Biomedical Engineering Reference
In-Depth Information
*
1
cc
c
FT Pt
ba
c
+
π−
−
()
*
*
33
12
2
0
2
1
*
ε= ββ +
c
[
T
pt
( )]
+ϖ+
FTc
θθ
33
0
13
013
*
2
F
(
)
3
11
(3.33)
2
*
*
+
ββ +
−
a
[
T
pt
( )]
+
ϖ
[ln( /) 1]
ra
c
−
1
2
0
2
rc
(
c
)
11
12
11
*
+−ββ +
1
FT Pt
ba
+
π−
( )
*
2
0
2
*
*
ε=
FT
−
(
c
c
)
2
c
[
T
pt
()]
zz
1
0
11
12
13
1
2
0
F
*
(
2
)
3
(3.34)
2
cc
c
ϖ
13
12
−
11
e
rc
(
ϕ−ϕ
)
ln(/)
15
b
a
ε=−
(3.35)
rz
ba
44
=−
ϕ−ϕ
(
)
ln(/)
b
a
(3.36)
E
r
rba
Then, substituting the solutions (3.32)-(3.36) into Equation (3.4) yields
ε
*
2
A
F
cc
c
FT Pt
ba
c
+
π−
−
()
=
*
rr
*
*
33
12
2
0
2
1
*
eAe
()
+
c
ββ +
[
T
pt
( )]
+ϖ+
FTc
33
0
13
013
*
2
(
)
3
11
ε
ε
*
A
ϖ
[2 ln(/) ]
r
a
−
A
F
FT Pt
ba
+
π−
( )
rr
zz
*
2
0
2
+
+
FT
−
(
c
+
c
)
(3.37)
1
0
11
12
*
2
c
(
)
11
3
2
cc
c
ϖ
−
ϕ−ϕ
e
c
*
*
13
12
b
a
E
15
ε
−ββ+ −
2
c
[
T
pt
()]
ba
A
+
A
13
1
2
0
r
zr
r
ln(/)
11
44
Since we do not know the exact expressions of the material functions
A
*
(
e
),
ε
AeAe
E
ij
,
c
ij
,
d
j
,
λ
j
,
κ
j
,
and χ
3
, the following approximate forms of them, as
proposed by Cowin and Van Buskirk [4] for small values of
e,
are used here:
(),
( )
i
*
2
E
E
0
E
1
ε
ε
0
ε
1
(3.38)
Ae
()
=++
CCeCeAeA eA
,
( )
=
+
,
Ae
()
=
AeA
+
0
1
2
i
i
i
ij
ij
ij
and
e
e
ce c
=+
ξ
0
cc ee e
1
−
0
(
)
=
0
+
ξ
(
ee
1
−
0
),
()
(
),
ij
ij
ij
ij
ij
ij
ij
ij
0
0
e
e
(3.39)
0
1
0
0
1
0
λ=λ+
ξ
λ−λκ=κ +
ξ
κ−κ
()
e
(
),
( )
e
(
),
i
i
i
i
i
i
i
i
0
0
e
0
1
0
χ=χ+
ξ
χ−χ
()
e
(
)
3
0
