Biomedical Engineering Reference
In-Depth Information
K
e
on
function values
∼
. This can be done by introducing an auxiliary matrix
element level such that
e
K
e
∼
e
=
∼
T
K
e
∼
.
∼
(14.41)
To illustrate this, consider once more the element distribution of Fig.
14.4
. For the
second element it holds that
w
2
K
11
u
1
u
2
w
1
K
12
2
K
2
∼
2
=
∼
(14.42)
K
21
K
22
w
2
w
3
K
11
K
12
u
2
u
3
.
=
(14.43)
K
21
K
22
Notice that in Eq. (
14.42
) the local nodal values have been used, while in Eq.
(
14.43
) the global values have been used. Eq. (
14.43
) may also be rewritten as
w
2
w
3
K
11
u
2
u
3
K
12
2
K
2
∼
2
=
∼
K
21
K
22
⎡
⎤
⎡
⎤
0000
0
K
11
K
12
0
0
K
21
K
22
0
0000
u
1
u
2
u
3
u
4
w
1
w
2
w
3
w
4
⎣
⎦
⎣
⎦
=
K
2
T
K
2
∼
.
=
∼
(14.44)
Consequently,
N
el
N
el
T
T
K
e
∼
,
∼
e
K
e
∼
e
=
∼
(14.45)
e
=
1
e
=
1
K
e
matrices the result:
and by summing the individual
N
el
T
T
K
∼
,
∼
e
K
e
∼
e
=
∼
(14.46)
e
=
1
is obtained, with
N
el
K
e
.
K
=
(14.47)
e
=
1
