Abstract The main aim of this paper is to investigate analytically nonlinear buckling and post-buckling of functionally graded stiffened circular cylindrical shells filled inside by Pasternak two-parameter elastic foundations in thermal environments and under axial compression load and external pressure by analytical approach. Shells are reinforced by closely spaced rings and stringers. The material properties of shell and the stiffeners are assumed to be continuously graded in the thickness direction. Using the Reddy third order shear deformation shell theory, stress function method and Lekhnitskii smeared stiffeners technique, the governing equations are derived. The closed form to determine critical axial load and post-buckling load-deflection curves are obtained by Galerkin method. The effects of temperature, stiffener, foundation, material and dimensional parameters on the stability behavior of shells are shown. The accuracy of the presented method is affirmed by comparisons with well-known results in references. The results shown for thick cylindrical shells, the use of TSDT for determining their critical buckling load is necessary and more suitable.

Abstract In this research work, an exact analytical solution for frequency characteristics of the free vibration of rotating functionally graded material (FGM) truncated conical shells reinforced by eccentric FGM stringers and rings has been investigated by the displacement function method. Material properties of shell and stiffeners are assumed to be graded in the thickness direction according to a simple power law distribution. The change of spacing between stringers is considered. Using the Donnell shell theory, Leckhnisky smeared stiffeners technique and taking into account the influences of centrifugal force and Coriolis acceleration the governing equations are derived. For stiffened FGM conical shells, it is difficult that free vibration equations are a couple set of three variable coefficient partial differential equations. By suitable transformations and applying Galerkin method, this difficulty is overcome in the paper. The sixth order polynomial equation for w is obtained and it is used to analyze the frequency characteristics of rotating ES-FGM conical shells. Effects of stiffener, geometrics parameters, cone angle, vibration modes and rotating speed on frequency characteristics of the shell forward and backward wave are discussed in detail. The present approach proves to be reliable and accurate by comparing with published results available in the literature.