 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| V.N. Paimushin and N.V. Polyakova, "The consistent equations of the theory of plane curvilinear rods for finite displacements and linearized problems of stability," J. Appl. Math. Mech. 73 (2), 220-236 (2009) |
| Year |
2009 |
Volume |
73 |
Issue |
2 |
Pages |
220-236 |
| Title |
The consistent equations of the theory of plane curvilinear rods for finite displacements and linearized problems of stability |
| Author(s) |
V.N. Paimushin (Kazan, Russia, dsm@dsm.kstu-kai.ru)
N.V. Polyakova (Kazan, Russia) |
| Abstract |
Based on a previously constructed, consistent version of the geometrically non-linear equations of elasticity theory, for small deformations and arbitrary displacements, and a Timoshenko-type model taking into account transverse shear and compressive deformations, one-dimensional equations of an improved theory are derived for plane curvilinear rods of arbitrary type for arbitrary displacements and revolutions and with loading of the rods by follower and non-follower external forces. These equations are used to construct linearized equations of neutral equilibrium that enable all possible classical and non-classical forms of loss of stability (FLS) of rods of orthotropic material to be investigated, ignoring parametric deformation terms in the equations. These linearized equations are used to find accurate analytical solutions of the problem of plane classical flexural-shear and non-classical flexural-torsional FLS of a circular ring under the combined and separate action of a uniform external pressure and a compression in the radial direction by forces applied to both faces. |
| Received |
27 May 2008 |
| Link to Fulltext |
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