Free vibration analysis of postbuckled arbitrary-shaped FG-GPL-reinforced porous nanocomposite plates

Abstract

Based upon the third-order shear deformation theory (TSDT) and a variational mixed formation, the postbuckling response and free vibration around buckled configurations of variously-shaped plates made of functionally graded graphene platelet (FG-GPL)-reinforced nanocomposite are numerically investigated considering the effect of porosity. The proposed numerical strategy is formulated according to the ideas of variational differential quadrature (VDQ) and finite element method (FEM), and can be employed for plates with different shapes (e.g. rectangular, skew or quadrilateral and annular) including arbitrary-shaped hole. The material properties of nanocomposite are approximated based upon the Halpin–Tsai model together with the closed-cell Gaussian Random field scheme for various distribution patterns of porosity and GPLs along the thickness direction. The governing equations are obtained according to Hamilton's principle by novel vector-matrix relations which can be readily used in numerical methods. One of the main novelties of developed numerical approach is proposing an efficient technique according to the mixed formulation to accommodate the continuity of first-order derivatives on the common boundaries of elements for the used TSDT model. A number of numerical examples are given to investigate the influences of porosity coefficient/distribution pattern, GPL weight fraction/dispersion pattern, cutout and edge conditions on the free vibrations of postbuckled FG-GPL-reinforced porous nanocomposite plates. © 2021 Elsevier Ltd