Abstract
We study the stress state in the vicinity of a planar surface crack whose boundary is described by the limaçon of pascal. The problem is solved by a conformal mapping of the region occupied by the crack onto part of a disk in the plane. This makes it possible to apply a numerical-analytic method for solving systems of double singular integral equations of the mathematical theory of cracks. We present the graphs of the dependence of the stress intensity factor on the angular coordinate for cracks that are part of a limaçon of Pascal.
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Literature Cited
I. V. Kalynyak, “The stress state in the vicinity of a planar crack whose boundary has points of negative curvature,”Mat. Met. Fiz.-Mekh. Polya, No. 33, 83–90 (1991).
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M. V. Khai and I. V. Kalynyak, “On an approach to numerical solution of problems of the mathematical theory of cracks,”Mat. Met Fiz.-Mekh. Polya, No. 20, 38–42 (1984).
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Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya. Vol. 38, 1995.
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Khai, M.V., Sushko, O.P. A study of the influence of the orientation of a planar surface crack in the shape of a limaçon of pascal on the stress concentration in a half-space. J Math Sci 81, 3069–3072 (1996). https://doi.org/10.1007/BF02362596
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DOI: https://doi.org/10.1007/BF02362596