 | | 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, "The equations of the geometrically non-linear theory of elasticity and momentless shells for arbitrary displacements," J. Appl. Math. Mech. 72 (5), 597-610 (2008) |
| Year |
2008 |
Volume |
72 |
Issue |
5 |
Pages |
597-610 |
| Title |
The equations of the geometrically non-linear theory of elasticity and momentless shells for arbitrary displacements |
| Author(s) |
V.N. Paimushin (Kazan, Russia, dsm@dsm.kstu-kai.ru) |
| Abstract |
To validate earlier results for the case of arbitrary deformations and displacements in orthogonal curvilinear coordinates, kinematic and static relations of the non-linear theory of elasticity are set up which, in the limit of small deformations, lead, unlike the known relations, to correct and consistent relations. The same relations are also constructed for momentless shells of general form for the case of arbitrary displacements and deformations on the basis of which the problem of the static instability of a cylindrical shell with closed ends, made of a linearly elastic material and under conditions of an internal pressure (the problem of the inflation of a cylinder), is considered. It is shown that, in the case of momentless shells, the components of the true sheat stresses are symmetrical, unlike the three-dimensional case. All the above-mentioned relations are constructed for the loading of deformable bodies both by conservative external forces of constant directions and, also, by two types of "following" forces. |
| Received |
18 September 2007 |
| Link to Fulltext |
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