 | | 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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| F. V. Loveikin and A. F. Ulitko, "Stress distribution in an elastic space weakened by two wedge-shaped cuts lying in one plane," Mech. Solids. 39 (1), 28-35 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
1 |
Pages |
28-35 |
| Title |
Stress distribution in an elastic space weakened by two wedge-shaped cuts lying in one plane |
| Author(s) |
F. V. Loveikin (Kiev)
A. F. Ulitko (Kiev) |
| Abstract |
The problem of equilibrium is considered for an elastic space with two
wedge-shaped cuts issuing from the same vertex, lying on the same plane, and
having a common bisectrix. Stress distribution near the cuts is studied on the
basis of homogeneous solutions of the corresponding problem. These solutions
are constructed in the spherical coordinates with the help of
transformations of Meler-Fock type [1, 2]. The analysis of these
homogeneous solutions allows us to describe the behavior of stresses near
the common vertex of the cuts. It is shown that the stresses at the vertex
have a local power-law singularity. We examine the dependence of the
exponent of this singularity on the angle of the cuts. Special attention is
given to the case of the classical root singularity at the vertex.
Previously [3-5], equilibrium problems were solved for an elastic space
with a single wedge-shaped cut
and with two cuts - one along a half-plane and the other wedge-shaped.
These problems are special cases of the
problem considered here. |
| References |
| 1. | N. N. Lebedev and I. P. Skal'skaya,
"Integral expansions related to the Meler-Fock transformations,"
Diff. Uravnenia, Vol. 22, No. 9, pp. 1515-1523, 1986. |
| 2. | D. N. Parfenenko and F. A. Ulitko,
"On a new integral transformation and its application in contact problems
of elasticity," Doklady AN UkrSSR, Ser. A, No. 11, pp. 53-58, 1988. |
| 3. | D. N. Parfenenko, "On singularities of the stress field in an
elastic material with a plane wedge-shaped cut," in Mathematical Modelling
of Dynamic Processes in Systems of Bodies with Fluids [in Russian],
pp. 72-76, Izd-vo In-ta Matem. AN UkrSSR, Kiev, 1988. |
| 4. | F. A. Ulitko and A. V. Loveikin, "Equilibrium of an elastic space
weakened by two wedge-shaped cuts," in Mechanics of Fracture of Materials
and Structures [in Ukranian], Vol. 2, No. 2, pp. 229-233, Kamenyar,
Lviv, 1999. |
| 5. | F. A. Ulitko and A. V. Loveikin, "Equilibrium problem for a space
with two cuts- along a plane and wedge-shaped- that lie in one
plane," Matem. Metodi ta Fiziko-mekhanichni Polya, Vol. 43,
pp. 109-114, 2001. |
| 6. | A. F. Ulitko, The Method of Vector-Valued Eigenfunctions in
Spatial Problems of Elasticity [in Russian], Naukova Dumka, Kiev, 1979. |
| 7. | N. N. Lebedev, Special Functions and Their Applications [in Russian],
Fizmatgiz, Moscow, Leningrad, 1963. |
| 8. | H. Bateman and A. Erdélyi, Higher Transcendental Functions.
Volume 1, McGraw-Hill Book Co., New York, 1953. |
| 9. | B. Noble, Methods Based on the Wiener-Hopf Technique for the
Solution of Partial Differential Equations, Pergamon Press, London, 1958. |
|
| Received |
17 May 2001 |
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