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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)
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.
Received: July 15, 2018 Revised: August 23, 2018 Accepted: September 3, 2018 First online: September 23, 2018
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
Linking options:
https://www.mathnet.ru/eng/vsgtu1635 https://www.mathnet.ru/eng/vsgtu/v222/i3/p504
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