A novel quadrilateral element for analysis of functionally graded porous plates/shells reinforced by graphene platelets

摘要

This paper firstly presents numerical analyses of functionally graded porous plates/shells with graphene platelets (GPLs) reinforcement using a novel four-node quadrilateral element with five degrees of freedom per node, namely SQ4P, based on the first-order shear deformation theory and Chebyshev polynomials. The novelty of the present element is to use the high-order shape functions which satisfy the interpolation condition at the points based on Chebyshev polynomials to build the new flat four-node element for analysis of plate/shell structures. The Chebyshev polynomials are a sequence of orthogonal polynomials that are described recursively and the values of these polynomials belong to the interval [-1,1] as well as vanish at the Gauss points. Full Gauss quadrature rule is used to establish the stiffness matrix, geometric stiffness matrix, mass matrix and load vector. Various dispersions of GPLs and internal pores into the metal matrix through the thickness of structure are considered with the rule of a mixture and the Halpin-Tsai model for evaluating effective material properties across the thickness. The influence of weight fraction, porosity coefficient and dimensions of GPLs, distribution of GPLs and porosity into metal matrix are fully studied via several numerical examples from static bending to free vibration and buckling response. Numerical results and comparison with other solutions from available references suggest that the present element has enough reliability and validity to use in structural analysis. With regular and irregular meshes, these results are in close agreement with the exact solutions by using the suitable value for the order of the shape functions.