Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
1/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
Organization (S):
EDF/AMA
Manual of Validation
V6.05 booklet: Nonlinear statics
Document: V6.05.100
SSNS100 - Nonlinear behavior of a tablecloth
reinforcements under thermal loading
Summary:
A tablecloth of reinforcements not offset compared to the layer average and embedded on its four sides east
subjected to a thermal loading. The orientations of the reinforcements are confused with the axes (X, Y) of
total reference mark.
The main interest of this test is to validate the numerical integration of the models of behavior
elastoplastic GRILL_ISOT_LINE, GRILL_CINE_LINE and GRILL_PINTO_MEN of a tablecloth of reinforcements
associated the finite element GRID (orthotropic plate with offsetting compared to the datum-line), in
general algorithm STAT_NON_LINE.
In order to obtain reference solutions, analytical solutions were established for both
elastoplastic behaviors with linear and kinematic work hardening isotropic linear. The behavior of
Pinto-Menegotto is validated by nonregression of the numerical results obtained with Aster in version 5-3
(cf [§1.3.3]).
Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
2/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
1
Problem of reference
1.1
Geometry of the plate
Y
X
1 m
1m
X
ref.
NO4
NO 1
NR O2
NO3
E
X
Z
Y
Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
3/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
1.2
Characteristics of modelings
This case test is composed of 7 modelings. The table below summarizes their characteristics:
Offsetting = 0 Thickness = 0,01m
Orientation of the reinforcements
longitudinal direction (L): OX
transverse direction (T): OY
Modeling Law of behavior
% braces
longitudinal
L
% braces
transversal
T
Mode of application of
the temperature
With
isotropic linear
1
0,1
with the nodes
B
linear kinematics
1
0,1
with the nodes
C
Pinto Menegotto
1
0,1
with the nodes
D
Pinto Menegotto
1
0,1
with the elements
E
Pinto Menegotto
1
0
with the elements
F
isotropic linear
1
0
with the nodes
G
linear kinematics
1
0
with the nodes
1.3
Properties of materials
1.3.1 Properties common to all modelings
Young modulus:
E
= 2 10
11
.
MPa
Poisson's ratio:
= 0
Elastic limit:
y
= 2 10
8
.
MPa
Thermal expansion factor:
=
-
10
5
(°C
- 1
)
1.3.2 Behavior
isotropic and kinematic plastic
For the behaviors isotropic (GRILL_ISOT_LINE) and kinematics (GRILL_CINE_LINE)
Slope of work hardening:
E
T
= 2 10
10
.
MPa
1.3.3 Behavior of Pinto Menegotto
For behavior PINTO MENEGOTTO (GRILL_PINTO_MEN)
EPSI_ULTM: 3,0.
10
2
SIGM_ULTM: 2,58.
10
8
EPSP_HARD: 0,0023
R_PM
: 20,0
EP_SUR_E
: 0,01
A1_PM
: 18,5
A2_PM
: 0,15
DASH
: 4,9
A6_PM
: 620,0
C_PM
: 0,5
A_PM
: 0,008
1.4
Boundary conditions and loading
The plate is entirely embedded.
Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
4/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
The loading is of origin thermal. The change of the temperature according to time is given
for each modeling in the following table. The temperature is applied to the nodes or to
elements, according to modeling.
Moment Evolution
With
T°
Evolution B
T°
Evolution C
T°
0 50 50 50
1 50 50 300
2 250 250 100
3 150 150
50
4 250 250 150
5 50 50 350
6.350.350 200
7 50 150
8 450 450
9 110 250
10.550.650
11 50 450
- 600
- 400
- 200
0
200
400
600
1
2
3
4
5
6
7
8
9
10
11
12
T
Tr
EFF
.
Evol_A
Evol_B
Evol_C
One took for all the tests a temperature of reference of 50°.
Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
5/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
2
Reference solutions
2.1
Isotropic plastic behavior
The reference solution is calculated analytically.
One notes
T
p
p
+
+
+
+
,
,
,
the temperature, plastic deformation, cumulated plastic deformation
and total deflection at the moment of calculation, and
T
p
p
-
-
-
,
,
same quantities at the moment
precedent. T
ref.
indicate the temperature of reference.
