Vol. 6, №1, 2014

CONTINUUM PHYSICS

MODELING OF THERMOELASTIC PROCESSES IN THREE-DIMENSIONAL MEDIA AND SHELLS BY MEANS OF THE COSSERAT CONTINUUM WITH MICROSTRUCTURE
Ivanova E. A.
Saint-Petersburg State Polytechnical University, http://www.spbstu.ru
195251, Saint-Petersburg, Russian Federation
Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, http://www.ipme.ru
199178, Saint-Petersburg, Russia Federation
ivanova@ei5063.spb.edu

Received 08.04.2013
Represented by a Academician of RANS V.I. Erofeev 08.04.2013
In continuum mechanics the temperature is considered to be a quantity measured by thermometer and any mechanical interpretation of temperature is left out. In kinetic theory and statistical physics the temperature is considered as average kinetic energy of the chaotic motion of molecules. The conception of thermal motion of molecules does not contradict continuum mechanics. However, it is very difficult to use this mechanical model of temperature for derivation of the equations of continuum mechanics since the chaotic motion of molecules is ignored in continuum mechanics and the temperature is connected with the internal energy. Our purpose is to propose the mechanical interpretation of the temperature which can be foundation for description of thermal processes within the framework of continuum mechanics and by using the methods of continuum mechanics. The main idea is to introduce the Cosserat continuum with internal structure and additional degrees of freedom. We believe that characteristics of rotational motions of internal structure and moment interactions connected with internal structure can be associated with the temperature and other thermodynamical quantities provided that the mathematical description of the proposed model can be reduced to the well-known equations of thermoelasticity.

Keywords: continuum mechanics, shell theory, Cosserat continuum, continuum with microstructure, thermoelasticity

PACS: 46.05.+b, 46.25.Cc, 46.25.Hf, 46.70.-p, 46.70.De, 65.40.Ba, 65.40.De, 65.40.G-, 65.40.Gr, 65.40.gd.

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RENSIT, 2013, 5(1):98-110

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