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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2018, Volume 22, Number 3, Pages 504–517
DOI: https://doi.org/10.14498/vsgtu1635
(Mi vsgtu1635)
 

This article is cited in 29 scientific papers (total in 30 papers)

Mechanics of Solids

The Lagrange multipliers method in covariant formulations of micropolar continuum mechanics theories

Yu. N. Radayev

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 107045, Russian Federation (published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: Linear model of micropolar elastic continuum (known also as the Cosserat continuum) is considered. Kinematics and strain measures are discussed. The symmetric small strains tensor, relative microrotation vector and spatial gradient of the total microrotation vector (the wryness tensor) are then employed for a covariant formulation of the micropolar theory. By means of the principle of virtual displacements much simplified by the lack of internal forces and couples contributions to the virtual work and the Lagrange multipliers method the micropolar theory of elasticity is developed. Hemitropic micropolar continuum model is investigated in further details. The paper is to be considered as a universal covariant script of equations of the linear micropolar theory of elasticity derived from the virtual displacements principle.
Keywords: micropolar continuum, force stress, couple stress, virtual displacements principle, Lagrange multipliers, virtual work, covariant formulation.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00844_а
Russian Academy of Sciences - Federal Agency for Scientific Organizations AAAA-A17-117021310381-8
This study was in part financially supported by the Federal Agency for Scientific Organizations (State Registration Number AAAA–A17–117021310381–8) and by the Russian Foundation for Basic Research (project no. 18–01–00844_a).
Received: July 15, 2018
Revised: August 23, 2018
Accepted: September 3, 2018
First online: September 23, 2018
Bibliographic databases:
Document Type: Article
UDC: 539.3
MSC: 74A60, 74F05
Language: Russian
Citation: Yu. N. Radayev, “The Lagrange multipliers method in covariant formulations of micropolar continuum mechanics theories”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 22:3 (2018), 504–517
Citation in format AMSBIB
\Bibitem{Rad18}
\by Yu.~N.~Radayev
\paper The Lagrange multipliers method in covariant formulations of micropolar continuum mechanics theories
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2018
\vol 22
\issue 3
\pages 504--517
\mathnet{http://mi.mathnet.ru/vsgtu1635}
\crossref{https://doi.org/10.14498/vsgtu1635}
\elib{https://elibrary.ru/item.asp?id=36497377}
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  • https://www.mathnet.ru/eng/vsgtu/v222/i3/p504
  • This publication is cited in the following 30 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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    Abstract page:602
    Full-text PDF :276
    References:60
     
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