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Code_Aster
®
Version
4.0
Titrate:
SSNV124 Analyzes limit. Law of Norton-Hoff
Date:
01/12/98
Author (S):
E. SCREWS, F.VOLDOIRE
Key:
V6.04.124-A
Page:
1/6
Manual of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
HI-75/98/040 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.124
SSNV124 - Analyze regularized limit.
Law of Norton-Hoff
Summary
This test makes it possible to validate the operators used analyzes regularized limit of it. One calculates the load limits by
a kinematic approach regularized by the method of Norton-Hoff-Friaâ.
One considers a rectangular plate (modeling A) or a cube (modeling B) or a cylinder
axisymmetric (modeling C). The constitutive material checks the criterion of von Mises and the structure is subjected
with loadings on the edges. Calculation makes it possible to obtain the limiting load in the direction of the loading.
The structure is modelized by incompressible elements and the loading is standardized.
The resolution by the regularized method of Norton-Hoff-Friaâ is carried out in the control
STAT_NON_LINE
[U4.32.01]. A postprocessing in the control
POST_ELEM
[U4.61.04] allows to obtain the value of a terminal
higher of the limiting load, .ainsi qu' an estimate.
The reference solution is analytical and the results are in perfect agreement with the values of reference.
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Code_Aster
®
Version
4.0
Titrate:
SSNV124 Analyzes limit. Law of Norton-Hoff
Date:
01/12/98
Author (S):
E. SCREWS, F.VOLDOIRE
Key:
V6.04.124-A
Page:
2/6
Manual of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
With
H
G
F
D
Z
y
3D
C
E
X
B
With
1
y
B
D
C
X
1
3
­ 1
2d_PLAN and AXIS
has
B
1.2
Material properties
Young modulus:
E =
MPa
200 000
.
Poisson's ratio:
= 0.5
Elastic limit:
y
MPa
=
10
.
Coefficient of the law of Norton-Hoff:
N
=
5
1.3
Boundary conditions and loadings
Conditions limit in 2D:
·
on AB: DX = 0.
·
on BC: DY = 0.
Conditions limit in 3D:
·
EFGH (FACEXINF): DX = 0.
·
ADEH (FACEYINF): DY = 0.
·
DCFE (FACEZINF): DZ = 0.
Conditions limit in AXIS:
·
on BC and AD: DY = 0.
The loading parameterized by
is:
·
in 2D:
FY = ­ 1. on AD
·
in 3D:
FX = ­ 0.2 on ABCD (FXSUP)
FY = ­ 0.8 on BCFG (FYSUP)
·
in AXIS:
FX = 1. on AB.
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Code_Aster
®
Version
4.0
Titrate:
SSNV124 Analyzes limit. Law of Norton-Hoff
Date:
01/12/98
Author (S):
E. SCREWS, F.VOLDOIRE
Key:
V6.04.124-A
Page:
3/6
Manual of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
HI-75/98/040 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
One considers a rectangular plate (modeling A) or a cube (modeling B) or a cylinder
axisymmetric (modeling C). The constitutive material checks the criterion of von Mises, with for
threshold
y
.
The structure is subjected to pressures on the edges horizontal
-
F
and vertical
(
)
- -
1
F
with
0.5
(
=
1.
in 2D,
=
0.8
in 3D). In plane 2D, one considers two ways of making: on the one hand in
amplifying the two pressures together, in addition while amplifying that horizontal pressure, and in
leaving the constant vertical. Into axisymmetric, the solid is subjected to the internal pressure
only
-
F
. One obtains the exact limiting load and that by the method of regularization [R7.07.01]
in this direction of loading, for the criterion of von Mises, with the threshold
y
.
Modeling
case
lim
lim
sup
lim
estimated
power
()
L
0
U
With
plane 2D
lim
.
=
-
2
3 2
1
y
F
2
3 2
1
-
.
y
F
2
3 2
1
1
has
. F. N
y
-
+
0
Abis
plane 2D
2 3
3
1
0
y
F
F
+ -
2 3
3
1
0
y
F
F
+ -
nothing
1
0
-
.
F
B
=
0 8
,
3D
lim
.
=
-
+
1
3
3
1
2
y
F
1
3
3
1
2
-
+
.
y
F
1
3
3
1
1
2
-
+
+
.
.
y
F
N
N
0
C
=
1
2D AXIS
lim
.
.ln
=
2 3
3
y
F
B
has
2 3
3.
.ln
y
F
B
has
2 3
3
1
2
.
.ln
.
y
F
B
has
N
N
+
0
2.2
Results of reference
Modeling
case
lim
lim
sup
lim
estimated
power
()
L
0
U
With
plane 2D
11.547
11.547
9.6225
0
Abis
plane 2D
14.6837
14.6837
nothing
0.25
B
3D
13.867
13.867
11.556
0
C
2D AXIS
12.685
12.685
8.5545
0
2.3 References
bibliographical
[1]
VOLDOIRE F., SCREWS E.: Calculation of load limits by the method of Norton-Hoff-Friaâ.
[R7.07.01]
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Code_Aster
®
Version
4.0
Titrate:
SSNV124 Analyzes limit. Law of Norton-Hoff
Date:
01/12/98
Author (S):
E. SCREWS, F.VOLDOIRE
Key:
V6.04.124-A
Page:
4/6
Manual of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
HI-75/98/040 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
One considers a rectangular plate modelized by element QUAD8 of an incompressible type:
miplqu8
. The two cases are studied: the first with the two amplified loads, the second with
amplified horizontal pressure and the constant vertical.
