Postbuckling nonlinear analysis of FGM truncated conical shells reinforced by orthogonal stiffeners resting on elastic foundations

This paper presents an analytical investigation on buckling and postbuckling of eccentrically stiffened functionally graded thin truncated conical shells subjected to axial compressive load and resting on elastic foundations. Shells are reinforced by rings and stringers attached to their inside. The shell material properties are graded in the thickness direction according to a volume fraction power-law distribution. The change in spacing between stringers in the meridional direction is taken into account. The theoretical formulations based on the Donnell shell theory with von Karman geometrical nonlinearity and the smeared stiffeners technique are derived. The resulting equations, which are a coupled set of three variable coefficients nonlinear partial differential equations in terms of displacement components, are solved by the Galerkin method. The closed-form expressions for determining the critical buckling load and for analyzing the postbuckling load–deflection curves are obtained. The influences of various parameters such as stiffeners, foundations, material properties and geometric dimensions on the stability of shells are considered in detail.