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CivilComp Proceedings
ISSN 17593433 CCP: 100
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping
Paper 87
Adaptive Model Reduction for Thermoelastic Problems M.G. Larson and H. Jakobsson
Department of Mathematics and Mathematical Statistics, Umeå University, Sweden M.G. Larson, H. Jakobsson, "Adaptive Model Reduction for Thermoelastic Problems", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Engineering Computational Technology", CivilComp Press, Stirlingshire, UK, Paper 87, 2012. doi:10.4203/ccp.100.87
Keywords: model reduction, component mode synthesis, adaptivity, a posteriori, error estimation.
Summary
Many important problems in industry are the so called multiphysics
problems which involve several different types of physics. One such
problem is thermoelastic stress analysis where the objective is to
predict the elastic strain of a material caused by heat flow in order
to prevent structural failure. A common technique for simulating
thermoelasticity is to connect two finite element solvers, one for
heat transfer and one for elastic deformation, into a network where
each physics is solved for and data exchanged between the solvers.
In this paper we present a method to automatically control the reduction error in both the thermal and elastic solver for a oneway coupled thermoelastic problem where each of the physics is approximated using the component mode synthesis (CMS) model reduction method. The method combines the methodology for a posteriori error estimation for CMS developed in [1,2], with that for a posteriori error estimation for multiphysics problems developed in [3,4,5]. The error estimate measures the difference between the reduced and the full finite element solution. A feature of the estimate is that it automatically gives a quantitative measure of the propagation of the error between the thermal and elastic solvers with respect to a certain computational goal. The results presented extend the results in [6] by allowing temperature dependendent elastic parameters, leading to a linearized thermal dual problem. The analytical results are accompanied with a numerical example. References
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