Civil Engineering Reference
In-Depth Information
Figure 4.6
Quadrilateral mesh by merging of triangles.
Figure 4.7
Quadrilateral mesh by Q-Morph scheme.
4.1.3 Surface meshing by means of intersection
Apart from the two approaches discussed, there is a third approach for the construction of
complex surface models of triangular elements. The first approach is the mapping approach,
which generates a mesh on the parametric domain followed by a mapping process of the
resulting mesh onto the surface. The second approach is to form triangles directly on the
surface by the well-known mesh generation techniques, such as the Octree method, the AFT,
the paving method and so forth. The third approach is to construct models by Boolean
operations such as intersection and union between groups of surfaces composed of trian-
gular facets. A great variety of meshes can be easily created by selectively putting together
various surface parts derived from surface intersections. This approach has been explored
and applied in the field of FE MG (Lo 1995; Coelho et al. 2000; Cebral et al. 2001; Lo and
Wang 2003, 2004, 2005a), molecular modelling (Laug and Borouchaki 2000, 2001, 2002,
2003b), engineering design (Bonet and Peraire 1991; Aftosmis et al. 1998), etc.
4.2 PARAMETRIC MAPPING METHOD
4.2.1 Introduction
4.2.1.1 The mapping
ϕ
from planar domain
Ω
to the surface S
Let ϕ be the mapping from a two-dimensional parametric domain
2
onto a curved
surface
S
3
in the three-dimensional space such that ϕ: Ω → S.
