Elastoplastic buckling of axially loaded functionally graded material cylindrical shells

In this paper, elastoplastic buckling behaviors of functionally graded material cylindrical shells under axial compression are investigated with Donnell shell theory and J2 flow constitutive relation of functionally graded materials. The nonlinear material properties vary smoothly through the thickness, and a multi-linear hardening elastoplasticity is considered in the analysis. The buckling government equations are solved by Galerkin method, and the semi-analytical solution of the critical load is given. Numerical results from the present theory are derived by an iterative procedure. The theoretical elastoplastic critical loads are well verified by those of ABAQUS code, which includes both the material and geometrical nonlinearities. The elastic, elastoplastic, and plastic buckling regions of functionally graded cylindrical shells can be effectively distinguished through the present method, and various effects of the material nonlinearity, the dimensional parameters and the power law exponent are investigated.