Dynamic Analysis - The Boundary Element Method with Programming - page 395

a range of values that depend on the time step size where the results are satisfactory i.e.,
stable and accurate. It can be observed, that the results are in good agreement with the
analytic solution and with the numerical results for single region problem published for
example by Schanz 11 . Excellent agreement with the analytic solution is obtained for the
time step E = 0.25, however the results for E = 0.10 are unstable. The larger time steps
(e.g., E = 1.50) tend to smooth the results due to larger numerical damping and introduce
some phase shift. Nevertheless, the results for all time step sizes inside the interval
0.20<E<1.50 are satisfactory.

Analytical:
C

2

= 1.50

C = 1.00

C = 0.50

node A

C = 0.25

= 0.10

C

1.5

node B

1

0.5

0

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

time [sec]

Figure 14.11 Longitudinal normalized displacements at nodes A and B .

Analytical:
C

2

= 1.50

C = 1.00

node C

C = 0.50

C = 0.25

1.5

C = 0.10

1

0.5

0

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

time [sec]

Figure 14.12 Longitudinal normalized tractions at the fixed end (node C) .