 | | 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
|
| In English (Mech. Solids): | | 4810 |
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| E. V. Murashkin and Yu. N. Radaev, "On Theory of Oriented Tensor Elements of Area for a Micropolar Continuum Immersed in an External Plane Space," Mech. Solids. 57 (2), 205-213 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
2 |
Pages |
205-213 |
| DOI |
10.3103/S0025654422020108 |
| Title |
On Theory of Oriented Tensor Elements of Area for a Micropolar Continuum Immersed in an External Plane Space |
| Author(s) |
E. V. Murashkin (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, evmurashkin@gmail.com)
Yu. N. Radaev (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia) |
| Abstract |
The paper deals with the problems of the tensor element of volume (area) of an M-cell for a manifold immersed in a "plane" multidimensional space. The corresponding considerations imply the choice of the reper orientation, which determines the volume (area) element. The latter circumstance is of exceptional importance in micropolar theories of elasticity. The indicated theories can be correctly developed only within the framework of the pseudotensor formalism. This is especially true for the theory of hemitropic elastic continua. The governing information from the algebra of pseudotensors is presented. Manifolds given by Gaussian parametrization are considered. The concept of an M-cell on a manifold and its orientation is introduced. An algorithm for comparing the orientations of M-dimensional cells is described. The concept of the tensor element of volume (area) for the M-cell is determined. The formula for transformation a natural volume element to an invariant volume element is shown. Important applications for the mechanics of the micropolar continuum are noted and discussed. |
| Keywords |
fundamental orienting pseudoscalar, pseudotensor, M-cell, volume tensor element, benchmark orientation, micropolar continuum power voltage, moment stress tensor |
| Received |
09 September 2021 | Revised |
10 October 2021 | Accepted |
11 October 2021 |
| Link to Fulltext |
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