In this study, the nonlinear thermomechanical buckling and postbuckling behavior of sandwich cylindrical shells with a graphene–origami (GOri) reinforced auxetic core and carbon nanotube (CNT)-reinforced face sheets is investigated. The shell is subjected to uniform torsional loading and a uniform temperature rise. The carbon nanotubes are dispersed within a temperature-dependent polymer matrix, while the auxetic core consists of multiple graphene-origami reinforced layers arranged either in a uniform distribution or a functionally graded (FG) pattern. The auxetic response of the core can be tuned by varying the weight fraction and folding degree of the graphene-origami structure.

The governing equations are formulated based on nonlinear Donnell thin shell theory with von Kármán geometric nonlinearity. An analytical solution for a simply supported cylindrical shell is obtained using a three-term displacement function and the Galerkin method to determine the critical buckling load and postbuckling path. The model’s accuracy is validated against published results. Parametric studies assess the effects of graphene–origami weight fraction, folding degree, and thermal conditions on buckling and postbuckling behavior. The results indicate that increasing the graphene–origami weight fraction significantly enhances buckling stability, with FG-X cores exhibiting greater enhancement compared to uniformly distributed cores.