A General Form Solution for Elastic Buckling of Thin Cylinders Made of FGM under Axial Loading

In this article, the axisymmetric mechanical buckling of thin cylindrical shell made of functionally graded material (FGM) is considered. The governing equations for a thin cylinder based on the first-order shell theory and Timoshenko's assumptions are obtained. The equations are derived using the Sanders simplified kinematic relations and the principle of work and energy. The constituent material of the functionally graded shell is assumed to be a mixture of ceramic and metal. It is assumed that the mechanical properties vary continuously through the shell thickness. The thin cylindrical shell is under uniform axial compressive load. The expression for the critical mechanical buckling load is obtained analytically and is given by closed form solution. The results are validated with the Timoshenko's formula in the literature.