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IssuesArchive of Issues2004-4pp.55-60

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L. V. Vakhonina and V. G. Popov, "The stress concentration near a delaminated thin rigid inclusion in the interaction with a torsional wave," Mech. Solids. 39 (4), 55-60 (2004)
Year 2004 Volume 39 Number 4 Pages 55-60
Title The stress concentration near a delaminated thin rigid inclusion in the interaction with a torsional wave
Author(s) L. V. Vakhonina (Odessa)
V. G. Popov (Odessa)
Abstract The stress concentration near a delaminated thin circular rigid inclusion which interacts with harmonic torsional waves is analyzed. The method of solution is based on representing the angular displacements, which are caused by waves reflected from the inclusion, in the form of a discontinuous solution of the corresponding equation of elasticity. This discontinuous solution expresses the angular displacements of the medium in terms of the unknown displacement and stress discontinuities at the inclusion. By satisfying the boundary conditions at the delaminated and attached surfaces of the inclusion, we obtain the system of singular equations for these discontinuities. This system is solved approximately by the collocation method using specific quadrature formulas for singular integrals. The approximate solution obtained made it possible to analyze the coefficient of the stress singularity and angle of rotation of the inclusion depending on the parameters of the incident wave.
References
1.  G. Ya. Popov, Concentration of Elastic Stresses Near Punches, Cuts, Rigid Inclusions, and Stiffeners [in Russian], Nauka, Moscow, 1982.
2.  V. M. Alexandrov, B. I. Smetanin, and B. V. Sobol', Thin Stress Concentrators in Elastic Bodies [in Russian], Nauka, Moscow, 1993.
3.  A. N. Guz', V. D. Kubenko, and N. A. Cherevko, Diffraction of Elastic Waves [in Russian], Naukova Dumka, Kiev, 1978.
4.  G. Ya. Popov, "Constructing the discontinuous solution of the dynamic equations of elasticity for a laminar medium with interphase defects," Doklady AN, Vol. 364, No. 6, pp. 763-769, 1999.
5.  S. M. Belotserkovskii and I. K. Lifanov, Numerical Methods in Singular Integral Equations and their Application in Aerodynamics, Elasticity, and Electrodynamics [in Russian], Nauka, Moscow, 1967.
6.  V. I. Krylov, Approximate Calculation of Integrals [in Russian], Nauka, Moscow, 1967.
Received 31 January 2002
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