Civil Engineering Reference
In-Depth Information
f/f
ο
(node 31)
q =
0.5
q =
0.75
q =
1.0
2D series solution
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
T
Figure 8.18
Typical solutions from Program 8.2 with varying
θ
(
t
=
0
.
4)
t
is increased, the explicit
algorithm will lead to unstable results (the stability limit for the chosen problem is about
t
crit
=
It must, however, be remembered that as the time step
.
θ
=
.
5 will tend to produce oscillatory
results, which can be damped, at the expense of average accuracy, by increasing
0
02). At that time step, Program 8.2 with
0
θ
towards
1.0. Typical behaviour of the implicit algorithm is illustrated in Figure 8.18.
Program 8.5, while retaining the storage economies of Program 8.4, allows the time
step to be increased well beyond the explicit limit. For example, in the selected prob-
lem, reasonable results are still produced at
is increased
still further, accuracy becomes poorer and Program 8.2 yields the best solutions for very
large
t
=
10
t
crit
. However, as
t
.
It will be clear that algorithm choice in this area is not a simple one and depends on
the nature of the problem (degree of non-linearity, etc.) and on the hardware employed.
All the mesh-free methods afford much scope for parallelisation and this is exploited in
Chapter 12.
t
