Modeling the Stressed state of Anisotropic Bodies under the Influence of Volumetric Forces

The paper presents a mathematical model for constructing elastic fields for transversally isotropic bodies of revolution, subject to the action of volumetric forces of a cyclic nature and varying according to the law of sine or cosine. The solution to the problem was carried out using the boundary state method. The basis of the space of internal states is formed using fundamental polynomials. The polynomial is placed at any position of the displacement vector of the flat auxiliary state, and a spatial state is formed using the transition formulas. The set of such states forms a finite-dimensional basis, according to which, after orthogonalization, the desired state is expanded into Fourier series with the same coefficients. The coefficients of the series are scalar products of the vectors of the given and basic body forces. Finally, the search for the elastic state comes down to solving quadratures. Solutions to problems in the theory of elasticity for a transversally isotropic circular cylinder under the action of body forces specified according to a cyclic law are analyzed. An analysis of the convergence of series and an assessment of the accuracy of the solution in graphical form are given.