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

A Family of C0 Quadrilateral Plate Elements Based on the Refined Zigzag Theory for the Analysis of Thin and Thick Laminated Composite and Sandwich Plates

“…For the implementation and the convergence analysis of this approximate method, see Reference [69]. In particular, as it is shown in Reference [69], 10 orthogonal polynomials in both x1 and x2 directions are enough to assure the converged Ritz solution. It is clear that when the numerical analyses are performed using the RZT (analytical or with FEM) for the isotropic plate (I), the zigzag terms vanish.…”

“…Thick (a/h = 10) and very thin (a/h = 10 3 ) square plates, simply supported on all edges, under uniform pressure of intensity q 0 , are considered for this analysis: A sandwich plate with thin two-layered cross-ply face-sheet (S), a five-layered cross-ply plate (L), and an isotropic plate (I). The reference (analytical) solutions (Table 4) have been obtained using the Ritz method [69] for the deflection. For the implementation and the convergence analysis of this approximate method, see Reference [69].…”

“…The reference (analytical) solutions (Table 4) have been obtained using the Ritz method [69] for the deflection. For the implementation and the convergence analysis of this approximate method, see Reference [69]. In particular, as it is shown in Reference [69], 10 orthogonal polynomials in both x 1 and x 2 directions are enough to assure the converged Ritz solution.…”

“…Two square plates (S) are considered, both loaded with the load distribution C1 (uniform transverse load) and C2 (uniform constant edge load) and meshed with 17 × 17 elements: (i) A thick plate (a/h = 8; a/b = 1) and (ii) a thin plate (a/h = 10 2 ; a/b = 1). The analytical solutions have been obtained using the Ritz method [69] with 10 orthogonal functions in x 1 direction and 10 orthogonal functions in x 2 direction. Plots of the distributions of shear force and bending moment along the midline of the plates parallel to x 1 axis are given in Figure 14 (thick sandwich plate) and Figure 15 (thin sandwich plate) for the C1 load condition and in Figure 16 (thick sandwich plate) and Figure 17 (thin sandwich plate) for the C2 load condition.…”

“…In order to show the ability of FEM solutions to capture also the local behaviour (distribution of the stresses along the thickness), we consider bending under transverse uniform pressure of simply supported sandwich plate (S) for a/h = 8. Figure 18 compares the distributions of in-plane stresses at the centre of the plates and the transverse shear stress at the midpoint of the left edge, computed using the Ritz method [69] and the family of C 0 RZT plate elements. For this study, in order to have a better distribution of the stresses, a regular mesh 16 × 16 for a quarter of plate has been adopted.…”