 | | 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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| A. V. Loveikin and A. F. Ulitko, "On the Stress Field Singularity in an Incompressible Half-Space Weakened by Two Near-Surface Wedge-Like Cracks," Mech. Solids. 44 (4), 585-595 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
4 |
Pages |
585-595 |
| DOI |
10.3103/S0025654409040098 |
| Title |
On the Stress Field Singularity in an Incompressible Half-Space Weakened by Two Near-Surface Wedge-Like Cracks |
| Author(s) |
A. V. Loveikin (National Taras Shevchenko Kyiv University, Vladimirskaya 60, Kiev, 01033 Ukraine, alov@univ.kiev.ua)
A. F. Ulitko (National Taras Shevchenko Kyiv University, Vladimirskaya 60, Kiev, 01033 Ukraine, igor_ulitko@infomania.com.ua) |
| Abstract |
We consider the equilibrium problem for an elastic incompressible half-space weakened by two near-surface wedge-like cracks, whose lie in the same plane perpendicular to the half-space surface and have a common vertex. We use the Papkovich-Neuber representation to reduce the problem to finding two harmonic functions satisfying the mixed boundary conditions. These functions are constructed in spherical coordinates by using a Mehler-Fock type integral representation in Legendre functions. The analytic solution thus obtained permits finding the character of the stress distribution near the common tip of the cracks. |
| Keywords |
crack, Papkovich-Neuber representation, integral transform |
| References |
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[Mech. Solids (Engl. Transl.)
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| 7. | A. V. Loveikin and A. F. Ulitko,
"Stress-Strain State Analysis for an Incompressible Half-Space with a Near-Surface Wedge-Shaped Crack,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 136-148 (2006)
[Mech. Solids (Engl. Transl.)
31 (1), 104-113 (2006)]. |
| 8. | G. B. Sinclair,
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[in Russian]. |
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| 11. | D. M. Parfenenko and A. F. Ulitko,
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No. 11, 53-58 (1988). |
| 12. | H. Batemen and A. Erde'lyi,
Higher Transcendental Functions, Vol. 1
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| 14. | B. Noble,
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|
| Received |
19 December 2006 |
| Link to Fulltext |
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