Mixed lagrangian formulation for linear thermoelastic response of structures / Georgios Apostolakis in Journal of engineering mechanics, Vol. 138 N° 5 (Mai 2012)  

Public ISBD [article]  inJournal of engineering mechanics > Vol. 138 N° 5 (Mai 2012) . - pp.508-518 Titre : Mixed lagrangian formulation for linear thermoelastic response of structures Type de document : texte imprimé Auteurs : Georgios Apostolakis, Auteur ; Gary F. Dargush, Auteur Année de publication : 2012 Article en page(s) : pp.508-518 Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Thermoelasticity, Variational methods, Mixed Lagrangian formulation Hamilton’s principle, Discrete variational calculus methods Flexibility Symplectic algorithms Résumé : Although a complete unified theory for elasticity, plasticity, and damage does not yet exist, an approach on the basis of thermomechanical principles may be able to serve as the foundation for such a theory. With this in mind, as a first step, a mixed formulation is developed for fully coupled, spatially discretized linear thermoelasticity under the Lagrangian formalism by using Hamilton’s principle. A variational integration scheme is then proposed for the temporal discretization of the resulting Euler-Lagrange equations. With this discrete numerical time-step solution, it becomes possible, for proper choices of state variables, to restate the problem in the form of an optimization. Ultimately, this allows the formulation of a principle of minimum generalized complementary potential energy for the discrete-time thermoelastic system. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000346 [article] Mixed lagrangian formulation for linear thermoelastic response of structures [texte imprimé] / Georgios Apostolakis, Auteur ; Gary F. Dargush, Auteur . - 2012 . - pp.508-518. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 138 N° 5 (Mai 2012) . - pp.508-518 Mots-clés : Thermoelasticity, Variational methods, Mixed Lagrangian formulation Hamilton’s principle, Discrete variational calculus methods Flexibility Symplectic algorithms Résumé : Although a complete unified theory for elasticity, plasticity, and damage does not yet exist, an approach on the basis of thermomechanical principles may be able to serve as the foundation for such a theory. With this in mind, as a first step, a mixed formulation is developed for fully coupled, spatially discretized linear thermoelasticity under the Lagrangian formalism by using Hamilton’s principle. A variational integration scheme is then proposed for the temporal discretization of the resulting Euler-Lagrange equations. With this discrete numerical time-step solution, it becomes possible, for proper choices of state variables, to restate the problem in the form of an optimization. Ultimately, this allows the formulation of a principle of minimum generalized complementary potential energy for the discrete-time thermoelastic system. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000346

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