Moment-Membrane model of a plate as a continual model of graphene deformations and a finite element method for its calculation

In this work the moment-membrane theory of elastic thin shells from the point of view of a variation interpretation is presented; the variational principles of Hu-Washizu, Lagrange and Castigliano types are established. Further, the moment-membrane theory of elastic thin plates is presented: a model of a plane stress state and a model of bending deformation, as deformation continuum models of graphene, respectively, for deformations in its plane and bending deformations from its plane. For numerical studies of these models, on the basis of the variational principle of Lagrange type, variants of the application of the finite element method are developed.