ИСТИНА

The new parametrization of the three-dimensional thin domain of an arbitrary body of revolution is considered, consisting in using several base surfaces in contrast to the classical approaches. The vector parametric equation is given. The geometric characteristics inherent to the new parameterization are determined. Expressions for the translation components of the unit tensor of the second rank and also relations connecting different classes of bases and geometric characteristic generated by them are written. Using the basic recurrence formulas for Legendre polynomials, several additional relations, which play an important role in the construction of various versions of the theory of thin bodies, have been obtained. The determination of the moment of the tensor quantity, as well as their derivatives and repeated derivatives, is given. The moments of the k-th order of several expressions with respect to the Legendre polynomials are written out. Several representations of differential operators, systems of motion equations, heat inflow equations, the constitutive relations of the micropolar theory of elasticity, the Fourier’s law of thermal conductivity and boundary conditions of the physical and thermal contents under the new parameterization of a thin body of rotation are obtained. In addition, from the presented relations in turn, the corresponding relations are obtained in the moments of the unknown quantities with respect to the Legendre polynomials. The statements of initial-boundary value problems in moments are given. As special cases cylindrical and spherical bodies are considered. Acknowledgements: this research was supported by the Shota Rustaveli National Science Foundaiton (project no. DI-2016-41).