Nonlinear dynamic analysis of eccentrically stiffened imperfect functionally graded doubly curved thin shallow shells

This paper presents a semi-analytical approach to investigate the nonlinear dynamic of imperfect eccentrically stiffened functionally graded shallow shells taking into account the damping subjected to mechanical loads. The functionally graded shallow shells are simply supported at edges and are reinforced by transversal and longitudinal stiffeners on internal or external surface. The formulation is based on the classical thin shell theory with the geometrical nonlinearity in von Karman–Donnell sense and the smeared stiffeners technique. By Galerkin method, the equations of motion of eccentrically stiffened imperfect functionally graded shallow shells are derived. Dynamic responses are obtained by solving the equation of motion by the Runge–Kutta method. The nonlinear critical dynamic buckling loads are found according to the Budiansky–Roth criterion. Results of dynamic analysis show the effect of stiffeners, damping, pre-loaded compressions, material and geometric parameters on the dynamical behavior of these structures.