A novel variational formulation for thermoelastic problems

•Hamilton–Pontryagin principle is used to derive a new variational formulation for thermo-elastic systems.•The concept of thermal displacement is considered to describe thermal part of the problem.•There is not extra assumptions and it is in conformity with the Clausius–Duhem inequality as a stateme...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2015-05, Vol.22 (1-3), p.263-268
Main Authors: Ebrahimzadeh, Zahra, Leok, Melvin, Mahzoon, Mojtaba
Format: Article
Language:English
Subjects:
Computer simulation
Conservation laws
Constitutive equations
Displacement
Hamilton–Pontryagin principle
Inequalities
Mathematical analysis
Mathematical models
Thermal displacement
Thermoelastic problems
Thermoelasticity
Variational formulation
Variational principles
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Summary:•Hamilton–Pontryagin principle is used to derive a new variational formulation for thermo-elastic systems.•The concept of thermal displacement is considered to describe thermal part of the problem.•There is not extra assumptions and it is in conformity with the Clausius–Duhem inequality as a statement for the second law of thermodynamics.•In final relations, all balance laws for a thermoelastic body were derived.•The second law of thermodynamics is satisfied in an equality constraint, too. A novel variational formulation for thermoelasticity is proposed in this paper. The formulation is based on the Hamilton–Pontryagin principle and the concept of temperature displacement. Although there are many other papers that have a similar goal, most of the proposed approaches are quite complicated, and contain assumptions that curtail their applicability. The proposed variational principle in this paper is straightforward with no extra assumptions and it is in conformity with the Clausius–Duhem inequality as a statement of the second law of thermodynamics. Conservation laws for linear momentum and energy, and the constitutive equation for thermoelasticity are consequences of this variational formulation.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2014.09.027