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Few researches have focused on elastoplastic mechanical performances of functionally graded plates and shells. In this paper, elastoplastic and plastic buckling behaviors of externally pressured cylindrical shells made from functionally graded materials are investigated by using Donnell shell theory. Either J2J2 flow theory or J2J2 deformation theory helps to found the constitutive relation of functionally graded materials. The material properties vary smoothly through the thickness, and a multi-linear hardening elastoplasticity is used in the analysis. The buckling governing equations are solved by Galerkin method, and the expression of the elastoplastic critical external pressure is given analytically. Numerical results from the present theory are derived by an iterative arithmetic developed in MATHEMATICA code. The theoretical critical loads of the present J2J2 deformation theory are well verified by experimental and numerical results in literature. The elastic, elastoplastic, and plastic buckling regions of functionally graded cylindrical shells can be effectively distinguished by the present method, and various effects of the dimensional parameters, the power law exponent, and the elastoplastic material parameters are investigated.
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