Page 110 - The Combined Finite-Discrete Element Method

SCREENING CONTACT DETECTION ALGORITHM 93

Further mapping of discrete elements onto the cells after the discrete elements have
moved does not require initialisation. Instead, discrete elements are simply removed from
the singly connected lists, and all singly connected lists are thus made empty before the
mapping process (step 1) starts again.
Removing of discrete elements from the singly connected lists is done by looping over
all discrete elements, integerising its coordinates and setting the corresponding number
of array C and also the corresponding number of array E to −1, indicating empty lists:

Loop over discrete elements (k=1; k≤N; k++)
{ Integerise current coordinates using equation (26) and set

int x k − x min
i = x k = 1 + Int
d
(3.36)

int y k − y min
j = y k = 1 + Int
d
Empty the corresponding singly connected list by
setting E[k] =−1
(3.37)
and C[i][j] =−1
}
Once the discrete elements have been mapped onto the cells, detection of contacts is
performed. This involves looping over all discrete elements, and finding out which cell a
particular discrete element is mapped onto. Once the particular cell has been identified,
direct check against all discrete elements from the central and neighbouring cells (as
shown in Figure 3.18) is performed:

Loop over discrete elements (k=1; k≤N; k++)
{ Integerise current coordinates using equation (26) and set

int x k − x min
i = x k = 1 + Int (3.38)
d

y k − y min
int
j = y k = 1 + Int
d
if C[i][j]≤N (3.39)
{ C[i][j]=C[i][j]+N
loop over all discrete elements from C[i][j]list
{ loop over all discrete elements from neighbouring
cells, i.e. lists C[i-1][j-1],C[i][j-1],
C[i+1][j-1],C[i-1][j],C[i][j]
{ direct check for contact between discrete elements
}} }
}

Note that no loop over cells is used. Loops over discrete elements are used instead. In
this way, the total number of algebraic operations involved is made independent of the
total number of cells, i.e. independent of the size of array C.