Nonlinear bending of axially functionally graded microbeams reinforced by graphene nanoplatelets in thermal environments

The present work investigates the nonlinear bending behavior of an axially functionally graded graphene nanoplatelet reinforced composite (AFG-GPLRC) microbeam in thermal environments. It is assumed that the weight fractions of the graphene nanoplatelets (GPLs) vary continuously and smoothly follow the polynomial forms in the axial direction of the microbeam. The effective Young's modulus of the composite is determined according to the modified Halpin-Tsai micromechanics model. Moreover, Poisson's ratio is considered to be constant. Timoshenko beam theory (TBT), in conjunction with the modified couple stress theory, is implemented to derive the nonlinear governing equations of the AFG-GPLRC microbeams subjected to a uniform distributed load. The Ritz method is applied to account for the various boundary conditions of the beam, while the Newton-Rapson (NR) method is implemented to solve the nonlinear equations associated with the bending behaviors. Some efforts are devoted to showing the effects of the size dependence, distribution patterns, weight fractions and geometries of the GPLs, and the thermal environments on the bending response of the AFG-GPLRC microbeams.