Abstract
The paper focuses on the method of calculation of evolution shells beyond the elastic limit. The conclusion of the basic system of differential equations is based on the linear shell theory with regard to the Hirchhoff-Lave hypothesis and on the physical equations for small elastic-plastic deformation theory using the method of elastic decisions. The boundary conditions are formulated for Cauchy problem: rigid attachment, hinged support, and free margin. The spherical shell boundary conditions in the pole are obtained from the conditions of symmetry and antisymmetry functions. The convergence of the elastic method and the method of the occurrence of superficial plastic deformations are studied. Also the stress-strain state in the spherical shell is determined and the convergence of the obtained solutions was studied. The results are presented on the symmetric load ring applied to the middle of the Meridian and on the load that can be considered as a concentrated force. The sufficient quantity of iterations is established to achieve the accuracy of 0.1%. The graphs are presented for radial displacement and for meridional bending moment as the functions that converge more rapidly and more slowly respectively.
Highlights
The paper focuses on the method of calculation of evolution shells beyond the elastic limit
The conclusion of the basic system of differential equations is based on the linear shell theory with regard to the Hirchhoff-Lave hypothesis and on the physical equations for small elasticplastic deformation theory using the method of elastic decisions
The boundary conditions are formulated for Cauchy problem: rigid attachment, hinged support, and free margin
Summary
The work is dedicated to the calculation of the isotopic shells of revolution of constant thickness under the action of symmetrical and assimetrical loads beyond the elastic limit. Long and short, closed and ring shells are considered with different hypothesis about contour intersection. The conclusion of the basic system of differential equations is based on the linear shell theory with regard to the Hirchhoff-Lave hypothesis and on the physical equations for small elastic-plastic deformation theory using the method of elastic decisions [1 - 3]. It is supposed that the shell mid-surface is the surface of rotation about the axis z without special points escluding points where the speciality is prevented. Shell generator is a quite smooth curve that curvature is too small comparing to 1/h. On the basis of the linear theory and Kirchhoff-Lave hypothesis the deformations are presented as two first power series expentions at ς, i.e. excluding values above the second order of smallness
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