Investigation of mechanical performance of bidirectional functionally graded graphene nanoplatelet reinforced composite beams using the Fredholm integral method

This study conducts a mechanical analysis of bidirectional functionally graded graphene nanoplatelet reinforced composite (BiFG-GPLRC) beams. The distribution of graphene nanoplatelets along the length of the beam is smoothly varying, while various distribution patterns are employed for the thickness direction. Using Hamilton’s principle, the governing equations are formulated, and material properties are characterized via the Halpin-Tsai model and the rule of mixtures. Different weight fractions of graphene nanoplatelets are assigned to each side of the beam to determine the volume fractions. Vibration and buckling analyses are conducted, utilizing a power law function for axial distribution with the gradient parameter k . Changing k leads to a corresponding change in the beam stiffness. Further, distribution patterns in thickness direction also have a considerable effect on the mechanical performance. Parametric studies involve altering volume fractions, gradient parameters, and boundary conditions to evaluate the beam’s behavior. The results reveal improved beam performance with increased GPL concentration.