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On the Validation of the Proper Generalized Decomposition Method with Finite Element Method: 3D Heat Problem Under Cyclic Loading

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Mechanism, Machine, Robotics and Mechatronics Sciences

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 58))

Abstract

Polymers are widely used in machine design, biomedical engineering, aircraft, and mechatronics. Certainly, these products are subjected to thermo-mechanical loading. For this reason, dealing with the fatigue criteria for viscous polymers is essential. In fact, this requires a large number of cycles to reach the accommodated cycle. These materials have a thermoviscoelastic behavior that has already been studied within the Finite Element Method (FEM). However, a very large computation time or a non-convergence has been noticed. In this paper, we considered a 3D thermal problem under cyclic load in which three main parts are considered. Firstly, the problem is studied using the Proper Generalized Decomposition method (PGD) where it shows a gain in the computation time compared to the classical FEM with a relative error less than 5%. Secondly, different time scales are taken into consideration: the cyclic time (load) and the characteristic one (material properties), where different relaxation times lead to various responses of the polymer. A link between these times should be established. Finally, the effect of the spatial point position on the evolution of the temperature within the domain is investigated.

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Authors and Affiliations

  1. International University of Beirut, Beirut, Lebanon

    A. AL Takash & M. Hammoud

  2. Institut Pprime, ISAE-ENSMA Poitiers, Poitou, France

    A. AL Takash, M. Beringhier & J. C. Grandidier

Authors
  1. A. AL Takash
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  2. M. Beringhier
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  3. M. Hammoud
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  4. J. C. Grandidier
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Corresponding author

Correspondence to M. Hammoud .

Editor information

Editors and Affiliations

  1. Faculty of Engineering, CRSI, Lebanese University , Roumieh, Lebanon

    Rany Rizk

  2. Department of Electrical and Computer Engineering, American University of Beirut, Beirut, Lebanon

    Mariette Awad

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AL Takash, A., Beringhier, M., Hammoud, M., Grandidier, J.C. (2019). On the Validation of the Proper Generalized Decomposition Method with Finite Element Method: 3D Heat Problem Under Cyclic Loading. In: Rizk, R., Awad, M. (eds) Mechanism, Machine, Robotics and Mechatronics Sciences. Mechanisms and Machine Science, vol 58. Springer, Cham. https://doi.org/10.1007/978-3-319-89911-4_1

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  • DOI: https://doi.org/10.1007/978-3-319-89911-4_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-89910-7

  • Online ISBN: 978-3-319-89911-4

  • eBook Packages: EngineeringEngineering (R0)

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