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IssuesArchive of Issues2004-1pp.21-27

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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 Layer of Variable Thickness. Preprint 6-96 [in Russian], pp. 1-39, In-t 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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