Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2004-4pp.92-101

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Total articles in the database: 10864
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G. A. Vanin, "Couple-stress mechanics of thin shells," Mech. Solids. 39 (4), 92-101 (2004)
Year 2004 Volume 39 Number 4 Pages 92-101
Title Couple-stress mechanics of thin shells
Author(s) G. A. Vanin (Moscow)
Abstract On the basis of couple-stress or gradient theory of elasticity of composite media [1-3], we construct couple-stress mechanics of thin double-curvature shells. For the sake of definiteness, we consider the problem for shells strengthened by hollow cylindrical fibers orthogonal to the middle surface and forming a nearly hexagonal simple lattice on a shallow surface. Fibers with a cylindrical cavity typically occur in nano-composites. The basic relations of the theory are constructed by direct generalization of the equations of Vlasov's theory of homogeneous shells. In an asymptotic approximation, the desired relations are obtained in an explicit form.
References
1.  G. A. Vanin, "Gradient theory of shear in multi-level composites," Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 120-128, 1985.
2.  G. A. Vanin, "Plane strain gradient theory of multilevel media," Izv. AN. MTT [Mechanics of Solids], No. 3, pp. 5-15, 1996.
3.  G. A. Vanin, "Gradient theory of elasticity," Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 46-53, 1999.
4.  G. A. Vanin, Micromechanics of Composites [in Russian], Naukova Dumka, Kiev, 1985.
5.  G. N. Savin, Fundamentals of the Plane Problem in Couple-stress Elasticity [in Russian], Izd-vo Kievsk. Un-ta, Kiev, 1965.
6.  E. L. Aero and E. V. Kuvshinskii, "Basic equations for materials with rotational interaction of particles," Fizika Tverdogo Tela, Vol. 11, No. 7, pp. 1399-1409, 1960.
7.  V. A. Pal'mov, "Plane problem of nonsymmetric elasticity," PMM [Applied Mathematics and Mechanics], Vol. 28, No. 6, pp. 117-1120, 1964.
8.  R. D. Mindlin, "Influence of couple-stresses on stress concentration," Mekhanika, No. 4, pp.  115-128, 1964.
9.  A. K. Eringen, "Micropolar Elasticity," in Fracture [Russian translation], pp. 646-751, Mir, Moscow, 1975.
10.  G. V. Kolosov, Applications of Complex Variables in Elasticity [in Russian], Glavn. Red. Obshchetekhn. Distsciplin, Moscow, Leningrad, 1935.
11.  G. A. Vanin, "Gradient interphase interaction of a nonhomogeneous plate with an inclusion," Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 146-151, 1998.
12.  A. L. Goldenveizer, Theory of Thin Elastic Shells [in Russian], Nauka, Moscow, 1975.
13.  V. V. Novozhilov, K. F. Chernykh, and E. I. Mikhailovskii, Linear Theory of Thin Shells, Izd-vo Politekhnika, Leningrad, 1991.
Received 04 May 2003
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