On the stability of functionally graded truncated conical shells reinforced by functionally graded stiffeners and surrounded by an elastic medium

This paper presents an analytical approach to investigate the mechanical buckling load of eccentrically stiffened functionally graded truncated conical shells surrounded by elastic medium and subjected to axial compressive load and external uniform pressure. Shells are reinforced by stringers and rings in which material properties of shell and stiffeners are graded in the thickness direction according to a volume fraction power-law distribution. The elastic medium is assumed as two-parameter elastic foundation model proposed by Pasternak. The change of spacing between stringers in the meridional direction is taken into account. The equilibrium and linearized stability equations for stiffened shells are derived based on the classical shell theory and smeared stiffeners technique. The resulting equations which they are the couple set of three variable coefficient partial differential equations in terms of displacement components are investigated by Galerkin method and the closed-form expression for determining the buckling load is obtained. Four cases of stiffener arrangement are analyzed. Carrying out some computations, effects of foundation, stiffener and input factors on stability of shell have been studied. The effectiveness of FGM stiffeners in enhancing the stability of cylindrical shells comparing with homogenuos stiffener is shown.