Civil Engineering Reference
In-Depth Information
elements in one go when the limit of the memory is to be exceeded. For a tetrahedral
mesh of Ne elements with element node labels V, neighbours T and array F flagging
the elements to be deleted, an algorithm to consolidate the tetrahedral mesh is given as
follows.
Algorithm Compress_T4 (Ne, V, T, F)
// Consolidate a tetrahedral mesh
// Ne is the number of elements in the mesh.
// Input: V = Vertices of the elements, Neighbours of tetrahedra T,
// Flag array Fi
i
= 0 or 1, i = 1,Ne, tetrahedron i will be deleted if Fi
i
= 1.
// Output: A consolidated tetrahedral mesh {Ne*,
V
*,
T
*}
{
n = Ne
Loop: i = 1,Ne
If (F
i
≠ 0)then
n = n + 1
1
n = n - 1
If (n < i) go to 2
If (F
n
≠ 0) go to 1
Loop: j = 1,4
;
j
j
j
j
V=V;k=T;T=k
i
n
n
i
If(k≠0)find m such that T=n and set T=i
k
m
m
k
End loop j
F
i
= 0; F
n
= 1; n = n - 1
End If
End loop i
2
Ne = n }
2.5.11 Find the tetrahedral elements within the boundary surface
For constrained boundary problems, following the boundary recovery process, all the
tetrahedral elements within the closed boundary surface of triangular facets have to be
identified. The same problem may be faced if the FE mesh and the boundary surface are
constructed independent of each other. A simple algorithm based solely on adjacency rela-
tionship for a rapid retrieval of the elements within a bounded surface is given as follows.
Algorithm RBR3D (s, Ne, F, T, B, Z)
// Retrieve tetrahedral elements within a bounded surface
// s = seed tetrahedron inside the boundary surface, Ne = Number of
// elements in the mesh.
// Input:
F=a
k
a h
face of element k,
T=a
k
a h
neighbour of element k,
// Boundary surface
B
.
// Output: Zonal label Zi
i
= 0: outside or Zi
i
= 1: inside boundary surface,
// i = 1, Ne.
// Working array: A = List of active tetrahedra
{
n = 0; Set zero to array
Z
: (Z
i
= 0, i = 1, Ne); Z
s
= 1
Loop: a = 1,4
If
(F
a
B)then
s
j=T
a
; n = n + 1; A
n
= j; Z
j
= 1
