Coupled systems mechanics

  • 제4권3호
  • /
  • Pages.263-277
  • /
  • 2015
  • /
  • 2234-2184(pISSN)
  • /
  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Elastodynamic analysis by a frequency-domain FEM-BEM iterative coupling procedure

  • Soares, Delfim Jr. (Structural Engineering Department, Federal University of Juiz de Fora) ;
  • Goncalves, Kleber A. (Department of Civil Engineering, Federal University of Rio de Janeiro) ;
  • de Faria Telles, Jose Claudio (Department of Civil Engineering, Federal University of Rio de Janeiro)
  • 투고 : 2014.11.06
  • 심사 : 2015.09.15
  • 발행 : 2015.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents a coupled FEM-BEM strategy for the numerical analysis of elastodynamic problems where infinite-domain models and complex heterogeneous media are involved, rendering a configuration in which neither the Finite Element Method (FEM) nor the Boundary Element Method (BEM) is most appropriate for the numerical analysis. In this case, the coupling of these methodologies is recommended, allowing exploring their respective advantages. Here, frequency domain analyses are focused and an iterative FEM-BEM coupling technique is considered. In this iterative coupling, each sub-domain of the model is solved separately, and the variables at the common interfaces are iteratively updated, until convergence is achieved. A relaxation parameter is introduced into the coupling algorithm and an expression for its optimal value is deduced. The iterative FEM-BEM coupling technique allows independent discretizations to be efficiently employed for both finite and boundary element methods, without any requirement of matching nodes at the common interfaces. In addition, it leads to smaller and better-conditioned systems of equations (different solvers, suitable for each sub-domain, may be employed), which do not need to be treated (inverted, triangularized etc.) at each iterative step, providing an accurate and efficient methodology.

키워드

참고문헌

  1. Bathe, K.J. (1996), Finite Element Procedures, Prentice Hall Inc., New Jersey.
  2. Ben Belgacem, F. (1999), "The mortar finite element methodwith Lagrange multipliers", Numerische Mathematik, 84, 173-197. https://doi.org/10.1007/s002110050468
  3. Bendali, A., Boubendir, Y. and Fares, M. (2007), "A FETI-like domain decomposition method for coupling finite elements and boundary elements in large-size problems of acoustic scattering", Comput. Struct., 85(9), 526-535. https://doi.org/10.1016/j.compstruc.2006.08.029
  4. Bernardi, C., Maday, Y. and Patera, A.T. (1990), A New Non Conforming Approach to Domain Decomposition: The Mortar Element Method. College de France Seminar, Pitman, H. Brezis, J.-L Lions.
  5. Beskos, D.E. (2003), "Dynamic analysis of structures and structural systems", (Eds., Beskos, D.E. and Maier, G.), Boundary Element Advances in Solid Mechanics, CISM International Centre for Mechanical Sciences No. 440, Springer-Verlag, Wien, New York.
  6. Boumaiza, D. and Aour, B. (2014), "On the efficiency of the iterative coupling FEM-BEM for solving the elasto-plastic problems", Eng. Struct., 72, 12-25 https://doi.org/10.1016/j.engstruct.2014.03.036
  7. Dominguez, J. (1993), Boundary elements in dynamics, Computational Mechanics Publications, Southampton and Boston.
  8. Elleithy, W. (2012), "Multi-region adaptive finite element-boundary element method for elasto-plastic analysis", Int. J. Comput.Math., 89(11), 1525-1539. https://doi.org/10.1080/00207160.2012.695352
  9. Elleithy, W.M., Al-Gahtani, H.J. and El-Gebeily, M. (2001), "Iterative coupling of BE and FE methods in elastostatics", Eng. Anal. Bound. Elem., 25(8), 685-695. https://doi.org/10.1016/S0955-7997(01)00054-6
  10. Elleithy, W. and Grzhibovskis, R. (2009), "An adaptive domain decomposition coupled finite element-boundary element method for solving problems in elasto-plasticity", Int. J. Numer. Meth. Eng., 79, 1019-1104. https://doi.org/10.1002/nme.2608
  11. Godinho, L. and Soares, D. (2013), "Frequency domain analysis of interacting acoustic-elastodynamic models taking into account optimized iterative coupling of different numerical methods", Eng. Anal. Bound. Elem., 37, 1074-1088. https://doi.org/10.1016/j.enganabound.2013.04.006
  12. Gosselet, P. and Rey, C. (2006), "Non-overlapping domain decomposition methods in structural mechanics", Arch. Comput. Meth. Eng., 13(4), 515-572. https://doi.org/10.1007/BF02905857
  13. Hughes, T.J.R. (2000), The Finite Element Method - Linear Static and Dynamic Finite Element Analysis, Dover Publications, New York.
  14. Jahromi, H.Z., Izzuddin, B.A. and Zdravkovic, L. (2009), "A domain decomposition approach for coupled modelling of nonlinear soil-structure interaction", Comput. Method. Appl. M., 198(33-36), 2738-2749. https://doi.org/10.1016/j.cma.2009.03.018
  15. Lin, C.C., Lawton, E.C., Caliendo, J.A. and Anderson, L.R. (1996), "An iterative finite element-boundary element algorithm", Comput. Struct., 59(5), 899-909. https://doi.org/10.1016/0045-7949(95)00285-5
  16. Soares, D. (2008), "An optimised FEM-BEM time-domain iterative coupling algorithm for dynamic analyses", Comput. Struct., 86(19-20), 1839-1844. https://doi.org/10.1016/j.compstruc.2008.04.001
  17. Soares, D. (2012), "FEM-BEM iterative coupling procedures to analyze interacting wave propagation models: fluid-fluid, solid-solid and fluid-solid analyses", Coupled Syst. Mech., 1(1), 19-37. https://doi.org/10.12989/csm.2012.1.1.019
  18. Soares, D. and Godinho, L. (2012), "An optimized BEM-FEM iterative coupling algorithm for acoustic-elastodynamic interaction analyses in the frequency domain", Comput. Struct., 106-107, 68-80. https://doi.org/10.1016/j.compstruc.2012.04.010
  19. Soares, D. and Godinho, L. (2014), "An overview of recent advances in the iterative analysis of coupled models for wave propagation", J. Appl. Math., 2014, Article ID 426283.
  20. Soares, D., von Estorff, O. and Mansur, W.J. (2004), "Iterative coupling of BEM and FEM for nonlinear dynamic analyses", Comput. Mech., 34, 67-73.
  21. Vion, A. and Guezaine, C. (2014), "Double sweep preconditionner for optimized Scwarz methods applied to Helmholtz problem", J. Comput. Phys., 266, 171-190. https://doi.org/10.1016/j.jcp.2014.02.015

피인용 문헌

  1. Iterative coupling of precise integration FEM and TD-BEM for elastodynamic analysis vol.67, pp.4, 2015, https://doi.org/10.12989/sem.2018.67.4.317
  2. Transversely isotropic thick plate with two temperature & GN type-III in frequency domain vol.8, pp.1, 2015, https://doi.org/10.12989/csm.2019.8.1.055
  3. Thermomechanical interactions in a transversely isotropic magneto thermoelastic solids with two temperatures and rotation due to time harmonic sources vol.8, pp.3, 2015, https://doi.org/10.12989/csm.2019.8.3.219