In this paper the fundamental solutions for an infinite poroelastic moderately thick plate and analytical solutions for a circular plate saturated by a incompressible fluid are derived in the Laplace transform domain. In order to obtain the solutions in the time domain, the Durbin’s Laplace transform inverse method has been used with high accuracy. The formulations using the boundary integral equation method can be derived directly with these fundamental solutions. In addition, the analytical solutions for a circular plate can be used to validate the accuracy of numerical algorithms such as the boundary element method and the method of fundamental solution. The deflection, moment, and equivalent moment in the time domain for a circular plate, subjected to uniform load and a concentrated force are presented, respectively. The analytical solutions demonstrate that interaction between the solid and flow is significant.

References

References
1.
Richardson
,
J.
, and
Power
,
H.
, 1996, “
A Boundary Element Analysis of Creeping Flow Past Two Porous Bodies of Arbitrary Shape
,”
Eng. Anal. Boundary Elements
,
17
, pp.
193
204
.
2.
Biot
,
M. A.
, 1941, “
General Theory of Three-Dimensional Consolidation
,”
J. Appl. Phys.
,
12
, pp.
155
164
.
3.
Biot
,
M. A.
, 1955, “
Theory of Elasticity and Consolidation for a Porous Anisotropic Solid
,”
J. Appl. Phys.
,
26
, pp.
182
185
.
4.
Kenyon
,
D. E.
, 1976, “
The Theory of an Incompressible Solid-Fluid Mixture
,”
Arch. Rat. Mech. Anal.
,
62
, pp.
131
147
.
5.
Mow
,
V. C.
,
Holmes
,
M. H.
, and
Lai
,
W. M.
, 1984, “
Fluid Transport and Mechanical Properties of Articular Cartilage: A Review
,”
J. Biomech.
,
17
, pp.
377
394
.
6.
Hou
,
J. S.
,
Holmes
,
M. H.
,
Lai
,
W. M.
, and
Mow
,
V. C.
, 1989, “
Boundary Conditions at the Cartilage-Synovial Fluid Interface for Joint Lubrication and Theoretical Verifications
,”
J. Biomech. Eng
,,
111
, pp.
78
87
.
7.
Barry
,
S. I.
,
Parker
,
K. H.
, and
Aldis
,
G. K.
, 1991, “
Fluid-Flow Over a Thin Deformable Porous Layer
,”
Z. Angew. Math. Phys.
,
42
, pp.
633
648
.
8.
Nowinski
,
J. L.
, and
Davis
,
C. F.
, 1972, “
The Flexure and Torsion of Bones Viewed as Anisotropic Poroelastic Bodies
,”
Int. J. Eng. Sci.
,
10
, pp.
1063
1079
.
9.
Taber
,
L. A.
, 1992, “
A Theory for Transverse Deflection of Poroelastic Plate
,”
ASME J. Appl. Mech.
,
59
, pp.
628
634
.
10.
Zhang
,
D.
, and
Cowin
,
S. C.
, 1994, “
Oscillatory Bending of a Poroelastic Beam
,”
J. Mech. Phys. Solids
,
42
, pp.
1575
1599
.
11.
Wen
,
P. H.
,
Hon
,
Y. C.
, and
Wang
,
W.
, 2009, “
Dynamic Responses of Shear Flows Over a Deformable Porous Surface Layer in a Cylindrical Tube
,”
Appl. Math. Model.
,
33
, pp.
423
436
.
12.
Theodorakopoulos
,
D. D.
, and
Bescos
,
D. E.
, 1994, “
Flexural Vibration of Poroelastic Plate
,”
Acta Mech.
,
103
, pp.
191
203
.
13.
Biot
,
M. A.
, and
Willis
,
D. G.
, 1957, “
The Elastic Coefficients of the Theory of Consolidation
,”
J. Appl. Mech.
,
24
, pp.
594
601
.
14.
He
,
L.
, and
Yang
,
X.
, 2008, “
A Dynamic Bending Model of Incompressible Saturated Poroelastic Plates With In-Plane Diffusion
,”
Chin. J. Solid Mech.
,
29
(
2
), pp.
121
128
.
15.
Kirchhoff
,
G.
, 1850, “
Uber das Gleichgewicht und die Bewegung Einer Elastichen Scheibe
,”
J. Reine Angew. Math.
,
40
, pp.
51
88
.
16.
Mindlin
,
R. D.
, 1951, “
Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic Elastic Plates
,”
J. Appl. Mech.
,
18
, pp.
31
38
.
17.
Vander Weeën
,
F.
, 1982, “
Application of the Boundary Integral Equation Method to Reissner’s Plate Model
,”
Int. J. Numer. Methods Eng
,
18
, pp.
1
10
.
18.
Wen
,
P. H.
, and
Aliabadi
,
M. H.
, 2006, “
Boundary Element Frequency Domain Formulation for Dynamic Analysis of Mindlin Plates
,”
Int. J. Numer. Meth. Eng
,
67
, pp.
1617
1640
.
19.
Atluri
,
S. N.
, 2004,
The Meshless Method (MLPG) for Domain and BIE Discretizations
,
Tech Science
,
Forsyth, GA
.
20.
Wen
,
P. H.
, and
Liu
,
Y. W.
, 2010, “
The Fundamental Solution of Poroelastic Plate Saturated by Fluid and its Applications
,”
Int. J. Numer. Anal. Methods Geomech.
,
34
, pp.
689
709
.
21.
Boer
,
R.
, 2005, “
Theoretical Poroelasticity—A New Approach
,”
Chaos Solitons Fractals
,
25
, pp.
861
878
.
22.
Sih
,
G. C.
, and
Hagendorf
,
H. C.
, 1977,
On Cracks in Shells With Shear Deformation
,
Mechanics of Fracture
, Vol.
3
,
G. C.
Sih
, ed.,
Noordhoff International
,
Leyden, The Netherlands
.
23.
Durbin
,
F.
, 1974, “
Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate’s Method
,”
Comput. J.
,
17
(
4
), pp.
371
376
.
24.
Wen
,
P. H.
,
Aliabadi
,
M. H.
, and
Rooke
,
D. P.
, 1996, “
The Influence of Elastic Waves on Dynamic Stress Intensity Factors (Three Dimensional Problem)
,”
Arch. Appl. Mech.
,
66
(
6
), pp.
385
384
.
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