Civil Engineering Reference
In-Depth Information
A
A
A
F
F
F
B
B
B
C
E
E
E
C
C
D
D
D
N
1
≥ N
2
+ 3 and N
3
≥ N
2
N
1
≥ 9
N
1
≥ N
3
+ 3 and N
2
≥ N
3
Figure 3.83
Swapping of diagonal.
If N
1
≥ 9, diagonal AD will be swapped with BE if
N
1
≥ N
2
+ 3 and N
3
≥ N
2
(3.8)
or with CF if
N
1
≥ N
3
+ 3 and N
2
≥ N
3
(3.9)
There will be no diagonal swap if neither Equation 3.8 nor 3.9 is satisfied.
3.9.5.4 Elimination of segment
All the line segments connected to two interior nodes are examined in turn. Line segment
AB will be eliminated if the connectivity numbers of both nodes A and B are equal to three,
i.e. N
A
= 3 and N
B
= 3. The segment elimination is completed by the elimination of quadri-
lateral ABCD and AFGB, as shown in Figure 3.84. A new diagonal DG will be formed if
N
C
+ N
F
≥ N
D
+ N
G
Otherwise, diagonal CF will be formed.
3.9.6 Examples of quadrilateral meshes
The conversion of the triangular mesh of 13,171 nodes and 26,094 triangles into a quadri-
lateral mesh of 15,463 nodes and 15,342 elements is shown in Figure 3.85. The increase in
the number of nodes is probably due to the additional nodes introduced in the splitting of
E
E
E
D
D
D
F
F
F
A
B
G
G
C
C
G
C
H
H
H
N
C
+ N
F
≥ N
D
+ N
G
N
C
+ N
F
< N
D
+ N
G
Figure 3.84
Elimination of segment.
