 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| E.V. Murashkin and Yu.N. Radayev, "The Schouten Force Stresses in Continuum Mechanics Formulations," Mech. Solids. 58 (1), 153-160 (2023) |
| Year |
2023 |
Volume |
58 |
Number |
1 |
Pages |
153-160 |
| DOI |
10.3103/S0025654422700029 |
| Title |
The Schouten Force Stresses in Continuum Mechanics Formulations |
| Author(s) |
E.V. Murashkin (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, evmurashkin@gmail.com)
Yu.N. Radayev (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, radayev@ipmnet.ru) |
| Abstract |
The paper deals with the force stress pseudotensor as proposed by Schouten and a derivation of equilibrium equations in terms of the Schouten stress pseudotensor of positive weight. The definition of Schouten's force stress pseudotensor is based on the notion of a pseudoinvariant area element. Conventional and unconventional definitions of the force stress tensor are recalled and discussed. The tensor area elements of a M-manifold immersed in N-dimensional parent (outer) plane space are revisited. The notions of vector, pseudovector, invariant and pseudo-invariant elementary areas in three-dimensional plane space are thoroughly discriminated. The usability of pseudotensor elementary volume of any given integer weight is discussed. Three realizations of the covariant differentiation of pseudotensor fields are considered and compared. Equations of equilibrium and dynamics are derived in terms of the Schouten force stress pseudotensor from the virtual displacements principle. |
| Keywords |
pseudotensor, manifold, elementary volume, elementary area, Schouten force stress pseudotensor, virtual displacements principle, fundamental orienting pseudoscalar |
| Received |
29 June 2022 | Revised |
18 July 2022 | Accepted |
31 August 2022 |
| Link to Fulltext |
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