Abstract
The problem of the limiting equilibrium of a closed cylindrical shell with evenly spaced longitudinal cuts, stated in the context of the analogy with the δk-model of Leonov-Panasyuk-Dagdeil, is reduced to a system of singular integral equations. An algorithm is constructed for the numerical solution of this system. For a shell under internal pressure we study the influence of the number of cuts, the magnitude of the applied load, and the length of a cut on the opening of its ends. Two figures. Bibliography: 4 titles.
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Literature cited
A. I. Kalandiya,Mathematical Methods of Two-dimensional Elasticity [in Russian], Nauka, Moscow (1973).
V. A. Osadchuk,The Stress-deformed State and Limiting Equilibrium of Shells with Cuts [in Russian], Naukova Dumka, Kiev (1985).
P. Ergodan and M. Ratwani, “Plasticity and the crack opening displacement in shells,”Int. J. Fract. Mech.,8, No. 4, 413–416 (1972).
N. I. Ioakimidis, “The numerical solution of crack problems in plane elasticity in the case of loading discontinuities,”Eng. Fract. Mech.,13, 709–716 (1980).
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Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 50–55.
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Nikolishin, M.M., Shabo, A.G. The interaction of a system of longitudinal cuts in a closed cylindrical shell taking account of plastic strain. J Math Sci 63, 350–354 (1993). https://doi.org/10.1007/BF01255741
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DOI: https://doi.org/10.1007/BF01255741