 | | 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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| V. M. Alexandrov, "Longitudinal crack in an orthotropic elastic strip with free faces," Mech. Solids. 41 (1), 88-94 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
1 |
Pages |
88-94 |
| Title |
Longitudinal crack in an orthotropic elastic strip with free faces |
| Author(s) |
V. M. Alexandrov (Moscow) |
| Abstract |
The problem of plane deformation of a strip with a longitudinal crack the
surfaces of which are loaded by uniform pressure is considered. The crack is
assumed to be arranged symmetrically with respect to the stress-free faces of
the strip. By means of the integral Fourier transform this problem is reduced
to an integral equation of the first kind with singular kernel for the
derivative of the function that describes the crack opening. Regular and
singular asymptotic methods are used to construct solutions of this integral
equation for large and small values of the dimensionless parameter
characterizing the strip thickness, respectively. A numerical example is given.
A similar problem for a crack in an isotropic plane has been previously
considered in [1, 2]. |
| References |
| 1. | V. M. Alexandrov and B. I. Smetanin, "On equilibrum longitudinal
cracks in plates," in Proceedings of the 6th All-Union Conference on the Theory
of Plates and Shells [in Russian], pp. 20-24, Nauka, Moscow, 1966. |
| 2. | B. I. Smetanin, "Some problems of slots in an elastic wedge and
layer," Inzh. Zh. MTT [Mechanics of Solids], No. 2, pp. 115-122, 1968. |
| 3. | S. G. Lekhnitskii, Theory of Elasicity of an Anisotropic Body [in
Russian], Nauka, Moscow, 1977. |
| 4. | I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko, Nonclassical
Mixed Problems of Elasticity [in Russian], Nauka, Moscow, 1974. |
| 5. | V. M. Alexandrov, B. I. Smetanin, and B. V. Sobol', Thin Stress
Concentrators in Elastic Bodies [in Russian], Nauka, Moscow, 1993. |
| 6. | G. Ya. Popov, Concentration of Elastic Stresses near Punches, Slots,
Inclusions, and Stiffening Elements [in Russian], Nauka, Moscow, 1982. |
| 7. | V. B. Zelentsov, "On the solution of some integral equations of mixed
problems in the theory of plate bending," PMM [Applied Mathematics and
Mechanics], Vol. 48, No. 6, pp. 983-991, 1984. |
| 8. | S. Bochner, Lectures on Fourier Integrals, Univ. Press, Princeton,
1959. |
| 9. | Yu. A. Brychkov and A. P. Prudnikov, Intergral Transforms of
Generalized Functions [in Russian], Nauka, Moscow, 1977. |
| 10. | B. Noble, Methods Based on the Wiener-Hopf Technique for the Solution
of Partial Differential Equations, Pergamon Press, London, 1958. |
| 11. | V. A. Ditkin and A. P. Prudnikov, A Handbook on the Operational
Calculus [in Russian], Vysshaya Shkola, Moscow, 1965. |
| 12. | N. F. Morozov, Mathematical Issues of the Theory of Cracks [in
Russian], Nauka, Moscow, 1984. |
|
| Received |
21 May 2004 |
| << Previous article | Volume 41, Issue 1 / 2006 | Next article >> |
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