Biomedical Engineering Reference
In-Depth Information
e ¼ e
0
+ e
NL
ð
2
:
72
Þ
which can also be presented as,
h
þ
1
¼ L
þ
1
e ¼ L h
2
A h
2
A
ð
2
:
73
Þ
|{z}
e
0
|{z}
e
NL
Matrix L is defined as,
2
4
3
5
e
1
0
1
3
0
1
3
½
½
2
3
e
2
0
1
3
0
1
3
100000000
000010000
000000001
010100000
000001010
001000100
½
½
4
5
e
3
0
1
3
0
1
3
½
½
L ¼
¼
ð
2
:
74
Þ
e
2
e
1
0
1
3
½
e
3
e
2
0
1
3
½
e
3
e
1
0
1
3
½
Being e
i
the coordinate i director column vector,
I ¼ e
1
½
e
2
e
3
ð
2
:
75
Þ
The column vector h is defined by,
h ¼ Gu
ð
2
:
76
Þ
The geometric matrix G is defined by,
2
3
o
u
ox
00
o
u
oy
00
o
u
oz
00
4
5
G
T
¼
o
u
ox
00
o
u
oy
00
o
u
oz
0
0
ð
2
:
77
Þ
00
o
u
ox
00
ou
oy
00
o
u
oz
which produces the following column vector h,
2
4
3
5
2
4
3
5
ou
on
ov
on
o
w
on
h
x
h
y
h
z
h ¼
being
h
n
¼
ð
2
:
78
Þ
The current configuration displacement is considered in matrix A, which cor-
responds in Eq. (
2.73
) to the actualized component.
