 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ĎĚĚ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| V.M. Aleksandrov and D.A. Pozharskii, "Problems of cuts in a composite elastic wedge," J. Appl. Math. Mech. 73 (1), 103-108 (2009) |
| Year |
2009 |
Volume |
73 |
Issue |
1 |
Pages |
103-108 |
| Title |
Problems of cuts in a composite elastic wedge |
| Author(s) |
V.M. Aleksandrov (Moscow)
D.A. Pozharskii (Rostov-on-Don, Russia) |
| Abstract |
Problems of strip and elliptical cuts (tensile cracks) in the middle of a three-layer elastic wedge are investigated in a three-dimensional formulation. Free or rigid clamping conditions or the stress-free condition are stipulated on the outer surfaces of the composite wedge. The problems are assumed to be symmetrical about the plane of the cut. The wedge-shaped layer containing the cut is incompressible and hinged along both faces with two other layers. The integral equations of the problems with respect to the opening of the cut are derived. Inverse operators are obtained for the operators occurring in the kernels of these equations. The relation between problems on cuts and the corresponding contact problems for a composite wedge of half the aperture angle is used. The method of paired integral equations is used for the case of a strip cut emerging from the edge of the wedge. The problems are reduced to Fredholm integral equations of the second kind in certain auxiliary functions, in terms of the values of which the normal stress intensity factors are expressed. A regular asymptotic solution is constructed for the case of an elliptic cut. |
| References |
| 1. | D.A. Pozharskii, The three-dimensional problem for an elastic wedge with a strip cut, Prikl Mat Mekh 58 (5) (1994), pp. 148–153. |
| 2. | D.A. Pozharskii, An elliptic crack in a three-dimensional elastic wedge, Izv Akad Nauk MTT 6 (1993), pp. 105–112. |
| 3. | V.M. Aleksandrov, B.I. Smetanin and B.V. Sobol’, Thin Stress Concentrators in Elastic Solids, Nauka, Moscow (1993). |
| 4. | A.F. Ulitko, The Method of Vector Eigenfunctions in Three-Dimensional Problems of the Theory of Elasticity, Naukova Dumka, Kiev (1979). |
| 5. | V.M. Aleksandrov and D.A. Pozharskii, Nonclassical Three-Dimensional Problems of the Mechanics of Contact Interactions of Elastic Bodies, Faktorial, Moscow (1998). |
| 6. | N.N. Lebedev and I.P. Skal'skaya, Paired integral equations related to the Kontorovich–Lebedev transformation, Prikl Mat Mekh 38 (6) (1974), pp. 1090–1097. |
| 7. | D.A. Pozharskii and Ye.Yu. Adamchukova, Contact problems for a three-dimensional composite wedge, Abstracts of Papers Presented at the International Conference "18th Session of the International School on Models of Continuum Mechanics", Izd SGU, Saratov (2007), pp. 87–88. |
| 8. | M. Rappoport Yu, Tables of Modified Bessel Functions K1/2+iβ(x), Nauka, Moscow (1979). |
| 9. | B.I. Smetanin and B.V. Sobol’, Stretching of an elastic half-space with cracks perpendicular to its surface, Prikl Mat Mekh 45 (5) (1981), pp. 940–943. |
| 10. | V.V. Panasyuk, Limiting Equilibrium of Brittle Bodies with Cracks, Michigan Information Service, Detroit (1971). |
|
| Received |
11 March 2008 |
| Link to Fulltext |
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