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
The paper presents a review of Haar wavelet methods and an application of the higher-order Haar wavelet method to study the behavior of multilayered composite beams under static and buckling loads. The Refined Zigzag Theory (RZT) is used to formulate the corresponding governing differential equations (equilibrium/ stability equations and boundary conditions). To solve these equations numerically, the recently developed Higher-Order Haar Wavelet Method (HOHWM) is used. The results found are compared with those obtained by the widely used Haar Wavelet Method (HWM) and the Generalized Differential Quadrature Method (GDQM). The relative numerical performances of these numerical methods are assessed and validated by comparing them with exact analytical solutions. Furthermore, a detailed convergence study is conducted to analyze the convergence characteristics (absolute errors and the order of convergence) of the method presented. It is concluded that the HOHWM, when applied to RZT beam equilibrium equations in static and linear buckling problems, is capable of predicting, with a good accuracy, the unknown kinematic variables and their derivatives. The HOHWM is also found to be computationally competitive with the other numerical methods considered.
The paper presents an enhancement in Refined Zigzag Theory (RZT) for the analysis of multilayered composite plates. In standard RZT, the zigzag functions cannot predict the coupling effect of in-plane displacements for anisotropic multilayered plates, such as angle-ply laminates. From a computational point of view, this undesirable effect leads to a singular stiffness matrix. In this work, the local kinematic field of RZT is enhanced with the other two zigzag functions that allow the coupling effect. In order to assess the accuracy of these new zigzag functions for RZT, results obtained from bending of angle-ply laminated plates are compared to the three-dimensional exact elasticity solutions and other plate models used in the open literature. The numerical results highlight that the enhanced zigzag functions extend the range of applicability of RZT to the study of general angle-ply multilayered structures, maintaining the same seven kinematic unknowns of standard RZT.
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