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
Rotational Invariance of Non-Linear Lagrangians of Type-II Micropolar Thermoelastic Continuum
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.
- Cosserat E. et F. The´ orie des corps de´ formables. Paris, Librairie Scientifique A. Hermann et Fils, 1909, 226 p.
- Toupin R. A. Theories of Elasticity with Couple-stress. Arch. Rational Mech. Anal. 1964, vol. 17, no. 5, pp. 85–112.
- Sedov L. I. Vvedenie v mekhaniku sploshnykh sred [Introduction to Mechanics of Continuos Media]. Moscow, Fizmatgiz, 1962, 284 p. (in Russian).
- Illyushin A. A. Mekhanika sploshnykh sred [Mechanics of Continuos Media]. Moscow, Moscow Univ. Press., 1978, 287 p. (in Russian).
- 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).
- Berdichevskii V. L. Variatsionnye printsipy mekhaniki sploshnoi sredy [Variational Principles of Mechanics of Continua]. Moscow, Nauka, 1983, 448 p. (in Russian).
- 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
- 1131 reads