Civil Engineering Reference
In-Depth Information
Figure 4.4
Surface meshes by 3D direct construction.
Direct 3D surface mesh generation of quadrilateral elements is also possible. A direct 3D
implementation of the
paving
algorithm over curved surfaces was presented by Cass et al.
(1996). Figure 4.5 shows a quadrilateral mesh of two intersecting cylinders by direct con-
struction of quadrilateral elements. Heuristic
sticky space
is introduced to detect intersec-
tion and overlapping quadrilaterals. Nevertheless, it is considerably much more flexible to
generate triangular meshes over curved surfaces, and by the systematic merging of triangles,
unstructured quadrilateral meshes can be conveniently generated by a two-step process with
much better control on the size and shape of the quadrilateral elements.
Quadrilateral-dominated meshes for curved surfaces can also be obtained by combin-
ing pairs of adjacent triangles. Gradation quadrilateral meshes over curved surfaces can be
obtained by conversion of surface triangulation with particular care taken to maintain cor-
rect surface curvature. Similar to planar meshes discussed in Section 3.9, all-quadrilateral
meshes on curved surfaces can be generated by systematic merging of triangular meshes.
Figure 4.6 shows examples of quadrilateral meshes from the conversion of triangulated
surfaces. The Q-morph scheme proposed by Owen et al. (1999) can also be used to gener-
ate quadrilateral meshes on triangulated curved surfaces. Q-morph can be considered as a
remeshing process, which converts a background triangulation into a quadrilateral mesh.
This method is applicable to 2D domains as well as over curved surfaces to generate grada-
tion unstructured quadrilateral meshes, as shown in Figure 4.7.
Figure 4.5
A quadrilateral mesh by 3D direct construction.
