Abstract
An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique (MITC) for triangular elements, named as ES-MITC3, was recently proposed to enhance the accuracy of the original MITC3 for analysis of plates and shells. In this study, the ES-MITC3 is extended to the static and vibration analysis of functionally graded (FG) porous plates reinforced by graphene platelets (GPLs). In the ES-MITC3, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains created by two adjacent triangular elements sharing an edge. The effective material properties are variable through the thickness of plates including Young’s modulus estimated via the Halpin–Tsai model and Poisson’s ratio and the mass density according to the rule of mixture. Three types of porosity distributions and GPL dispersion pattern into the metal matrix are examined. Numerical examples are given to demonstrate the performance of the present approach in comparison with other existing methods. Furthermore, the effect of several parameters such as GPL weight fraction, porosity coefficient, porosity distribution, and GPL dispersion patterns on the static and free vibration responses of FG porous plates is discussed in detail.
Highlights
In recent years, functionally graded (FG) porous material has attracted a great interest from many researchers over the world due to their superior mechanical properties such as lightweight, wear resistance, and high strength. ese properties make FG porous structures to be very suitable to apply for civil engineering, aerospace structures, nuclear plants, and other applications
Several numerical examples are verified to illustrate new contributions including (1) verifying the accuracy of the present method for the free vibration and static bending analyses of the FG porous plates reinforced by graphene platelets (GPLs) by comparing with results in [25] and (2) investigating the influences of the porosity distributions, the GPL dispersion patterns, GPL weight fraction, and the porosity coefficients on the free vibration and static response of the FG porous plates
It can be seen that the ES-MITC3 is a good competitor to quadrilateral shell element MITC4 and gives better accuracy compared with the original triangular elements MITC3
Summary
FG porous material has attracted a great interest from many researchers over the world due to their superior mechanical properties such as lightweight, wear resistance, and high strength. ese properties make FG porous structures to be very suitable to apply for civil engineering, aerospace structures, nuclear plants, and other applications. Ese properties make FG porous structures to be very suitable to apply for civil engineering, aerospace structures, nuclear plants, and other applications In this regard, Rezaei et al [1] presented the analytical approach based on Reddy’s third-order shear deformation theory to analyse the free vibration of thick porous plates. Nguyen et al [5] studied the dynamic response of FG porous plates resting on elastic foundation under thermal and mechanical loads by the Mathematical Problems in Engineering analytical method and the first-order shear deformation theory (FSDT). Barati used the analytical approach based on nonlocal strain gradient theory to investigate the free vibration of FG porous nanoshells [7] and the forced vibration of FG porous nanoplates [8]. Barati and Shahverdi [16] proposed the higher-order refined four-variable plate theory to examine the nonlinear vibration of the FG porous nanoplates
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