 | | 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
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| In English (Mech. Solids): | | 4810 |
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| B. D. Annin and A. E. Alekseev, "Equations of deformation of an inhomogeneous layered oval elastic body," Mech. Solids. 39 (1), 21-27 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
1 |
Pages |
21-27 |
| Title |
Equations of deformation of an inhomogeneous layered oval elastic body |
| Author(s) |
B. D. Annin (Novosibirsk)
A. E. Alekseev (Novosibirsk) |
| Abstract |
We construct equations describing deformation of an elastic inhomogeneous layered
body of oval shape. Each layer coincides with a region bounded by convex equidistant
surfaces. Various methods for the construction of the theory of elastic deformation
of multi-layer structural elements are described in [1-4]. A technique
for the construction of equations of elastic deformation of a layer is proposed in [5-7]
in the case of arbitrary boundary conditions on its faces. For the same unknown quantities
several approximations in the form of segments of the series in terms of Legendre polynomials are used.
In [8-10], this approach is applied for the construction and the solution of
equations describing elastic deformation of layered plates and shells; at the
interfaces between the layers, the matching conditions should hold for the
displacements and the stresses. In the present paper, this technique is used
for the construction of the equations describing elastic deformation of an
oval-shaped layered body in nonorthogonal curvilinear coordinates. |
| References |
| 1. | A. A. Dudchenko, S. A. Lur'e, and I. F. Obraztsov,
"Anisotropic multi-layered plates and shells," in Advances in Science and
Technology. Ser. Mechanics of Solids [in Russian],
Vol. 15, pp. 3-68, VINITI, Moscow, 1983. |
| 2. | S. A. Ambartsumyan, General Theory of Anisotropic Shells [in Russian],
Nauka, Moscow, 1974. |
| 3. | B. L. Pelekh, A. V. Maksimuk, and I. M. Korovaichuk,
Contact Problems for Layered Structural Elements and Coated Bodies [in Russian],
Naukova Dumka, Kiev, 1988. |
| 4. | E. I. Grigolyuk, E. A. Kogan, and V. I. Mamii,
"Problems of deformation of thin-walled layered structures with delamination,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 6-32, 1994. |
| 5. | G. V. Ivanov, Theory of Plates and Shells [in Russian], Izd-vo Novosibirsk.
Un-ta, Novosibirsk, 1980. |
| 6. | A. E. Alekseev, Linear Theory of Elastic Deformation of a
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Gidrodinamiki SO RAN, Novosibirsk, 1996. |
| 7. | Yu. M. Volchkov, L. A. Dergileva, and G. V. Ivanov,
"Numerical modelling of stress states in plane elasticity problems by the
layer method," Zh. Prikl. Mekhaniki i Tekhn. Fiziki, Vol. 35, No. 6,
pp. 129-138, 1994. |
| 8. | A. E. Alekseev, "Bending of a three-layered orthotropic beam,"
Zh. Prikl. Mekhaniki i Tekhn. Fiziki, Vol. 36, No. 3, pp. 158-166, 1995. |
| 9. | A. E. Alekseev, V. V. Alekhin, and B. D. Annin,
"Plane elasticity problem for an inhomogeneous layered body,"
Zh. Prikl. Mekhaniki i Tekhn. Fiziki, Vol. 42, No. 6, pp. 136-141, 2001. |
| 10. | A. E. Alekseev and B. D. Annin,
"Equations of deformation of an elastic inhomogeneous layered body of revolution,"
Zh. Prikl. Mekhaniki i Tekhn. Fiziki, Vol. 44, No. 3, pp. 157-163, 2003. |
| 11. | B. Blyashke, Differential Geometry and Geometrical Principles of
Einstein's Relativity Theory [Russian translation], Vol. 1, ONTI, Moscow, Leningrad, 1935. |
| 12. | A. A. Ligun, S. V. Timchenko, and A. A. Shumeiko,
"On the geometry of convex surfaces," Vistn. Dnipropetrovsk. Un-tu.
Matematika, Vol. 3, pp. 85-92, 1998. |
| 13. | A. A. Ligun, A. A. Shumeiko, and S. V. Timchenko,
"On a representation of convex surfaces in n-dimensional spaces,"
Doklady AN, Vol. 377, No. 1, pp. 17-19, 2001. |
| 14. | I. N. Vekua, Some General Methods for the Construction of Different Versions of
the Theory of Shells [in Russian], Nauka, Moscow, 1982. |
| 15. | P. M. Naghdy, "Foundation of elastic shell theory," in
Progress in Solid Mechanics, Vol. 4, pp. 1-90, North-Holland, Amsterdam,1963. |
|
| Received |
09 September 2003 |
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