Revisting the pertinence of theory of little elasto-plastic strain when calculating shells in the process of inelastic behavior of material
Abstract: The article is devoted to verification of competence of application of the before developed method on determination of the resiliently-plastic tensely-deformed state of shells of arbitrary form on the basis of theory of small resiliently-plastic deformations at linear approximations of decision of tasks the method of resilient decisions. In every progressive approximation at the decision of resilient task, the variation equalization of Lagranzha is used in moving of points of middle surface of shell in eventual differences. At the record of variation equalization of Lagranzha connection between tensions and deformations is presented in form of Hookers law, but with additional members, taking into account plastic deformations. Geometrical equa-lizations are accepted in the linear raising in form of Cauchy relations. Material is characterized by the proper diagram of tension of cylindrical standard, module of normal resiliency and Poisson ratio. Kinematics scope terms are satisfied exactly, and static, on the free of fixing edges of shell, is approximately. The task about the competence of application of method of resilient decisions for the unreserved cylindrical shell of permanent thickness, hardly jammed in circuitous direction and joint fastened in meridional direction with the large joint fastened opening at operating on it of the evenly distributed normal to the middle surface loading, is considered. It is confirmed by the construction of trajectory of deformation in three-dimensional subspace of the fivemeasured vector space of A. A. Il’yushina for the elements of shell being in the resiliently-plastic state. For this purpose the calculation of this shell is carried out at three values of loading, that allows to build the trajectory of deformation. Work is devoted to the up-to-date question of structural mechanics of shells at the action of loading at resiliently-plastic deformation at the active process of loading.
Keywords: barrel shell, variation and difference method, method of linear approximation, density of shear stress, plasticity function, strain path.
Pages: 221-234.
For citation: Demidov, A. I. Revisting the pertinence of theory of little elasto-plastic strain when calculating shells in the process of inelastic behavior of material. – Text : electronic. – In: Metal Constructions. – 2014. – Vol. 20, N 4. – Р. 221-234. – URL: https://donnasa.ru/publish_house/journals/mk/2014-4/04_demidov.pdf (date of access: 27.11.2024). – ISSN 1993-3517.
Vol. 20, N 4 (2014)
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