Biomedical Engineering Reference
In-Depth Information
T
=σ=σ =σ =ϕ=ϕ ψ=ψ
0,
0,
,
at
r
=
a
,
rr
r
θ
rz
a
a
(3.77)
TT
=σ=− σ=σ= ϕ=ϕψ=ψ
,
p
,
0,
,
at
r
=
b
0
rr
r
θ
rz
b
b
The solutions to the governing equations (3.7), (3.74), and (3.75) satisfying
boundary conditions (3.6) and (3.77) 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
(
)
(3.78)
+
ββ +
−
a
2
*
[
*
T
pt
( )]
+
ϖ
rra
c
[ln( /) 1]
−
1
2
0
rc
(
c
)
11
12
11
2
*
z
F
FT Pt
ba
+
π−
()
+−ββ +
0
2
*
*
*
u
=
FT
−
(
c
c
)
2
c
[
T
pt
()]
z
1
0
11
12
13
1
2
0
*
2
(
)
3
(3.79)
2
cc
c
ϖ
−
e
(
ϕ−ϕ
)ln( /)
ln(/)
r
a
−
αψ−ψ
(
) ln(/)
ln(/)
ra
13
12
11
15
b
a
15
b
a
−
c
b
a
c
b
a
44
44
ln(/)
ln(/)
(
ra
ba
ln(/)
ln(/)
(
ra
ba
ϕ=
ϕ−ϕ+ϕψ=
)
,
ψ −ψ +ψ
)
(3.80)
b
a
a
b
a
a
ln(/)
ln(/)
ra
ba
T
T
=
0
(3.81)
The strains, electric, and magnetic field intensity can be found by introduc-
ing Equations (3.78)-(3.81) into Equation (3.71). 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
(3.82)
2
*
*
−
ββ +
−
a
[
T
pt
( )]
+
ϖ
ln(/)
ra
1
2
0
2
rc
(
c
)
c
11
12
11
*
1
cc
c
FT Pt
ba
c
+
π−
−
()
*
*
33 12
11
2
0
2
*
ε= ββ +
c
[
T
pt
( )]
+ϖ+
FTc
θθ
33
1
2
0
13
1
013
F
*
(
2
)
3
(3.83)
+
ββ +
−
a
2
*
[
*
T
pt
( )]
+
ϖ
[ln( /) 1]
ra
c
−
1
2
0
2
rc
(
c
)
11
12
11
*
+−ββ +
1
FT Pt
ba
+
π−
( )
2
cc
c
ϖ
ε=
(3.84)
*
2
0
2
*
*
13
12
FT
−
(
c
c
)
2
c
[
T
pt
()]
−
zz
1
0
11
12
13
1
2
0
*
2
F
(
)
3
11
