Evaluation of Layerwise Mixed Theories for Laminated Plates Analysis

Abstract

The evaluation of mixed layerwise theories to calculate the in-plane and out-of-plane responses of thick plates in two-dimensional modeling of multilayered structures is made. The employed models, which were proposed by the author in earlier works, a priori fulfill the continuity of transverse shear and normal stress components at the interface between two adjacent layers. A Reissner's mixed variational equation is used to derive the governing equations, in terms of introduced stress and displacement variables. The interface continuity conditions are imposed by writing the governing equations at a multilayered level. The related standard displacement formulations are also discussed for comparison purpose. Closed-form solutions are presented for plates made of orthotropic lamina and bent by harmonic distribution of transverse pressure. Symmetrically and unsymmetrically laminated, as well as sandwich, plates have been investigated. A comparison with a three-dimensional-elasticity analysis shows that present mixed layerwise models furnish a better description of the in-plane and out-of-plane response of thick plates with respect to existing layerwise and equivalent single-layer theories. In particular, the proposed models describe, with excellent accuracy, the transverse shear and normal stress fields. Unlike available current models, these fields are herein determined a priori without requiring implementation of any postprocessing procedures. The distribution of the transverse displacement and transverse normal stress in the plate thickness direction are also shown for most of the problems.