Page 125 - The Combined Finite-Discrete Element Method

108 CONTACT DETECTION

10

9

8
7
6

5 7 1 4

4
10
3
2

1

Figure 3.43 All x-lists of discrete elements for row 7 of cells.

Integer array A

−1 −1 7 1 4 −1 −1 −1 −1 −1

2 −1 −1 −1 −1 −1 −1 −1 −1 −1

Integer array X

Figure 3.44 Representation of all singly connected lists for row 7 of cells using two integer arrays.

Discrete elements are mapped by looping over all the discrete elements in ascend-
ing order.
List y 7 (Figure 3.42) contains all discrete elements in row 2 of cells, i.e. discrete
elements 10, 7, 4 and 1. No discrete element from list y 2 has an integerised coordinate
i x equal to 1 or 2, thus singly connected lists x 1,7 and x 2,7 are empty, i.e. A[1] =−1
and A[2] =−1. Only discrete element 4 has an integerised coordinate i x equal to 5, thus
A[5] = 4and X[4] =−1. Only discrete element 7 has an integerised coordinate i x equal
to 3, thus A[3] = 7, X[7] =−1. Discrete elements 1 and 10 have integerised coordinates
i x equal to 4, thus A[4] = 1, X[1] = 10, X[10] =−1.
It is important to note how lists y iy and x ix are assembled:

• First a loop over all discrete elements is performed, and inside the loop a particular
discrete element j is added to the corresponding y iy list, depending on its integerised
coordinate i y .