Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Radayev Y. N., Kovalev V. A. Rotational Invariance of Non-Linear Lagrangians of Type-II Micropolar Thermoelastic Continuum. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 4, pp. 96-102. DOI: 10.18500/1816-9791-2013-13-4-96-102

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
15.12.2013
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Language: 
Russian
Heading: 
Mechanics
UDC: 
539.374
DOI: 
10.18500/1816-9791-2013-13-4-96-102

Rotational Invariance of Non-Linear Lagrangians of Type-II Micropolar Thermoelastic Continuum

Autors: 
Radayev Yuri Nickolaevich, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Kovalev Vladimir Aleksandrovich, Moscow City Government University of Management Moscow, Russia
Abstract: 

The paper contains new results related to extension of the field theoretical approach and its formalism to non-linear coupled micropolar thermoelastic media. A mathematical model of micropolar (MP) type-II (GNII) thermoelastic (TE) continuum is considered. A formulation of the least thermoelastic action principle is discussed. Partial differential equations subsequent to the least action principle are derived. The translational symmetries of non-linear Lagrangians are adopted. Those include an additional symmetry: translations of the thermal displacement. The rotational invariance of the action and corresponding Lagrangian is then studied. For micropolar type-II thermoelastic Lagrangians following the usual procedure independent rotationally invariant functional arguments are obtained. Objective forms of the Lagrangians satisfying the frame indifference principle are given.

Key words: 
type-II micropolar thermoelasticity
field
extra field
action
Lagrangian
d-vector
invariance
rotation
frame indifference principle
deformation
extra deformation
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