Free vibration and buckling analyses of edge-cracked functionally graded multilayer graphene nanoplatelet-reinforced composite beams resting on an elastic foundation

This study investigates the linear free vibration and elastic buckling behaviors of functionally graded (FG) multilayer graphene platelet (GPL)-reinforced composite beams containing a single edge crack and resting on a Pasternak-type elastic foundation. GPLs are randomly oriented, and their concentration varies layer-wisely through the beam thickness. A modified Halpin-Tsai model is employed to estimate Young's modulus of the GPL-reinforced composite (GPLRC). The first-order shear deformation beam theory is applied in structural modeling. The bending stiffness of the cracked section is assumed to be equivalent to that of a massless rotational spring, which is related to the stress intensity factor (SIF) at the crack tip. SIFs of the cracked FG multilayer GPLRC beams are calculated by the finite element method. The differential quadrature method is used to discretize the equations of motion of the cracked beams. A parametric study is performed after a validation study for the present approach to illustrate the effects of crack location, crack length, boundary condition, GPL weight fraction, GPL distribution pattern, GPL size and geometry, and foundation stiffnesses on the fundamental frequencies and critical buckling loads.