An appraisal of Voigt and Mori–Tanaka models for free vibration and buckling analyses of FG shallow curved shell panels reinforced with GPLs and resting on Kerr foundation using an improved FSDT

To improve the dynamic performance and structural stability of functionally graded material (FGM) shallow curved panels, reinforcing the functionally graded (FG) matrix with graphene platelets (GPLs) is a highly effective approach. Therefore, this study presents a nanocomposite for FG shallow curved panels reinforced with GPLs. The Kerr foundation model is incorporated into the analytical formulation. The effective Young’s modulus of the FG matrix is evaluated using the Voigt (V) and Mori–Tanaka (M–T) models, while that of the GPL-reinforced nanocomposite is estimated via the Halpin–Tsai (H–T) approach. Hamilton’s principle is utilized to derive the governing equations based on an improved first-order shear deformation theory (FSDT), incorporating a shear correction factor for improved accuracy. The numerical results, presented in terms of natural frequencies and buckling loads, are obtained by Navier’s solution technique. The comparison studies reveal significant discrepancies between the two micromechanical models in predicting the behavior of FG matrices reinforced with GPLs. Specifically, the M–T model gives lower absolute values for natural frequencies and critical buckling loads compared to the V model, whereas the percentage increases, relative to the unreinforced FGM case, predicted by the M–T model are higher than those obtained from the V model. Furthermore, the geometry of shallow curved panels plays a decisive role, with the hyperbolic configurations being the most sensitive to free vibration and buckling.