A port-Hamiltonian formulation of linear thermoelasticity and its mixed finite element discretization

Andrea Brugnoli (1) , Daniel Alazard (2) , Valérie Pommier-Budinger (2) , Denis Matignon (3)

1 University of Twente
2 DCAS - Département Conception et conduite des véhicules Aéronautiques et Spatiaux
3 DISC - Département d'Ingénierie des Systèmes Complexes

A port-Hamiltonian formulation for general linear coupled thermoelasticity and for the thermoelastic bending of thin structures is presented. The construction exploits the intrinsic modularity of port-Hamiltonian systems to obtain a formulation of linear thermoelasticity as an interconnection of the elastodynamics and heat equations. The derived model can be readily discretized by using mixed finite elements. The discretization is structure-preserving, since the main features of the system are retained at a discrete level. The proposed model and discretization strategy are validated against a benchmark problem of thermoelasticity, the Danilovskaya problem.

Mots clés: Port-Hamiltonian systems; Linear coupled thermoelasticity; Mixed finite elements; Structure preserving discretization

Domaines: Mathématiques générales [math.GM]

Andrea Brugnoli, Daniel Alazard, Valérie Pommier-Budinger, Denis Matignon. A port-Hamiltonian formulation of linear thermoelasticity and its mixed finite element discretization. Journal of Thermal Stresses, 2021, 44 (6), pp.643-661. ⟨10.1080/01495739.2021.1917322⟩. ⟨hal-03230436⟩