 | | 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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| << Previous article | Volume 44, Issue 2 / 2009 | Next article >> |
| D. N. Sheidakov, "On the influence of the gravity force on the stability of an inhomogeneous layer under biaxial extension-compression," Mech. Solids. 44 (2), 244-250 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
2 |
Pages |
244-250 |
| DOI |
10.3103/S0025654409020095 |
| Title |
On the influence of the gravity force on the stability of an inhomogeneous layer under biaxial extension-compression |
| Author(s) |
D. N. Sheidakov (South Scientific Centre, Russian Academy of Sciences, Chekhova 41, Rostov-on-Don, 344006, Russia, sheidakov@mail.ru) |
| Abstract |
In the present paper, in the framework of the three-dimensional nonlinear theory of elasticity, we study the stability of a heavy layer under biaxial extension-compression. The elastic properties of the layer are assumed to be inhomogeneous along thickness and are described by a semilinear material model. We study the stability by using the bifurcation approach. By solving the linearized equilibrium equations, we obtain the critical curves and the stability domain in the plane of the loading parameters, for which we take the material elongation ratios along the coordinate axes lying in the layer plane. We analyze the influence of the layer thickness, specific weight, and material parameters on buckling. In particular, we find that, when studying stability, it is expedient to take the gravity force into account only if the layer rigidity decreases with increasing depth. |
| References |
| 1. | A. I. Lurie, Nonlinear Theory of Elasticity (Nauka, Moscow, 1980) [in Russian]. |
| 2. | F. John, "Plane Strain Problem for a Perfectly Elastic Materials of Harmonic Type," Comm. Pure Appl. Math. 13(2), 239–296 (1960). |
| 3. | M. A. Biot, Mechanics of Incremental Deformations (Wiley, New York, 1965). |
| 4. | S. I. Boyarchenko and L. M. Zubov, "Surface Instability of Elastic Inhomogeneous Heavy Half-Space," Izv. Akad. Nauk SSSR. Fiz. Zemli, No. 1, 11–19 (1984) [Izv. Phys. Solid Earth (Engl. Transl.)]. |
| 5. | L. M. Zubov, "Variational Principles of the Nonlinear Theory of Elasticity. Case of Superposition of a Small Deformation on a Finite Deformation," Prikl. Mat. Mekh. 35(5), 848–852 (1971) [J. Appl. Math. Mech. (Engl. Transl.) 35 (5), 802–806 (1971)]. |
| 6. | L. M. Zubov and S. I. Moiseenko, "Buckling of an Elastic Cylinder under Torsion and Compression," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 5, 78–84 (1981) [Mech. Solids (Engl. Transl.) 16 (5), 67–72 (1981)]. |
| 7. | L.M. Zubov and D. N. Sheidakov, "The Effect of Torsion on the Stability of an Elastic Cylinder under Tension," Prikl. Mat. Mekh. 69(1), 53–60 (2005) [J. Appl. Math. Mech. (Engl. Transl.) 69 (1), 49–56 (2005)]. |
| 8. | V. N. Bakulin and A. G. Protosenya, "Nonlinear Effects in Propagation of Elastic Waves through Rocks," Dokl. Akad. Nauk SSSR 263(2), 314–316 (1982). |
|
| Received |
16 May 2006 |
| Link to Fulltext |
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