Biomedical Engineering Reference
In-Depth Information
Table 17.3 Integration points in the triangles.
n
int
point
location of the integration points
weight factors
λ
1
λ
2
λ
3
W
i
3
1
0.5
0.5
0
0.16667
2
0
0.5
0.5
0.16667
3
0.5
0
0.5
0.16667
7
1
0.3333333333
0.3333333333
0.3333333333
0.11250
2
0.0597158717
0.4701420641
0.4701420641
0.00662
3
0.4701420641
0.0597158717
0.4701420641
0.00662
4
0.4701420641
0.4701420641
0.0597158717
0.00662
5
0.7974269853
0.1012865073
0.1012865073
0.00630
6
0.1012865073
0.7974269853
0.1012865073
0.00630
7
0.1012865073
0.1012865073
0.7974269853
0.00630
λ
2
λ
2
6
2
2
1
4
1
7
λ
1
3
5
λ
1
3
Figure 17.12
Position of the integration points in the triangles.
the coordinate
λ
3
these can represented in a rectangular coordinate system as given
in Fig.
17.11
. It can easily be seen that the surface integral of a function
φ
λ
1
,
λ
2
)
(
can be written as
1
1
−
λ
1
φ
λ
1
,
λ
2
)
d
λ
2
d
λ
1
.
(
(17.41)
0
0
Despite a problem with a variable integral limit, it appeared possible to derive
numerical integration rules for triangles. In Table
17.3
the position of integration
points in triangular coordinates as well as weight factors are given for two higher-
order elements.
