An Elastic-Plastic Stressed-Deformed State of a Thin Unclosed Toroidal Shell
O. I. Demidov
Donbas National Academy of Civil Engineering and Architecture
Annotation: The work is devoted to the application of the earlier developed methods of determining an elastic-plastic stressed-deformed state of arbitrary shape shells in terms of the theory of small elastic-plastic deformations. There are considered the problems under a simple shell loading. The problem linearization is done by the method of elastic solutions. In every approximation, there are considered the problems of the theory of thin elastic shells by the method of d finite differences in terms of the Lagrange variational equation in the median surface points travel. When writing the Lagrange variational equation, the relation between stresses and deformations is given in the form of the Hooke’s law but with additional terms considering plastic deformations. Geometrical equations are accepted in the linear formulation in the form of Саuсhу’s correlations. The material is characterized by a corresponding tension diagram of a cylindrical specimen, by the standard modulus of elasticity, and by the Poisson’s ratio. The equations of a toroidal shell medium surface are written in a parametric form. The shell inner and outer edges are absolutely rigidly packed, and the sides are jointed. There is given a numerical design of a thin unclosed elastic-plastic toroidal shell of a constant thickness under the action of an equally distributed normal load in the in the median surface points travels. There is applied a method of elastic solutions together with the variational- differential method in the median surface points travels. The problem solution is brought to numerical results. There are presented the fields of intensity of tangential stress through the shell thickness at an elastic-plastic solution of the problem for the whole net domain for three values of an equally distributed load. There was determined the load value under which there appear the first plastic deformations. In the figures there is shown a development of plastic zones as an equally distributed standard load grows. The work is devoted to an urgent question of the shells structural mechanics at their elastic-plastic deformation in terms of a shell simple loading.
Keywords: an unclosed toroidal shell, the variational-differential method, boundary conditions, the method of elastic solutions, an intensity of a shift deformations, an intensity of tangential stresses, the function of plasticity.
Pages: 163-176.
Link for citation: Demidov, O. I. An Elastic-Plastic Stressed-Deformed State of a Thin Unclosed Toroidal Shell. – Text : electronic. – In: Modern Industrial and Civil Construction. – 2006. – Vol. 2, N 4. – Р. 163-176. – URL: https://donnasa.ru/publish_house/journals/spgs/2006-4/01_demidov.pdf (date of access: 16.09.2024). (in Russian)
Vol. 2, N 4 (2006)Journal: Modern Industrial and Civil Construction
Publish house: Donbas National Academy of Civil Engineering and Architecture