Structural Engineering and Mechanics

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A decoupling FEM for simulating near-field wave motion in two-phase media

  • Chen, S.L. (College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics) ;
  • Liao, Z.P. (Institute of Engineering Mechanics, China Seismological Bureau) ;
  • Chen, J. (The State Key Laboratory of Vibration, Shock & Noise, Shanghai Jiao Tong University)
  • Received : 2004.11.16
  • Accepted : 2006.08.14
  • Published : 2007.01.30
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Abstract

A decoupling technique for simulating near-field wave motions in two-phase media is introduced in this paper. First, an equivalent but direct weighted residual method is presented in this paper to solve boundary value problems more explicitly. We applied the Green's theorem for integration by parts on the equivalent integral statement of the field governing equations and then introduced the Neumann conditions directly. Using this method and considering the precision requirement in wave motion simulation, a lumped-mass FEM for two-phase media with clear physical concepts and convenient implementation is derived. Then, considering the innate attenuation character of the wave in two-phase media, an attenuation parameter is introduced into Liao's Multi-Transmitting Formula (MTF) to simulate the attenuating outgoing wave in two-phase media. At last, two numerical experiments are presented and the numerical results are compared with the analytical ones demonstrating that the lumped-mass FEM and the generalized MTF introduced in this paper have good precision.

