Biomedical Engineering Reference
In-Depth Information
FIGURE 5.18
A cylindrical bone with a medullary pin inserted [64].
Assuming that the radius of the pin is
a
0
+ δ/2, where
a
0
is the radius of the
cylindrical bone, we obtain Equation (3.63) and rewrite it here for the sake of
convenience
+
δ
+=+
a
u
au
2
(5.34)
0
1
0
2
where
u
1
is given by the following [64]:
a
E
vP
ba
1
(
)
(5.35)
u
=
π−
−−
1
vpt
( )
1
2
2
(
)
for an isotropic pin, where
E
and
v
are, respectively, Young's modulus and
Poisson's ratio. Making use of Equations (5.33)-(5.35), we obtain the solution
of contact force
p
(
t
) as
δ
+
π−
−
⋅
π−
vP
Eb a
c
F
P
ba
1
13
3
2
a
(
2
2
)
*
(
2
2
)
pt
()
=
(5.36)
2
c
Fc
1
⋅
b
ba
1
−
v
13
+
+
*
2
2
−
c
−
E
3
11
12