 | | 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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| I. V. Kirillova and L. Yu. Kossovich, "Hyperbolic boundary layers in compound cylindrical shells," Mech. Solids. 44 (3), 409-420 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
3 |
Pages |
409-420 |
| DOI |
10.3103/S0025654409030108 |
| Title |
Hyperbolic boundary layers in compound cylindrical shells |
| Author(s) |
I. V. Kirillova (Chernyshevskii Saratov State University, Astrakhanskaya 83, Saratov, 410012 Russia, ivkirillova@yandex.ru)
L. Yu. Kossovich (Chernyshevskii Saratov State University, Astrakhanskaya 83, Saratov, 410012 Russia, rector@sgu.ru) |
| Abstract |
A survey of papers dealing with the mathematical modeling of
transient wave propagation in compound and stiffened shell
constructions by asymptotic methods based on exact three-dimensional elasticity equations can be found in [1]. Longitudinal actions of tangential and bending types are
considered. An asymptotic model of wave propagation in a
semi-infinite shell of rotation is used, which employs the
two-dimensional Kirchhoff-Love (tangential and flexural)
components, the solutions of the quasiplane problem of elasticity, the parabolic boundary layer near the quasifront, and the hyperbolic boundary layer near the expansion wave front. The boundary value contact problems for the incident, reflected, and transmitted waves are posed and solved on the basis of approximate theories for the corresponding components. If the boundary conditions are satisfied at the shell faces in the exact three-dimensional form in small neighborhoods of the shell end contact region, then the construction of the quasistatic boundary layer satisfying the boundary conditions together with the two-dimensional component is completed. Methods proposed for solving boundary value problems by using integral transforms and asymptotic approaches to their inversion are described. But the methods developed for constructing hyperbolic boundary layers near the wave fronts are not described in [1].
The present paper supplements the materials presented in [1] with the description of hyperbolic boundary layers for all types of shell face actions including the case of NW-type forces, which have not yet been described. |
| References |
| 1. | L.Yu. Kossovich,
"Asymptotic Analysis of Nonstationary SSS of Compound and Stiffened Shells under Impact Boundary Actions,"
in Mixed Problems of Mechanics of Solid.
Proceedings of V Russian Conf. with Intern. Participation,
Ed. by Acad. N.F. Morozov (Izd. Saratov Univ., Saratov, 2005),
pp. 199-210 [in Russian]. |
| 2. | U. Nigul,
"Regions of Effective Applications of the Methods of Three-Dimensional and Two-Dimensional Analysis of Transient Stress Waves in Shells and Plates,"
Int. J. Solids Struct. 5 (6), 607-627 (1969). |
| 3. | L.Yu. Kossovich,
Nonstationary Problems of Theory of Elastic Thin Shells
(Izd-vo Saratov Univ., Saratov, 1986) [in Russian]. |
| 4. | J.D. Kaplunov, L.Yu. Kossovich, and E.V. Nolde,
Dynamics of Thin Walled Elastic Bodies (Acad. Press, London, 1988). |
| 5. | L.Yu. Kossovich and Yu.D. Kaplunov,
"Asymptotic Analysis of Nonstationary Elastic Waves in Thin Shells of Rotation under Impact Boundary Actions,"
Izv. Saratov Univ. 1 (2), 111-131 (2001). |
| 6. | I.V. Kirillova,
"Domains of Compatibility of Dynamical Boundary Layer
and Short-Wave High-Frequency Approximation,"
in Mathematical Modeling and Control in Technical Systems,
No. 2 (Izd-vo Saratov Univ., Saratov, 1998),
pp. 3-11 [in Russian]. |
| 7. | I.V. Kirillova,
"Applicability Regions of Wave Front Boundary Layers in Shells of Revolution of Zero Gaussian Curvature,"
Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 117-125 (2003)
[Mech. Solids (Engl. Transl.) 38 (6), 95-101 (2003)]. |
| 8. | V.V. Novozhilov and L.I. Slepian,
"On Saint-Venant's Principle in the Dynamics of Beams,"
Prikl. Mat. Mekh. 29 (2), 261-281 (1965)
[J. Appl. Math. Mech. (Engl. Transl.) 29 (2), 293-315 (1965)]. |
| 9. | L.I. Slepyan,
Unsteady Elastic Waves
(Sudostroenie, Leningrad, 1972) [in Russian]. |
| 10. | A.Yu. Kopnin, L.Yu. Kossovich, and S.A. Petrokovskii,
"Nonstationary Bending Wave Processes in Stiffened Shells of Revolution Subjected to an Impact at the Edge,"
Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 127-138 (1996)
[Mech. Solids (Engl. Transl.) 31 (6), 107-116 (1996)]. |
| 11. | A.Yu. Kopnin and L.Yu. Kossovich,
"Study of Nonstationary SSS of Stiffened Shells of Rotation under Impact Longitudinal Actions of Tangential Type,"
in Mechanics of Deformable Media, No. 12
(Izd. Saratov Univ., Saratov, 1995), pp. 9-29 [in Russian]. |
| 12. | L.Yu. Kossovich and A.N. Kushekkaliev,
"Analysis of Approximations in the Lamb Problem for an Infinite Elastic Layer,"
Izv. Vyssh. Uchebn. Zaved. Sev.-Kavkaz. Region. Estestv. Nauki, No. 9, 10-22 (2003). |
| 13. | L.Yu. Kossovich and A.N. Kushekkaliev,
"Rayleigh Field in Infinite Elastic Layer,"
in Mathematics. Mechanics
(Izd-vo Saratov Univ., Saratov, 2003),
No. 5, pp. 159-161 [in Russian]. |
| 14. | A.N. Kushekkaliev,
"Solution of Wave Propagation Problem in Transversal-Isotropic Cylindrical Shell under Normal Actions,"
in Mechanics of Deformable Media, No. 14,
(Izd-vo Saratov Univ., Saratov, 2002), pp. 106-115 [in Russian]. |
| 15. | I.V. Kirillova and L.Yu. Kossovich,
"Boundary Layers in Shells of Revolution with Discontinuity in the Thickness,"
in Proc. ICOVP-2001 (Moscow, 2001), pp. 263-266. |
| 16. | E. Kamke,
Handbook on Ordinary Differential Equations
(Fizmatgiz, Moscow, 1961) [in Russian]. |
|
| Received |
13 December 2006 |
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