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Variational Integrators for Thermomechanical Coupled Dynamic Systems with Heat Conduction
Author(s) -
Kern Dominik,
Bär Sebastian,
Groß Michael
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410016
Subject(s) - variational integrator , discretization , variational principle , mathematics , hamilton's principle , thermal conduction , integrator , thermoelastic damping , mathematical analysis , calculus of variations , classical mechanics , equations of motion , physics , thermal , thermodynamics , quantum mechanics , voltage
Abstract Variational integrators are modern time‐integration schemes based on a discretization of the underlying variational principle. They thus skip the direct formulation and time discretization of partial differential equations. In mechanics, Hamilton's Principle is approximated by an action sum whose variation should be equal to zero, resulting in discrete Euler‐Lagrange Equations or equivalently in discrete Position‐Momentum Equations. Variational integrators are, by design, structure preserving (symplecticity) and show excellent long‐time behavior. In order to consider the coupling between mechanical and thermal quantities, Hamilton's principle is extended by using the notion of thermacy as thermal analogue to mechanical displacements. From this variational formulation, a variational integrator using the generalized trapezoidal rule is constructed exemplarily. A thermoelastic double pendulum with heat conduction serves as a model problem. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)