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

The paper presents a numerical assessment of the performance of the Refined Zigzag Theory (RZT) to the analysis of bending (deflection and stress distributions) and free vibration of functionally graded materials (FGM) plates, monolayer and sandwich, under a set of different boundary conditions. The numerical assessment is performed comparing results from RZT using Ritz method with those from 3-D, quasi 3-D and 2-D theories and finite element method (FEM). In the framework of 2D theories, equivalent single layer theories (ESL) of different order (sinusoidal, hyperbolic, inverse- hyperbolic, third-order (TSDT), first-order (FSDT) and classical (CPT)) have been used to investigate deformation, stresses, and free vibration and compared with results from the RZT. 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 FGM square and rectangular plates of 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 (P-FGM), exponential law (E-FGM) and sigmoidal-law (S-FGM)) is studied. Monolayer and sandwich plates with homogeneous core and functionally graded face-sheets are considered for the assessment. It is concluded that the RZT generally predicts the global (deflection and frequencies) and local (displacement and stress distributions) response of FGM sandwich plates, more accurately than first-order (FSDT) and third-order (TSDT) shear deformation theories, while retaining its simplicity.