Code_Aster ®
Version
4.0
Titrate:
Limiting SSNV124 Analyze. Law of Norton-Hoff
Date:
01/12/98
Author (S):
E. SCREWS, F.VOLDOIRE
Key:
V6.04.124-A Page:
1/6
Organization (S): EDF/IMA/MN
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.124
SSNV124 - Regularized limiting Analyze.
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 modelled by incompressible elements and the loading is standardized.
The resolution by the regularized method of Norton-Hoff-Friaâ is carried out in command STAT_NON_LINE
[U4.32.01]. A postprocessing in command POST_ELEM [U4.61.04] makes it possible 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.
Handbook of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Limiting SSNV124 Analyze. Law of Norton-Hoff
Date:
01/12/98
Author (S):
E. SCREWS, F.VOLDOIRE
Key:
V6.04.124-A Page:
2/6
1
Problem of reference
1.1 Geometry
Z
H
G
y
With
D
B
1
With
E
F
1
3
X
y
B
D
1
C
C
has
B
X
2d_PLAN and AXIS
3D
1.2
Material properties
Young modulus: E = 200.000 MPa.
Poisson's ratio: = 0.5
Elastic limit: =
y
10 MPa.
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.
Handbook of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Limiting SSNV124 Analyze. Law of Norton-Hoff
Date:
01/12/98
Author (S):
E. SCREWS, F.VOLDOIRE
Key:
V6.04.124-A Page:
3/6
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.en 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 threshold Y.
Modeling
case
sup
estimated
power
lim
lim
lim
L0 (U)
With
plane 2D
2
2
0
y
N
=
y
2
y
.
.
lim
3
.
2 - 1
F
3 2 -.
1
F
3 2a - 1
F
1 + N
Abis
plane 2D
2 3
nothing
-
y
1 -
y
-
1
+
2 3
1
F
+
F
.0 F
3
0
F
3
0
F
B
3D
1
0
=
y
1
y
1
y
N
0 8
,
=
lim
.
.
.
.
3 2 -
3 + 1 F
3 2
- 3 +1 F
3 2
- 3 +
F
+
1
1 N
C
2D AXIS
2
0
=
y
B
2 3
y
B
2 3
B
N
1
= 2 3
y
lim
.
.ln
.
.ln
.
.ln
.
3
F
has
3
F
has
3
F
1 + N has
2.2
Results of reference
Modeling
case
sup
estimated
lim
power L0 (U)
lim
lim
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]
Handbook of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Limiting SSNV124 Analyze. Law of Norton-Hoff
Date:
01/12/98
Author (S):
E. SCREWS, F.VOLDOIRE
Key:
V6.04.124-A Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
One considers a rectangular plate modelled by an element QUAD8 of the 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 grid
A number of nodes: 8
A number of meshs and types: 1 mesh of the incompressible type QUAD8.
3.3 Functionalities
tested
Commands
Key word factor
Single-ended spanner word
Argument
Keys
DEFI_MATERIAU
NORTON-HOFF
NR
[U4.23.01]
SY
AFFE_CHAR_MECA
LIAISON_CHAMNO
CHAM_NO
[U4.25.01]
NUME_LAGR
“APRES”
STAT_NON_LINE
COMP_INCR
RELATION
“NORTON_HOFF”
[U4.32.01]
SOLVEUR
METHODE
“LDLT”
AFFE_CHAR_MECA
LIAISON_CHAMNO
CHAM_NO
[U4.25.01]
POST_ELEM
CHAR_LIMITE
TOUT
“OUI”
[U4.61.04]
TEST_TABLE
TABLE
“CHAR_LIMI_SUP”
[U4.72.01]
“CHAR_LIMI_ESTIM”
“PUIS_PERMANENTE”
4
Results of modeling A
4.1 Values
tested
Identification
Case
Reference
Aster
% difference
Tolerance
Charge higher limit
With
11.547
11.547
0.0
0.1%
Abis
14.6837
14.6837
0.0
0.1%
Charge estimated limit
With
9.6225
9.6225
0.0
0.1%
Abis
nothing
nothing
Permanent power
With
0
0
0.0
0.1%
Abis
0.25
0.25
0.0
0.1%
4.2 Parameters
of execution
Version: 4.03
Machine: CRAY C98
System: 9.0
UNICOS
Obstruction memory:
8 megawords
Time CPU To use:
8.7 seconds
Handbook of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Limiting SSNV124 Analyze. Law of Norton-Hoff
Date:
01/12/98
Author (S):
E. SCREWS, F.VOLDOIRE
Key:
V6.04.124-A Page:
5/6
5 Modeling
B
5.1
Characteristics of modeling
One considers a cube modelled by an element HEXA20 of the incompressible type: minc_hexa20.
5.2
Characteristics of the grid
A number of nodes: 20.
A number of meshs and types: 1 mesh of the incompressible type HEXA20.
5.3 Functionalities
tested
Commands
Key word factor
Single-ended spanner word
Argument
Keys
DEFI_MATERIAU
NORTON-HOFF
NR
[U4.23.01]
SY
AFFE_CHAR_MECA
LIAISON_CHAMNO
CHAM_NO
[U4.25.01]
NUME_LAGR
“APRES”
STAT_NON_LINE
COMP_INCR
RELATION
“NORTON_HOFF”
[U4.32.01]
SOLVEUR
METHODE
“LDLT”
AFFE_CHAR_MECA
LIAISON_CHAMNO
CHAM_NO
[U4.25.01]
POST_ELEM
CHAR_LIMITE
TOUT
“OUI”
[U4.61.04]
TEST_TABLE
TABLE
“CHAR_LIMI_SUP”
[U4.72.01]
“CHAR_LIMI_ESTIM”
“PUIS_PERMANENTE”
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
Obstruction memory:
8 megawords
Time CPU To use:
5.3 seconds
Handbook of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Limiting SSNV124 Analyze. Law of Norton-Hoff
Date:
01/12/98
Author (S):
E. SCREWS, F.VOLDOIRE
Key:
V6.04.124-A Page:
6/6
7 Modeling
C
7.1
Characteristics of modeling
One considers a cylinder modelled by axisymmetric elements QUAD8 of the incompressible type:
miaxqu8, according to a regulated grid.
7.2
Characteristics of the grid
A number of nodes: 96
A number of meshs and types: 25 meshs of the incompressible type QUAD8.
7.3 Functionalities
tested
Commands
Key word factor
Single-ended spanner word
Argument
Keys
DEFI_MATERIAU
NORTON-HOFF
NR
[U4.23.01]
SY
AFFE_CHAR_MECA
LIAISON_CHAMNO
CHAM_NO
[U4.25.01]
NUME_LAGR
“APRES”
STAT_NON_LINE
COMP_INCR
RELATION
“NORTON_HOFF”
[U4.32.01]
SOLVEUR
METHODE
“LDLT”
AFFE_CHAR_MECA
LIAISON_CHAMNO
CHAM_NO
[U4.25.01]
POST_ELEM
CHAR_LIMITE
TOUT
“OUI”
[U4.61.04]
TEST_TABLE
TABLE
“CHAR_LIMI_SUP”
[U4.72.01]
“CHAR_LIMI_ESTIM”
“PUIS_PERMANENTE”
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
Obstruction 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 into 1/R in
analytical solution, which is not included/understood in the base of the selected finite elements.
Handbook of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
HI-75/98/040 - Ind A