Civil Engineering Reference
In-Depth Information
8.5.2.4 Cutting of intersecting edges
Partly due to nodes not all being projected onto the boundary surface and partly due to
the fact that the boundary surfaces in general may not be contained in the refined mesh
(i.e. boundary surfaces are covered with triangular facets of the refined mesh), there are
edges of the refinement mesh cutting across the boundary surface. To create a conforming
mesh by getting rid of these intersecting edges, the edge bisection procedure described in
Section 8.4.3.1 can be applied. To this end, the intersection point on the penetrating edge is
determined, and the ring of tetrahedra around this edge will be divided by the introduction
of an extra node at the intersection point. Effectively, an additional point is created at the
boundary surface with faces of tetrahedra in good alignment with the boundary surface.
Of course, intersection point too close to an end point of the edge will not be introduced,
which indeed would rarely happen due to close point projection discussed in Section 8.5.1.3.
Anyway, a point too close to an existing point will not be created, and this situation will be
dealt with in the phase of boundary point projection. In the current formulation, intersec-
tion points within 5% to an end point of the cutting edge will not be created so as to prevent
elements of poor quality being formed near the object boundary.
8.5.2.5 Elimination of elements not belonging to the object
By the procedures discussed in Sections 8.5.1.3 and 8.5.1.4, the object boundary is virtually
in place to within a few percentages depending on the actual situation. Tetrahedral elements
outside the object boundary can be readily eliminated by checking their centres of gravity
relative to the object boundary, as shown in Figure 8.100. The boundary surface of the same
object would be much more irregular with an indentation of half an element on the average
if boundary preparation procedures discussed in Sections 8.5.1.3 and 8.5.1.4 have not been
applied, as shown in Figure 8.101. It is noted that further mesh refinement will only reduce
the size but not the pattern of boundary irregularity.
8.5.2.6 Boundary point projection
With the elimination of elements outside the object, the boundary of the meshed object is
formally defined as a result. The boundary nodes can now be identified, which are vertices
belonging to one of the boundary triangular facets. As a final step, the boundary nodes are
all projected onto the analytical boundary surfaces to further match the geometry between
Figure 8.100
Elements within boundary retained.
