Large deflection geometrically nonlinear bending of sandwich beams with flexible core and nanocomposite face sheets reinforced by nonuniformly distributed graphene platelets

Abstract

This study investigates the nonlinear bending response of a novel class of sandwich beams with flexible core and face sheets reinforced with graphene platelets that are functionally graded distributed through the thickness. Nonlinear governing equations are established based on extended high-order sandwich panel theory and Von Kármán type of geometrical nonlinearity. In this theory, the face sheets follow the first-order shear deformation theory, and the two-dimensional elasticity is adopted for the core. These nonlinear differential equations are discretized into algebraic systems by means of the Ritz-based method from which the static bending solution can be achieved. The effective Young’s modulus of functionally graded graphene platelet-reinforced composite (GPLRC) face sheets is determined through the modified Halpin–Tsai micromechanics model, and associated Poisson’s ratio is evaluated by employing the rule of mixture. Comparison studies are provided for a sandwich beam with graphene-reinforced face sheets and conventional nanocomposite beam reinforced by graphene platelets due to lack of results for introduced sandwich beams. Besides, three-point bending test was carried out in order to assure the validity of nonlinear bending analysis of a sandwich beam based on extended high-order sandwich panel theory. Afterwards, parametric studies are given to examine the influences of graphene platelet distribution pattern, weight fraction, and core-to-face sheet thickness ratio together with the total number of layers on the linear and nonlinear bending performances of the sandwich beams. Numerical results demonstrate that distributing more graphene platelets near the upper and lower surface layers of the face sheets, named X-GPLRC, is capable to improve the bending strength and decrease the local deflection of the top face sheet, and this recovery effect becomes more significant as graphene platelet weight fraction increases. The results also reveal that the graphene platelet distribution pattern of the face sheets plays an important role to decrease the transverse shear stress of the core by dispersing more graphene platelets near surfaces of the face sheets (X-GPLRC). So, reducing the local deflection of the top face sheet tends to be much more safety of the soft core from any failure. Besides, sandwich beams with a lower weight fraction of graphene platelets in face sheets that are symmetrically distributed in such a way, called O-GPLRC, are also less sensitive to the nonlinear deformation.