Civil Engineering Reference
In-Depth Information
(a)
(b)
(c)
(d)
(1)
(2)
(Initial)
(e)
(1)
(2)
(Initial)
(4)
(5)
(3)
Figure 5.34
Boundary edge recovery: (a) the support model; (b and c) missing edge with five Steiner
points; (d) Steiner points removed simultaneously in a group; (e) Steiner points removed by a
random order.
The third example is an impeller model with 172 Steiner points inserted, as shown in
Figure 5.36a. Point relocation is an essential step in removing flat elements. Magnified views
of a critical recovery zone in the form of a concave polyhedron are shown in Figure 5.36b
and c. The node reposition aims at relocating the Steiner point shown in red in Figure 5.36b
and c so as to remove the flat elements connected to it. The feasible region of the Steiner
point is a polyhedron that is marked green in Figure 5.36d. The Steiner point is repositioned
at the barycentre of the region, which is marked red in Figure 5.36e. Consequently, all flat
elements connected to the Steiner point are opened up, as shown in Figure 5.36f.
The well-known falcon model, as shown in Figure 5.37a, is quoted here to discuss the
main features of the boundary recovery procedure. There are 141,470 triangles on the
boundary, including 19,738 (14%) sharp triangles with an angle less than 5°. The result
of MG is shown in Figure 5.37b. To compare with available tetrahedral mesh generators,
