A general framework of higher-order shear deformation theories with a novel unified plate model for composite laminated and FGM plates

Abstract

A novel unified framework of higher-order shear deformation theories is developed for modeling and analysis of laminated and functionally graded plates. The major objective of this study is to (1) unify all higher-order shear deformation plate theories in a unique formulation; (2) propose a new higher-order shear deformation model based on the unified plate model. In this study, the existing displacement fields in the equivalent single layer theories are classified into three categories based on the present unified method. Some of the existing equivalent single-layer plate theories are unified according to different types of transverse displacements and transverse shear strains based on the present method and several new plate theories are proposed and assessed. The Reddy shear strain function and a changeable shear function proposed by Li et al. are applied to represent the distribution of transverse shear strains through the thickness of composite laminated and FGM plates, respectively. One of the new higher-order shear deformation theory is then ascertained by comparing the obtained bending, free vibration and buckling results of composite laminated and FGM plates with other published ones. The results show that the unified plate model can theoretically cover all existing equivalent single-layer models and is able to encourage interested readers to search for more feasible and accurate plate theories.