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IssuesArchive of Issues2008-5pp.597-610

Archive of Issues

Total articles in the database: 1813
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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 http://www.sciencedirect.com/science/journal/00218928
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