On the Calculation of Thin Shells Beyond the Elastic Limit

This paper presents the results of the calculation of a thin spherical shell, the material of which operates beyond the elastic limit. Thin isotropic shells of rotation of constant thickness h are considered. The complete system of the equations contains the equilibrium equations, the geometric relations of linear theory, and the physical relations of the small elastic-plastic deformations theory. The problem is solved using the elastic decisions method. By decomposing the functions of forces, deformations, displacements, and loads into Fourier series in the circumferential coordinate θ and then converting the complete system of equations, the system of eight first-order differential equations with respect to the Fourier series coefficients of the selected resolving functions is obtained. The integration of the resolving system of differential equations is carried out by the run-through method with discrete orthogonalization. In this paper, we study the change in the stress-strain state and the region of occurrence of plastic deformations when changing the place of application of three ring loads. A significant role in the formation of plastic deformations is played not only by the size of the ring loads, but also by their location on the surface of the shell.