Moment-Membrane Theory of Elastic Shells of Large Deflection as a Continuum Model of Deformation Behavior of Two-Dimensional Nanomaterials

Abstract

This paper uses the assumption on the smallness of deformations, flexural-torsional characteristics and angles of rotation of the shell elements, as well as the assumption on shell’s shallowness. Based on this assumption, a geometrically nonlinear moment-membrane theory of elastic shells is constructed with the help of the three-dimensional geometrically nonlinear moment theory of elasticity and by preserving only those nonlinear terms that come from normal displacement (deflection) and its derivatives. The constructed theory is interpreted as a continuum theory of the deformation behavior of flexible two-dimensional nanomaterials, in particular, of carbon nanotubes and graphene.