Discretisation and Interpolation - The Boundary Element Method with Programming - page 41

The corner node functions are constructed in a similar way as for the previous
elements

1 1

N 1 [K N N

1 4 6

2 2

1 1

N [ N N

(3.23)

2 4 5

2 2

1 1

N K N N

3 5 6

2 2

K

3

K 1

6

1
2

K

5

1

[

4 2 [ 0

1
2

[ 1

[

Figure 3.15 Triangular quadratic element

3.4 THREE-DIMENSIONAL CELLS

For the description of cells for 3-D problems three-dimensional elements are used.
Their derivation is analogous to that of the two-dimensional elements described
previously, except that now three intrinsic coordinates ([ , K , ]) are used, as shown in
Figure 3.16. The Cartesian coordinates of a point with intrinsic coordinates ([ , K , ]) are
obtained by

8

¦

e

x N [K] ,, x

(3.24)

n n

n 1

Bilinear shape functions are used for the quadrilateral element in Figure 3.16

1

]

N 1 [ [ 1 K K 1 ]

(12.1) n n n n

8