The solution is calculated in the following way:
(
)
[
]
(
)
[
]
(
)
E
ref.
p
T
T
y
E
p
p
E
E
p
T
ref.
y
T
p
p
p
p
T
ref.
E
T
T
R p
E E
E E p
R p
p
p
R p
E E
E
T
T
E
E
E
p
p
p
R p
E E
E
T
T
=
-
-
-
=
-
+
=
=
=
>
=
-
-
-
-
+
-
=
+
-
=
=
-
-
-
+
+
+
-
-
+
-
+
-
+
-
+
+
+
-
-
+
-
+
-
+
+
+
+
+
()
.
(
)
;
;
(
)
(
)
if
if not
if
if not
[
]
y
T
p
p
p
E
E
E
p
p
p
R p
+
+
=
-
+
= -
-
-
+
-
+
-
+
+
(
)
This calculation is made in each direction. For the treated case,
+
= 0
at any moment.
In the longitudinal direction, the stress memorized in Aster is the real stress existing
in each grid of this direction.
In the transverse direction, the stress memorized in Aster is the real stress existing
in each grid of this direction multiplied by the coefficient
T
L
.
Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
6/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
2.2
Kinematic plastic behavior
The reference solution is calculated analytically.
One notes
T
X
p
+
+
+
+
,
,
,
the temperature, plastic deformation and the variable of work hardening
kinematics at the moment of calculation, and
T
X
p
-
-
-
,
same quantities at the previous moment.
The solution is calculated in the following way:
(
)
[
]
(
)
(
)
(
)
[
]
(
)
E
ref.
p
E
y
p
p
E
E
y
p
T
ref.
y
T
ref.
y
T
ref.
T
y
p
T
ref.
y
E
T
T
X
X
X
X
E
E
E
T
T
E
X
E
T
T
E
E
T
T
E
E
E
E
E
E
T
T
E
=
-
-
-
-
=
=
=
-
>
=
-
-
-
-
=
-
-
-
=
-
-
+
-
=
-
-
-
+
+
+
-
-
+
-
+
-
+
-
+
+
+
+
+
+
+
+
+
+
+
+
if
if not
if
if not
;
;
(
)
(
)
[
]
=
-
-
+
=
-
-
-
-
+
+
+
+
+
+
X
E
T
T
E
E
T
T
E
E
E
T
ref.
y
T
ref.
T
y
This calculation is made in each direction. For the treated case,
+
= 0
at any moment.
In the longitudinal direction, the stress memorized in Aster is the real stress existing
in each grid of this direction.
In the transverse direction, the stress memorized in Aster is the real stress existing
in each grid of this direction multiplied by the coefficient
T
L
.
Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
7/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
2.3
Behavior Pinto Ménégotto
The reference solution is that obtained by an Aster calculation with the same mesh on which one
apply cycles of load/discharge, in imposed displacement, allowing to recreate them
deformations resulting from mechanical thermo calculations presented hereafter. The test corresponding is not
thus that a test of nonregression, by comparing the stresses obtained by these two types of
modeling: on the one hand mechanical, and on the other hand thermomechanical.
In the longitudinal direction, the stress memorized in Aster is the real stress existing
in each grid of this direction.
In the transverse direction, the stress memorized in Aster is the real stress existing
in each grid of this direction multiplied by the coefficient
T
L
.
3 Modeling
With
The test-tube is with a grid with two elements `GRID `with three nodes.
NO1
NO3
NO2
NO4
4 Functionalities
tested
Controls
AFFE_CARA_ELEM ROASTS
DEFI_MATERIAU ECRO_LINE
PINTO_MENEGOTTO
STAT_NON_LINE COMP_INCR
RELATION
“GRILL_ISOT_LINE”
“GRILL_CINE_LINE”
“GRILL_PINTO_MEN”
NEWTON
STAMP
“TANGENT”
CALC_ELEM OPTION
SIGM_ELNO_VARI
Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
8/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
5
Results modeling A (linear isotropic work hardening)
5.1
Thermal loading for modeling A
Temperature of reference: 50
History of the loading: Evolution_A (cf [§1.4])
The temperatures re-entered like a field to the nodes.
