Bending and free vibration analysis of functionally graded sandwich plates: An assessment of the Refined Zigzag Theory

Abstract

The paper presents a numerical assessment of the performance of the Refined Zigzag Theory to the analysis of bending (deflection and stress distributions) and free vibration of functionally graded material plates, monolayer and sandwich, under a set of different boundary conditions. The numerical assessment is performed comparing results from Refined Zigzag Theory using Ritz method with those from 3D, quasi-3D, and 2D theories and finite element method. In the framework of 2D theories, equivalent single-layer theories of different orders (sinusoidal, hyperbolic, inverse-hyperbolic, third-order shear deformation theory, first-order shear deformation theory, and classical plate theory) have been used to investigate deformation, stresses, and free vibration and compared with results from the Refined Zigzag Theory. After validating the convergence characteristics and the numerical accuracy of the developed approach using orthogonal admissible functions, a detailed parametric numerical investigation is carried out. Bending under transverse pressure and free vibration of functionally graded material square and rectangular plates of a different aspect ratio under various combinations of geometry (core-to-face sheet thickness ratio and plate to thickness ratio), boundary conditions and law of variation of volume fraction constituent in the thickness direction (power-law functionally graded material, exponential law functionally graded material, and sigmoidal-law functionally graded material) is studied. Monolayer and sandwich plates with homogeneous core and functionally graded face sheets are considered for the assessment. It is concluded that the Refined Zigzag Theory generally predicts the global (deflection and frequencies) and local (displacement and stress distributions) response of functionally graded material sandwich plates, more accurately than first-order shear deformation theory and third-order shear deformation theory, while retaining its simplicity.