Abstract:
The paper deals with the problems of ordering the reper orientations for a micropolar continuum immersed in an external plane space. Based on the concept of an elementary tensor volume (area) \(M\)-cells, an algorithm for comparing and matching external spatial orientations of \(M\)-cells is proposed. The process of continuous transfer of reper directions associated with a \(M\)-cell is considered. As a result, we can talk about the orientation of micropolar continuum itself and its boundary. The oriented continuum plays an important role in micropolar elasticity. This is especially true for the theory of hemitropic elastic media. The pseudotensor formulation of Stokes' theorem is discussed.
This study was supported by the Ministry of Science and Higher Education of the Russian Federation (State Registration Number AAAA–A20–120011690132–4) and by the Russian Foundation for Basic Research (projects nos. 18–01–00844, 20–01–00666).
Citation:
E. V. Murashkin, Yu. N. Radayev, “On a ordering of area tensor elements orientations in a micropolar continuum immersed in an external plane space”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 25:4 (2021), 776–786
\Bibitem{MurRad21}
\by E.~V.~Murashkin, Yu.~N.~Radayev
\paper On a ordering of area tensor elements orientations in a micropolar continuum immersed in an external plane space
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2021
\vol 25
\issue 4
\pages 776--786
\mathnet{http://mi.mathnet.ru/vsgtu1883}
\crossref{https://doi.org/10.14498/vsgtu1883}
\zmath{https://zbmath.org/?q=an:7499972}
\elib{https://elibrary.ru/item.asp?id=47942928}
\edn{https://elibrary.ru/ZKIAAJ}
Linking options:
https://www.mathnet.ru/eng/vsgtu1883
https://www.mathnet.ru/eng/vsgtu/v225/i4/p776
This publication is cited in the following 13 articles:
E. V. Murashkin, Yu. N. Radaev, “Dvumernye figury Naya dlya gemitropnykh mikropolyarnykh uprugikh tel”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 24:1 (2024), 109–122
E. V. Murashkin, Y. N. Radayev, “On Algebraic Triple Weights Formulation of Micropolar Thermoelasticity”, Mech. Solids, 59:1 (2024), 555
E. Yu. Krylova, E. V. Murashkin, Y. N. Radaev, “The Nye Cells and Figures for Athermic Hemitropic, Isotropic, and Ultraisotropic Micropolar Elastic Solids”, Mech. Solids, 59:3 (2024), 1311
E. V. Murashkin, Y. N. Radayev, “Characteristic Constitutive Numbers in Semi-Isotropic Coupled Thermoelasticity”, Mech. Solids, 59:4 (2024), 1856
E. Yu. Krylova, E. V. Murashkin, Yu. N. Radaev, “The nye cells and figures for athermic hemitropic, isotropic and ultraisotropic micropolar elastic solids”, Izvestiâ Rossijskoj akademii nauk. Mehanika tverdogo tela, 2024, no. 3
E. V. Murashkin, Yu. N. Radaev, “Termomekhanicheskie sostoyaniya girotropnykh mikropolyarnykh tel”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 27:4 (2023), 659–678
E. V. Murashkin, Yu. N. Radaev, “Teploprovodnost mikropolyarnykh tel, chuvstvitelnykh k zerkalnym otrazheniyam prostranstva”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 165, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2023, 389–403
E.V. Murashkin, Yu.N. Radaev, “On the polyvariance of the base equations of coupled micropolar thermoelasticity”, Vestnik Chuvashskogo gosudarstvennogo pedagogicheskogo universiteta im. I.Ya. Yakovleva. Seriya: Mekhanika predelnogo sostoyaniya, 2023, no. 3(57), 112
E. V. Murashkin, Y. N. Radayev, “Two-Dimensional Nye Figures for Some Micropolar Elastic Solids”, Mech. Solids, 58:6 (2023), 2254
E. V. Murashkin, Yu. N. Radayev, “Heat Transfer in Anisotropic Micropolar Solids”, Mech. Solids, 58:9 (2023), 3111
D. E. Bykov, M. V. Nenashev, V. P. Radchenko, “K 60-letiyu so dnya rozhdeniya prof. Yuriya Nikolaevicha Radaeva”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:2 (2022), 207–221
E. V. Murashkin, Yu. N. Radaev, “K teorii gemitropnykh tenzorov chetvertogo ranga v trekhmernykh prostranstvakh Evklida”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:3 (2022), 592–602
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