 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| I.Ya. Zhbadinskii, "Interaction of One-Periodic Disk-Shaped Cracks under an Incident Elastic Harmonic Wave," Mech. Solids. 51 (1), 127-134 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
1 |
Pages |
127-134 |
| DOI |
10.3103/S002565441601012X |
| Title |
Interaction of One-Periodic Disk-Shaped Cracks under an Incident Elastic Harmonic Wave |
| Author(s) |
I.Ya. Zhbadinskii (Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, ul. Naukova 3b, Lvov, 79060 Ukraine, zhbadynskyi.igor@gmail.com) |
| Abstract |
We study a symmetric problem of harmonic wave propagation in an elastic space with a one-periodic array of interacting disk-shaped cracks. Using the Green function obtained by the Fourier transform, we reduce the problem to a boundary integral equation (BIE) for the function characterizing the displacement discontinuity on one of the cracks and numerically determine the desired function by solving the BIE. We present graphs of the dynamic stress intensity factors near a circular crack versus the wave number for various distances between the defects. |
| Keywords |
elastic space, periodic arrays of disk-shaped cracks, periodic Green function, harmonic elastic wave, dynamic stress intensity factors, boundary integral equation method |
| References |
| 1. | R. V. Goldstein and N. M. Osipenko,
"On a Model of Structured Medium Fracture under Compression Conditions,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 86-97 (2010)
[Mech. Solids (Engl. Transl.)
45 (6), 835-843 (2010)]. |
| 2. | I. P. Laushnik and M. V. Khai,
"Three-Dimensional Problem of Thermoelasticity for a Body
with a Periodic System of Disk-Shaped Cracks,"
Prikl. Mekh.
16 (4), 29-34 (1980). |
| 3. | V. Buryachenko,
Micromechanics of Heterogeneous Materials
(Springer, New York, 2006). |
| 4. | L. I. Manevich, I. V. Andrianov, V. G. Oshmyan,
Mechanics of Periodically Heterogeneous Structures
(Springer, Berlin-Heidelberg, 2002). |
| 5. | Ch. Zhang and D. Gross,
On Wave Propagation in Elastic Solids with Cracks
(Computational Mechanics Publ., Southampton, 1998). |
| 6. | Y. Murai,
"Scattering Attenuation, Dispersion and Reflection of SH Waves in Two-Dimensional Elastic Media
with Densely Distributed Cracks,"
Geophys. J. Int.
168 (1), 211-223 (2007). |
| 7. | Y. Bao and X. Wang,
"Identification of Multiple Cracks Based on Optimization Methods
Using Harmonic Elastic Waves,"
Int. J. Fract.
172, 77-95 (2011). |
| 8. | E. Scarpetta,
"In-Plane Problem for Wave Propagation through Elastic Solids with a Periodic Array of Cracks,"
Acta Mech.
154 (4), 179-187 (2002). |
| 9. | E. Scarpetta and V. Tibulio,
"P-Wave Propagation through Elastic Solids with a Doubly Periodic Array of Cracks,"
Quart. J. Mech. Appl. Math.
58 (4), 535-550 (2005). |
| 10. | Y. Otani and N. Nishimura,
"An FMM for Periodic Boundary Value Problems for Cracks for Helmholtz' Equation in 2D,"
Int. J. Numer. Meth. Engng
73, 381-406 (2007). |
| 11. | Y. Pennec, J. O. Vasseur, B. D. Rouhani, et al.,
"Two-Dimensional Phononic Crystals: Examples and Applications,"
Surf. Sci. Rep.
65 (8), 229-291 (2010). |
| 12. | Zh. Yan and Ch. Zhang,
"Wave Localization in Two-Dimensional Porous Phononic Crystals
with One-Dimensional Aperiodicity,"
Ultrasonics
52 (5), 598-604 (2012). |
| 13. | F.-L. Li, Y.-S. Wang, Ch. Zhang, and G.-L. Yu,
"Boundary Element Method for Band Gap Calculation of Two-Dimensional Solid Phononic Crysrals,"
Engng Anal. Bound. Elem.
37, 225-235 (2013). |
| 14. | E. I. Shifrin,
Spatial Problems of Linear Fracture Mechanics
(Fizmatlit, Moscow, 2002)
[in Russian]. |
| 15. | V. V. Mykhas'kiv, Ch. Zhang, J. Sladek, and V. Sladek,
"A Frequency Domain BEM for 3-D Non-Synchronous Crack Interaction Analysis in Elastic Solids,"
Engng Anal. Bound. Elem.
30 (3), 167-175 (2006). |
| 16. | V. V. Mykhas'kiv, I. Zhbadynskyi, and Ch. Zhang,
"Elastodynamic Analysis of Multiple Crack Problem in 3-D Bi-Materials by a BEM,"
Int. J. Numer. Mech. Biomed. Engng
26 (12), 1934-1946 (2010). |
| 17. | V. T. Grinchenko and V. V. Meleshko,
Harmonic Vibrations and Waves in Elastic Bodies
(Naukova Dumka, Kiev, 1981)
[in Russian]. |
| 18. | H. S. Kit, M. V. Khaj, and V. V. Mykhas'kiv,
"Analysis of Dynamic Stress Concentration in an Infinite Body with
Parallel Penny-Shaped Cracks by BIEM,"
Engng Fract. Mech.
55 (2), 191-207 (1996). |
| 19. | I. S. Gradshtein and I. M. Ryzhik,
Tables of Integrals, Sums, Series, and Products
(Fizmatgiz, Moscow, 1971)
[in Russian]. |
|
| Received |
17 August 2013 |
| Link to Fulltext |
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