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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
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