dohrmann Episode 2 Part 3 pptx

Figure 6: Example 3.1 displaced geometry exaggerated for mesh configuration Q4Q4 obtained using the standardmaster-slave approach... Results arepresentedfor mesh configuration Q4Q4 using

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

7

4

1

8

3

5

1

9

4

6

2

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

Figure 6: Example 3.1 displaced geometry (exaggerated) for mesh configuration Q4Q4 obtained using the standardmaster-slave approach

1.15[ I I I I 1 I i I I

:

“\l \

;\.’

/ “A.1 \ ! ~ 1.” , /“ \ I

~ ‘(’

“Y’” \

/ 4’ “! ‘, /’ { “~.’ , 1 “’j “{ ‘\

I /\ .“ “/\ \

/ I\”’. lj I /\ .“ 1 \ \

/ / (

II \ 0- ‘ l,\”’”\ \

I //”\” ’\\

\ /. /\.”” /\, ,.l~\’ , l\, \

: OAA

‘ II.J

/ \ \ 1- bdl.+ii Lf?!b &e& LiLi k.A&:.dit i.J”o “~;

0.95

-0.9

I

‘2

Figure 7: Axial stress01 ~at centroids of elements with edges on the slave boundary Results arepresentedfor mesh configuration Q4Q4 using the standardmaster-slave approach

22

1.05

=1

o

0.95

0.9

1“ “.I

~;

~.1.

,1

‘2

Figure 8: Axial stress61 ~atcentroids of elements with edges on the slave boundary Results are presentedfor mesh configuration Q8Q8 using the standardmaster-slave approach

I I I I I I I [

1

2

1

. 3

Figure 9:

Iog(lh)

Energy norms of the error for Example 3.1 obtained

usingthe standardmaster-slaveapproach

*

*

.

24

-!3

F_

o

-l:?

–1:3

1

n

Q4Q4

1

[

Iog(lln)

10: Energy norms of the error for Example 3.2 obtained using the present method

–4.4

4.6

–4.8

~

>

0

~ –5.2

~

-5.4

n

Case 1 Case 2

-5.6

-5.8

1

Iog(lh)

Figure 11: Energy norms of the error for Example 3.3 obtained using the present method for mesh configura-tion Q4Q4 Casekrefers to the problem with Meshkdesignated as master

26

‘:-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 Casekrefers to the problem with Meshkdesignated as master

0.6

0.4

102

0.2

0

-0.2

exact

‘2

Figure 13: Normalized shear stress 612 at centroids of elements with edges on the slave boundary for mesh configuration Q4Q4 (Case 1)

,.

28