Numerical methods of calculation of thin isotropic rotation shells
Abstract
Numerical methods of calculation of thin isotropic rotation shells
Incoming article date: 24.07.2024Numerical 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