Effect of simultaneous compressive and inertia loads on the bifurcation stability of shear deformable functionally graded annular fabrications reinforced with graphenes

In the current study, the stability of a functionally graded annular plate reinforced with a limited content of graphene platelets (FG-GPLRC) resting on a two-parameter elastic foundation is investigated. The structure is under the coincident effect of radial compressive forces and inertial load due to angular velocity. It is considered that the GPL nanofillers are randomly oriented, and their weight fraction varies with a layer-wise pattern through the thickness direction. The equivalent Young's modulus and other material properties of the annular FG-GPLRC plate are evaluated by utilizing the Halpin–Tsai micromechanics rule. It is considered that the plate is resting on a two-parameter elastic foundation. The governing equations are extracted based on the first-order shear deformation theory (FSDT) and the von-Kármán type of geometric nonlinearity. Applying the virtual work principle and the adjacent equilibrium standard, the plate's equations of stability are established. The derived governing equations are solved using a combined analytical–numerical (TE-GDQ) method, including trigonometric expansion in the circumferential direction and the generalized differential quadratures method through the radial direction. Comprehensive novel numerical results is derived to evaluate the effect of weight fraction of nanoparticles, the type of FGM, geometric dimensions, various boundary conditions, and surrounding elastic foundation on the buckling behavior of the plate.