 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| A.V. Kaptsov, E.I. Shifrin, and P.S. Shushpannikov, "Identification of Parameters of a Plane Elliptic Crack in an Isotropic Linearly Elastic Body from the Results of a Single Uniaxial Tension Test," Mech. Solids. 47 (4), 433-447 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
4 |
Pages |
433-447 |
| DOI |
10.3103/S0025654412040085 |
| Title |
Identification of Parameters of a Plane Elliptic Crack in an Isotropic Linearly Elastic Body from the Results of a Single Uniaxial Tension Test |
| Author(s) |
A.V. Kaptsov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, kaptsov@ipmnet.ru)
E.I. Shifrin (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, shifrin@ipmnet.ru)
P.S. Shushpannikov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, shushpan@ipmnet.ru) |
| Abstract |
The method earlier developed by one of the authors for identifying
ellipsoidal defects is numerically tested for the applicability to
the problem of identification of a degenerate ellipsoidal defect,
i.e., an elliptic crack. The method is based on the reciprocity
functional and the assumption that the displacements are measured
in a uniaxial tension test of an isotropic linearly elastic body.
Calculations show that the earlier developed method is also efficient for identification of an elliptic crack and its parameters (the center coordinates, the normal to the crack plane, and the directions and lengths of the semiaxes) can be determined with high accuracy. Some examples where the crack has a non-elliptic shape are also considered. It is discovered that, in many cases, the ellipsoids that were constructed by formulas reconstructing the ellipsoidal crack from the data on the external boundary of the body that correspond to a nonelliptic crack, approximate the actual defect with sufficient accuracy. The method stability was investigated with respect to noise in the initial data. |
| Keywords |
linear elasticity, inverse problem, reciprocity principle, elliptic crack |
| References |
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| 10. | E. I. Shifrin,
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| 11. | E. I. Shifrin and P. S. Shushpannikov,
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48 (7-8), 1154-1163 (2011). |
| 12. | A. Morassi and E. Rosset,
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| 15. | V. Ph. Zhuravlev,
Fundamentals of Theoretical Mechanics
(Fizmatlit, Moscow, 2001)
[in Russian]. |
|
| Received |
09 February 2011 |
| Link to Fulltext |
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