Nonlinear Stability of FG-GPLRC Shallow Annular Spherical Caps and Annular Plates Stiffened by Circumferential Stiffener System

Abstract

For the first time, an analytical approach to the static stability problem of a shallow annular spherical cap stiffened by a system of circumferential stiffeners is presented in this study. Both the shell and the stiffeners are constructed from Functionally Graded Graphene Platelet Reinforced Composite (FG-GPLRC) material, which follows five common distribution laws: FG-X, FG-O, FG-A, FG-V, and UD. The stiffened shallow annular spherical caps are subjected to a uniform temperature change. An extended smeared stiffener technique is applied to the circumferential stiffener system of the SASC. Based on Donnell’s classical shell theory and von Kármán geometric nonlinearities, the fundamental expressions and governing equations of the problem are established. Novel displacement solutions satisfying the parallel-closed conditions are proposed. The load–deflection relationships are derived by applying the Ritz energy minimization method. Consequently, the significant effects of the stiffeners, material model, and geometric and material parameters are investigated.