Civil Engineering Reference
In-Depth Information
bounded volume, Vyas and Shimada (2009) employed a metric tensor field to generate hex
meshes. By this method, elements are formed from the boundary quad facets, and the con-
struction advances towards the volume interior. A set of heuristic procedures are devised to
determine the order in which elements should be created. Similar to the AFT for tetrahedral
meshing, the generation front for plastering is composed of quads. Hex elements are defined
by projecting quads on the generation front towards the interior of the volume. Of a more
complicated nature compared to the classical AFT, intersecting faces have to be checked and
carefully controlled, and the problems of when and how to connect existing nodes and to
seam faces have to be resolved. As the front advances, complex irregular internal voids may
occur, which in some cases cannot be filled with hex elements. Existing elements already
placed have to be removed or modified from time to time to cater for the formation of
new elements. The plastering algorithm has not yet been proved to be reliable and versatile
enough for general applications.
5.8.11 Whisker weaving method
The whisker weaving method (Murdoch and Benzley 1995; Murdoch et al. 1997), which
is based on the concept of the spatial twisting continuum (STC), is an attempt to mesh
objects with a prescribed boundary of quad facets (hex problem type II). Tautges et al. (1996)
described the STC as a dual of the hex mesh represented by intersecting surfaces, which
bisect hex elements in each direction. The principle behind the whisker weaving method
is to first construct the STC from the boundary quad faces. By means of the STC, hex
elements can be defined within the volume using the STC as a guide. The intersection of
the twisting planes with the volume will form a closed loop on the surface, which can be
deduced from the boundary quads. The objective of the whisker weaving algorithm is to
determine where the intersection of the twisting planes will occur within the volume, as
shown in Figure 5.103. This is entirely based on the topological consideration, and there are
no actual geometrical calculations involved (Folwell and Mitchell 1999; Calvo and Idelsohn
2000; Kawamura et al. 2008). Once a valid topological representation of the twisting plane
model has been established, hex elements are formed inside the volume at places where three
twist planes meet. Nodes can then be created within the volume afterwards to complete the
MG. Indeed, it is a method based on the STC loops on the boundary surface to deduce the
topological structure of the corresponding hex mesh. Given a hex mesh, it is easy to find its
boundary surface of quads; however, the inverse problem is less obvious, and it may not be
always possible to find out the internal structure of a mesh based merely on its boundary sur-
face. The whisker weaving algorithm faces problems of unresolved topological situations and
the formation of degenerated hex elements of zero volume. However, the method could help
in establishing the topological structure of a non-conforming hex mesh (Shepherd 2009).
Hexahedral
elements are defined
by the intersection of
STC loops in three
principal directions
Figure 5.103
Whisker weaving method.
