Civil Engineering Reference
In-Depth Information
Figure 8.94
Axis rotated along a diagonal.
some local topological operations to provide a compatible environment for the creation of
anisotropic elements, there is a limitation in the generation of anisotropic meshes merely
based on edge refinement alone. The works of Gruau and Coupez (2005), Remacle et al.
(2005), Alauzet and Frey (2005), Sahni et al. (2006), Loseille and Alauzet (2009), Loseille
and Lohner (2009) and Loseille et al. (2010) are referred to for details of those treatments
in anisotropic refinement and adaptation.
8.4.4 Refinement of non-simplicial elements
Non-simplicial meshes in 2D and 3D such as quad and hex meshes can be refined uniformly
across all the elements in the mesh along the principal directions, as shown in Figure 8.95.
In order to be compatible with adjacent elements, there is a severe restriction that each ele-
ment has to be subdivided in exactly the same manner. As for non-uniform refinement, it
seems that the only practical way is perhaps to refine quads (Tchon et al. 2004: Garimella
2009; Liang et al. 2009) and hex (Sun et al.
2011) elements around a point, as shown in
Figure 8.96. A quad is divided into three quads, and a hex is divided into four hex, a smaller
one close to the point and three bigger ones on the opposite faces. However, for the non-
uniform subdivision of quads and hex, distorted elements will inevitably be generated from
the original regular elements. Refer to Sections 5.8.14 and 5.8.15; in case we would like to
keep all the elements as regular as possible in the refinement process, transition quad and
hex elements can be employed, as shown in Figure 8.97.
Figure 8.95
Uniform refinement.
