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IssuesArchive of Issues2002-6pp.64-69

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V. N. Akopyan and A. V. Saakyan, "Stress state of an elastic half-plane containing a thin rigid inclusion," Mech. Solids. 37 (6), 64-69 (2002)
Year 2002 Volume 37 Number 6 Pages 64-69
Title Stress state of an elastic half-plane containing a thin rigid inclusion
Author(s) V. N. Akopyan (Erevan)
A. V. Saakyan (Erevan)
Abstract Various aspects of contact interaction of thin rigid or elastic inclusions (internal or/and boundary) with an elastic half-plane have been addressed in numerous publications [1-5]. In the present paper, we consider the stress state of a homogeneous elastic half-plane with a thin rigid boundary inclusion of finite length, one side of this inclusion being detached from the matrix. Mathematically, the problem is stated in the form of two singular integral equations of the second kind with fixed singularity and solved by the numerical-analytical discrete singularity method.
References
1.  B. L. Abramyan, "On one contact problem for a half-plane," Izv. AN SSSR. MTT [Mechanics of Solids], No. 5, pp. 4-10, 1972.
2.  E. Kh. Grigoryan, "Solution of the problem of an elastic finite boundary inclusion in a half-plane," Uchenye Zapiski EGY. Estestvennye Nauki, No. 3, pp. 32-43, 1981.
3.  V. M. Alexandrov and S. M. Mkhitaryan, Contact Problems for Bodies with Thin Coatings and Interlayers [in Russian], Nauka, Moscow, 1983.
4.  V. N. Akopyan, "Stress-strain state of a combined wedge reinforced by a thin inclusion," in Mechanics of Solids [in Russian], pp. 63-78, Izd-vo NAN RA, Erevan, 1993.
5.  V. N. Akopyan and A. V. Saakyan, "On one mixed problem for an elastic wedge weakened by a crack," Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 66-78, 1999.
6.  N. I. Muskhelishvili, Some Basic Problems of Mathematical Theory of Elasticity [in Russian], Nauka, Moscow, 1966.
7.  Ya. S. Uflyand, Integral Transforms in Problems of Elasticity [in Russian], Izd-vo AN SSSR, Moscow, Leningrad, 1963.
8.  F. Erdogan, G. D. Gupta, and T. S. Cook, "Numerical solution of singular integral equations," in G. C. Sih (Editor), Mechanics of Fracture. Volume 1, pp. 368-425, Noordoff, Leyden, 1983.
9.  V. Z. Parton and P. I. Perlin, Integral Equations of the Theory of Elasticity [in Russian], Nauka, Moscow, 1977.
10.  A. V. Saakyan, "Discrete singularity method for solving singular integral equations with a fixed singularity," Izv. NAN RA. Mekhanika, No. 3, pp. 12-19, 2000.
Received 29 May 2000
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