1. Introduction
Functionally graded (FGM) plate and shell structures have became
popular in engineering designs of coating of nuclear reactors and
space shuttle. The static and dynamic behavior of FGM cylindrical shell
attracts special attention of a lot of scientists in the world.
In static analysis of FGM cylindrical shells, many studies have been
focused on the buckling and post-buckling of shells under mechanic
and thermal loading. Shen [1] presented the nonlinear post-buckling
of perfect and imperfect FGM cylindrical thin shells in thermal
environments under lateral pressure by using the classical shell theory
with the geometrical nonlinearity in von Karman–Donnell sense. By
using higher order shear deformation theory; this author [2] continued to investigate the post-buckling of FGM hybrid cylindrical shells in
thermal environments under axial loading. Bahtui and Eslami [3]
investigated the coupled thermo-elasticity of FGM cylindrical shells.
Huang and Han [4–7] studied the buckling and post-buckling of unstiffened FGM cylindrical shells under axial compression, radial
pressure and combined axial compression and radial pressure based
on the Donnell shell theory and the nonlinear strain–displacement