Page 141 - The Combined Finite-Discrete Element Method

124 CONTACT DETECTION

Finding nonempty y-lists involves looping over all discrete elements from the z iz list.
Thus, no loop over cells is involved. For a given non-empty y iy,iz list only x-lists for rows

(i y − 1,i z ); (i y ,i z );
(3.78)
(i y − 1,i z − 1); (i y ,i z − 1); (i y + 1,i z − 1);

need to be assembled. It is important to separate elements from row (i y,iz ) from elements
from the other rows. Thus, two sets of singly connected x-lists are assembled –one set
of lists for discrete elements from row (i y,iz ), and one set of lists for discrete elements
from rows

(i y − 1,i z ); (3.79)
(i y − 1,i z − 1); (i y ,i z − 1); (i y + 1,i z − 1);

All these lists can be represented by two arrays:

• The two-dimensional array A[2][n x ] containing the head of each of the lists, i.e. the
first discrete elements in a particular list.
• The one-dimensional array X[N]; for each discrete element this array contains the next
discrete element in the same x-list.
To further aid understanding of the above described procedures, a visual representation
of the NBS contact detection algorithm in 3D is given in Figures 3.59–3.63. First, discrete
elements are mapped onto layers of cells. (Figure 3.59) and a nonempty layer is identified
and called the central layer (Figure 3.60).
The non-empty z-layer i z together with the layer immediately below it (layer i z− 1) is
divided into y-rows of cells (Figure 3.61).
By looping over discrete elements from layer i z , a non-empty row (i y ,i z ) is identified
and called the central row (Figure 3.62).

z

y

x
Figure 3.59 Layers of cells.