Page 101 - The Combined Finite-Discrete Element Method

84 CONTACT DETECTION

• Step 2: check which cell the current discrete element belongs to:

left–hand cell if x i >x mid
(3.17)
right–hand cell otherwise
• Step 3: place the current discrete element onto a list of discrete elements if the current
level equals b,i.e.
if j = b,
(3.18)
place current discrete element (element i) onto the list
The easiest way to achieve Step 3 is to use singly connected lists. For example, for the
discrete elements shown in Figure 3.11, a singly connected list for all cells at level 4
contain four discrete elements, as shown in Figure 3.12.
This list is easiest achieved by using an array of integer numbers of size N,where
N is the total number of discrete elements comprising the system. The array is called E
(short for element). The head of the list is remembered with the node of the binary tree,
as shown in Figure 3.12.
All successive discrete elements are shown using array E, as shown in Figure 3.13. All
the numbers of array E are initially assigned as −1, meaning the end of the list, i.e.

E[i] =−1; i = 1, 2, 3,. ..,N (3.19)

while all the heads are initially assigned −1, meaning an empty list.
Placing a new discrete element i onto the list is done by setting

E[i] = HEAD
(3.20)
HEAD = i

Discrete
element 9 Level 5
Discrete
element 7
Discrete
element 5 Level 3
Discrete
element 3
Level
4
Level 1

Level 2

Figure 3.11 Four discrete elements in a single cell.