Abstract
In the present work, under the assumption of smallness of deformations, bending-torsional characteristics and angles of rotation (including the angles of free rotation) of the elements of the plate, based on the three-dimensional geometrically-nonlinear moment theory of elasticity, preserving only those nonlinear terms, that come from normal displacement (deflection) and its derivatives, a geometrically nonlinear moment-membrane theory of elastic plates is constructed as a continual theory of deformations of a flexible graphene. For the indicated nonlinear theory of elastic plates, by introducing stress functions, the resolving equations are presented also in a mixed form: these are the system of equilibrium equations for transverse-bending deformation, compiled in the deformed state of the plate, and deformations continuity equations, expressed in stress functions and deflection functions. For the geometrically nonlinear moment-membrane theory of elastic plates Lagrange-type variational principle is established.
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