3.2
Characteristics of the mesh
A number of nodes: 8
A number of meshs and types: 1 mesh of the incompressible type QUAD8.
3.3 Functionalities
tested
Controls
Key word factor
Single-ended spanner word
Argument
Keys
DEFI_MATERIAU
NORTON-HOFF
NR
SY
[U4.23.01]
AFFE_CHAR_MECA
LIAISON_CHAMNO
CHAM_NO
NUME_LAGR
“AFTER”
[U4.25.01]
STAT_NON_LINE
COMP_INCR
SOLVEUR
RELATION
METHOD
“NORTON_HOFF”
“LDLT”
[U4.32.01]
AFFE_CHAR_MECA
LIAISON_CHAMNO
CHAM_NO
[U4.25.01]
POST_ELEM
CHAR_LIMITE
ALL
“YES”
[U4.61.04]
TEST_TABLE
COUNT
“CHAR_LIMI_SUP”
“CHAR_LIMI_ESTIM”
“PUIS_PERMANENTE”
[U4.72.01]
4
Results of modeling A
4.1 Values
tested
Identification
Case
Reference
Aster
% difference
Tolerance
Charge higher limit
With
Abis
11.547
14.6837
11.547
14.6837
0.0
0.0
0.1%
0.1%
Charge estimated limit
With
Abis
9.6225
nothing
9.6225
nothing
0.0
0.1%
Permanent power
With
Abis
0
0.25
0
0.25
0.0
0.0
0.1%
0.1%
4.2 Parameters
of execution
Version: 4.03
Machine: CRAY C98
System: 9.0
UNICOS
Overall dimension memory:
8 megawords
Time CPU To use:
8.7 seconds
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Code_Aster
®
Version
4.0
Titrate:
SSNV124 Analyzes limit. Law of Norton-Hoff
Date:
01/12/98
Author (S):
E. SCREWS, F.VOLDOIRE
Key:
V6.04.124-A
Page:
5/6
Manual of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
HI-75/98/040 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
One considers a cube modelized by element HEXA20 of an incompressible type:
minc_hexa20
.
5.2
Characteristics of the mesh
A number of nodes: 20.
A number of meshs and types: 1 mesh of the incompressible type HEXA20.
5.3 Functionalities
tested
Controls
Key word factor
Single-ended spanner word
Argument
Keys
DEFI_MATERIAU
NORTON-HOFF
NR
SY
[U4.23.01]
AFFE_CHAR_MECA
LIAISON_CHAMNO
CHAM_NO
NUME_LAGR
“AFTER”
[U4.25.01]
STAT_NON_LINE
COMP_INCR
SOLVEUR
RELATION
METHOD
“NORTON_HOFF”
“LDLT”
[U4.32.01]
AFFE_CHAR_MECA
LIAISON_CHAMNO
CHAM_NO
[U4.25.01]
POST_ELEM
CHAR_LIMITE
ALL
“YES”
[U4.61.04]
TEST_TABLE
COUNT
“CHAR_LIMI_SUP”
“CHAR_LIMI_ESTIM”
“PUIS_PERMANENTE”
[U4.72.01]
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
Tolerance
Charge higher limit
13.867505
13.867505
0.0
0.1%
Charge estimated limit
11.556
11.556
0.0
0.1%
6.2 Parameters
of execution
Version: 4.03
Machine: CRAY C98
System: 9.0
UNICOS
Overall dimension memory:
8 megawords
Time CPU To use:
5.3 seconds
background image
Code_Aster
®
Version
4.0
Titrate:
SSNV124 Analyzes limit. Law of Norton-Hoff
Date:
01/12/98
Author (S):
E. SCREWS, F.VOLDOIRE
Key:
V6.04.124-A
Page:
6/6
Manual of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
HI-75/98/040 - Ind A
7 Modeling
C
7.1
Characteristics of modeling
One considers a cylinder modelized by axisymmetric elements QUAD8 of the incompressible type:
miaxqu8
, according to a regulated mesh.
7.2
Characteristics of the mesh
A number of nodes: 96
A number of meshs and types: 25 meshs of the incompressible type QUAD8.
7.3 Functionalities
tested
Controls
Key word factor
Single-ended spanner word
Argument
Keys
DEFI_MATERIAU
NORTON-HOFF
NR
SY
[U4.23.01]
AFFE_CHAR_MECA
LIAISON_CHAMNO
CHAM_NO
NUME_LAGR
“AFTER”
[U4.25.01]
STAT_NON_LINE
COMP_INCR
SOLVEUR
RELATION
METHOD
“NORTON_HOFF”
“LDLT”
[U4.32.01]
AFFE_CHAR_MECA
LIAISON_CHAMNO
CHAM_NO
[U4.25.01]
POST_ELEM
CHAR_LIMITE
ALL
“YES”
[U4.61.04]
TEST_TABLE
COUNT
“CHAR_LIMI_SUP”
“CHAR_LIMI_ESTIM”
“PUIS_PERMANENTE”
[U4.72.01]
8
Results of modeling C
8.1 Values
tested
Identification
Reference
Aster
% difference
Tolerance
Charge higher limit
12.685
12.6866
0.0
0.1%
Charge estimated limit
8.5545
8.72227
1.96
2.0%
8.2 Parameters
of execution
Version: 4.03
Machine: CRAY C98
System: 9.0
UNICOS
Overall dimension memory:
8 megawords
Time CPU To use:
4.3 seconds
9
Summary of the results
The numerical results are in perfect agreement with the values of reference. In the case
axisymmetric, the light differences are explained by the fact why displacement is in
1/R
in
analytical solution, which is not included/understood in the base of the selected finite elements.