Civil Engineering Reference
In-Depth Information
Object to be meshed
Figure 8.98
Object inside a cube.
8.5.2.1 Initial embedding mesh
The object to be meshed defined by a collection of boundary surfaces is put in a cube, which
is divided into five or six tetrahedra, as shown in Figure 8.98.
8.5.2.2 Mesh refinement over object boundary
Mesh refinement algorithm presented in Section 8.4.3 is applied to the initial tetrahedral
mesh following the object boundary surfaces with a mesh refinement compatible with the
curvatures of the boundary surface and the size specifications, as shown in Figure 8.99.
8.5.2.3 Projection of nodes close to boundary surface
To recover the object boundary, nodes near the boundary have to be projected onto the
boundary surface. The main issue here is to devise an objective measure to judge whether a
point is close to the object boundary or not. Obviously, a distance measure will be problem-
dependent and subject to the geometrical characteristics of the object under consideration.
Instead of prescribing a specific threshold or tolerance, a more generic approach is to judge
based on the shape quality of the elements associated with the projection. To this end, a
node close to the object boundary will be projected if the minimum γ-quality of the patch
of elements incident to the node is not inferior to that prior to the nearest point projection.
Figure 8.99
Mesh refined along object boundary.
