Coupled systems mechanics

  • 제7권1호
  • /
  • Pages.5-25
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  • 2018
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  • 2234-2184(pISSN)
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  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Linear elastic mechanical system interacting with coupled thermo-electro-magnetic fields

  • Moreno-Navarro, Pablo (Sorbonne Universites-Universite de Technologie Compiegne, Laboratoire Roberval de Mecanique) ;
  • Ibrahimbegovic, Adnan (Sorbonne Universites-Universite de Technologie Compiegne, Laboratoire Roberval de Mecanique) ;
  • Perez-Aparicio, Jose L. (Department of Continuum Mechanics & Theory of Structures, Universitat Politecnica de Valencia)
  • 투고 : 2016.12.19
  • 심사 : 2017.05.26
  • 발행 : 2018.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

A fully-coupled thermodynamic-based transient finite element formulation is proposed in this article for electric, magnetic, thermal and mechanic fields interactions limited to the linear case. The governing equations are obtained from conservation principles for both electric and magnetic flux, momentum and energy. A full-interaction among different fields is defined through Helmholtz free-energy potential, which provides that the constitutive equations for corresponding dual variables can be derived consistently. Although the behavior of the material is linear, the coupled interactions with the other fields are not considered limited to the linear case. The implementation is carried out in a research version of the research computer code FEAP by using 8-node isoparametric 3D solid elements. A range of numerical examples are run with the proposed element, from the relatively simple cases of piezoelectric, piezomagnetic, thermoelastic to more complicated combined coupled cases such as piezo-pyro-electric, or piezo-electro-magnetic. In this paper, some of those interactions are illustrated and discussed for a simple geometry.

키워드

참고문헌

  1. Aboudi, J. (2001), "Micromechanical analysis of fully coupled electro-magneto-thermo-elastic multiphase composites", Smart Mater. Struct., 10(5), 867. https://doi.org/10.1088/0964-1726/10/5/303
  2. Allik, H. and Hughes, T. (1970), "Finite element method for piezoelectric vibration", J. Numer. Meth. Eng., 2(2), 151-157. https://doi.org/10.1002/nme.1620020202
  3. Babuska, I., Szabo, B.A. and Katz, I. (1981), "The p-version of the finite element method", SIAM J. Numer. Analy., 18(3), 515-545. https://doi.org/10.1137/0718033
  4. Balanis, C. (1989), Advanced Engineering Electromagnetics, John Wiley & Sons.
  5. Chen, W., Lee, K. and Ding, H. (2004), "General solution for transversely isotropic magneto-electrothermoelasticity and the potential theory method", J. Eng. Sci., 42(13), 1361-1379. https://doi.org/10.1016/j.ijengsci.2004.04.002
  6. De Groot, S. and Mazur, P. (1984), Non-Equilibrium Thermodynamics, Dover.
  7. Duczek, S. and Gabbert, U. (2013), "Anisotropic hierarchic finite elements for the simulation of piezoelectric smart structures", Eng. Comput., 30(5), 682-706. https://doi.org/10.1108/EC-08-2013-0005
  8. Ferrari, A. and Mittica, A. (2013), "Thermodynamic formulation of the constitutive equations for solids and fluids", Energy Convers. Manage., 66, 77-86. https://doi.org/10.1016/j.enconman.2012.09.028
  9. Fung, R.F., Huang, J.S. and Jan, S.C. (2000), "Dynamic analysis of a piezothermoelastic resonator with various shapes", J. Vibr. Acoust., 122(3), 244-253. https://doi.org/10.1115/1.1303123
  10. Gornandt, A. and Gabbert, U. (2002), "Finite element analysis of thermopiezoelectric smart structures", Acta Mech., 154(1), 129-140. https://doi.org/10.1007/BF01170703
  11. Hou, P., Ding, H. and Leung, A. (2006), "The transient responses of a special non-homogeneous magnetoelectro- elastic hollow cylinder for axisymmetric plane strain problem", J. Sound Vibr., 291(1), 19-47. https://doi.org/10.1016/j.jsv.2005.05.022
  12. Ibrahimbegovic, A. (2009), Nonlinear Solid Mechanics: Theoretical Formulations and Finite Element Solution Methods, Springer Science & Business Media.
  13. Jiang, J.P. and Li, D.X. (2007), "A new finite element model for piezothermoelastic composite beam", J. Sound Vibr., 306(3), 849-864. https://doi.org/10.1016/j.jsv.2007.06.023
  14. Lezgy-Nazargah, M., Vidal, P. and Polit, O. (2013), "An efficient finite element model for static and dynamic analyses of functionally graded piezoelectric beams", Compos. Struct., 104, 71-84. https://doi.org/10.1016/j.compstruct.2013.04.010
  15. Li, J. (2000), "Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials", J. Eng. Sci., 38(18), 1993-2011. https://doi.org/10.1016/S0020-7225(00)00014-8
  16. Moreno-Navarro, P., Ibrahimbegovic, A. and Perez-Aparicio, J. (2017), "Plasticity coupled with thermoelectric fields: Thermodynamics framework and finite element method computations", Comput. Meth. Appl. Mech. Eng., 315, 50-72. https://doi.org/10.1016/j.cma.2016.10.038
  17. Pan, E. (2001), "Exact solution for simply supported and multilayered magneto-electro-elastic plates", J. Appl. Mech., 68(4), 608-618. https://doi.org/10.1115/1.1380385
  18. Perez-Aparicio, J.L., Palma, R. and Taylor, R.L. (2016), "Multiphysics and thermodynamic formulations for equilibrium and non-equilibrium interactions: Non-linear finite elements applied to multi-coupled active materials", Archiv. Comput. Meth. Eng., 23(3), 535-583. https://doi.org/10.1007/s11831-015-9149-9
  19. Ramirez, F., Heyliger, P.R. and Pan, E. (2006), "Free vibration response of two-dimensional magnetoelectroelastic laminated plates", J. Sound Vibr., 292(3), 626-644. https://doi.org/10.1016/j.jsv.2005.08.004
  20. Rao, S. and Sunar, M. (1993), "Analysis of distributed thermopiezoelectric sensors and actuators inadvanced intelligent structures", AIAA J., 31(7), 1280-1286. https://doi.org/10.2514/3.11764
  21. Ryu, J., Carazo, A., Uchino, K. and Kim, H. (2001), "Magnetoelectric properties in piezoelectric and magnetostrictive laminate composites", Jap. J. Appl. Phys., 40(8R), 4948. https://doi.org/10.1143/JJAP.40.4948
  22. Safari, A. and Akdogan, E. (2008), Piezoelectric and Acoustic Materials for Transducer Applications, Springer Science & Business Media.
  23. Smith, R. (2005), Smart Material Systems: Model Development, Siam.
  24. Wang, X. and Zhong, Z. (2003), "A finitely long circular cylindrical shell of piezoelectric/piezomagnetic composite under pressuring and temperature change", J. Eng. Sci., 41(20), 2429-2445. https://doi.org/10.1016/S0020-7225(03)00215-5
  25. Zienkiewicz, O. and Taylor, R. (2005), The Finite Element Method, Elsevier.

피인용 문헌

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