 | | 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: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| N. N. Shavlakadze, "Bending of an anisotropic elastic plate with an elastic inclusion," Mech. Solids. 38 (6), 83-87 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
6 |
Pages |
83-87 |
| Title |
Bending of an anisotropic elastic plate with an elastic inclusion |
| Author(s) |
N. N. Shavlakadze (Tbilisi) |
| Abstract |
Problems of contact interaction of isotropic elastic plates with thin elastic elements, such as stringers or inclusions, have been considered in detail in the monographs [1, 2], which also contain the relevant bibliography. Contact tangential stresses on the edges of a patch of constant or elliptically varying cross-sectional areas have a singularity of square root type [3]. For an isotropic elastic wedge stiffened by a rod that has a finite length and linearly varying cross-sectional area, a solution is constructed in [4], and it is shown that the contact stress near the thin end of the patch has a singularity of order less than 1/2. If the variation of the cross-sectional area of the plate is parabolic, then the contact stress near its thin end is bounded [5].
Contact problems of bending of isotropic plates reinforced by thin inclusions (rigid or elastic) are considered in [6, 7]. These problems can be reduced to integral equations with a special characteristic part, and the solution is sought in the class of integrable functions.
Contact problems for finite or infinite plates with elastic patches of variable thickness (variable flexural rigidity) were investigated in [8-10], where an integro-differential equation is obtained for the unknown contact stresses. The characteristic part of these equations is an integro-differential equation of Prandtl type. This equations is studied in [11, 12]. However, if the coefficient of the singular operator has a zero of any order at the ends of the integration line, the equation undergoes a qualitative change, in particular, it becomes equivalent to a singular integral equation of the third kind. |
| References |
| 1. | V. M. Alexandrov and S. M. Mkhitaryan,
Contact Problems for Bodies with Thin Covers and Interlayers [in Russian],
Nauka, Moscow, 1983. |
| 2. | G. Ya. Popov, Elastic Stress Concentration near Punches, Cuts, Thin Inclusions,
and Stiffening Elements [in Russian], Nauka, Moscow, 1982. |
| 3. | G. A. Morar' and G. Ya. Popov,
"On a contact problem for a half-space with a finite elastic attachment,"
PMM [Applied Mathematics and Mechanics], Vol. 34, No. 3, pp. 412-421, 1970. |
| 4. | B. M. Nuller, "An elastic wedge stiffened by a finite beam of variable cross-section," Izv. AN SSSR. MTT [Mechanics of Solids], No. 5,
pp. 98-100, 1972. |
| 5. | N. N. Shavlakadze, "An isotropic elastic half-plane stiffened by a finite beam of variable cross-section," Soobshch. AN GSSR, Vol. 130,
No. 3, pp. 509-512, 1988. |
| 6. | O. V. Onishchuk and G. Ya. Popov,
"On some problems of bending of plates with cracks and thin inclusions,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 4, pp. 141-150, 1980. |
| 7. | O. V. Onishchuk, G. Ya. Popov, and P. G. Farshait,
"On singularities of contact stresses in plates subjected to bending and containing thin inclusions," PMM [Applied Mathematics and Mechanics], Vol. 50, No. 2, pp. 293-302, 1986. |
| 8. | N. Shavlakadze, "On some contact problems for bodies with elastic inclusions," Georg. Math. J., Vol. 5, No. 3, pp. 285-300, 1998. |
| 9. | N. Shavlakadze, "A contact problem of the interaction of semi-infinite inclusion with a plate," Georg. J. Math., Vol. 6, No. 5,
pp. 489-500, 1999. |
| 10. | N. Shavlakadze, "On singularities of contact stress upon tension and bending of plates with elastic inclusion," Trudy Matem. In-ta im A. Razmadze,
Vol. 120, pp. 135-147, 1999. |
| 11. | I. N. Vekua, "On Prandtl's integro-differential equation," PMM [Applied Mathematics and Mechanics],
Vol. 9, No. 2, pp. 143-150, 1945. |
| 12. | L. G. Magnaradze, "On a new integro-differential equation in the theory of airfoil," Soobsh. AN GSSR, Vol. 3, No. 6, pp. 503-508,
1942. |
| 13. | S. G. Lekhnitskii, Anisotropic Plates [in Russian], Gostekhizdat, Moscow,
Leningrad, 1947. |
| 14. | I. N. Muskhelishvili, Some Basic Problems in Mathematical Elasticity [in Russian],
Nauka, Moscow, 1966. |
| 15. | I. M. Gel'fand and G. E. Shilov, Generalized functions and Operations with Them [in Russian], Fizmatgiz, Moscow, 1958. |
| 16. | R. D. Banzuri, "On a boundary-value problem in the theory of analytic functions," Soobsh. AN GSSR, Vol. 73, No. 3, pp. 549-552,
1974. |
|
| Received |
04 May 2001 |
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