Biomedical Engineering Reference
In-Depth Information
d
11
d
12
d
14
=
p
d
7
d
8
d
10
=
p
d
4
d
4
d
6
=
p
Tri-Lock
d
1
d
1
d
3
=
p
Figure 10.4
Definition of the initial geometry and design
variables based on the Tri-Lock stem represented on the
right image (section dimensions are not scaled).
10.4.2
Objective Function for Interface Displacement
One of the requirements for the hip stem is to minimize the interface relative
displacements. With this objective, the single cost function
f
d
is considered:
u
re
t
P
NC
C
c
2
f
d
=
α
d
(10.4)
P
c
P
=
1
This function is a measure of the tangential displacement on the contact bound-
ary, where
NC
is the number of applied loads,
α
P
are the load weight factors, with
NC
P
α
P
=
1, and (
u
rel
t
)
P
is the relative tangential displacement on bone-stem
=
1
c
for load case
P
. The constant C is assumed equal to 10
5
interface
to avoid
numerical instabilities due to values of
f
d
close to zero.
10.4.3
Objective Function for Interface Stress
The control of interface contact stress is also crucial for prosthesis performance.
It is necessary to avoid stress peaks and also to maintain a low stress level on
all interfaces. To achieve this, a measure for the contact stress, given by
f
t
,is
