Moment-membrane theory of large deflection of elastic shells as a continuum model of deformed behavior of two-dimensional nanomaterials

S. O. Sarkissian

Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2024), pp. 48-58

Résumé

In this paper, based on the assumption on the smallness of deformations, flexural-torsional characteristics and angles of rotation of the shell elements as well as on the assumption on shell's shallowness, 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, a geometrically nonlinear moment-membrane theory of elastic shells is constructed, which is interpreted as a continuum theory of the deformation behavior of flexible two-dimensional nanomaterials (in particular, for carbon nanotubes and graphene).

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