Civil Engineering Reference
In-Depth Information
Figure 6.40
Elimination of nodes surrounded by three or four triangles.
Figure 6.41
Elimination of a short edge and a small triangle.
Figure 6.42
Swap of diagonal between two triangles.
6.4.1 Triangular meshes
For efficient operations, some topological structures such as element adjacency relationship
and the patch of elements surrounding each node have to be first retrieved from the mesh,
which have to be updated whenever there is a structural change in the mesh. In a triangular
mesh, nodes surrounded by three triangles are eliminated, as shown in Figure 6.40. For nodes
surrounded by four triangles, we have to consider the shape quality of the elements and the
length conformity of all the edges before and after the transformation. Short edges smaller
than a certain threshold are identified, which are eliminated by shrinking the two related
triangles to line segments, as shown in Figure 6.41. Similarly, small triangles are detected by
checking their areas relative to those of their neighbours, and a triangle with too small an area
is eliminated by shrinking it to a point, as shown in Figure 6.41. Diagonal swap within a quad-
rilateral formed by a pair of adjacent triangles is a common and effective measure in creating
meshes of different characteristics and in enforcing boundary compatibility requirements. In
shape optimisation, a diagonal swap can be carried out if the overall quality of the resulting
triangles is superior to that before transformation, as shown in Figure 6.42.
6.4.2 Quadrilateral meshes
When nodes surrounded by three quadrilaterals are detected in a mesh, as shown in Figure
6.43, we have to consider the shape quality of the elements and the length conformity of
all the edges before and after the transformation. Short edges much smaller than their
Figure 6.43
Elimination of nodes surrounded by three quadrilaterals.