5.2 Results
Variable: SIGXX and SIGYY with node NO1
SIGXX
SIGYY
Moment Code_Aster Reference
Variation Code_Aster Reference
Variation (%)
1 2,00000E+08 2,00000E+08 0 2,00000E+07 2,00000E+07 0
2 2,40000E+08 2,40000E+08 0 2,40000E+07 2,40000E+07 0
3 4,00000E+07 4,00000E+07 0 4,00000E+06 4,00000E+06 0
4 2,40000E+08 2,40000E+08 0 2,40000E+07 2,40000E+07 0
5 1,60000E+08 1,60000E+08 0 1,60000E+07 1,60000E+07
0
6 3,12000E+08 3,12000E+08 0 3,12000E+07 3,12000E+07
0
7 2,88000E+08 2,88000E+08 0 2,88000E+07 2,88000E+07 0
8 4,09600E+08 4,09600E+08 0 4,09600E+07 4,09600E+07 0
9 2,70400E+08 2,70400E+08 0 2,70400E+07 2,70400E+07
0
10 5,27680E+08 5,27680E+08 0 5,27680E+07 5,27680E+07
0
11 4,72320E+08 4,72320E+08 0 4,72320E+07 4,72320E+07 0
Note:
The results presented are given in the reference mark of reference (X
ref.
, Y
ref.
) forming an angle of 0°
compared to (X, Y).
Stresses SIGYY are equal to stresses SIGXX multiplied by the report/ratio of
percentages of reinforcement enters the directions transversal and longitudinal.
The case studied test corresponds to the diagrams following in a plan forced deformation:
- 6,000E+08
- 5,000E+08
- 4,000E+08
- 3,000E+08
- 2,000E+08
- 1,000E+08
0,000E+00
1,000E+08
2,000E+08
3,000E+08
4,000E+08
5,000E+08
- 6,00E-03 - 4,00E-03 - 2,00E-03 0,00E+00
2,00E-03
4,00E-03
6,00E-03
Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
9/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
6 Results modeling B (work hardening kinematic
linear)
6.1
Thermal loading for modeling B
Temperature of reference: 50°C
History of the loading: Evolution_B (cf [§1.4)
The temperatures re-entered like a field to the nodes.
6.2 Results
Variable: SIGXX and SIGYY with node NO1
SIGXX
SIGYY
Moment Code_Aster Reference
Variation Reference
Code_Aster Variation
(%)
1 2,00E+08
2,00E+08 0 2,00E+07 2,00E+07
0
2 2,40E+08
2,40E+08 0 2,40E+07 2,40E+07
0
3 4,00E+07
4,00E+07 0 4,00E+06 4,00E+06
0
4 2,40E+08
2,40E+08 0 2,40E+07 2,40E+07
0
5 1,60E+08
1,60E+08
0 1,60E+07 1,60E+07
0
6 2,40E+08
2,40E+08
0 2,40E+07 2,40E+07
0
7 1,60E+08
1,60E+08 0 1,60E+07 1,60E+07
0
8 2,80E+08
2,80E+08 0 2,80E+07 2,80E+07
0
9 1,20E+08
1,20E+08
0 1,20E+07 1,20E+07
0
10 3,00E+08 3,00E+08
0 3,00E+07 3,00E+07
0
11 1,00E+08 1,00E+08
0 1,00E+07 1,00E+07
0
Note:
The results presented are given in the reference mark of reference (X
ref.
, Y
ref.
) forming an angle of 0°
compared to (X, Y).
Stresses SIGYY are equal to stresses SIGXX multiplied by the report/ratio of
percentages of reinforcement enters the directions transversal and longitudinal.
The case studied test corresponds to the following diagram in a plan forced deformation:
- 3,00E+08
- 2,00E+08
- 1,00E+08
0,00E+00
1,00E+08
2,00E+08
3,00E+08
- 6,00E-03 - 4,00E-03 - 2,00E-03 0,00E+00
2,00E-03
4,00E-03
6,00E-03
Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
10/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
7
Results modeling C (model of Pinto Menegotto)
7.1
Thermal loading for modeling C
Temperature of reference: 50°C
History of the loading: Evolution_C (cf [§1.4])
The temperatures re-entered like a field to the nodes.
7.2 Results
Variable: SIGXX and SIGYY with node NO1
SIGXX
SIGYY
Code_Aster moment
Code_Aster
1
2.00000E+08
2.00000E+07
2
2.09416E+08
2.09416E+07
3
1.21555E+08
1.21555E+07
4
1.82862E+08
1.82862E+07
5
1.52164E+08
1.52164E+07
6
2.02506E+08
2.02506E+07
7
7.59307E+07
7.59307E+06
Note:
The results presented are given in the reference mark of reference (X
ref.
