 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| V. M. Alexandrov, D. A. Pozharskii, and V. V. Trepachev, "Contact problem for a conical valve," Mech. Solids. 41 (3), 69-74 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
3 |
Pages |
69-74 |
| Title |
Contact problem for a conical valve |
| Author(s) |
V. M. Alexandrov (Moscow)
D. A. Pozharskii (Moscow)
V. V. Trepachev (Moscow) |
| Abstract |
An integral equation of a three-dimensional contact problem for an
elastic conical valve in a conical cavity in an
elastic medium is obtained. The equation is solved by the regular and
singular asymptotic methods based on the introduction of a
non-dimensional parameter characterizing the relative distance between
the contact area and the vertex of the conical cavity. The asymptotic relations
obtained are valid in the entire range of this parameter. The solution of
the three-dimensional equilibrium problem for a circular cone is
based on the expansion of vector functions in terms of the
complete system of vector harmonics on the cone surface using the
Mellin integral transform and Fourier series [1].
Asymptotic methods [2, 3] have been applied earlier [4] to the solution of a
contact problem for a rigid ring band on an elastic cone. A three-dimensional
contact problem for a cone with unknown contact area was considered in [5] and
involved nonlinear boundary equations. The singularities of contact pressures
at the cone vertex were studied for the cases where this point is contacted by
the edges of several wedge-shaped punches [6] or a single wedge-shaped
punch [7]. |
| References |
| 1. | V. T. Grinchenko and A. F. Ulitko, Equilibrium of Elastic Solids of
Canonical Shape [in Russian], Naukova Dumka, Kiev, 1985. |
| 2. | V. M. Alexandrov and E. V. Kovalenko, Problems of Mechanics of
Continuous Media With Mixed Boundary Conditions [in Russian], Nauka,
Moscow, 1986. |
| 3. | V. M. Alexandrov and D. A. Pozharskii, Nonclassical Three-dimensional
Problems of Mechanics of Contact Interactions of Elastic Solids [in Russian],
Faktorial, Moscow, 1998. |
| 4. | D. A. Pozharskii, "On the spatial contact problem for an elastic cone,"
Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 51-60, 1997. |
| 5. | V. M. Alexandrov and D. A. Pozharskii, "On the 3D contact problem
for an elastic cone with unknown contact area,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 36-41, 1998. |
| 6. | D. A. Pozharskii,
"On singularities of contact pressures in the problem
of a periodic system of wedge-shaped punches on a cone,"
Dokl. RAN, Vol. 361, pp. 54-57, 1998. |
| 7. | D. A. Pozharskii and M. I. Chebakov,
"On the singularities of contact stresses in the problem of a
wedge-shaped punch on an elastic cone,"
Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 72-77, 1998. |
| 8. | I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums,
Series, and Products [in Russian], Nauka, Moscow, 1971. |
| 9. | M. I. Zhurina and L. M. Karmazina, Tables and Formulas for Spherical
Functions Pm−1/2+ir(z) [in Russian], Izd-vo VTs AN SSSR, Moscow,
1962. |
| 10. | P. S. Theocaris and E. E. Gdoutos, "Stress singilarities at vertices of
composite plates with smooth or rough interfaces," Arch. Mech.,
Vol. 28, No. 4, pp. 693-704, 1976. |
|
| Received |
21 April 2004 |
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