Code_Aster ®
Version
4.0
Titrate:
SSLV113 Estimateur of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A Page:
1/8
Organization (S): EDF/IMA/MN
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
V3.04.113 document
SSLV113 - Estimator of error on a cylinder
hollow Bi-materials
Summary:
This test validates the estimator of error in pure residue, applied to linear elasticity 2D, in statics. One is considered
hollow roll made up of two materials and subjected to internal and external pressures.
2 modelings are axisymmetric, on quadrangles with 8 nodes.
The interest of the test lies in the comparison between the exact and calculated constraints, on the one hand, the error
estimated and the exact error, in addition. This test also makes it possible to show the validity of the estimator in residue
on a structure bimatériau, contrary to the estimator of Zhu-Zienkiewicz which is not applicable on
structures presenting of discontinuities in the stress field (here with the interface material).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV113 Estimateur of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A Page:
2/8
1
Problem of reference
1.1 Geometry
Z
With
D
C
1
chechmate. 1
chechmate. 2
p
Q
With
E
B
0.
1.
3/2
2.
R
1.2
Material properties
chechmate. 1:
E = 2.
= 0 3
.
chechmate. 2:
E = 1.
= 0 3
.
1.3
Boundary conditions and loadings
On AB, UZ = 0.
on cd., UZ = 0.91333 = A.
Pressure interns on AD, p = 1.
External pressure on BC, Q = 2.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV113 Estimateur of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A Page:
3/8
2
Reference solution
2.1
Method of calculation used for the reference solution
µ
I
E
=
I
(
2 1 +)
I
E
=
I
(1 -
2) (1+)
has
= - 0.98097
B
= - 1.11741
1
1
calculated numerical data
has
= - 1.34405
B
= -
2
2
0.30048 starting from the equations of Navier
For the material “I”, one a:
B
U
= R has
I
+
R
I
R
U
= A
Z
I
B
=
2
+
+ 2
-
rr
I (ia
) A µi ia
r2
I
B
= 2 + + 2
+
I (
I
has
) A µi ia
r2
= 2
+
+
zz
I ia (I 2 µi) A
2.2
Uncertainty on the solution
Analytical solution.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV113 Estimateur of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A Page:
4/8
3 Modeling
With
3.1
Characteristics of modeling
M1
M2
M3
M4
With
E
B
3.2
Characteristics of the grid
A number of nodes: 23.
A number of meshs and types: 4 QUAD8.
3.3 Functionalities
tested
Commands
Keys
CALC_ELEM
OPTION
“SIRE_ELNO_DEPL”
[U4.61.02]
OPTION
“ERRE_ELGA_NORE”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV113 Estimateur of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A Page:
5/8
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
tolerance
With
1.00003
1.06833
6.83
7.0
rr
4.43821
4.46731
0.66
2.0
0.19518
0.16596
14.9
15.0
zz
E
2.37%
5.0
rel
E chechmate. 1
1.95508
1.97893
1.22
2.0
rr
3.48316
3.49330
0.29
2.0
0.19518
0.18498
5.22
6.0
zz
E
1.05%
5.0
rel
E chechmate. 2
1.95508
1.98398
1.48
2.0
rr
2.16049
2.13394
1.23
2.0
0.32135
0.32204
0.22
2.0
zz
E
0.152%
5.0
rel
B
1.99999
2.00095
0.048
2.0
rr
2.11555
2.11595
0.012
2.0
0.32135
0.32174
0.12
2.0
zz
E
0.057%
5.0
rel
4.2 Remarks
Grid being coarse (4 elements according to Gold), certain constraints close to the axis of axisymetry
are badly approximated. The jump of and zz to the interface of 2 materials are on the other hand well detected.
4.3 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
4.7 seconds
4.4 Remarks
Relative error considered total = 1.40%.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV113 Estimateur of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A Page:
6/8
5 Modeling
B
5.1
Characteristics of modeling
M1
M10
M20
M11
With
E
B
5.2
Characteristics of the grid
A number of nodes:
A number of meshs and types: 20 QUAD8.
5.3 Functionalities
tested
Commands
Keys
CALC_ELEM
OPTION
“SIRE_ELNO_DEPL”
[U4.61.02]
OPTION
“ERRE_ELGA_NORE”
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV113 Estimateur of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A Page:
7/8
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
tolerance
With
1.00003
1.00351
0.35
0.5
rr
4.43821
4.43970
0.034
0.05
0.19518
0.19369
0.76
0.8
zz
E
0.57%
0.6
rel
E chechmate. 1
1.95508
1.95583
0.039
0.05
rr
3.48316
3.48347
0.009
0.01
0.19518
0.19486
0.16
0.2
zz
E
0.14%
0.2
rel
E chechmate. 2
1.95508
1.96166
0.34
0.5
rr
2.16049
2.15403
0.299
0.5
0.32135
0.32138
0.009
0.01
zz
E
0.027%
0.03
rel
B
1.99999
2.00003
0.002
0.01
rr
2.11555
2.11558
0.001
0.01
0.32135
0.32135
0.002
0.01
zz
E
0.0084%
0.01
rel
6.2 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
5.3 seconds
6.3 Notice
Relative error considered total = 0.24%.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV113 Estimateur of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A Page:
8/8
7
Summary of the results
The estimator of error in residue “ERRE_ELGA_NORE' gives good results on the problems in bi-
materials.
Note:
The estimator of error of Zhu-Zienkiewicz does not give correct results. Indeed, with
the interface it detects a strong error because it carries out a continuous smoothing of the constraints whereas it
exist a jump for zz and.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A