Nonlinear Stability and Vibration Analyses of Functionally Graded Variable Thickness Toroidal Shell Segments Reinforced with Spiral Stiffeners

Abstract

In this study, an analysis of nonlinear stability and vibration of functionally graded (FG) variable thickness toroidal shell segments (TSSs) reinforced with spiral stiffeners exposed to axial loading is presented using a combination of semi-analytical and analytical methods. Three types of variable thickness TSSs, including concave, convex, and cylindrical shells (CSs), are studied. Moreover, these structures are reinforced by external spiral stiffeners with various angles whose material properties are considered to be continuously graded along the thickness direction. In this regard, the smeared stiffeners technique is utilized to model the stiffeners, and the Donnell shell theory and the von Kármán equation are applied to derive the nonlinear governing equation for variable thickness TSSs reinforced with spiral stiffeners. Galerkin’s method is then used to obtain a discretized nonlinear governing equation to analyze the shells’ behavior. Also, the fourth-order P-T method is applied to analyze the nonlinear dynamic behaviors and the Budiansky–Roth criteria are used to examine the dynamic post-buckling (DPB) behavior. In this regard, it is noted that in terms of reliability and accuracy, the fourth-order P-T method has demonstrated advantages over the other numerical methods. Results are reported to evaluate the influences of stiffeners with different angles and input factors on the nonlinear vibration, dynamic and static post-buckling (SPB) behaviors of FG variable thickness TSSs reinforced with spiral stiffeners.