On the Cauchy Problem in the Theory of Coefficient Inverse Problems for Elastic Bodies

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Home Editorial board Publication ethics Peer review guidelines Current Archive Rules for authors Send an article Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2016.2.5916 On the Cauchy Problem in the Theory of Coefficient Inverse Problems for Elastic Bodies Vatulyan A. O. , Gukasyan L. S. , Nedin R. D. Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 2. Abstract: The inverse problems on the identification of inhomogeneous material properties of an elastic plate is considered. The condition of uniqueness of the inverse problems statements are analyzed. Direct problem on finding displacements to formulate the additional input data of the inverse problem is investigated; the accuracy of the direct problem solution is estimated by means of comparison with finite-element computation. A scheme of the inverse problem solving is proposed based on the application of the weak statement of the initial boundary problem and the projection method. A series of computation experiments on a reconstruction of various types of inhomogeneity laws of the Lame' coefficients is performed. Keywords: coefficient inverse problem, the Lame' coefficients, weak statement, projection method, finite element method, biharmonic polynomials. Language: Russian Download the full text For citation: Vatulyan A. O., Gukasyan L. S., Nedin R. D. On the Cauchy problem in the theory of coefficient inverse problems for elastic bodies // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 2, pp. 31-40. DOI 10.23671/VNC.2016.2.5916 + References 1. Vatulyan A. O. Obratnye zadachi v mehanike deformiruemogo tverdogo tela [Inverse Problems in Mechanics of Deformable Solids]. Moscow: Physmatlit, 2007. 233 p. [Russian]. 2. Vatulyan A. O. On the Theory of Inverse Problems in Linear Mechanics of Deformable Body, Prikladnaja matematika i mehanika [J. Appl. Math. Mech.], 2010, vol. 74, no. 6, p. 909-916 [Russian]. 3. Bonnet M., Constantinescu A. Inverse problems in elasticity. Inverse Probl., 2005, no. 21, pp. 1-50. 4. Bocharova O.V., Vatulyan A.O. On a Reconstruction of Density and Young Modulus for an Inhomogeneous Rod. Akusticheskij zhurnal [Acoust. J.], 2009, vol. 55, no. 3, pp. 275-282 [Russian]. 5. Sanches-Palencia E. Neodnorodnye sredy i teorija kolebanij [Inhomogeneous Media and Vibration Theory]. Moscow: Mir, 1984. 472p. [Russian]. 6. Tikhonov A.N., Arsenin V.Ya. Metody reshenija nekorrektnyh zadach [Methods of Solving Ill-Posed Problems]. Moscow: Nauka, 1986. 287p. [Russian]. 7. Philippov A.P. Kolebanija deformiruemyh system [Vibration of Deformable Systems]. Moscow: Mashinostroyenie, 1970. 736 p. [Russian]. 8. Gunter H.M. Integrirovanie uravnenij pervogo porjadka v chastnyh proizvodnyh [Integrating of First Order Equations in Partial Derivatives]. Leningrad: Gostekhizdat, 1934. 359 p. [Russian]. 9. Dudarev V.V., Nedin R.D., Vatulyan A.O. Nondestructive dentification of inhomogeneous residual stress state in deformable bodies on the basis of the acoustic sounding method, Advanced Materials Research, 2014, vol. 996, pp. 409-414. 10. Nedin R.D., Vatulyan A.O. Inverse Problem of Non-homogeneous Residual Stress Identification in Thin Plates. Int. J. Solids Struct, 2013, no. 50, pp. 2107-2114. 11. Vatulyan A.O., Gukasyan L.S. On the Cauchy Problem for an Equation of the First Order and its Applications in the Theory of Inverse Problems. Bulletin of DGTU. Rostov-on-Don, 2012, vol. 7, no. 68, pp. 11-20. ← Contents of issue


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