Dynamic equations of thermoelastic Cosserat rods

A thermoelastic Cosserat rod with a heat flux along its length is modeled after reviewing a simple Cosserat rod model. Extended Kirchhoff constitutive relations that include thermal effects, and the associated heat conduction equation, are derived using the first law of thermodynamics. The rate of i...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2013-07, Vol.18 (7), p.1880-1887
Main Authors: Cao, D.Q., Song, M.T., Tucker, R.W., Zhu, W.D., Liu, D.S., Huang, W.H.
Format: Article
Language:English
Subjects:
Beams (structural)
Cosserat rod
Dissipation
Dynamic equations
Heat conduction
Heat transfer
Inequalities
Kirchhoff constitutive relations
Mathematical analysis
Mathematical models
Nonlinear dynamics
Thermodynamics
Thermomechanics
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Summary:A thermoelastic Cosserat rod with a heat flux along its length is modeled after reviewing a simple Cosserat rod model. Extended Kirchhoff constitutive relations that include thermal effects, and the associated heat conduction equation, are derived using the first law of thermodynamics. The rate of internal dissipation of the Cosserat rod is estimated by the Clausius–Duhem inequality. Nonlinear dynamic equations of the thermoelastic Cosserat rod, which extend the simple Cosserat rod model, are obtained. Dynamic equations of a planar thermoelastic Cosserat rod, the Timoshenko thermoelastic beam, and the planar Euler–Bernoulli thermoelastic beam are derived as a special case within the framework of the thermoelastic Cosserat rod.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2012.11.011