On modeling of three-layered thin bodies

Abstract

Abstract Some questions about the new parameterization of three-dimensional thin body with one small size are considered. The vector parametric equations of the multilayered thin body are given. The geometric characteristics are considered. The representations of several differential operators, the equations of motion, the boundary conditions and the constitutive relations (CR) of classic and micropolar theories of elasticity are given. Some interlayer contact conditions are obtained. The definition of the k-order moment of any quantity with respect to the system of Legendre polynomials is given. The problems of the classic and micropolar theories of one-, two- and three-layered prismatic elastic thin bodies in moments of displacement and rotation vectors with respect to the system of Legendre polynomials are formulated. The problem of one-layered two-dimensional rectangular plate with two pinched edges under the distributed load are solved.