Semi-analytical approach for analyzing the nonlinear dynamic torsional buckling of stiffened functionally graded material circular cylindrical shells surrounded by an elastic medium

In this study, we propose a semi-analytical method for analyzing the nonlinear dynamic behavior of functionally graded material (FGM) thin circular cylindrical shells surrounded by an elastic medium under a time-dependent torsional load. The shell is stiffened by a closely spaced orthogonal FGM stiffeners system, which is attached to the inner surface of the shell. The elastic medium is assumed to follow the two-parameter elastic foundation model proposed by Pasternak. The fundamental relations and governing equations for stiffened cylindrical shells are derived using the Donnell shell theory with von Karman geometrical nonlinearity and the smeared stiffeners technique. A deflection function with three terms is employed to consider the nonlinear buckling shape in a more correct manner. The Galerkin method is used. The critical dynamic torsional load is found by using the fourth order Runge–Kutta method and Budiansky–Roth criterion. Based on computations, we investigated the effects of the stiffener, foundations, material, and dimensional parameters on the dynamic buckling behavior of the shell.