In this paper, the boundary finite element method (BFEM) is applied to dynamic fluid-structure interaction problems. The BFEM is employed to model the infinite fluid medium, while the structure is modeled by the finite element method (FEM). The relationship between the fluid pressure and the fluid velocity corresponding to the scattered wave is derived from the acoustic modeling. The BFEM is suitable for both finite and infinite domains, and it has advantages over other numerical methods. The resulting system of equations is symmetric and has no singularity problems. Two numerical examples are presented to validate the accuracy and efficiency of BFEM-FEM coupling for fluid-structure interaction problems.
Issue Section:
Technical Papers
1.
Hamdan
, F. H.
, 1999, “Near-Field Fluid-Structure Interaction Using Lagrangian Fluid Elements
,” Comput. Struct.
0045-7949, 71
, pp. 123
–141
.2.
Belytschko
, T.
, 1980, “Fluid-Structure Interaction
,” Comput. Struct.
0045-7949, 12
, pp. 459
–469
.3.
Bathe
, K. J.
, Nitikitpaiboon
, C.
, and Wang
, X.
, 1995, “A Mixed Displacement-Based Finite Element Formulation for Acoustic Fluid-Structure Interaction
,” Comput. Struct.
0045-7949, 56
, pp. 225
–237
.4.
Morand
, H.
, and Ohayon
, R.
, 1979, “Substructure Variational Analysis of the Vibrations of Coupled Fluid-Structure Systems. Finite Element Results
,” Int. J. Numer. Methods Eng.
0029-5981, 14
, pp. 741
–755
.5.
Mellado
, M.
, and Rodriguez
, R.
, 2001, “Efficient Solution of Fluid-Structure Vibration Problems
,” Appl. Numer. Math.
0168-9274, 36
, pp. 389
–400
.6.
Biswal
, K. C.
, Bhattacharyya
, S. K.
, and Sinha
, P. K.
, 2003, “Free-Vibration Analysis of Liquid-Filled Tank With Baffles
,” J. Sound Vib.
0022-460X, 259
, pp. 177
–192
.7.
Olson
, L. G.
, and Bathe
, K. J.
, 1985, “Analysis of Fluid-Structure Interactions. A Direct Symmetric Coupled Formulation Based on the Fluid Velocity Potential
,” Comput. Struct.
0045-7949, 21
, pp. 21
–32
.8.
Pal
, N. C.
, Bhattacharyya
, S. K.
, and Sinha
, P. K.
, 2003, “Non-Linear Coupled Slosh Dynamics of Liquid-Filled Laminated Composite Containers: A Two Dimensional Finite Element Approach
,” J. Sound Vib.
0022-460X, 261
, pp. 729
–749
.9.
Nitikitpaiboon
, C.
, and Bathe
, K. J.
, 1993, “An Arbitrary Lagrangian-Eulerian Velocity Potential Formulation for Fluid-Structure Interaction
,” Comput. Struct.
0045-7949, 47
, pp. 871
–891
.10.
Mindlin
, R. D.
, and Bleich
, H. H.
, 1953, “Response of an Elastic Cylindrical Shell to a Transverse Step Shock Wave
,” ASME J. Appl. Mech.
0021-8936, 20
, pp. 189
–195
.11.
DiMaggio
, F. L.
, Sandler
, I. S.
, and Rubin
, D.
, 1981, “Uncoupling Approximations in Fluid-Structure Interaction Problems with Cavitation
,” ASME J. Appl. Mech.
0021-8936, 48
, pp. 753
–756
.12.
Hamdan
, F. H.
, and Dowling
, P. J.
, 1995, “Far-Field Fluid-Structure Interaction Formulation and Validation
,” Comput. Struct.
0045-7949, 56
, pp. 949
–958
.13.
Fan
, S. C.
, Wang
, K.
, Yu
, G. Y.
, and Lie
, S. T.
, 2001, “Spline Shell Element and Plane-Wave Approximation for Dynamic Response of Submerged Structures
,” Comput. Struct.
