Biomedical Engineering Reference
In-Depth Information
In the case of the element distribution of Fig.
14.4
, it holds that
⎡
⎤
K
11
K
12
00
⎣
⎦
K
21
K
22
00
K
1
=
(14.48)
0
0
0
0
0
0
0
0
⎡
⎤
0000
0
K
11
K
12
0
0
K
21
K
22
0
0000
⎣
⎦
K
2
=
(14.49)
⎡
⎤
00 0 0
00 0 0
00
K
11
⎣
⎦
K
3
=
,
(14.50)
K
12
00
K
21
K
22
such that
K
=
K
1
+
K
2
+
K
3
,
(14.51)
leading to
⎡
⎣
⎤
⎦
K
11
K
12
0
0
K
21
K
22
+
K
11
K
12
0
K
=
.
(14.52)
K
21
K
22
+
K
11
K
12
0
K
21
K
22
0
0
In computer codes, however, the individual matrices
K
i
are never formed explic-
itly. The non-trivial components of
K
i
are supplied directly to the appropriate
position within
K
. This process of assembling the global matrix
K
based on the
contributions of the individual element matrices
K
e
is called the
assembly
process.
For the right-hand side the same procedure is followed. For element 2 it can be
written analogously:
w
2
f
1
w
2
w
3
f
1
w
1
2
f
∼
∼
2
=
=
f
2
f
2
⎡
⎣
⎤
0
f
1
f
2
0
w
1
w
2
w
3
w
4
⎦
f
∼
T
=
=
∼
2
.
(14.53)
f
∼
2
