Civil Engineering Reference
In-Depth Information
J
P
2
P
nā1
K
P
1
P
n
I
Figure 8.78
Bisecting a ring of tetrahedra.
Start: k = 0; i = 1; j = 1;
T
T
End
j > m?
i > n?
F
T
j > m?
F
F
F
T
k = k + 1; L
k
* = E
j
; j = j + 1;
r
i
< s
j
?
k = k + 1; L
k
* = L
i
; i = i + 1;
Figure 8.79
Flow chart for merging of sets
L
and
E
.
generated are IK, KJ, KP
1
, ā¦, KP
n
. Those new edges satisfying criterion 8.4, which need fur-
ther refinement, are stored in the set
E
.
8.4.3.1.5 Merging of the two sets
L
and
E
The number of edges in
L
decreases as refinement is carried out by bisecting lines in
L
.
Suppose that there are n edges remaining in
L
; then
L
can be expressed as
L
= {L
i
, i = 1,n}.
Subdivision of edges in
L
is suspended if there is a line segment in
E
that is longer than the
edge L
n
currently under consideration. Before merging, the edges in
E
are ordered in the
same way as described in Section 8.4.3.1.3. Let m be the number of line segments in
E
; then
E
can be written as
E
= {E
j
, j = 1,m}. These two ordered sets can be merged easily to form a
new set
L
* = {L
k
*, k = 1,m + n} consisting of edges from the sets
L
and
E
. Replacing
L
by
L
*,
go back to Section 8.4.3.1.4, and the refinement process continues. Let ri
i
and s
j
be, respec-
tively, the lengths of edges L
i
ā
L
and E
j
ā
E
. A simple algorithm for the merging of the two
ordered sets
L
and
E
is given by the flow chart shown in Figure 8.79.
8.4.3.2 Optimisation of element shape
The quality of the refined mesh can be significantly improved through cycles of element
shape optimisation. As discussed in Chapter 6, mesh optimisation procedures can be clas-
sified into two main categories: (i) those that do not involve a change in mesh topology
(node-element connectivity relationship), for instance, node repositioning; and (ii) those
that involve a structural modification of the mesh such as face/edge-swapping operations.
