On the Modeling of Thin Bodies of Revolution

Abstract

Abstract The new parametrization of the three-dimensional thin domain of an arbitrary body of rotation 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 bases and geometric characteristic generated by them are written. The determination of the moment of an arbitrary function is given. The motion equations and CR of the micropolar theory of elastic rotation bodies without a symmetry center of variable thickness are obtained under the new parametrization, from which equations are obtained for very thin and shallow rotation bodies, both variable and constant thickness. The equations of motion and CR of any approximation in the moments of unknown functions with respect to an arbitrary system of orthogonal polynomials and, in particular, for the system of Legendre polynomials are derived. The questions of setting initial-boundary problems are discussed.