Civil Engineering Reference
In-Depth Information
idea to go right back to the early conceptual stage, as after cycles of simulation, modification
and update, the FE mesh might have a substantial departure from the CAD model, or simply
the CAD model is already outdated or not even available at all for one reason or another.
Furthermore, very often the new demands would require just some minor adjustments from
the original design, and a few modifications of the existing FE mesh will produce a new
model for engineering simulation addressing all the changes required.
Lou et al. (2010) put forward an FE merging scheme to enrich FE triangular meshes for
rapid prototyping of alternate solutions for industrial maintenance. On the introduction of
a feature to a triangulated surface mesh, a cavity at the vicinity of the new feature will be
created in the existing surface mesh, where triangular elements could be generated to fill up
the gap linking the two parts together. Another possibility to combine two surface parts
is to consider the intersection of the given surfaces (Lo 1995). The interaction of curved
surfaces discretised into triangles and/or quadrilaterals will produce intersection segments,
which could always be grouped into structural loops for analysis and further manipulation.
Triangles intersected by the intersection loops are removed to produce gaps between the
intersection loops and the curved surfaces. By filling up the void with triangles, all intersec-
tion loops will be incorporated into the given surfaces. The surfaces will be automatically
merged together as all intersection segments exist on both of the given surfaces to ensure
compatibility. This method has been proved to be versatile and efficient in generating new
surface meshes from existing discretised objects (Shostko and Lohner 1999; Lo and Wang
2003, 2004).
In response to the demands for maintenance and update of products in service similar
to those of the triangular surface meshes, there is an urgent need to develop automatic
algorithms to merge solid tetrahedral meshes. Apart from the aforementioned needs for a
versatile solid mesh merger, such a tool could also offer the following applications.
1. Handling minor modifications and mesh update of existing meshed objects
2. Working as a supplementary MG tool for objects that could only be conveniently
defined by a combination of some fundamental shapes put together
3. Incorporating foreign parts into an existing meshed object (Mouton et al. 2010)
4. Putting existing meshes together in a variety of ways to create new models
5. Opening up a way to merge other solid meshes that can be converted into tetrahedral
meshes
Not much research work has been reported in the literature so far in the development of
such an automatic scheme in merging arbitrary tetrahedral meshes (Yamakawa and Shimada
2009), although there are robust algorithms proposed for the merging of triangulated surfaces
(Cebral et al. 2002; Lo and Wang 2005a) and the insertion of surface mesh into a tetrahedral
mesh (Ebeida et al. 2009; Cuillière et al. 2010). The major difficulty lies in the finding of a reli-
able way for the determination of intersections and in formulating a systematic plan in filling
up any cavity to accommodate all the intersection parts. For a consistent treatment of intersec-
tions between two solid objects, we have to concentrate on their patterns and structural form.
In the algorithm to be presented in this section, rather than focusing on the intersection points
and segments as individual components, we aim at finding distinct non-overlapping intersec-
tion loops as a single entity on the boundary of the 3D objects under consideration. Instead
of micro-management in linking up broken intersected tetrahedral elements one by one, the
intersection parts will be recorded and treated as volumes of intersection. In terms of regions
of intersection, we could exercise a tight control and have a much better understanding on the
geometry and the topology of the intersection parts. Apart from the determination of intersec-
tion loops, which is an integral part for the interaction of two meshed objects, the operations