, Y
ref.
) forming an angle of 0°
compared to (X, Y).
Stresses SIGYY are equal to stresses SIGXX multiplied by the report/ratio of
percentages of reinforcement enters the directions transversal and longitudinal.
The case studied test corresponds to the following diagram in a plan forced deformation:
- 2,00E+08
- 1,50E+08
- 1,00E+08
- 5,00E+07
0,00E+00
5,00E+07
1,00E+08
1,50E+08
2,00E+08
2,50E+08
0,0E+00 5,0E-04 1,0E-03 1,5E-03 2,0E-03 2,5E-03 3,0E-03 3,5E-03 4,0E-03
Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
11/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
8
Results modeling D (model of Pinto-Menegotto)
Modeling D is the same one as modeling C, with the difference which the temperatures are
defined by a card.
The results are identical.
9
Results modeling E (model of Pinto-Menegotto)
Modeling E approaches modeling D, with the difference that it there not of reinforcement
transversal (
T
= 0).
9.1 Results
Variable: SIGXX and SIGYY with node NO1
SIGXX SIGYY
Moment
Code_Aster
Code_Aster
1
2.00000E+08
0,0
2
2.09416E+08
0,0
3
1.21555E+08
0,0
4
1.82862E+08
0,0
5
1.52164E+08
0,0
6
2.02506E+08
0,0
7
7.59307E+07
0,0
Note:
The results presented are given in the reference mark of reference (X
ref.
, Y
ref.
) forming an angle of 0°
compared to (X, Y).
Stresses SIGYY are null, since there are not any more transverse reinforcements.
Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
12/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
10 Results modeling F (linear isotropic work hardening)
Modeling F approaches modeling A, with the difference that it there not of reinforcement
transversal (
T
= 0).
10.1 Results
Variable: SIGXX and SIGYY with node NO1
SIGXX SIGYY
Moment
Code_Aster
Code_Aster
1
2.00000E+08
0,0
2
2.40000E+08
0,0
3
4.00000E+07
0,0
4
2.40000E+08
0,0
5
1.60000E+08
0,0
6
3.12000E+08
0,0
7
2.88000E+08
0,0
8
4.09600E+08
0,0
9
2.70400E+08
0,0
10
5.27680E+08
0,0
11
4.72320E+08
0,0
Note:
The results presented are given in the reference mark of reference (X
ref.
, Y
ref.
) forming an angle of 0°
compared to (X, Y).
Stresses SIGYY are null, since there are not any more transverse reinforcements.
10.2 Parameters
of execution
Version: 5.03.13
Machine: SGI ORIGIN 2000 - R 12000
Overall dimension memory: 32 Mo
Time CPU To use: 6, 43 S
Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
13/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
11 Results modeling G (linear kinematic model)
Modeling F approaches modeling B, with the difference that it there not of reinforcement
transversal (
T
= 0).
11.1 Results
Variable: SIGXX and SIGYY with node NO1
SIGXX
SIGYY
Moment
Code_Aster
Code_Aster
1
2,00E+08
0,0
2
2,40E+08
0,0
3
4,00E+07
0,0
4
2,40E+08
0,0
5
1,60E+08
0,0
6
2,40E+08
0,0
7
1,60E+08
0,0
8
2,80E+08
0,0
9
1,20E+08
0,0
10
3,00E+08
0,0
11
1,00E+08
0,0
Note:
The results presented are given in the reference mark of reference (X
ref.
, Y
ref.
) forming an angle of 0°
compared to (X, Y).
Stresses SIGYY are null, since there are not any more transverse reinforcements.
11.2 Parameters
of execution
Version: 5.03.13
Machine: SGI ORIGIN 2000 - R 12000
Overall dimension memory: 32 Mo
Time CPU To use: 7, 52 S
Code_Aster
®
Version 5.0
Titrate:
Nonlinear SSNS100 Behavior of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT
Key
:
V6.05.100-A
Page:
14/14
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A
12 Summary of the results
For elastoplastic behaviors with linear work hardening, the analytical solution is
perfectly found.
The behavior of Pinto-Menegotto is validated by nonregression.