Abstract
In the context of an analog of the Leonov-Panasyuk-Dagdeil model we consider the problem of limit equilibrium of a nonshallow transversally isotropic cylindrical shell weakened by a nonthrough surface longitudinal crack. Based on the equations that take account of the initial stresses, we reduce the problem to a system of two singular integral equations with unknown limits of integration. We carry out a numerical analysis of the dependence of the opening of the edges of the crack on the load and the geometric and physico-mechanical parameters of the shell.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature Cited
M. Ya. Leonov and V. V. Panasyuk, “Development of minuscule cracks in a solid body,”Prikl. Mekh.,5, No. 4, 391–401 (1959).
V. A. Osadchuk,The Stress-strain State and Limit Equilibrium of Shells with Slits [in Russian], Naukova Dumka, Kiev (1985).
V. A. Osadchuk, V. I. Kir'yan, and M. M. Nikolishin, “The opening of the end of a through longitudinal crack in a cylindrical shell subject to internal pressure,”Probl. Prochn., No. 10, 64–67 (1984).
V. A. Osadchuk and M. M. Nikolishin, “The stress state of a closed transversally isotropic cylindrical shell and an infinite plate with cracks,”Mat. Met. Fiz.-mekh. Polya, No. 3, 30–36 (1976).
V. A. Osadchuk, M. M. Nikolishin, and V. I. Kir'yan, “Application of the analog of the δk-model to determine the opening of a nonthrough crack in a closed cylindrical shell,”Fiz.-khim Mekh. Mater., No. 1, 88–92 (1986).
V. A. Osadchuk and Ya. S. Podstrigach, “The stress state and limit equilibrium of shells with cracks,”Itogi Nauki i Tekhniki. Ser. Mekh. Tver. Tela,18, 3–32 (1986).
V. V. Panasyuk, M. P. Savruk and A. P. Datsyshin,The Distribution of Stresses near Cracks in Plates and Shells [in Russian], Naukova Dumka, Kiev (1976).
W. Prager,An Introduction to Plasticity, Addison-Wesley, Reading (1959).
D. S. Dugdale, “Yielding of steel sheets containing slits,”J. Mech. Phys. Solids,8, No. 2, 100–108 (1960).
F. E. Erdogan and F. Delale, “Ductile fracture of pipes and cylindrical containers with a circumferential flaw,”Trans. ASME J. Pressure Vessel Technol.,103, No. 2, 160–168 (1981).
F. E. Erdogan and M. Ratwani, “Plasticity and the crack opening displacement in shells,”Intern. J. Fract. Mech.,8, No. 4, 413–426 (1972).
N. J. Ioakimidis, “The numerical solution of crack problems in plane elasticity in the case of loading discontinuities,”Eng. Fract. Mech.,13, No. 4, 709–716 (1980).
Additional information
Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 31–36.
Rights and permissions
About this article
Cite this article
Nikolishin, M.M. Limit equilibrium of a closed transversally isotropic cylindrical shell with a nonthrough longitudinal crack. J Math Sci 86, 2547–2551 (1997). https://doi.org/10.1007/BF02356094
Issue Date:
DOI: https://doi.org/10.1007/BF02356094