Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 245170, 28 pages
http://dx.doi.org/10.1155/2011/245170
Review Article

Coupled Numerical Methods to Analyze Interacting Acoustic-Dynamic Models by Multidomain Decomposition Techniques

Structural Engineering Department, Federal University of Juiz de Fora, Cidade Universitária, 36036-330 Juiz de Fora, MG, Brazil

Received 11 May 2011; Accepted 12 July 2011

Academic Editor: Luis Godinho

Copyright © 2011 Delfim Soares. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, vol. 1, Butterworth-Heinemann, Oxford, UK, 5th edition, 2002.
  2. J. Virieux, “P- SV wave propagation in heterogeneous media: velocity- stress finite-difference method,” Geophysics, vol. 51, no. 4, pp. 889–901, 1986. View at Google Scholar · View at Scopus
  3. B. Lombard and J. Piraux, “Numerical treatment of two-dimensional interfaces for acoustic and elastic waves,” Journal of Computational Physics, vol. 195, no. 1, pp. 90–116, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. H. Y. Lee, S. C. Lim, D. J. Min, B. D. Kwon, and M. Park, “2D time-domain acoustic-elastic coupled modeling: a cell-based finite-difference method,” Geosciences Journal, vol. 13, no. 4, pp. 407–414, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. K. M. Lim and H. Li, “A coupled boundary element/finite difference method for fluid-structure interaction with application to dynamic analysis of outer hair cells,” Computers and Structures, vol. 85, no. 11-14, pp. 911–922, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. O. Von Estorff and H. Antes, “On FEM-BEM coupling for fluid-structure interaction analyses in the time domain,” International Journal for Numerical Methods in Engineering, vol. 31, no. 6, pp. 1151–1168, 1991. View at Google Scholar · View at Scopus
  7. S. Amini, P. J. Harris, and D. T. Wilton, Coupled Boundary and Finite Element Methods for the Solution of the Dynamic Fluid-Structure Interaction Problem, Springer, Berlin, Germany, 1992.
  8. X. G. Zeng and F. Zhao, “A coupled FE and boundary integral equation method based on exterior domain decomposition for fluid-structure interface problems,” International Journal of Solids and Structures, vol. 31, no. 8, pp. 1047–1061, 1994. View at Google Scholar · View at Scopus
  9. H. M. Koh, J. K. Kim, and J. H. Park, “Fluid-structure interaction analysis of 3-D rectangular tanks by a variationally coupled BEM-FEM and comparison with test results,” Earthquake Engineering and Structural Dynamics, vol. 27, no. 2, pp. 109–124, 1998. View at Google Scholar · View at Scopus
  10. S. T. Lie, G. Yu, and Z. Zhao, “Coupling of BEM/FEM for time domain structural-acoustic interaction problems,” Computer Modeling in Engineering and Sciences, vol. 2, no. 2, pp. 171–181, 2001. View at Google Scholar · View at Scopus
  11. O. Czygan and O. Von Estorff, “Fluid-structure interaction by coupling BEM and nonlinear FEM,” Engineering Analysis with Boundary Elements, vol. 26, no. 9, pp. 773–779, 2002. View at Publisher · View at Google Scholar · View at Scopus
  12. L. Gaul and W. Wenzel, “A coupled symmetric BE-FE method for acoustic fluid-structure interaction,” Engineering Analysis with Boundary Elements, vol. 26, no. 7, pp. 629–636, 2002. View at Publisher · View at Google Scholar · View at Scopus
  13. A. Márquez, S. Meddahi, and V. Selgas, “A new BEM-FEM coupling strategy for two-dimensional fluid-solid interaction problems,” Journal of Computational Physics, vol. 199, no. 1, pp. 205–220, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. D. Soares, O. von Estorff, and W. J. Mansur, “Efficient non-linear solid-fluid interaction analysis by an iterative BEM/FEM coupling,” International Journal for Numerical Methods in Engineering, vol. 64, no. 11, pp. 1416–1431, 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. D. Soares and W. J. Mansur, “An efficient time-domain BEM/FEM coupling for acoustic-elastodynamic interaction problems,” Computer Modeling in Engineering and Sciences, vol. 8, no. 2, pp. 153–164, 2005. View at Google Scholar · View at Scopus
