An ES-MITC3 Finite Element Method Based on Higher-Order Shear Deformation Theory for Static and Free Vibration Analyses of FG Porous Plates Reinforced by GPLs

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.