Civil Engineering Reference
In-Depth Information
1
5
RL = 0
1
2
2
7
6
4
3
4
3
RL = 1
RL = 2
Mesh (iii)
Mesh (iii)
11
12
5
1
5
2
8
1
2
8
13
7
10
7
10
6
9
6
9
RL = 1
4
4
3
3
Mesh (iii)
Mesh (iv)
Figure 5.106
Mesh refinement following the 1-LR rule.
checked. It is found that the RL (=0) of element 2 is lower than that (RL = 1) of element 5.
As a result, subdivision of element 5 has to be suspended, and element 2 ought to be divided
first. After checking the RLs of the neighbours of element 2, the restriction criterion is sat-
isfied for element 2, and it is divided as shown in mesh iii of Figure 5.106. RLs of the four
smaller quadrilateral elements 2, 8, 9 and 10 are set to 1, which is the result of increasing the
RL of the previous element 2 in mesh ii. The subdivision procedure for element 5 can now
be reactivated to generate elements 5, 11, 12 and 13 with RL = 2, as shown in mesh iv of
Figure 5.106. In summary, before dividing an element, we have to make sure that the 1-LR
mesh refinement criterion is satisfied by checking the RL values of its neighbouring elements,
which can be done locally without much effort.
Although the 1-LR refinement scheme based merely on a check on the refined levels of
neighbouring elements is simple enough, it is quite efficient even for the most general node
Figure 5.107
Refinement of quadrilateral meshes based on different node-spacing functions.