  16. A. Warszawski, D. Soares, and W. J. Mansur, “A FEM-BEM coupling procedure to model the propagation of interacting acoustic-acoustic/acoustic-elastic waves through axisymmetric media,” Computer Methods in Applied Mechanics and Engineering, vol. 197, no. 45–48, pp. 3828–3835, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. D. Soares, “Fluid-structure interaction analysis by optimised boundary element-finite element coupling procedures,” Journal of Sound and Vibration, vol. 322, no. 1-2, pp. 184–195, 2009. View at Publisher · View at Google Scholar · View at Scopus
  18. O. C. Zienkiewicz and P. Bettess, “Fluid-structure dynamic interaction and wave forces. An introduction to numerical treatment,” International Journal for Numerical Methods in Engineering, vol. 13, no. 1, pp. 1–16, 1978. View at Google Scholar · View at Scopus
  19. D. Komatitsch, C. Barnes, and J. Tromp, “Wave propagation near a fluid-solid interface: a spectral-element approach,” Geophysics, vol. 65, no. 2, pp. 623–631, 2000. View at Google Scholar · View at Scopus
  20. K. C. Park, C. A. Felippa, and R. Ohayon, “Partitioned formulation of internal fluid-structure interaction problems by localized lagrange multipliers,” Computer Methods in Applied Mechanics and Engineering, vol. 190, no. 24-25, pp. 2989–3007, 2001. View at Publisher · View at Google Scholar · View at Scopus
  21. L. Godinho, A. Tadeu, and F. J. Branco, “Wave scattering by infinite cylindrical shell structures submerged in a fluid medium,” Wave Motion, vol. 38, no. 2, pp. 131–149, 2003. View at Publisher · View at Google Scholar · View at Scopus
  22. X. Feng and Z. Xie, “A priori error estimates for a coupled finite element method and mixed finite element method for a fluid-solid interaction problem,” IMA Journal of Numerical Analysis, vol. 24, no. 4, pp. 671–698, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. D. Soares and W. J. Mansur, “Dynamic analysis of fluid-soil-structure interaction problems by the boundary element method,” Journal of Computational Physics, vol. 219, no. 2, pp. 498–512, 2006. View at Publisher · View at Google Scholar · View at Scopus
  24. D. Soares, W. J. Mansur, and D. L. Lima, “An explicit multi-level time-step algorithm to model the propagation of interacting acoustic-elastic waves using finite element/finite difference coupled procedures,” Computer Modeling in Engineering and Sciences, vol. 17, no. 1, pp. 19–34, 2007. View at Google Scholar · View at Scopus
  25. D. Soares, “Numerical modelling of acoustic-elastodynamic coupled problems by stabilized boundary element techniques,” Computational Mechanics, vol. 42, no. 6, pp. 787–802, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. M. R. Ross, C. A. Felippa, K. C. Park, and M. A. Sprague, “Treatment of acoustic fluid-structure interaction by localized Lagrange multipliers: formulation,” Computer Methods in Applied Mechanics and Engineering, vol. 197, no. 33-40, pp. 3057–3079, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. D. Soares, “An iterative time-domain algorithm for acoustic-elastodynamic coupled analysis considering meshless local Petrov-Galerkin formulations,” Computer Modeling in Engineering and Sciences, vol. 54, no. 2, pp. 201–221, 2009. View at Google Scholar · View at Scopus
  28. D. Soares, G. G. Rodrigues, and K. A. Gonçalves, “An efficient multi-time-step implicit-explicit method to analyze solid-fluid coupled systems discretized by unconditionally stable time-domain finite element procedures,” Computers & Structures, vol. 88, no. 5-6, pp. 387–394, 2010. View at Publisher · View at Google Scholar · View at Scopus
  29. Z. C. He, G. R. Liu, Z. H. Zhong, G. Y. Zhang, and A. G. Cheng, “Coupled analysis of 3D structuralacoustic problems using the edge-based smoothed finite element method/finite element method,” Finite Elements in Analysis and Design, vol. 46, no. 12, pp. 1114–1121, 2010. View at Publisher · View at Google Scholar
