Open AccessStress-stain state in elastic spherical shells under the action some asymmetrical of circular loads
Author(s) -
Avgustina Astakhova
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1015/1/012021
Subject(s) - shell (structure) , isotropy , action (physics) , linear elasticity , rotation (mathematics) , spherical shell , mathematical analysis , stress (linguistics) , elasticity (physics) , differential equation , geometry , mechanics , physics , materials science , mathematics , structural engineering , optics , finite element method , composite material , engineering , linguistics , quantum mechanics , philosophy
The paper presents the basic differential equations for calculating shells of rotation. It is considered that the material of the shell works beyond the elastic limit. The conclusion of the resolving system of differential equations is based on the linear shell theory and the Kirchhoff-Love hypothesis. The physical correlations are based on the small elastic-plastic deformation theory. With the construction of the solution of the load function, also unknown resolving functions expand to the Fourier series along the circumferential coordinate. In the present work, the action of the asymmetrical distribution along the parallel loads is considered. The solution is approached by the elastic decisions method. The study of stress-stain state in the isotropic spherical shells is presented in the work. The results of the calculation are presented in the example of a spherical shell. The work of the material beyond the elastic limit is taken into account using assuming linear hardening of the material. The shell is loaded with ring distributed loads, and they are applied on a certain segment in a parallel circle. The diagrams of bending moments and areas of the appearance of plastic deformations along the thickness of the shell are presented. The areas of plastic deformations for ring loads distributed along the parallel relative to the zero meridian in the range of 45, 90,135 degrees are shown.