Buckling and free vibration analysis of shear deformable graphene-reinforced composite laminated plates

Abstract

Within the framework of the first-order shear deformation theory (FSDT), semi-analytical solutions for buckling and free vibration analysis of graphene-reinforced composite (GRC) laminated plates are presented by the means of the multi-term Kantorovich-Galerkin method. The method begins with expanding the displacements as the products of trial and unknown functions, in which the trigonometric trial functions fulfill all the boundary conditions at two opposite edges. Then, the Galerkin technique is adopted to reduce the governing partial differential equations into the ordinary differential equations, which are solved with the spectral element method (SEM). With the excitation approach, the critical buckling loads and natural frequencies are identified from the response curves and validated with the existing solutions. Then, the effects of graphene distribution pattern, graphene volume fraction, aspect ratio, thickness ratio, and shear correction factor are examined. It is interesting to find that the two uniaxial buckling loads for simply-supported square GRC laminated plates are same, which are twice of the biaxial buckling load. It is also found that the buckling mode under the uniaxial compression along the x direction for the simply-supported GRC laminated plates will change from mode (1,1) to mode (2,1) as the aspect ratio increases from 1 to 1.5.