The construction of continuous models for nanomaterials (graphene, nanotubes, etc) is currently one of the topical problems. It is assumed that in the interatomic interactions of graphene (as well as nanotubes) there exist force independent moment interactions. This is logical, otherwise, in case of out of plane deformation (also in case of deformation of nanotube ) graphene would not be endowed with rigidity. In this respect, it is essential to construct an atomic discrete model of graphene (or of one-layered nanotube) where, besides force interactions, moment interactions are also taken into account. When the interatomic interactions of graphene (nanotube) are replaced by the beam system, it becomes essential to construct a model of thin beams based on the moment theory of elasticity, where the beam deformation subjects to the concept “shear plus free rotation.” The present paper demonstrates the construction of such a beam model. Further, by replacing the interatomic interactions of graphene by the constructed model, the discrete-continuous model of graphene is constructed. After, by passing the limit, continuous – moment model of graphene (both for its in plane and out of plane deformations) is constructed. The latter is represented by the model of a thin plate based on moment theory of elasticity. In the result, the constants of the moment theory of elasticity are determined. Further, the paper demonstrates the construction of the general model of thin shells based on the moment theory of elasticity, where the shell deformation (similar to the deformation model of graphene as a plate) is subject to the concept “shear plus independent rotation”. In specific cases this model can serve as a continuous-moment model for one-layered nanotubes. Based on the constructed two models for graphene and nanotube, specific applied problems on in plane deformation and out-of-plane bending deformations of graphene, as well as problems on the deformation of nanotubes, are solved.
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