dohrmann Episode 2 Part 6 ppt

Figure 2: Projection of F1 onto an element face of the master surface (see top left comer of Figure 1). In the
coordinate system of the element face, the triangularregions have straightedges and lie in a single plane. The
domain of the projection of Fl onto the element face is divided into triangularregions for the purpose of cal-
culating surface integralsover
Fm.
19
*

\
Figure 3: An edge of F1 (solid line) and its projection onto the mastersurface (dashedline) viewed from a
direction nearly orthogonal to F1. The edge shown spans threedifferent element faces on the mastersurface.
The projection of the edge onto the master surface is a piecewise continuous line with possible discontinui-
ties in slope at edges on the master surface. The solid and dashed lines appearas straightlines in the coordi-
nate systems of element faces on the slave and mastersurfaces, respectively.
20
e3
k
(2hl,h2,h3)
e2
el
Mesh 2
Mesh
(2hl,h2,0)
(o
(a)
(b)
Figure 4: (a) Mesh configuration H8T4 with nl 1= n21= n31= 2
and FZ12= 7222= n32= 3, (b) openedview of
meshes revealing sharedboundary.
21
10

9
1.104
0.92465
1.1049 1.1049
0.92465 1.104
8
0.92465
0.76437
0.92385
0.92385 0.92385
0.76437 0.92465
7
6
1.1049
1.1049
1.1064
1.1064
1.1084
1.1064
0.92385
0.92385
1.1049
1.1049
m5
*
0.92385
4
3
2
0.92465

0.76437
0.92385 0.92385 0.76437 0.92465
1
1.104
0.92465
1.1049 1.1049
0.92465
I
I
7
8
1.104
2 3
4
5 6
9 10
Figure 7: Stress component G1, at centroids of elements with faces on the slave surface for Example 3.1.
Results presented are for mesh configuration H20H20 using the standardmaster-slaveapproach.
I I I
I I 1 I
BEl
0.527
0.514
0.511
0.505
–2 –1 .8 –1 .6
-1.4 –1 .2 –1
-0.8 -0.6
log(lhz)
Figure 8: Energy norms of the errorfor Example 3.1 obtained using the standardmaster-slaveapproach.

Slopes of lines connecting the data points are shown above the line segments.
25
I I
I
I
I I
I
0.977
0.993
0.997
1.836
1.803
1.762
-11
-2.2 -2
-1.8
-1.6
–1 .4
-1.2 -1
-0.8 -0.6
log(lln)
Figure 9: Energy norms of the error for Example 3.2 obtained using the presentmethod. Slopes of lines
connecting the datapoints are shown above the line segments.
26
-1.8 -1.6 -1.4 -1.2
-1
-0.8 -0.6
-0.4
log(lln)
Figure 10: Energy norms of the error for Example 3.3 obtained using thepresentmethod.

27
10
-0.060954 –0.060954
1
0.041871 0.041871
8
9
-0.052381
-0.052381
T
,
I
0.047454
I
0.047454
I
RI
1
I
-0.048586
-0.048586
0.049262
0.049262
7
-0.048806
-0.048806
0.048954 0.048954
6
-0.048929
-0.048929

0.048913
0.048913
*N 5
-0.048924 -0.048924
I
0.048919
I
0.048919
I
-0.04892 -0.04892
0.04892
0.04892
Q
u
-0.04892
-0.04892
I
0.04892
I
0.04892
I
2
-0.04892
-0.04892
0.04892
0.04892
1
-0.04892
–0.04892
0.04892

0.04892
0
I
I
I
I
I I
o 0.1 0.2
0.3
0.4 0.5
0.6
0.7 0.8 0.9
1
x3
Figure 11: Stresscomponent olzat centroids ofelements with faces onthe slave surface forCasel of
Example 3.3.
28
I
0.00086069
I
0.00086069
I
:) .
0.0019521
0.0019521
8
I
0.00029844
0.00029844
-r

I
–5.5033e-05
-5.5033e-05
6
I
–5.855e-06
-5.855e-06
f?
5
1.0282e-06
1.0282e-06
4
I
‘ 2.0026e-07
I
2.0026e–07
I
I
-3.6555e–08
I
-3.6555e-08
I
I
-2.5823e-09
I
-2.5823e-09
I
-1t
I
2.6216e–10

2.6215e-10
()-
I
I
I I I ! !
I
o 0.1 0.2 0.3
0.4
0.5 0.6
0.7
0.8 0.9 1
x3
Figure 12: Stresscomponento12at centroidsofelements withfaces onthe slave surface forCase 2of
Example 3.3.
29
Internal Distribution:
1 MS 9042
1 MS 9042
1 MS 9042
1 MS 9042
1
N’fs9405
1 11S 9042
1 hfs 9405
1 lls 0828
1 llS 0826
1 hlS 0835
1 \fs o-143
1 \Iso4-i3
1 MS 0443

1 31S 0443
10 hfso443
10 hls 0443
1 hlso443
1 L1S0443
1 Lls 0443
1 hlS 0836
1 MS0836
1 JIS0819
1 MS0819
1 hlS0819
1 hls 0443
1
}1s0441
1 hIS0441
1 hlso439
10 MS0439
1 MS0439
1 MS0439
1 MS0439
1 MS9018
2 MS0899
1 MS0619
E. P. Chen, 8742
R. E. Jones, 8742
L. E. Voelker,8742
L. I. Weingarten, 8742
P. E. Nielan,8743
M. L. Chiesa,8743
J. F. Lathrop, 8743

F. J. Mello, 9104
D. K. Gartling, 9111
R. J. Cochran,9113
H. S. Morgan, 9117
S. W. Attaway, 9117
11. L. Blanford,9117
K. H. Brown, 9117
lf. W. Heinstein, 9117
S. W. Key, 9117
J. R. Koteras,9117
J. W. Swegle, 9117
C. M. Stone, 9117
J. R. Stewart, 9121
L. M. Taylor, 9121
K. G. Budge, 9231
J. S. Peery,9231
J. R. Weatherby, 9231
J. Jung, 9135
R. W. Leland, 9226
S. A. Mitchell, 9226
D. R. Martinez, 9234
C. R. Dohrmann, 9234
C. W. Fulcher, 9234
G. M. Reese, 9234
D. J. Segalman, 9234
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1