Non-polynomial shear deformation theory-based analysis for bending, free vibration, and buckling in graphene nano platelet-reinforced composite plates

Abstract This study deals with bending, free vibration and buckling analysis of functionally graded composite plates reinforced with graphene nano platelets (GPL). A higher order non-polynomial shear deformation theory known as the trigonometric shear deformation theory is used which satisfy traction-free boundary condition at the top and bottom of the plate, hence no shear correction factor is required. These problems are solved numerically using in finite element analysis (FEA) by developing inhouse MATLAB codes. The 8-noded serendipity element with C 0 continuity is used for the mesh generation. The Hamilton’s principle is the primary variational principle used in this formulation to derive the plate governing equations. The structural behaviours of plate are analysed, focusing on the effects of stacking sequences, number of layers, weight percentage of GPL, size of GPL and ratio of length to thickness plate. The study explores both uniaxial and biaxial loading scenarios for buckling analysis and validates the results against existing literature for buckling and free vibration. The study reveals that, incorporating 1% of GPL to pure epoxy composite, the FG-X pattern exhibits a substantial reduction in static deflection by 81.7%, a marked increase in natural frequency by 133.8% and a significant enhancement in critical buckling load by 444.5%.