Nonlinear static and dynamic buckling analysis of imperfect eccentrically stiffened functionally graded circular cylindrical thin shells under axial compression

• Nonlinear buckling of axial loaded stiffened FGM cylindrical shells is studied.
• Smeared stiffeners technique and Galerkin method are applied.
• Static buckling loads and post-buckling curves are found explicitly.
• Dynamic responses with different load types are analyzed.
• Effectiveness of stiffeners in enhancing the stability of shells is shown.

An analytical approach is presented to investigate the nonlinear static and dynamic buckling of imperfect eccentrically stiffened functionally graded thin circular cylindrical shells subjected to axial compression. Based on the classical thin shell theory with the geometrical nonlinearity in von Karman–Donnell sense, initial geometrical imperfection and the smeared stiffeners technique, the governing equations of motion of eccentrically stiffened functionally graded circular cylindrical shells are derived. The functionally graded cylindrical shells with simply supported edges are reinforced by ring and stringer stiffeners system on internal and (or) external surface. The resulting equations are solved by the Galerkin procedure to obtain the explicit expression of static critical buckling load, post-buckling load–deflection curve and nonlinear dynamic motion equation. The nonlinear dynamic responses are found by using fourth-order Runge–Kutta method. The dynamic critical buckling loads of shells under step loading of infinite duration are found corresponding to the load value of sudden jump in the average deflection and those of shells under linear-time compression are investigated according to Budiansky–Roth criterion. The obtained results show the effects of stiffeners and input factors on the static and dynamic buckling behavior of these structures.