Civil Engineering Reference
In-Depth Information
Figure 3.60
Triangular mesh generated by the ADF-Delaunay scheme.
A triangular mesh of a multi-connect planar domain is generated by the ADF-Delaunay
scheme, as shown in Figure 3.60. There are 253 line segments on the interior and the exte-
rior boundary loops, and the final mesh consists of 9793 nodal points and 19,333 triangles.
The α mesh quality after two cycles of smart Laplace smoothing improves to 0.924 from
the original value of 0.89 before optimisation. It is seen that all triangles in the mesh are
Delaunay triangles except a few of those constrained by the boundary of the domain. It is
noted that the system of interior nodes is generated from some mathematical functions by a
separate program, and the ADF-Delaunay scheme has been applied to connect the nodes on
the boundary with those at the interior of the domain.
3.7.3 Delaunay-advancing-front scheme
Another possibility to merge the DT and the AFT is to insert interior points proposed by
the AFT using the Delaunay insertion kernel. A constrained DT is constructed using nodes
on the boundary of the domain. Analogous to the classical ADF approach, the initial gen-
eration front consists of all the boundary segments of the planar domain. A line segment
is taken from the generation front as the base segment. Based on the specified element size,
an interior node is generated by the AFT, which is then inserted to the constrained DT of
frontal nodes by means of the Delaunay insertion kernel. In case the proposed node is too
close to the generation front, no interior node will be generated. Whichever the case, the
triangle connected to the base segment is deleted from the DT, and the generation front is
updated accordingly resulting in another constrained DT bounded by the generation front
without any nodes in its interior. Obviously, this procedure can be repeated until there is no
more line segment on the generation front, and the region bounded by the generation front
reduces to nothing. The final mesh is given by all the triangles removed one by one from the
system for each frontal base segment considered.
The procedure of the Delaunay-ADF scheme is elucidated by an example of triangular
mesh of non-uniform element size. An FE mesh of variable element size is going to be gener-
ated over a rectangular domain. Following the specified nodal spacing, the boundary of the
rectangular domain is decomposed into line segments of different lengths. Using nodes on
the domain boundary, a DT is constructed, as shown in Figure 3.61.
An intermediate stage of MG is depicted in Figure 3.62 where the boundary segments
are represented by arrows, which divided the rectangular domain into the meshed region
and the unmeshed region. The meshed region consists of those triangles connected to the
base segments removed one by one from the unmeshed region, and the unmeshed region is
