Nowadays, numerical methods are widely used to realise complex calculations.Verification of the correctness of the numerical calculation results is a relevant task. The validity of the results can be confirmed by determining the stress-strain state by various methods. This paper presents the results of the calculation of thin isotropic ring spherical shells of constant thickness with half-shell angle in the range of (90-170) degrees by two numerical methods. The results of solving the system of differential equations of the general moment theory of shells with the use of the computer mathematics system (Maple 2017) and the finite element method (FEM) are discussed. The given examples show that the calculation results with the use of the selected finite element KE-44 coincide with an accuracy of 10-15 % for shells with a half-shell angle of 120 degrees. When the angle is increased to 170 degrees, the difference in function values becomes significant. The paper gives some examples of calculation of ring spherical shells under the action of one and three annular loads. The variation of axial and radial displacements, of meridional bending moment for shells with the ratio of radius of the curvature to shell thickness 25, 50, 100, 200 is shown. Plots of meridional bending moment and moment isopole are given.

Keywords: elastic, spherical shell, numerical method, computer mathematics system, finite element method.

Numerical methods for calculating shells provide a wide range of solutions when varying various parameters. The object of this study is a mathematical model of thin isotropic elastic shells of revolution of constant thickness. The problem is solved from the position of moment theory.To determine the stress-strain-state of the shell, the solving system is obtained by transforming the basic systems of equations of rotational shells by moment theory and the variables separation. All SSS and load components are decomposed into Fourier series along the circumferentail coordinate. A programme in the Python programming language was written to verify the numerical solution by a computer mathematics system (CMS-Maple 17). Matplotlib library was used for plotting graphs. Examples of numerical calculation of ring spherical shells for the action of ring loads are given. The variants of action of one and two ring loads on shells with different conditions of support along the contours and different half shell angles are presented. The difference between the calculation results of the two methods for bending moment functions and displacement functions is tabulated. The highest value of the difference is 0.0015%. Plots of the variation of meridional bending moment under the action of two ring loads are presented. The variants of rigid pinching along the contours and hinged support are considered. Exsmples are given for shells with the ratio of radius of curvature to shell thickness equal o R/h = 25, 50, 150, 200. Considered of the half shell angles equal to 90, 100, 130 degrees.

Keywords: rotation shell, spherical, isotropic, elastic, computer mathematics system, Python programming language