Cite this article as:
Radaev Y. N. Rotational Invariance of Non-Linear Lagrangians of Type-II Micropolar Thermoelastic Continuum. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 4, pp. 96-102. DOI: https://doi.org/10.18500/1816-9791-2013-13-4-96-102
Language:
Russian
Heading:
UDC:
539.374
Rotational Invariance of Non-Linear Lagrangians of Type-II Micropolar Thermoelastic Continuum
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:
References
1. Cosserat E. et F. The´ orie des corps de´ formables. Paris, Librairie Scientifique A. Hermann et Fils, 1909, 226 p.
2. Toupin R. A. Theories of Elasticity with Couple-stress. Arch. Rational Mech. Anal. 1964, vol. 17, no. 5, pp. 85–112.
3. Sedov L. I. Vvedenie v mekhaniku sploshnykh sred [Introduction to Mechanics of Continuos Media]. Moscow, Fizmatgiz, 1962, 284 p. (in Russian).
4. Illyushin A. A. Mekhanika sploshnykh sred [Mechanics of Continuos Media]. Moscow, Moscow Univ. Press., 1978, 287 p. (in Russian).
5. Green A. E., Adkins J. E. Bol’shie uprugie deformatsii i nelineinaia mekhanika sploshnoi sredy [Large Elastic Deformations and Non-Linear Continuum Mechanics]. Moscow, Mir, 1965, 456 p. (in Russian).
6. Berdichevskii V. L. Variatsionnye printsipy mekhaniki sploshnoi sredy [Variational Principles of Mechanics of Continua]. Moscow, Nauka, 1983, 448 p. (in Russian).
7. Kovalev V. A., Radayev Y. N. Volnovye zadachi teorii polia i termomekhanika [Wave Problems of Field Theory and Thermomechanics]. Saratov. Saratov Univ. Press., 2010, 328 p. (in Russian). Mechanics
Short text (in English):
39
Full text:
60