Biomedical Engineering Reference
In-Depth Information
2
*
*
a
ββ +
−
[
T
pt
( )]
0
Bt
()
=
(3.24)
c
c
11
12
*
1
FT Pt
ba
+
π−
( )
2
cc
c
ϖ
*
2
0
2
*
*
13
12
11
Ct
()
=
FT
−
(
c
+
c
)
−ββ+ −
2
c
[
T
pt
()]
(3.25)
1
0
11
12
13
1
2
0
F
*
(
2
)
3
e
c
(
ϕ−ϕ
)
ln(/)
15
b
a
Dt
()
=−
(3.26)
b
a
44
=
ϕ−ϕ
b
a
Ft
()
(3.27)
ln(/)
ba
where
2
b
ab
β=
λ
c
c
*
2
*
*
1
12
Fcc
=
(
+
c
)
−
2,
c
β =
)
,
−
1
(3.28)
3
33
11
12
13
1
2
2
2
(
−
2
11
Using Equations (3.23)-(3.27), the displacements
u
r
,
u
z
,
and electrical poten-
tial φ are given by
*
r
F
cc
c
FT Pt
ba
c
+
π−
−
()
*
*
33
12
11
2
0
2
*
u
=
c
β β+ +ϖ
[
T
pt
( )]
+
FTc
r
33
1
2
0
13
1
013
3
*
2
(
)
(3.29)
2
*
*
+
ββ +
−
a
[
T
pt
( )]
+
ϖ
rra
c
[ln( /) 1]
−
1
2
0
rc
(
c
)
11
12
11
*
+−ββ +
z
F
FT Pt
ba
+
π−
()
*
2
0
2
*
*
u
=
FT
−
(
c
c
)
2
c
[
T
pt
()]
z
1
0
11
12
13
1
2
0
*
2
(
)
3
(3.30)
2
cc
c
ϖ
−
e
(
ϕ−ϕ
)ln( /)
ln(/)
r
a
13
12
15
b
a
−
c
b
a
11
44
ln(/)
ln(/)
(
ra
ba
a
(3. 31)
ϕ=
ϕ−ϕ+ϕ
)
b
a
The strains and electric field intensity appearing in Equation (3.4) can be
found by substituting Equations (3.29)-(3.31) into Equation (3.2). They are,
respectively,
*
1
cc
c
FT Pt
ba
c
+
π−
−
()
*
*
33
12
2
0
2
*
ε= ββ +
c
[
T
pt
( )]
+ϖ+
FTc
rr
33
1
2
0
13
1
013
*
2
F
(
)
3
11
(3.32)
2
*
*
−
ββ +
−
a
[
T
pt
( )]
+
ϖ
ln(/)
ra
1
2
0
2
rc
(
c
)
c
11
12
11
