Civil Engineering Reference
In-Depth Information
is effectively,
−
v
∂φ
∂y
=
∂φ
∂t
(8.9)
in the region 0
≤
y
≤
2, subject to the boundary conditions
φ
=
1at
y
=
0 for 0
≤
t
≤
0
.
2,
φ
=
.
Comparing with Program 8.7, the usual geometry subroutine for 4-noded elements num-
beredinthe
0at
y
=
0for
t>
0
.
2and
∂φ/∂y
=
0at
y
=
2 for all
t
-direction,
geom rect
with
'dir = 'x'
is used. Arrays
node
and
storpb
are used to read in the numbers of fixed freedoms and to store information about them dur-
ing the time-stepping process. The system
kb
matrix is now unsymmetrical and stored as
a rectangular array with the full bandwidth using subroutine
formtb
(see Figure 3.18).
Although
pb
is symmetrical, it too is stored as a full band to be compatible with
kb
.
x
There are 202 equations and the half-bandwidth is 3
Time Concentration(node 3)
0.0000E+00 0.0000E+00
0.4000E-01 0.3660E+00
0.8000E-01 0.1116E+01
0.1200E+00 0.1066E+01
0.1600E+00 0.9285E+00
0.2000E+00 0.1017E+01
(some results omitted here)
0.8800E+00 -0.6148E-02
0.9200E+00 -0.3116E-02
0.9600E+00 0.8138E-02
0.1000E+01 -0.4934E-02
Distance Concentration(time=0.1000E+01)
0.0000E+00 0.3289E-24
-0.2000E-01 -0.4934E-02
-0.4000E-01 0.1548E-01
-0.6000E-01 -0.4225E-02
-0.8000E-01 -0.2975E-01
-0.1000E+00 0.3345E-01
(some results omitted here)
-0.7000E+00 -0.9004E-01
-0.7200E+00 0.1104E+00
-0.7400E+00 0.3613E+00
-0.7600E+00 0.6202E+00
-0.7800E+00 0.8459E+00
-0.8000E+00 0.1009E+01
-0.8200E+00 0.1095E+01
-0.8400E+00 0.1105E+01
-0.8600E+00 0.1051E+01
-0.8800E+00 0.9513E+00
-0.9000E+00 0.8246E+00
-0.9200E+00 0.6881E+00
-0.9400E+00 0.5551E+00
-0.9600E+00 0.4344E+00
-0.9800E+00 0.3306E+00
-0.1000E+01 0.2453E+00
-0.1020E+01 0.1779E+00
-0.1040E+01 0.1262E+00
-0.1060E+01 0.8776E-01
-0.1080E+01 0.5989E-01
-0.1100E+01 0.4017E-01
-0.1120E+01 0.2650E-01
(some results omitted here).
-0.1900E+01 0.1688E-11
-0.1920E+01 0.8274E-12
-0.1940E+01 0.4025E-12
-0.1960E+01 0.1973E-12
-0.1980E+01 0.9360E-13
-0.2000E+01 0.4779E-13
Figure 8.26
Results from Program 8.8 example
