Page 130 - The Combined Finite-Discrete Element Method

MUNJIZA-NBS CONTACT DETECTION ALGORITHM IN 2D 113

6 Detection time -- packing A
Time for 10 loops (s) - (R4600 133.0 MHz) 4 Legend
5

3

2
Experiment

1

0 Approximation
0 10 20 30 40 50 60 70 80 90
Total number of discrete elements (N x 1000)
Figure 3.47 Example I: CPU time as a function of the total number of discrete elements
(A. Munjiza and K.R.F. Andrews, International Journal for Numerical Methods in Engineering,
43/1). Reproduced by permission John Wiley & Sons, Ltd).

The results shown are obtained by changing N from N = 100 to N = 90,000. The
results accurately fit a linear relation, which confirms that the total detection time is
indeed proportional to the total number of discrete elements.
Example II consists of N = 10,000 circular discrete elements of diameter D spaced
at distance 2D in the y-direction and at variable distance S (spacing) in the x-direction
(packing ‘B’), (Figure 3.48).
The packing density ρ changes with spacing S as

1
ρ ∝ (3.66)
S

i.e. the packing density is reduced by increasing spacing S. In Figure 3.49, the total CPU
time for 10 repeated detections of all contacts is shown as a function of spacing.
The results obtained in this numerical experiment confirm that the total detection time
does not depend upon packing density (which is the same as predicted in Chapter 6).
Example III consists of N = 10,000 circular discrete elements of diameter D spaced
at distance S in the x-direction and at distance S in the y-direction. (Figure 3.50).
The packing density ρ changes with spacing S as

1
ρ ∝ (3.67)
S 2
Contact detection for various values of S is repeated 10 times, and the total CPU time for
all 10 detections of all contacts is recorded as shown in Figure 3.51.