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IssuesArchive of Issues2006-1pp.114-123

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A. O. Vatul'yan and A. N. Solov'ev, "On the reconstruction of plane cracks in an elastic heat-conducting solid with the interaction of crack surfaces being taken into account," Mech. Solids. 41 (1), 114-123 (2006)
Year 2006 Volume 41 Number 1 Pages 114-123
Title On the reconstruction of plane cracks in an elastic heat-conducting solid with the interaction of crack surfaces being taken into account
Author(s) A. O. Vatul'yan (Rostov-on-Don)
A. N. Solov'ev (Rostov-on-Don)
Abstract An approach to the identification of plane cracks in an elastic heat-conducting solid, based on the reconstruction of heat sources which model the impact and frictional interaction of the crack surfaces under external harmonic mechanical excitation, is presented. The steady-state temperature field established on the material boundary after maintaining the excitation for a long enough time provides the necessary input for the reconstruction procedure. With the use of the reciprocity functional, the problem of identifying the parameters of the plane on which the cracks are located is reduced to the solution of transcendental equations. The planar case is studied in more details, and results of the computational experiments are discussed.
References
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2.  T. Bannour, A. Ben Abda, and M. Jaouo, "A semi-explicit algorithm for the reconstruction of 3D planar cracks," Inverse Problems, Vol. 13, No. 4, pp. 899-917, 1997.
3.  C. J. S. Alves and T. Ha Duong, "On inverse scattering by screens," Inverse Problems, Vol. 13, No. 5, pp. 1161-1176, 1997.
4.  A. O. Vatul'yan and A. N. Solov'ev, "Determination of planar crack orientation in an elastic solid," Teoret. Prikl. Mekhanika, No. 37, pp. 141-145, 2003.
5.  A. O. Vatul'yan, "On the determination of the crack configuration in an anisotropic solid," PMM [Applied Mathematics and Mechanics], Vol. 68, No. 1, pp. 180-188, 2004.
6.  I. N. Ermolov, Yu. V. Lange, and V. G. Shcherbinskii, "Progress in ultrasonic control. Proc. of 15th Int. Conference. 1. New methods and equipment," in Control. Diagnostics [in Russian], No. 3, 2002.
7.  A. V. Kovalev, "Diagnostic tools based on the introscopy method," in Acoustic Diagnostic Systems. Special Equipment [in Russian], No. 2, 2000 (http://st.ess.ru/publications/articles/kovalev4/kovalev.htm).
8.  R. V. Goldstein and M. N. Perel'muter, Crack on the Interface Between Materials with Non-linear Interaction of Crack Surfaces. Preprint No. 619 [in Russian], In-t Problem Mekhaniki RAN , Moscow, 1998.
9.  V. M. Alexandrov and M. I. Chebakov, Analytical Methods in Contact Problems of Elasticity [in Russian], Fizmatlit, Moscow, 2004.
10.  V. V. Zozulya and A. V. Men'shikov, "On a 3D contact problem of fracture mechanics in the case of normal action of tension-compression wave," Intern. Appl. Mech., V. 38, No. 7, pp. 74-78, 2002.
11.  V. V. Zozulya and A. V. Men'shikov, "Contact of the surfaces of a planar elliptic crack subjected to an incident harmonic tension-compression wave," Teoret. Prikl. Mekhanika, No. 37, pp. 168-172, 2003.
12.  A. O. Vatul'yan and A. N. Solov'ev, "On the flaw detection in a composite solid," Defectoskopiya, Vol. 5, pp. 15-23, 2004.
13.  A. N. Solov'ev, "Identification of interfacial cracks," Modern Issues of Continuum Mechanics. Proc. 8th Int. Conference. Volume 1 [in Russian], pp. 163-169, Rostov-on-Don, 2002.
14.  A. O. Vatul'yan and A. N. Solov'ev, "Some semi-implicit algorithms for interfacial crack reconstruction," Izv. Vuzov. Sev.-Kavk. Region. Estestv. Nauki, No. 3, pp. 20-24, 2003.
15.  W. Nowacki, Dynamic Problems of Thermoelasticity [Russian translation], Mir, Moscow, 1970.
16.  A. V. Belokon', V. A. Eremeev, A. V. Nasedkin, and A. N. Solov'ev, "Block finite element schemes for dynamic problems of acoustoelectroelasticity," PMM [Applied Mathematics and Mechanics], Vol. 64, No. 3, pp. 381-393, 2000.
Received 02 August 2004
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