Non-classical approach to mathematical modeling of plate bending

Abstract

This work is devoted to constructing a modified non-classical theory of plates without preliminary hypotheses about the distribution of the displacement vector and the deformation tensor on the basis of three-dimensional equations of the nonlinear elasticity theory of V.V. Novozhilov. The proposed approach is applicable to deformation of non-canonical plates and shallow shells. The recurrent relations have been obtained; they will be further used in determining the ratios of interlayer variables in layered composites