Browse > Article
http://dx.doi.org/10.12989/sem.2007.25.2.181

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)
Publication Information
Structural Engineering and Mechanics / v.25, no.2, 2007 , pp. 181-200 More about this Journal
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
two-phase media; transmitting boundary; near-field wave motion; decoupling technique;
Citations & Related Records

Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
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   DOI   ScienceOn
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   DOI   ScienceOn
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   DOI
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   DOI   ScienceOn
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   DOI   ScienceOn
7 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   DOI   ScienceOn
8 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   DOI
9 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   DOI   ScienceOn
10 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   DOI   ScienceOn
11 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)
12 Liao, Z.P. (1984), 'The simulation of near-field wave motion using FEM', Earthq. Eng Eng Vib., 2(1), 1-14, (in Chinese)   DOI
13 Liao, Z.P. (1996), 'Extrapolation non-reflection boundary conditions', Wave Motion, 24(1),117-138   DOI   ScienceOn
14 Men, F.L. (1982), 'On wave propagation in fluid-saturated porous media', In: Soil Dynamics and Earthquake Engineering Conference. Spain, Vol. 1
15 Liao, Z.P. (1999), 'Dynamic interaction of natural and man-made structures with earth medium', Earthq. Res. in China, 13(3), 367-408
16 Liao, Z.P. (2001), 'Transmitting boundary and radiation conditions at infinity', Science in China (Series E), 44(2),177-186   DOI   ScienceOn
17 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   DOI   ScienceOn
18 Prevost, J.H. (1985), 'Wave propagation in fluid-saturated porous media: An efficient finite element procedure', Soil. Dyn. Earthq. Eng., 4(4), 183-201   DOI   ScienceOn
19 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   DOI   ScienceOn
20 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   DOI   ScienceOn
21 Zienkiewicz, O.C. and Taylor, R.L. (1989), The Finite Element Method, London:McGraw-Hili
22 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   DOI   ScienceOn
23 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   DOI   ScienceOn
24 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   DOI   ScienceOn
25 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   DOI
26 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   DOI   ScienceOn