The Convergence of the Elastic-Plastic State of a Cylindrical Shell by the Method of Elastic Solutions under the Action of a Distributed Load Along its Lines of Symmetry
Abstract: The article presents a numerical calculation of an inelastic open cylindrical shell by the method of successive approximations based on the elastic solution method based on the previously developed technique [3]. The elasticity problem in each approximation is solved by the difference method based on the variational equation of J. Lagrange in the displacements of points on the middle surface. Moreover, the matrix of the system of equations does not change from approach to approximation. Only the right parts, which depend on plastic deformations, change. First, the statement of the problem is given: we consider a circular open cylindrical shell with pivotally fixed meridional edges and rigidly fixed edges in the circumferential direction under the action of a uniformly distributed load normal to the middle surface, acting along the lines of symmetry. The boundary conditions are formulated. The validity of using shell symmetry is proved. The convergence of the solution of the elastic problem by doubling the grid is established. The moment of appearance of the first plastic deformations in the most loaded node of the grid region is established. The definition of the magnitude of the effective load, to which the solution converges for a predetermined elasto-plastic state of a given shell by the method of elastic solutions, is given: the shear stress intensity field over the shell thickness over the entire grid region is given. The field of shear stress intensity over the entire grid area is presented in tabular form and in the form of volumetric-flat graphs. The influence of the choice of the number of points over the shell thickness when determining additional terms depending on plastic strains by the Simpson method is shown. It is proved that a significant refinement of the elastic-plastic solution for the VAT shell by this criterion is not achieved. It is shown that, taking into account plastic deformations, the percentage of stress reduction is less where, in the case of an elastic solution, the stress S is greater. A numerical experiment was carried out to determine the convergence of solutions of an elastoplastic stress-strain state in the most loaded node 2-34 with a grid of 27×35 nodes with five points along the shell thickness at z = h / 2. The values of the load q, which correspond to the elastic solutions of the problem for the intensity of the tangential stresses S from the tensile diagram, are determined.
Keywords: closed inelastic cylindrical shell, Lagrange equations, boundary conditions, intensity of tangent stresses, Simpson method.
Pages: 137-149.
For citation: Mushchanov, V. F.; Demidov, A. I.; Orzhekhovsky, A. N. [et al.]. The Convergence of the Elastic-Plastic State of a Cylindrical Shell by the Method of Elastic Solutions under the Action of a Distributed Load Along its Lines of Symmetry. – Text : electronic. – In: Metal Constructions. – 2019. – Vol. 25, N 4. – Р. 137-149. – URL: https://donnasa.ru/publish_house/journals/mk/2019-4/01_mushchanov_demidov_orzhekhovsky_fomenko_tanasoglo.pdf (date of access: 21.11.2024). – ISSN 1993-3517.
Vol. 25, N 4 (2019)
Journal: Metal Constructions
Publish house: Donbas National Academy of Civil Engineering and Architecture
Journal: Metal Constructions
Publish house: Donbas National Academy of Civil Engineering and Architecture