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IssuesArchive of Issues2014-2pp.175-186

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V.I. Ostrik, "Edge Crack Opening in an Elastic Plane with a Wedge-Like Cut in Contact with a Punch," Mech. Solids. 49 (2), 175-186 (2014)
Year 2014 Volume 49 Number 2 Pages 175-186
DOI 10.3103/S0025654414020071
Title Edge Crack Opening in an Elastic Plane with a Wedge-Like Cut in Contact with a Punch
Author(s) V.I. Ostrik (Institute of Applied Physics, National Academy of Sciences of Ukraine, Petropavlovskaya†St.,†58, Sumy, 40030 Ukraine, ostrik_v@rambler.ru)
Abstract The equilibrium of an elastic plane with a wedge-like cut and an internal or edge crack on the symmetry axis was studied in [1] in the case of punch indentation in the lateral faces of the cut at a distance from the cut tip. In [1], the system of singular integral equations of the problem was solved numerically by the mechanical quadrature method.

In this paper, the generalized Wiener-Hopf method [2] is used to obtain the analytic solution of a similar problem in the case of an edge crack under punch pressure on parts of the cut lateral faces adjacent to the cut tip. Some special cases of this problem were considered earlier without a crack [3, 4] or a punch [5, 6].
Keywords elastic wedge, crack, punch, stress, Wiener-Hopf method, factorization
References
1.  F. Erdogan and M. B. Civelek, "Stress Intensity Factors in a Cracked Infinite Elastic Wedge Loaded by a Rigid Punch," Int. J. Engng Sci. 17 (8), 973-989 (1979).
2.  Yu. A. Antipov, "Exact Solution of the Problem of Ring Punch Indentation into Half-Space," Dokl. Akad. Nauk Ukr. SSR, No. 7, 29-33 (1987).
3.  E. I. Ivchenko, N. E. Kachalovskaya, and A. F. Ulitko, "Smooth Contact of a Rigid Wedge with the Shores of a Wedge-Like Cut in an Elastic Plane," Dokl. Ukr. Akad. Nauk. Mekh., No. 12, 23-29 (1991).
4.  V. I. Ostrik, "Problems of Friction Contact between an Elastic Wedge and a Rigid Attachment," Vestnik Kiev Nats. Un-tu. Ser. Fiz.-Mat. Nauki, No. 4, 119-126 (2002).
5.  A. A. Khrapkov, "An Infinite Triangular Wedge with a Cut on the Bisectrix under the Action of Concentrated Forces Applied to the Cut Shores," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 5, 88-97 (1972) [Mech. Solids (Engl. Transl.)].
6.  F. Quchterlony, "Some Stress Intensity Factors for Self-Similar Cracks, Derived from Path-Independent Integrals," J. Elasticity 8 (3), 259-271 (1978).
7.  I. M. Gelfand and G. E. Shilov, Generalized Functions and Operations over Them (Fizmatgiz, Moscow, 1958) [in Russian].
8.  G. Ya. Popov, Elastic Stress Concentration near Punches, Thin Inclusions, and Stiffeners (Nauka, Moscow, 1982) [in Russian].
9.  M. V. Fedoryuk, Asymptotics: Integrals and Series (Nauka, Moscow, 1987) [in Russian].
10.  G. P. Cherepanov, Mechanics of Brittle Failure (Nauka, Moscow, 1974) [in Russian].
Received 05 April 2011
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