Civil Engineering Reference
In-Depth Information
These equations can be rewritten as [
I
sf
]
V
s
(M
2
)
+
[
J
sf
]
V
f
(M
3
)
=
0, with
0100
0010
0001
0
1
10
00
−
,
[
I
sf
]
=
[
J
sf
]
=
(11.71)
Matrices [
I
]and[
J
] must be interchanged for a fluid - solid interface. The same
matrices can be used for a solid - thin plate interface.
Porous - fluid interface
The continuity conditions are given by
(
1
− φ
)v
3
(
M
2
)
+ φ
v
3
(
M
2
)
=
v
3
(
M
3
)
σ
33
(
M
2
)
=−
(
1
− φ
)
p
(
M
3
)
σ
13
(
M
2
)
=
0
σ
33
(
M
2
)
(11.72)
=−φ
p
(
M
3
)
where
φ
is the porosity of the porous layer. These equations can be rewritten in the form
[
I
pf
]
V
p
(M
2
)
+
[
J
pf
]
V
f
(M
3
)
=
0, with
0
(
1
− φ
)
φ
000
0
−
1
0
0
0100
(
1
− φ
)
0
[
I
pf
]
=
,
[
J
pf
]
=
(11.73)
0
0
0010
0
0
0
0
0001
φ
0
Matrices [
I
]and[
J
] must be interchanged for a fluid - porous interface.
Solid - porous interface
The continuity conditions are given by
υ
1
(
M
2
)
υ
1
(
M
3
)
=
υ
3
(
M
2
)
υ
3
(
M
3
)
=
υ
3
(
M
2
)
υ
3
(
M
3
)
=
(11.74)
σ
33
(
M
2
)
σ
33
(
M
3
)
σ
33
(
M
3
)
=
+
σ
13
(
M
2
)
σ
13
(
M
3
)
=
which can be rewritten as [
I
sp
]
V
s
(M
2
)
+
[
J
sp
]
V
p
(M
3
)
=
0, with
1000
0100
0100
0010
0001
100000
010000
001000
000101
000010
[
I
sp
]
=
,
[
J
sp
]
=−
(11.75)
Matrices [
I
]and[
J
] must be interchanged for a porous - solid interface. Note that
these matrices can be used to interface an impervious screen in mechanical contact.
