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.

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
.
You do not currently have access to this content.