Keywords

Acknowledgement

Supported by : Natural Science Foundation of China

References

  1. Chen, J. (1994), 'Time domain fundamental solution to Biot's complete equations of dynamic poroelasticity, Part I: Two-dimensional solution', Int. J Solids Struct., 31(10), 1447-1490 https://doi.org/10.1016/0020-7683(94)90186-4
  2. Chen, J. (1994), 'Time domain fundamental solution to Biot's complete equations of dynamic poroelasticity, Part II: Three-dimensional solution', Int. J Solids Struct., 31(2), 169-202 https://doi.org/10.1016/0020-7683(94)90049-3
  3. Chen, S.L. (2002), 'Numerical simulation for near-field wave motion in two-phase media', Ph.D Dissertation, Institute of Engineering Mechanics, China Seismological Bureau, Harbin, China
  4. Chen, S.L. and Liao, Z.P. (2003), 'Multi-transmitting fonnula for attenuating waves', Acta Seismological Sinica, 16(3), 283-291 https://doi.org/10.1007/s11589-003-0032-7
  5. Degrande, G and Roeck, GD. (1993), 'An absorbing boundary condition for wave propagation in saturated poroelastic media -Part II: Finite element fonnulation', Soil Dyn. Earthq. Eng, 12, 423-432 https://doi.org/10.1016/0267-7261(93)90005-C
  6. Degrande, G and Roeck, GD. (1993), 'An absorbing boundary condition for wave propagation in saturated poroelastic media-Part I: Fonnulation and efficiency evaluation', Soil Dyn. Earthq. Eng, 12,411-421 https://doi.org/10.1016/0267-7261(93)90004-B
  7. Diebels, S. and Ehlers, W. (1996), 'Dynamic analysis of a fully saturated porous medium accounting for geometrical and material non-linearities', Int. J Numer. Meth. Eng, 39(1), 81-97 https://doi.org/10.1002/(SICI)1097-0207(19960115)39:1<81::AID-NME840>3.0.CO;2-B
  8. Gajo, A. and Mongiovi, L. (1995), 'An analytical solution for the transient response of saturated linear elastic porous medium', Int. J Numer. Anal. Meth. Geomech., 19,399-413 https://doi.org/10.1002/nag.1610190603
  9. Gajo, A., Saetta, A. and Vitaliani, R. (1996), 'Silent boundary conditions for wave propagation in saturated porous media', Int. J Numer. Anal. Meth. Geomech., 20, 253-273 https://doi.org/10.1002/(SICI)1096-9853(199604)20:4<253::AID-NAG820>3.0.CO;2-N
  10. Huang, M.S., Yue, Z.Q., Tham, L.G et al. (2004), 'On the stable finite element procedures for dynamic problems of saturated porous media', Int. J Numer. Meth. Eng, 61(9), 1421-1450 https://doi.org/10.1002/nme.1115
  11. Karim, M.R., Nogami, T. and Wang, J.G (2002), 'Analysis of transient response of saturated porous elastic soil under cyclic loading using element-free Galerkin method', Int. J Solids Struct., 39, 6011-6033 https://doi.org/10.1016/S0020-7683(02)00497-3
  12. Kim, S.H., Kim, K.J. and Blouin, S.E. (2002), 'Analysis of wave propagation in saturated porous media. I. Theoretical solution', Comput. Meth. Appl. Mech. Eng, 191(37-38),4061-4073 https://doi.org/10.1016/S0045-7825(02)00339-0
  13. Li, C., Borja, R.I. and Regueiro, R.A. (2004), 'Dynamics of porous media at finite strain', Comput. Meth. Appl. Mech. Eng., 193, 3837-3870 https://doi.org/10.1016/j.cma.2004.02.014
  14. Li, X.J., Liao, Z.P. and Du, X.L. (1992), 'A explicit integration procedure for dynamic system with damping', Engineering Mechanics, Science Press, (in Chinese)
  15. Liao, Z.P. (1984), 'The simulation of near-field wave motion using FEM', Earthq. Eng Eng Vib., 2(1), 1-14, (in Chinese) https://doi.org/10.1007/BF02857534
  16. Liao, Z.P. (1996), 'Extrapolation non-reflection boundary conditions', Wave Motion, 24(1),117-138 https://doi.org/10.1016/0165-2125(96)00010-8
  17. Liao, Z.P. (1999), 'Dynamic interaction of natural and man-made structures with earth medium', Earthq. Res. in China, 13(3), 367-408
  18. Liao, Z.P. (2001), 'Transmitting boundary and radiation conditions at infinity', Science in China (Series E), 44(2),177-186 https://doi.org/10.1007/BF02879660
  19. Liao, Z.P. and Wong, H.L. (1984), 'A transmitting boundary for the numerical simulation of elastic wave propagation', Soil Dyn. Earthq. Eng., 3(1), 174-183 https://doi.org/10.1016/0261-7277(84)90033-0
  20. Men, F.L. (1982), 'On wave propagation in fluid-saturated porous media', In: Soil Dynamics and Earthquake Engineering Conference. Spain, Vol. 1
  21. Prevost, J.H. (1985), 'Wave propagation in fluid-saturated porous media: An efficient finite element procedure', Soil. Dyn. Earthq. Eng., 4(4), 183-201 https://doi.org/10.1016/0261-7277(85)90038-5
  22. Sandhu, R.S. and Hong, S.J. (1987), 'Dynamics of fluid-saturated soils variational fonnulation', Int. J Numer. Anal. Methods Geomech., 11(1), 241-255 https://doi.org/10.1002/nag.1610110303
  23. Yiagos, A.N. and Prevost, J.H. (1991), 'Two-phase elasto-plastic seismic response of earth dams: Appliation', Soil. Dyn. Earthq. Eng., 10(7), 371-381 https://doi.org/10.1016/0267-7261(91)90026-V
  24. Zhao, C.G, Li, W.H. and Wang, J.T. (2005), 'An explicit finite element method for Biot dynamic fonnulation in fluid-saturated porous media and its application to a rigid foundation', J Sound Vib., 282, 1169-1181 https://doi.org/10.1016/j.jsv.2004.03.073
  25. Zienkiewicz, O.C. and Shiomi, T. (1984), 'Dynamic behaviour of saturated porous media; the generalized biot fonnulation and its numerical solution', Int. J Numer. Meth. Geomech., 8(1), 71-96 https://doi.org/10.1002/nag.1610080106
  26. Zienkiewicz, O.C. and Taylor, R.L. (1989), The Finite Element Method, London:McGraw-Hili