Civil Engineering Reference
In-Depth Information
7
6
8
3
5
2
4
1
Figure 8.133
Hexahedron H(1, 2, 3, 4, 5, 6, 7, 8).
and tetrahedral elements, a pyramid element has to be introduced at the interface between
hexahedral and tetrahedral elements, as shown in Figure 8.134. As hexahedral elements
are retrieved from a valid tetrahedral mesh, a quadrilateral face of a hexahedron can only
be connected to two tetrahedra, as shown in Figure 8.135. There are two cases to consider.
1. If the two tetrahedra share a common opposite node E, as shown in Figure 8.135a,
then the two tetrahedra can be merged to form pyramid element ABCDE.
2. In case the two tetrahedra do not share a common node, as shown in Figure 8.135b,
node I has to be inserted at the mid-point of edge BD. All the tetrahedra connected to
line BD are each divided into two tetrahedra by the standard edge-subdivision process.
Node I is then lifted slightly away from the quadrilateral face ABCD to create pyramid
element ABCDI.
Hexahedron
Te trahedra
Pyramids
Figure 8.134
Pyramid as an interface between hexahedral and tetrahedral elements.
E
E
F
D
D
I
C
C
A
A
B
B
(a)
(b)
Figure 8.135
Connection between tetrahedral elements and a quadrilateral face: (a) two tetrahedra form
a pyramid at face ABCD; (b) tetrahedral elements cannot merge into a pyramid at face ABCD.
