 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 51, Issue 5 / 2016 | Next article >> |
| E.I. Shifrin, "Factorization Method in the Geometric Inverse Problem of Static Elasticity," Mech. Solids. 51 (5), 562-570 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
5 |
Pages |
562-570 |
| DOI |
10.3103/S0025654416050083 |
| Title |
Factorization Method in the Geometric Inverse Problem of Static Elasticity |
| Author(s) |
E.I. Shifrin (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, shifrin@ipmnet.ru) |
| Abstract |
The factorization method, which has previously been used to solve inverse scattering problems, is generalized to geometric inverse problems of static elasticity. We prove that finitely many defects (cavities, cracks, and inclusions) in an isotropic linearly elastic body can be determined uniquely if the operator that takes the forces applied to the body outer boundary to the outer boundary displacements due to these forces is known. |
| Keywords |
geometric inverse problems, factorization method, linear elasticity, static problem |
| References |
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Inv. Probl.
16 (4), 1029-1042 (2000). |
| 6. | I. N. Grinberg,
"Obstacle Visualization via the Factorization Method for the Mixed Boundary Value Problem,"
Inv. Probl.
18 (6), 1687-1704 (2002). |
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"Linear Sampling Methods for 2D Inverse Elastic Wave Scattering,"
Inv. Probl.
17 (5), 1445-1464 (2001). |
| 9. | C. J. S. Alves and R. Kress,
"On the Far-Field Operator in Elastic Obstacle Scattering,"
IMA J. Math.
67 (1), 1-21 (2002). |
| 10. | A. Charalambopoulos, A. Kirsch, K. A. Anagnostopoulos, et al.,
"The Factorization Method in Inverse Elastic Scattering from Penetrable Bodies,"
Inv. Probl.
23 (1), 27-51 (2007). |
| 11. | R. Potthast,
"A Survey on Sampling and Probe Methods for Inverse Problems,"
Inv. Probl.
22 (2), R1-R47 (2006). |
| 12. | A. Kirsch,
"The Factorization Method for a Class of Inverse Elastic Problems,"
Mathematische Nachrichten
278 (3), 258-277 (2005). |
|
| Received |
21 April 2016 |
| Link to Fulltext |
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