Nonlinear static and dynamic buckling of eccentrically stiffened functionally graded cylindrical shells under axial compression surrounded by an elastic foundation

Abstract

This paper presents an analytical approach to investigate the nonlinear buckling of imperfect eccentrically stiffened functionally graded thin circular cylindrical shells subjected to axial compression and surrounded by an elastic foundation. Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, initial geometrical imperfection, the smeared stiffeners technique and Pasternak's twoparameter elastic foundation, the governing equations of eccentrically stiffened functionally graded cylindrical shells are derived. The functionally graded cylindrical shells are reinforced by homogeneous ring and stringer stiffener system on internal iand (or) external surface. The resulting equations are solved by the Galerkin method. 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 ldads of shells are considered for step loading of infinite duration and linear-time compression. The obtained results show the effects of foundation, stiffeners and input factors on t,he nonlinear buckling behavior of these structures.