An elastic-plastic state of a circle toroidal shell with a rectangular opening
V. P. Muschanov, A. I. Demidov
Donbas National Academy Civil Engineering Architecture
Annotation: This article is devoted to the use of the technique developed for determining a plasto-elastic stress-strain state of arbitrary curvature shells on the base of the theory of small plasto-elastic deformations. Linearization of task solution is done by the method of elastic solutions. Lagrange's variational equation in the form of point displacements of a shell middle surface in finite differences is used in every approximation. When writing down Lagrange's variational equation a functional dependence between stresses and strains is given in the form of Hooke's law but with additional members taking into account plastic deformations. Geometrical equations are used in a linear form as Cauchy correlations. A material is characterized by a corresponding tension diagram of a cylindrical specimen, by a normal elasticity modulus, and Poisson's ratio. Cinematic boundary conditions are exactly met, and static ones on free loose shell edges are met approximately. There is considered an example of calculating a toroidal shell middle surface equations of which are written in a parametrical form. Shell internal and external edges are fastened quite rigidly, and its side faces are hingedly fastened. A shell is weakened by a large unsupported rectangular opening and is loaded with a normal uniformly distributed load. The task is solved by the elastic solution method and the variation-difference method of point displacements of a shell middle surface. The solution is taken as far as numerical results. There are given the fields of intensity of shearing stresses by a shell internal light surface, displacements, axial forces, and bending moments at a plasto-elastic solution of the task for the whole net area. The paper is devoted to an actual problem of structural mechanics of the shells weakened by large openings at the plasto-elastic deformation in a simple loading.
Keywords: loose toroidal shell, variation-difference method, boundary conditions, elastic solution method, intensity of shear strains, intensity of shearing stresses, plasticity function
Pages: 67-77.
Link for citation: Muschanov, V. P.; Demidov, A. I. An elastic-plastic state of a circle toroidal shell with a rectangular opening. – Text : electronic. – In: Modern Industrial and Civil Construction. – 2007. – Vol. 3, N 2. – Р. 67-77. – URL: https://donnasa.ru/publish_house/journals/spgs/2007-2/01_muschanov_demidov.pdf (date of access: 19.09.2024). (in Russian)
Vol. 3, N 2 (2007)Journal: Modern Industrial and Civil Construction
Publish house: Donbas National Academy of Civil Engineering and Architecture