0045-7949, 79
, pp. 1635
–1644
.14.
Geers
, T. L.
, 1969, “Excitation of an Elastic Cylindrical Shell by a Transient Acoustic Wave
,” ASME J. Appl. Mech.
0021-8936, 36
, pp. 459
–469
.15.
Ranlet
, D.
, DiMaggio
, F. L.
, Bleich
, H. H.
, and Baran
, M. L.
, 1977, “Elastic Response of Submerged Shells with Internally Attached Structures to Shock Wave Loading
,” Comput. Struct.
0045-7949, 7
, pp. 355
–364
.16.
Zilliacus
, S.
, 1983, “Fluid-Structure Interaction and ADINA
,” Comput. Struct.
0045-7949, 17
, pp. 763
–773
.17.
Givoli
, D.
, 1991, “Non-Reflecting Boundary Conditions: A Review
,” J. Comput. Phys.
0021-9991, 94
, pp. 1
–29
.18.
Estorff
, O. V.
, and Antes
, H.
, 1991, “On FEM-BEM Coupling for Fluid-Structure Interaction Analyses in the Time Domain
,” Int. J. Numer. Methods Eng.
0029-5981, 31
, pp. 1151
–1168
.19.
Czygan
, O.
, and Estorff
, O. V.
, 2002, “Fluid-Structure Interaction by Coupling BEM and Nonlinear FEM
,” Eng. Anal. Boundary Elem.
0955-7997, 26
, pp. 773
–779
.20.
Yu
, G. Y.
, Lie
, S. T.
, and Fan
, S. C.
, 2002, “A Stable BEM/FEM Coupling Procedure Applied in Time Domain Fluid-Structure Interaction Problems
,” J. Eng. Mech.
0733-9399, 128
, pp. 909
–915
.21.
Song
, C.
, and Wolf
, J. P.
, 1996, “Consistent Infinitesimal Finite-Element Cell Method: Three-Dimensional Vector Wave Equation
,” Int. J. Numer. Methods Eng.
0029-5981, 39
, pp. 2189
–2208
.22.
Wolf
, J. P.
, and Song
, C.
, 1996, “Consistent Infinitesimal Finite-Element Cell Method: Three-Dimensional Scalar Wave Equation
,” ASME J. Appl. Mech.
0021-8936, 63
, pp. 650
–654
.23.
Wolf
, J. P.
, and Song
, C.
, 1996, Finite-Element Modeling of Unbounded Media
, Wiley
, Chichester.24.
Dasupta
, G.
, 1982, “A Finite Element Formulation for Unbounded Homogeneous Continua
,” ASME J. Appl. Mech.
0021-8936, 49
, pp. 136
–140
.25.
Song
, C.
, and Wolf
, J. P.
, 1997, “The Scaled Boundary Finite-Element Method-Alias Consistent Infinitesimal Finite-Element Cell Method-for Elastodynamics
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 147
, pp. 329
–355
.26.
Deeks
, J. A.
, and Wolf
, J. P.
, 2002, “A Virtual Work Derivation of the Scaled Boundary Finite-Element Method for Elastostatics
,” Comput. Mech.
0178-7675, 28
, pp. 489
–504
.27.
Lamb
, H.
, 1932, Hydrodynamics
, 6th ed., Dover
, New York, pp. 476
–477
.28.
Mansur
, W. J.
, Yu
, G. Y.
, Carrer
, J. A. M.
, Lie
, S. T.
, and Siqueira
, E. F. N.
, 2000, “The θ Scheme for Time-Domain BEM/FEM Coupling Applied to the 2-D Scalar Wave Equation
,” Commun. Numer. Methods Eng.
1069-8299, 16
, pp. 439
–448
.29.
Huang
, H.
, 1970, “An Exact Analysis of the Transient Interaction of Acoustic Plane Waves with a Cylindrical Elastic Shell
,” ASME J. Appl. Mech.
0021-8936, 37
, pp. 1091
–1099
.Copyright © 2005
by American Society of Mechanical Engineers
You do not currently have access to this content.
