ИСТИНА

We consider several questions about the new parameterization of three-dimensional thin body with one small size. 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 of classic and micropolar theories of elasticity are given. Several interlayer contact conditions are obtained. The definition of the k-order moment of tensor quantity with respect to the system of Legendre polynomials is given. We have obtained the formulations of the problems of the classic and micropolar theories of elasticity for one-, two- and three-layered prismatic thin bodies with respect to the moments of displacement and rotation vectors. The problems of one-, two- and three-layered two-dimensional rectangular cantilever plate and plate with two pinched edges under the distributed load are solved. Acknowledgements: This work was supported by the Shota Rustaveli National Science Foundation (project no. DI-2016-41).