Review of research on the vibration and buckling of functionally graded spherical shells

Spherical shells are important components in many aerospace and engineering structures. A functionally graded material (FGM) spherical shell can have its material distribution varied with the change of the radius direction, which can enhance the bearing capacity and the stability of the thin-walled shells. However, due to the special geometric characteristics of the spherical shell, the simplicity of its geometry will lead to great complexity in its vibration and buckling analysis processes. This paper mainly reviews the previous analytical and numerical research on the vibration and buckling of the FGM spherical shell. The shell's middle plane equilibrium equations are derived from plate theory. The Galerkin method, the Ritz method, the power series solution method, and other methods are introduced to carry out the vibration and buckling analysis. The frequencies, mode shapes, and the critical buckling load of the FGM spherical shells, which are under various boundary conditions and external pressure.