Prestressed vibration and buckling analysis of graphene platelets reinforced composite plates using the dynamic stiffness method

The article presents the use of the dynamic stiffness method (DSM) for analyzing the buckling and prestressed vibration of advanced composite plates subjected to uniaxial and biaxial in-plane loads. The plate consists of laminated layers reinforced with graphene platelets and the effective material properties of the plate are computed using the Halpin-Tsai micromechanical model. Through the application of Hamilton's principle, the governing differential equations (GDEs), based on the first order shear deformation theory, are obtained for the GPL-reinforced plate resting on elastic foundations. For a segment of the plate, the dynamic stiffness matrix is obtained by solving the GDEs with the Levy form of boundary conditions. Subsequently, the assembled global dynamic stiffness matrix is solved using the Wittrick-Williams algorithm to compute the buckling and prestressed vibration behavior of the plates. Convergence and comparative studies are performed to show that the DSM is efficient and produces very accurate results as it is formulated based on closed-form solutions. Several parametric studies are carried out to study the effect of different edge loads, foundation parameters, and plate boundary conditions. Results for non-uniform plate configurations are also presented to highlight the applicability and efficacy of the present DSM to fairly complex plate configurations.