Calculation of spherical shells under ring loads
Abstract
Calculation of spherical shells under ring loads
Incoming article date: 01.07.2024Nowadays, 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.