Civil Engineering Reference
In-Depth Information
as described in Section 2.4.7. More explicitly, the intersection between tetrahedron J
1
J
2
J
3
P
and the generation front Γ can be determined by checking the intersections of line segments
{J
1
P, J
2
P, J
3
P} with Γ = {Δ
i
, i = 1,N
Γ
} and line segments {L
j
, j = 1,N
L
} in Γ with {ΔJ
1
J
2
P, ΔJ
2
J
3
P,
ΔJ
3
J
1
P}, where Δ
i
and L
j
are, respectively, the triangular facets and the line segments (edges)
on the generation front Γ.
5.5.3 Efficiency consideration and mesh quality
The most time-consuming step in ADF meshing is to check whether the proposed tetrahe-
dral elements have penetrated into the generation front. As all the triangles on the genera-
tion front have to be examined, the computation may become excessive if there are many
nodes in the system. Supposing there are N nodes in the mesh, since the generation front is
one dimension less, a rough estimate of the number of triangles on the generation front is
N
2/3
, and the processing time is of order N
5/3
. As a result, the computation time will increase
rapidly with the number of nodes in the system unless the intersection checks can be made
localised. Similar to 2D ADF meshing presented in Section 3.6, a dynamic grid scheme can
be applied to facilitate 3D ADF meshing for fairly large systems within a reasonable meshing
time. As the shape and size of each tetrahedral element are well controlled in the MG, the
quality of the resulting mesh is
guaranteed
. Usually, tetrahedral elements of good quality
tend to form at the boundary as MG is operated from the surface of the volume towards
its interior, which is quite an important factor for some finite element applications where
boundary stresses or gradient values are of primary concern.
5.5.4 ADF meshing of 3D objects
Four volumes of machine parts bounded by triangulated surfaces meshed by the ADF
method are presented in this section, as shown in Figures 5.68-5.71. The statistics of these
example meshes are listed in Table 5.4. ADF meshing was carried out by reading in the
co-ordinates of the nodes on the boundary surface and the node numbers of the boundary
triangles. Interior nodes were first generated before ADF meshing, and for some meshes,
remedial actions were needed with additional interior nodes generated as indicated in Table
5.4. Objects 1 and 4 characterised with many internal features and elongated boundary
Figure 5.68
Object with many internal features.
