Nikolishin, M. M.; Maselko, T. E. Limit equilibrium of a flat cylindrical shell with longitudinal crack taking account of plastic deformations. (Russian) Zbl 0591.73120 Mat. Metody Fiz.-Mekh. Polya 23, 80-84 (1986). Summary: On the basis of an analogue of the \(\delta_ k\)-model of M. Ya. Leonov and V. V. Panasyuk [Prikl. Mekh. 5, No.4, 391-401 (1959)] for an effective construction of thin-walled elements with cracks, the stress deformation state of a flat cylindrical shell made of an ideal elastic-plastic material with a longitudinal through crack is studied. The stress state is assumed to be symmetric with respect to the centre of the crack. Using the apparatus of generalized functions the problem is reduced to a system of singular integral equations which is solved by the method of small parameters. Expressions for the determination of the vertex aperture of the defect and of the length of the zone of plastic deformation are stated. Shells under an internal pressure are also included into the investigations. MSC: 74R05 Brittle damage 74K15 Membranes 74R20 Anelastic fracture and damage 74C99 Plastic materials, materials of stress-rate and internal-variable type Keywords:thin-walled elements with cracks; stress deformation state; flat cylindrical shell; ideal elastic-plastic material; longitudinal through crack; stress state; symmetric; system of singular integral equations; method of small parameters; vertex aperture; defect; length of the zone of plastic deformation; internal pressure PDFBibTeX XMLCite \textit{M. M. Nikolishin} and \textit{T. E. Maselko}, Mat. Metody Fiz.-Mekh. Polya 23, 80--84 (1986; Zbl 0591.73120)