On the linear stability of eccentrically stiffened functionally graded annular spherical shell on elastic foundations

The study deals with the formulation of governing equations of eccentrically stiffened functionally graded materials annular spherical shells resting on elastic foundations and based upon the classical shell theory and the smeared stiffeners technique taking into account geometrical nonlinearity in Von Karman-Donnell sense. The annular spherical shells are reinforced by eccentrically longitudinal and transversal stiffeners made of full metal or full ceramic depending on situation of stiffeners at metal-rich side or ceramic-rich side of the shell respectively. Approximate solutions are assumed to satisfy the simply supported boundary condition and Galerkin method is applied to obtain closed-form relations of bifurcation type of buckling loads. Numerical results are given to evaluate effects of inhomogeneous, dimensional parameters, outside stiffeners and elastic foundations to the buckling of structures.