 | | 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. O. Vatul'yan and V. V. Krasnikov, "Vibrations of an orthotropic half-plane with a curvilinear crack," Mech. Solids. 37 (5), 68-74 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
5 |
Pages |
68-74 |
| Title |
Vibrations of an orthotropic half-plane with a curvilinear crack |
| Author(s) |
A. O. Vatul'yan (Rostov-on-Don)
V. V. Krasnikov (Rostov-on-Don) |
| Abstract |
An effective approach is developed for solving the problem of
steady-state vibrations of an orthotropic half-plane with a curvilinear crack.
A system of boundary integral equations is constructed for this problem.
Discretization of these equations is performed on the basis of
the method of boundary elements. The dependence of
stress intensity factors on vibration frequencies is described for cracks with
various types of geometrical structure, and the results obtained for
isotropic and anisotropic materials are compared.
Stress distribution in elastic media with cracks and operational integrity of
such structures in complex dynamical situations form the subject matter of
numerous publications. A review of the relevant methods and an extensive
bibliography which, apparently, is most complete for today can be found
in [1, 2]. In spite of the variety of approaches to the analysis of
vibrations of bodies with cracks, most of them can be effectively applied
to elasticity problems for bodies with simple geometry (the crack is
assumed rectilinear and is either parallel or orthogonal to the canonical
boundary of the domain), and the efficiency of these approaches is limited
with regard to wave processes in bodies with near-surface defects of
non-canonical structure (curvilinear and branching cracks). The most
efficient method for solving problems of the latter type is the method of
boundary integral equations and the related method of boundary elements. |
| References |
| 1. | V. Z. Parton and V. G. Boriskovskii,
Dynamic Fracture Mechanics [in Russian], Mashinostroenie, Moscow, 1985. |
| 2. | S. Murakami (Editor), Stress Intensity Factors Handbook [Russian translation],
Volume 1, p. 448; Volume2, pp. 449-1013, Mir, Moscow, 1990. |
| 3. | I. I. Vorovich and V. A. Babeshko,
Mixed Dynamical Problems of Elasticity in Nonclassical Domains [in Russian],
Nauka, Moscow, 1979. |
| 4. | A. O. Vatul'yan, I. A. Guseva, and I. M. Syunyakova,
"On fundamental solutions for orthotropic media and their applications,"
Izv. SKNTs. Ser. Estestv. Nauki, No. 2, pp. 81-85, 1989. |
| 5. | V. S. Budaev,
"On a class of solutions of a system of second-order partial differential
equations in the dynamics of anisotropic elastic media,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 5, pp. 127-135, 1976. |
| 6. | L. D. Landau and E. M. Lifshits,
Theoretical Physics. Volume 7. Theory of Elasticity [in Russian],
Nauka, Moscow, 1987. |
| 7. | W. Nowacki, Theory of Elasticity [Russian translation], Mir, Moscow, 1975. |
| 8. | S. M. Belotserkovskii and I. K. Lifanov,
Numerical Methods in the Theory of Singular Integral Equations and
Their Applications to Aerodynamics, Elasticity, and Electrodynamics [in Russian],
Nauka, Moscow, 1985. |
| 9. | P. Banerjee and R. Butterfield,
Boundary-Element Methods in Engineering Science [Russian translation], Mir, Moscow, 1984. |
| 10. | K. Brebbia, G. Telles, and L. Vrowbel,
Boundary-Element Methods [Russian translation], Mir, Moscow, 1987. |
|
| Received |
17 April 2000 |
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