 | | 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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| N. N. Shavlakadze, "Contact problem of bending for a plate with a thin reinforcement," Mech. Solids. 36 (3), 122-127 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
3 |
Pages |
122-127 |
| Title |
Contact problem of bending for a plate with a thin reinforcement |
| Author(s) |
N. N. Shavlakadze (Tbilisi) |
| Abstract |
The problem of bending is considered for an infinite isotropic plate
stiffened by a thin elastic finite rib with varying bending
stiffness. The plate is loaded by a bending moment at infinity, while the
rib is not loaded. The problem is reduced to the solution of the
Prandtl integro-differential equation analyzed in [1-2] for some
cases. Singularities of the contact stresses are analyzed. The
effective solutions are constructed.
Similar problems for the cases where the stiffening is provided by ribs
(finite or infinite) or inclusions with constant stiffness have been
considered in [3-5]. In the present paper, the dependence of the behavior of
the contact stresses on the law of change of the stiffness of a rib or an
inclusion is established. |
| References |
| 1. | V. M. Alexandrov and S. M. Mkhitaryan, Contact Problems for
Solids with Thin Coatings and Interlayers [in Russian], Nauka,
Moscow, 1983. |
| 2. | V. M. Alexandrov and E. V. Kovalenko, Problems of Continuum
Mechanics with Mixed Boundary Conditions [in Russian], Nauka,
Moscow, 1986. |
| 3. | G. Ya. Popov and Yu. S. Protserov, "Bending of stiffened
plates lying on a linearly deformable base," Prikl. Mekhanika,
Vol. 15, No. 7, pp. 68-73, 1979. |
| 4. | O. V. Onishchuk, G. Ya. Popov, and Yu. S. Protserov, "On
some contact problems for stiffened plates," PMM [Applied Mathematics and
Mechanics], Vol. 48, No. 2, pp. 307-314, 1984. |
| 5. | G. Ya. Popov, Concentration of Elastic Stresses Near
Punches, Notches, Thin Inclusions, and Stiffeners [in Russian],
Nauka, Moscow, 1982. |
| 6. | M. M. Fridman, "On some problems of the theory of bending
of thin isotropic slabs," PMM [Applied Mathematics and Mechanics],
Vol. 5, No. 1, pp. 93-102, 1941. |
| 7. | O. V. Onishchuk, G. Ya. Popov, and P. G. Farshait, "On the
singularities of the contact stresses in plates with thin
inclusions subjected to bending," PMM [Applied Mathematics and Mechanics],
Vol. 50, No. 2, pp. 293-302, 1986. |
| 8. | N. I. Muskhelishvili, Some Basic Problems of
Mathematical Theory of Elasticity [in Russian], Nauka, Moscow, 1966. |
| 9. | I. M. Gel'fand and G. E. Shilov, Generalized Functions and
Operations on them [in Russian], Fizmatgiz, Moscow, 1958. |
| 10. | I. N. Vekua, "On the Prandtl integro-differential
equation," PMM [Applied Mathematics and Mechanics], Vol. 9, No. 2,
pp. 143-150, 1945. |
|
| Received |
04 February 1999 |
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