A comprehensive analysis of porous graphene-reinforced curved beams by finite element approach using higher-order structural theory: Bending, vibration and buckling

In this paper, the bending, vibration and buckling characteristics of functionally graded porous graphene-reinforced nanocomposite curved beams are studied based on a trigonometric shear deformation theory. The effect of various theories deduced from the proposed formulation on the static and dynamic behavior of curved nanocomposite beams is also studied. The governing equilibrium equations are formed by applying Lagrangian equations of motion coupled with the finite element approach employing a 3-noded C-1 continuous curved beam element. The methodology developed here is tested for problems having known solutions in the open literature. A detailed investigation involving various parameters such as coefficient of porosity, type of distribution pattern for the porosity and graphene platelets, radius of curvature of curved beam, length-to-thickness ratio, the platelet geometry, and boundary conditions on the static bending, free vibration and elastic stability behavior of nanocomposite curved beams is conducted. New results for certain boundary conditions of graphene reinforced curved beams are presented. Participation of various types of in-plane and transverse bending modes responsible for yielding the lowest critical buckling loads/natural frequencies are also highlighted.