Civil Engineering Reference
In-Depth Information
5.5.2 ADF meshing procedures
5.5.2.1 The generation front
Let Ω be the given domain (object) and B = ∂ Ω be the discretised boundary surface of Ω. By
virtue of the orientation of the triangular facet on B, the domain to be triangulated has an
interior volume always situated in the direction of the normal vectors of the boundary trian-
gular facets, as shown in Figure 5.62. At the beginning of the triangulation, the generation
front Γ is exactly equal to the boundary of the object, i.e. Γ = B. While the domain boundary
remains the same, the generation front Γ evolves continuously throughout the MG process
and has to be updated whenever a new tetrahedral element is created.
5.5.2.2 Generation of interior node
For ADF on 2D domains, interior nodes are created simultaneously as triangular elements are
formed. For tetrahedral meshes of more or less uniform element size, in an earlier attempt,
a convenient and efficient way for ADF meshing over 3D domains is to generate a system of
uniformly spaced interior nodes within the problem domain before the construction of tetra-
hedral elements (Lo 1991c; Bajaj et al. 1999). Interior nodes within the given domain Ω are
generated layer by layer. Planar cross sections can be defined when a series of parallel planes
cut across the 3D object to be discretised. Interior nodes are generated on these cut sections,
as shown in Figure 5.63 (refer to Section 3.5.6 for details). The following are the procedures
to obtain parallel cut sections of a bounded volume, as shown in Figure 5.64.
i. The z
min
and z
max
of the domain are determined.
ii. Imaginary horizontal planes at various levels between z
min
and z
max
are allowed to cut
across the 3D domain.
Γ
Ω
Surface normal pointing
inwards towards volume
Figure 5.62
Orientation of boundary triangular facets.
Figure 5.63
Generation of interior points on a cut section.
