Civil Engineering Reference
In-Depth Information
for the creation of the new element always comes from the set Υ of potential line segments
for intersection, for the boundary update, it is sufficient to search over the set Υ in lieu of
the entire set of line segments on the generation front. The set Υ, which has been obtained
earlier in the creation of the new element, is a much reduced set compared to all the line seg-
ments on the generation front (
N
s
vs.
N
b
). The gain in computation time for the boundary
update as a by-product in boosting intersection checks is also very significant.
3.6.4 Test examples
The effectiveness of the dynamic grid was tested systematically using two series of adaptive
meshes progressively refined with an increasing number of elements and nodes. The MG was
coded on a standard PC, Intel(R) Core™2 i7, CPU870 at 2.93 GHz, running on Windows 7
with Intel FORTRAN VS2010 on XP mode. The domain employed is a 150 × 100 rectangle
whose boundary is decomposed uniformly into line segments of length 10 units. The first
node spacing function has been given by Equation 3.6, which specifies a higher-element
density around a circle and an ellipse, as shown in Figure 3.50.
As for the second node spacing function, it requires elements to be concentrated on the
perimeter of five intersecting circles, as shown in Figure 3.51. The mathematical expressions
for this node spacing function are given by
1
2
2
2
ρ
=−+
rR
ρ
min
,
r
= −+−
(
xxy
)(
y
),
i
i
i
i
i
π
π
xxR
=+
cos
+
i
α
,
y
=
yR
+
sin
+
i
α
,
i
=
15
,
i
0
x
i
0
y
2
2
απ
=
2
5
,
R
=
18
,
R
=
30
,
R
=
24
,
x
=
75
,
y
=
48
x
y
0
0
ρ
=
min( ,
ρ ρ
),
ρ
max
= 20
i
max
i
=
15
,
For the series of five meshes corresponding to the first node spacing function, ρ
max
= 20
and the minimum node spacing ρ
min
varies from 0.1 to 0.005, which represents a variation
Figure 3.50
FE mesh for the first nodal spacing function,
N
n
= 75,740,
N
e
= 151,428.
