Self-weight and Thermal Bifurcation Analysis of Functionally Graded Vertical Annular Plates

The present paper thoroughly investigates the influence of structural weight on the thermal buckling of standing circular and annular plates. The structure is composed of symmetrically functionally graded materials (FGM) in terms of its thickness. The first-order theory of shear deformation along with nonlinear strain–displacement equations has been employed to derive the governing equations of the FG plate. First, the asymmetric pre-buckling path of the structure under the influence of weight and heat is calculated by a semi-analytical method. The plate's stability relations are extracted using the adjacent equilibrium criterion and virtual work principle. Then, the stability equations are analyzed by the 2D generalized differential quadrature (GDQ) method. Parametric results are presented based on the analysis of the FGM power-law index, geometric ratios, and edge constraints on the buckling of the vertical plate. The study reveals the critical power-law index and thickness at which the structure becomes unstable, shedding light on the previously neglected calculation of weight-induced buckling in vertical structures. Also, the effect of weight on the buckling mode shapes of heavy plates and disturbing its symmetry is demonstrated. Additionally, this study presents the first investigation into the effect of weight on the thermal stability of annular FG plates.