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The nonlinear buckling behavior of functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical shells reinforced by ring, stringer and/or spiral FG-GPLRC stiffeners under torsional loads is studied by an analytical approach. The governing equations are based on the Donnell shell theory with geometrical nonlinearity of von Kármán-Donnell-type, combining the improvability of Lekhnitskii’s smeared stiffeners technique for spiral FG-GPLRC stiffeners. The effects of mechanical and thermal loads are considered in this paper. The number of spiral stiffeners, stiffener angle, and graphene volume fraction, are numerically investigated. A very large effect of spiral FG-GPLRC stiffeners on the nonlinear buckling behavior of shells in comparison with orthogonal FG-GPLRC stiffeners is approved in numerical results.