Code_Aster
®
Version
4.0
Titrate:
SSLV113 Estimator of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A
Page:
1/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Organization (S):
EDF/IMA/MN
Manual 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 stresses, 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).
Code_Aster
®
Version
4.0
Titrate:
SSLV113 Estimator of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A
Page:
2/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
1
Problem of reference
1.1 Geometry
1
Z
0.
D
1.
3/2
2.
chechmate. 1
chechmate. 2
E
With
p
With
C
Q
B
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,
U
Z
= 0.
on cd.,
U
Z
= 0.91333 = A.
Pressure interns on AD, p = 1.
External pressure on BC, Q = 2.
Code_Aster
®
Version
4.0
Titrate:
SSLV113 Estimator of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A
Page:
3/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
(
)
(
) (
)
µ
I
I
I
I
E
E
=
+
=
-
+
2 1
1 2
1
has
B
has
B
1
1
2
2
=
=
=
=
-
-
-
-
0.98097
1.11741
1.34405
0.30048
calculated numerical data
starting from the equations of Navier
For material
''
I
, one a:
U
R has
B
R
U
With
R
I
I
Z
=
+
=
(
)
(
)
(
)
µ
µ
µ
rr
I
I
I
I
I
I
I
I
I
I
zz
I
I
I
I
has
With
has
B
R
has
With
has
B
R
has
With
=
+
+
-
=
+
+
+
=
+
+
2
2
2
2
2
2
2
2
2.2
Uncertainty on the solution
Analytical solution.
Code_Aster
®
Version
4.0
Titrate:
SSLV113 Estimator of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A
Page:
4/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
M1
M2
M3
M4
With
E
B
3.2
Characteristics of the mesh
A number of nodes: 23.
A number of meshs and types: 4
QUAD8
.
3.3 Functionalities
tested
Controls
Keys
CALC_ELEM
OPTION
“SIRE_ELNO_DEPL”
[U4.61.02]
OPTION
“ERRE_ELGA_NORE”
Code_Aster
®
Version
4.0
Titrate:
SSLV113 Estimator of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A
Page:
5/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
tolerance
With
rr
1.00003
1.06833
6.83
7.0
4.43821
4.46731
0.66
2.0
zz
0.19518
0.16596
14.9
15.0
E
rel
2.37%
5.0
E chechmate. 1
rr
1.95508
1.97893
1.22
2.0
3.48316
3.49330
0.29
2.0
zz
0.19518
0.18498
5.22
6.0
E
rel
1.05%
5.0
E chechmate. 2
rr
1.95508
1.98398
1.48
2.0
2.16049
2.13394
1.23
2.0
zz
0.32135
0.32204
0.22
2.0
E
rel
0.152%
5.0
B
rr
1.99999
2.00095
0.048
2.0
2.11555
2.11595
0.012
2.0
zz
0.32135
0.32174
0.12
2.0
E
rel
0.057%
5.0
4.2 Remarks
Mesh being coarse (4 elements according to
However
), certain stresses close to the axis of axisymetry
are badly approximated. The jump of
and
zz
with the interface of 2 materials is on the other hand well detected.
4.3 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
System:
UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use:
4.7 seconds
4.4 Remarks
Relative error considered total = 1.40%.
Code_Aster
®
Version
4.0
Titrate:
SSLV113 Estimator of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A
Page:
6/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
M1
With
E
B
M10
M11
M20
5.2
Characteristics of the mesh
A number of nodes:
A number of meshs and types: 20
QUAD8
.
5.3 Functionalities
tested
Controls
Keys
CALC_ELEM
OPTION
“SIRE_ELNO_DEPL”
[U4.61.02]
OPTION
“ERRE_ELGA_NORE”
Code_Aster
®
Version
4.0
Titrate:
SSLV113 Estimator of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A
Page:
7/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
tolerance
With
rr
1.00003
1.00351
0.35
0.5
4.43821
4.43970
0.034
0.05
zz
0.19518
0.19369
0.76
0.8
E
rel
0.57%
0.6
E chechmate. 1
rr
1.95508
1.95583
0.039
0.05
3.48316
3.48347
0.009
0.01
zz
0.19518
0.19486
0.16
0.2
E
rel
0.14%
0.2
E chechmate. 2
rr
1.95508
1.96166
0.34
0.5
2.16049
2.15403
0.299
0.5
zz
0.32135
0.32138
0.009
0.01
E
rel
0.027%
0.03
B
rr
1.99999
2.00003
0.002
0.01
2.11555
2.11558
0.001
0.01
zz
0.32135
0.32135
0.002
0.01
E
rel
0.0084%
0.01
6.2 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
System:
UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use:
5.3 seconds
6.3 Notice
Relative error considered total = 0.24%.
Code_Aster
®
Version
4.0
Titrate:
SSLV113 Estimator of error on a hollow roll Bi-materials
Date:
26/01/98
Author (S):
X. DESROCHES
Key:
V3.04.113-A
Page:
8/8
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
7
Summary of the results
The estimator of error in residue “
ERRE_ELGA_NORE'
give 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 stresses whereas it
exist a jump for
zz
and
.