of classical and advanced theories for laminated structures are formulated and the related governing equations are written in terms of so-called fundamental nuclei with only nine terms each. Navier-type, closed form solutions of these equations are presented for orthotropic plates by expanding the applied pressure loading in Fourier series. A number of conclusions have been traced as far as performance and limitations of compared theories is concerned. Quoted results could be used as benchmarks to assess available theories not considered in this paper as well as approximated solution techniques, such as finite element applications.