Buckling and vibration of FG graphene platelets/aluminum sandwich curved nanobeams considering the thickness stretching effect and exposed to a magnetic field

This paper studies the buckling and vibration analyses of a new model composed of a homogeneous ceramic curved nanobeam sandwiched between two reinforced composite layers. The face layers are made of an aluminum matrix reinforced with functionally graded (FG) graphene nanosheets (nanoplatelets) (GNShs). The present model is assumed to be embedded in an elastic substrate, exposed to an axial magnetic field and axial compressive external loads. Moreover, various boundary conditions are considered. The faces contain multi-composite nanolayres. Each nanolayer is composed of an aluminum matrix reinforced with uniformly distributed GNShs. The material properties of each face layer as a whole are graded through the thickness according to a piecewise micromechanical model. A refined higher-order curved beam theory is introduced in the polar coordinates considering the thickness stretching effect. Based on the proposed theory, four motion equations are presented containing Lorentz magnetic force and beam-foundation interaction. These equations are analytically solved to obtain the mechanical buckling load as well as the natural frequencies of the sandwich curved nanobeam. Since the general form of the strain-displacement relations is considered in the polar coordinates, the present formulation gives precise results for both shallow and deep curved beams. The effects of the different parameters such as arc angle, magnetic field parameter, elastic substrate parameters, boundary conditions, graphene wight fraction and core thickness on the buckling load and free vibration of the sandwich curved composite beams are investigated.