Civil Engineering Reference
In-Depth Information
4
8
7
5
6
3
(b)
1
4
5
3
2
6
(a)
2
1
4
4
3
5
3
(c)
1
1
2
(d)
2
Figure 2.6
Node labeling of 3D FE elements: (a) tetrahedral element; (b) hexahedral element; (c) penta-
hedral element; (d) pyramid element.
For a mixed mesh consisting of elements of various types, an additional pointer array has
to be used to mark the starting point of each 3D solid element. Alternatively, a linear array
of length 8N
E
can also be reserved for a mixed mesh of N
E
elements in such a way that each
element is allocated eight nodal spaces irrespective of its type, and the excessive space can be
filled up with zeros. At the expense of slightly more memory, there is an additional flexibility
in deleting and adding elements to a mesh in the second storage scheme.
2.4 GEOMETRICAL OPERATIONS AND FORMULAS
2.4.1 Distance from a point P to a line segment AB, d(P, AB)
As shown in Figure 2.7, the unit vector along direction AB is given by
u
=
AB
AB
Compute α = AP ⋅
u
d = ∣∣PC∣∣ = ∣∣AP − α
u
∣∣
B
u
C
α
d
A
P
Figure 2.7
Distance between point P and segment AB.
