Static and free vibration analyses of functionally graded porous skew plates reinforced by graphene platelet based on three-dimensional elasticity theory

Abstract

This paper deals with the static and free vibration analyses of FG porous skew plates reinforced by graphene platelets (GPL). The plate comprises of a layered model with uniform or non-uniform dispersion of graphene platelets in a metallic matrix including open-cell interior pores. The extended rule of mixture in conjunction with the modified Halpin–Tsai approach is used to obtain the equivalent properties of the porous nanocomposite plate. Three various types of porosity distributions are assumed through the plate thickness including uniform and two kinds of symmetric functionally graded distributions. Besides, five various kinds of GPL dispersion patterns are assumed along the plate thickness. By substituting in the expression for functional of element and Rayleigh–Ritz method, the equations of motion are derived and a 3D FEM approach is applied to solve the governing equation of motions. The influences of different parameters including various porosity coefficients, porosity distribution in conjunction with GPL pattern and the weight fraction of GPL as nanofiller, different boundary conditions and various angles of skew plates on static response, and free vibration behavior of the skew nanocomposite plate have been surveyed.