  30. Z. C. He, G. R. Liu, Z. H. Zhong, G. Y. Zhang, and A. G. Cheng, “A coupled ES-FEM/BEM method for fluidstructure interaction problems,” Engineering Analysis with Boundary Elements, vol. 35, no. 1, pp. 140–147, 2011. View at Publisher · View at Google Scholar
  31. R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 2007.
  32. G. C. Cohen, Higher-Order Numerical Methods for Transient Wave Equations, Springer, Berlin, Germany, 2002.
  33. T. J. R. Hughes, The Finite Element Method, Dover, New York, NY, USA, 1987.
  34. K. J. Bathe, Finite Element Procedures, Prentice-Hall, Englewood Cliffs, NJ, USA, 1996.
  35. M. A. Crisfield, Non-linear Finite Element Analysis of Solid Structures, vol. 1-2, John Wiley & Sons, Chichester, UK, 1991.
  36. T. Belytschko, W. K. Liu, and B. Moran, Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons, Chichester, UK, 2000.
  37. S. Atluri, The Meshless Method (MLPG) for Domain & BIE Discretizations, Tech Science Press, Encino, Calif, USA, 2004.
  38. G. R. Liu, Meshfree Methods, Moving beyond the Finite Element Method, CRC Press, Boca Raton, Fla, USA, 2nd edition, 2010.
  39. D. Soares and W. J. Mansur, “A time domain FEM approach based on implicit Green's functions for non-linear dynamic analysis,” International Journal for Numerical Methods in Engineering, vol. 62, no. 5, pp. 664–681, 2005. View at Publisher · View at Google Scholar · View at Scopus
  40. D. Soares, “A time-marching scheme based on implicit Green's functions for elastodynamic analysis with the domain boundary element method,” Computational Mechanics, vol. 40, no. 5, pp. 827–835, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  41. D. Soares, “A new family of time marching procedures based on Green's function matrices,” Computers & Structures, vol. 89, no. 1-2, pp. 266–276, 2011. View at Publisher · View at Google Scholar · View at Scopus
  42. J. C. Houbolt, “A recurrence matrix solution for the dynamic response of elastic aircraft,” Journal of the Aeronautical Sciences, vol. 17, pp. 540–550, 1950. View at Google Scholar
  43. N. M. Newmark, “A method of computation for structural dynamics,” ASCE Journal of Engineering Mechanics Division, vol. 85, pp. 67–94, 1959. View at Google Scholar
  44. W. J. Mansur, A time-stepping technique to solve wave propagation problems using the boundary element method, Ph.D. thesis, University of Southampton, England, UK, 1983.
  45. J. Dominguez, Boundary Elements in Dynamics, International Series on Computational Engineering, Computational Mechanics Publications, Southampton, UK, 1993.
  46. Boundary Elements in Acoustics, vol. 9 of Advances in Boundary Elements, WIT Press, Southampton, UK, 2000.
  47. D. Beskos and G. Maier, Boundary Element Advances in Solid Mecha, Springer, New York, NY, USA, 2003.
  48. J. A. M. Carrer and J. C. F. Telles, “A boundary element formulation to solve transient dynamic elastoplastic problems,” Computers & Structures, vol. 45, no. 4, pp. 707–713, 1992. View at Google Scholar · View at Scopus
  49. J. A. M. Carrer and W. J. Mansur, “Alternative time-marching schemes for elastodynamic analysis with the domain boundary element method formulation,” Computational Mechanics, vol. 34, no. 5, pp. 387–399, 2004. View at Publisher · View at Google Scholar · View at Scopus
  50. D. Soares, “Acoustic modelling by BEM-FEM coupling procedures taking into account explicit and implicit multi-domain decomposition techniques,” International Journal for Numerical Methods in Engineering, vol. 78, no. 9, pp. 1076–1093, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  51. J. W. Milles, “Integral transforms,” in Modern Mathematics for the Engineer, E. F. Beckenbach, Ed., pp. 82–84, McGraw-Hill, London, UK, 1961. View at Google Scholar
  52. G. Cohen and P. Joly, “Fourth order schemes for the heterogeneous acoustics equation,” Computer Methods in Applied Mechanics and Engineering, vol. 80, pp. 397–407, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  53. D. L. Lima, Through-riser acoustic communication system for ultra-deep water completion, M.S. thesis, Federal University of Rio de Janeiro, Brazil, 2004.