Civil Engineering Reference
In-Depth Information
(b)
(a)
Figure 8.104
Mesh of volume bounded by two ellipsoids: (a) entire mesh; (b) half section.
to the two boundary surfaces. Upon removal of elements outside the object, 278,860 tetrahe-
dra are left in the volume within the boundary surfaces, as shown in Figure 8.103d. The last
example is a volume defined by two analytical surfaces in which another ellipsoid with semi-
principal axes of 2, 3 and 5 units along x, y and z directions is added to the ellipsoid employed
in the second example. The initial tetrahedral mesh is refined on the ellipsoidal surfaces into
396,461 elements. On removal of elements outside the object, an FE mesh of 227,769 tetrahe-
dral elements is generated with a γ-quality of 0.646, as shown in Figure 8.104a. A half mesh
cross section revealing the internal structure of the mesh is shown in Figure 8.104b.
MG by refinement is a versatile and efficient scheme in meshing geometrical objects bounded
by analytical surfaces. As FEs only need to fit the geometrical boundary of the object, the
algorithm is applicable to objects of general topological shapes, simply or multi-connected,
with or without internal openings, bounded by one or several surfaces, and the object may even
be disjointed into a number of pieces. Exactly the same boundary rectification steps of node
projection and edge division can be applied to recover objects of the most general shapes and
topology. The computation time mainly depends on the number of elements in the mesh more
or less linearly but not on the geometry or the topology of the object. As shown by the exam-
ples, meshing a sphere using the same number of elements takes roughly the same CPU time as
meshing a volume bounded by two surfaces or with an internal void. Though more evidence
and an in-depth study are required, the quality of the mesh seems to depend on the number
of penetrating edges on the boundary surfaces as there is little difference in the quality of the
initial refined mesh. Anyway, though the proposed boundary treatment is simple enough, there
still is much room for improvement of the quality of the elements on the boundary through the
use of some more sophisticated techniques. In theory, volumes of different material types with
internal partition surfaces can also be meshed as long as the regions along with the internal
surfaces within the object are well defined and represented.
8.6 MERGING OF TETRAHEDRAL MESHES
8.6.1 Introduction
Nowadays, advanced industrial production often systematically goes through the cycle of
conception, CAD geometrical modelling, data preparation for simulation and meshing, FE
analysis and optimisation. For a proper maintenance of the products and possible upgrades
for additional features, another round of simulation and refinement has to be carried out to
meet the new requirements. However, for the sake of rapid turnaround, it may not be a good
