 | | 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
|
| In English (Mech. Solids): | | 4810 |
|
| << Previous article | Volume 44, Issue 4 / 2009 | Next article >> |
| 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 |
| 1. | E. S. Folias,
"On 3-Dimensional Theory of Cracked Plates,"
Trans. ASME Ser. E. J. Appl. Mech.
42 (3), 663-674 (1975). |
| 2. | J. P. Bentem,
"State of Stress at the Vertex of a Quarter-Infinite Crack in a Half-Space,"
Int. J. Solids Struct.
13 (5), 479-492 (1977). |
| 3. | J. P. Bentem,
"The Quarter-Infinite Crack in a Half-Space:
Alternative and Additional Solutions,"
Int. J. Solids Struct.
16 (2), 119-130 (1980). |
| 4. | Z. P. Bažant and L. F. Estenssoro,
"Surface Singularity and Crack Propagation,"
Int. J. Solids Struct.
15 (4), 405-426 (1979). |
| 5. | F. Ghahremani and C. F. Shih,
"Corner Singularities of 3-Dimensional Planar Interface Crack,"
Trans. ASME. Ser. E. J. Appl. Mech.
59 (1), 61-68 (1992). |
| 6. | E. V. Glushkov, N. V. Glushkova, and O. N. Lapina,
"Singularity Exponents of Elastic Stresses at the Point where the Crack Reaches the Surface,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 146-153 (1998)
[Mech. Solids (Engl. Transl.)
33 (5), 117-122 (1998)]. |
| 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,
"Stress Singularities in Classical Elasticity - II: Asymptotic Identification,"
Appl. Mech. Rev.
57 (5), 385-439 (2004). |
| 9. | Ya. S. Ufland,
Integral Transforms in Elasticity Problems
(Nauka, Leningrad, 1967)
[in Russian]. |
| 10. | N. N. Lebedev,
Special Functions and Their Applications
(Fizmatgiz, Moscow, 1963)
[in Russian]. |
| 11. | D. M. Parfenenko and A. F. Ulitko,
"On a New Integral Transform and Its Use in Contact Problems of Elasticity,"
Dokl. Akad. Nauk Ukrain. SSR. Ser. A,
No. 11, 53-58 (1988). |
| 12. | H. Batemen and A. Erde'lyi,
Higher Transcendental Functions, Vol. 1
(McGrow-Hill, New York etc., 1953). |
| 13. | V. F. Fedoryuk,
Asymptotics: Integrals and Series
(Nauka, Moscow, 1987)
[in Russian]. |
| 14. | B. Noble,
Methods Based on the Wiener-Hopf Technique
for the Solution of Partial Differential Equations
(Pergamon Press, London etc., 1958; Izd-vo Inostr. Lit., Moscow, 1962). |
|
| Received |
19 December 2006 |
| Link to Fulltext |
|
| << Previous article | Volume 44, Issue 4 / 2009 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English