Bending analysis of functionally graded graphene oxide powder-reinforced composite beams using a meshfree method

Abstract

In this paper, the linear bending response of straight, thin to moderately thick functionally graded (FG) composite beams reinforced with graphene oxide powder (GOP) and subjected to two types of static mechanical loads, with various boundary conditions is investigated using a meshfree collocation method based on multiquadric radial basis functions. The weight fractions of the GOP are considered to vary continuously through the thickness direction of the composite beams. To determine the effective Young's modulus of the FG-GOP reinforced composite beams, a modified Halpin–Tsai model is used, whereas the rule of mixture is adopted to estimate the equivalent Poisson's ratio. The first-order shear deformation (FSDT) beam theory is adopted to model the functionally graded graphene oxide powder (FG-GOP) reinforced composite beams. The static equilibrium equations and associated boundary conditions of the FG-GOP reinforced composite beams are obtained by using the principle of minimum potential energy. The governing equations are rewritten in a matrix-vector strong form and discretized using the multiquadric radial basis functions. Various comparisons studies are performed to demonstrate the robustness and accuracy of the proposed numerical model. Parametric studies are conducted to examine the effects of length-to-thickness ratio, GOP distribution patterns, weight fraction, and size of GOP, types of loads, and boundary conditions on the bending behavior of the FG-GOP reinforced composite beams.