A two-dimensional elasticity model for bending and free vibration analysis of laminated graphene-reinforced composite beams

Abstract

By assuming the plane-stress state in each layer, a two-dimensional elasticity model is proposed for laminated graphene-reinforced composite (GRC) beams. It is assumed that the graphene disperses uniformly in each layer but the graphene volume fraction may vary from layer to layer. For an arbitrary individual layer, the governing partial differential equations and boundary conditions are given directly from the two-dimensional elasticity theory. Then, the multi-term Kantorovich-Galerkin method is employed to build a state-space equation for the layer, in which the axial and transverse displacements are expressed as products of trial function matrix and unknown function matrix. Eventually, a global equation for the laminated beam is established by virtue of the displacement and stress continuity conditions at the interfaces. Non-dimensional displacements, stresses and natural frequencies are obtained for laminated GRC beams with different boundary conditions. The effects of graphene distribution patterns, boundary conditions, length-to-thickness ratios, layer fraction increments and the number of layers are examined. It is found that the laminated GRC beam with graphene distribution pattern X has the smallest deflection and largest fundamental frequency at high length-to-thickness ratios, but it has largest deflection and smallest fundamental frequency at a very low length-to-thickness ratio due to its reduced transverse shear stiffness.