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La nouvelle approche hybride MAX-FEM pour la modélisation thermomécanique des couches minces

Abstract : This work introduces a new simplified finite elements method MAX-FEM based on hybrid analytical-numerical coupling. This method is intended to the multi-scales analysis of transient thermomechanical behavior of mediums containing thin layers such as bounded and coated structures. The MAX-FEM consists in correcting the classical Finite Elements Method (FEM) by correction matrices taking into account the presence of thin layers without any mesh refinement. The proposed correction is based on the analytical approach of Matched Asymptotic Expansions (MAE) and the numerical method of Partition of Unity Method (PUM). The developed approach can easily implemented under different numerical codes (MATLAB, ABAQUS, ...) and can be used to perform mechanical, thermal and thermomechanical analyses of 1D and 2D bounded and coated structures. The obtained results show a good accuracy with short computation time, and without any required mesh refinement. Also, the developed method overcomes the limitation of the MAE and PUM methods by exploiting the advantages of their coupling. Finally, the MAX-FEM approach was also used to develop an experimental test bench intended to the thermal characterization of thin layers. Indeed, a simple confrontation between the heat transfer in an homogeneous structure and a second structure with thin layer allows identifying the thermal conductivity in both transient and stationary regimes. The test bench is simple to release and the obtained results for brazed structure show a good accuracy of the developed approach.
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Abderrazzaq Ifis. La nouvelle approche hybride MAX-FEM pour la modélisation thermomécanique des couches minces. Autre. Université de Lorraine, 2014. Français. ⟨NNT : 2014LORR0044⟩. ⟨tel-01750702⟩

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