dohrmann Episode 2 Part 3 pptx
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X2
t
Mesh 1
Mesh 2
(a)
(c)
x,
(b)
(d)
Figure 4: Mesh configurations (a) Q4Q4, (b) Q4T3, (c) T3Q4 and (d) T3T3 all with nl 1= n21= 2 and
19
X’2
7
4
1
8
3
5
1
22
23 24 25
9
4
6
2
2 3
11
8
8
4
5
0
12
9
9
5
6
1
13
0
10
6
7
2
Figure 5: Mesh configuration Q4Q4 showing element and node numbers.
20
-1
Figure 6: Example 3.1 displaced geometry (exaggerated)for mesh configuration Q4Q4 obtained using the
standardmaster-slaveapproach.
21
1.15[
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n=16
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2 3 4
5 6 7 8
9
10
‘2
Figure 7: Axial stress01 ~atcentroids of elements with edges on the slave boundary.Results arepresentedfor
mesh configuration Q4Q4 using the standardmaster-slave approach.
22
1.15
1.1
1.05
=1
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0.95
0.9
1 I
I-II
exact
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n=4
-*-
n=8
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n=16
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1 2 3
4 5
6
7 8 9
10
‘2
Figure 8: Axial stress61~atcentroidsof elements with edges on the slave boundary. Results arepresentedfor
mesh configuration Q8Q8 usingthe standardmaster-slave approach.
23
I
I
I I I I I [
I 1
1
2
1
-3
Figure 9:
–2.8 -2.6 -2.4 -2.2
-2
Iog(lh)
Energy norms of the error for Example 3.1 obtained
–1.8 –1.6
–1.4 -1.2
using
the standardmaster-slaveapproach.
*
*
.
24
–“7
–/3
-!3
F_
o
c
-l:?
–1:3
I
[
I
1
n
Q4Q4
“
Q8Q8
1
[
–14
I
I
I I
I I I I
3 –2.8 –2.6 -2.4 –2.2 -2 –1.8 -1.6 -1.4 -1.2
Iog(lln)
10: Energy norms of the errorfor Example 3.2 obtained using the presentmethod.
25
4.2
–4.4
4.6
–4.8
~
c
-5
>
p
0
~ –5.2
~
-5.4
n
Case 1
Case 2
-5.6
-5.8
1
-5.2
-2 –1 .8 -1.6
-1.4 -1.2
–1 -0.8 -0.6
Iog(lh)
Figure 11: Energy norms of the error for Example 3.3 obtained using the presentmethod for mesh configura-
tion Q4Q4. Case
k refers to the problem with Mesh k designated as master.
26
–7.2
‘:-2.2
-2
–1.8 –1.6 -1.4 –1 .2
-1 –0.8 -0.6
Iog(l/n)
Figure l12:Energy nomdensities of theenor for Exmple3.30bttined using thepresent method formesh
configuriition Q4Q4. Case
k refers to the problem with Mesh k designated as master.
27
1
0.8
0.6
0.4
102
0.2
0
-0.2
. II
exact
n
n=4
.–m -
n=8
-0.4 ~
1
I
o
1 2 3 4
5 6
7 8 9
10
‘2
Figure 13: Normalized shear stress 612 atcentroids of elements with edges on the slave boundary for mesh
configuration Q4Q4 (Case 1).
,.
28
