 | | 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): | | 4760 |
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| L. V. Nikitin and E. I. Ryzhak, "On stability and instability of a compressed block pressed to a smooth basement," Mech. Solids. 43 (4), 558-570 (2008) |
| Year |
2008 |
Volume |
43 |
Number |
4 |
Pages |
558-570 |
| DOI |
10.3103/S0025654408040055 |
| Title |
On stability and instability of a compressed block pressed to a smooth basement |
| Author(s) |
L. V. Nikitin (Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, B. Gruzinskaya 10, Moscow, 123995, Russia, niklv@gagarinclub.ru)
E. I. Ryzhak (Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, B. Gruzinskaya 10, Moscow, 123995, Russia, e_i_ryzhak@mail.ru) |
| Abstract |
We study the problem on the stability of the equilibrium of a compressed homogeneous nonlinearly elastic body having the shape of a rectangular parallelepiped (block). The conditions of free sliding along the block face planes (with possible separation) are posed on all but one block faces. On the remaining face, a normal pressing "dead" load uniformly distributed over the surface is given. We obtain strict upper and lower bounds for the critical values of compression stresses, which coincide in order of magnitude with the characteristic elastic moduli of the material in the equilibrium under study; these estimates are independent of the relations between the block dimensions in the entire range of possible variation of the latter. The result indirectly confirms that the primary instability in the problem under study has a surface character (is localized near the kinematically free face with a given load) for any relations between the block dimensions and is characterized by the absence of separation from the basement even for an arbitrarily thin plate. This also implies that the "cantilever approximation" (whose application to similar problems has been attempted in the literature) cannot be used for the stability analysis in this situation in principle. |
| Received |
10 December 2007 |
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