Code_Aster
®
Version
7.2
Titrate:
SSNL122 - Beam cantilever Multifibre subjected to an effort
Date:
01/03/04
Author (S):
J.L. FLEJOU
Key
:
V6.02.122-B
Page:
1/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.122
SSNL122 - Beam cantilever Multifibre subjected
with an effort
Summary:
This test relates to the validation of beam multifibre with a modeling in POU_D_TGM.
This problem makes it possible to test:
·
linear finite elements of beams type with a modeling in POU_D_TGM,
·
the taking into account of the orientation,
·
the calculation of the SIEF_ELGA and the SIEF_ELNO_ELGA.
Code_Aster
®
Version
7.2
Titrate:
SSNL122 - Beam cantilever Multifibre subjected to an effort
Date:
01/03/04
Author (S):
J.L. FLEJOU
Key
:
V6.02.122-B
Page:
2/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
With
X
Y
Z
B
C
Lo
Length of the bar: 3m
Embedding in A
Forces out of B
Section of the bar:
height: 0.04m
width: 0.02m
1.2
Properties of material
Material with elastoplastic behavior with a linear work hardening, for the linear element:
Elasticity:
·
Young modulus E = 2.1E+11 AP
Plasticity:
·
slope of the traction diagram in the plastic range
D
_
SIGM
_
EPSI
= 1.0E+08 AP
·
yield stress
SY
= 400.0E+06 AP
1.3
Boundary conditions and loadings
At the point A, perfect embedding (blocking of displacements and rotations),
·
blocking of the ddl: dx, Dy, dz, DRX, DRY, DRZ.
Loading at point b:
(
)
Z
y
X
F
F
F
,
,
=
F
.
Code_Aster
®
Version
7.2
Titrate:
SSNL122 - Beam cantilever Multifibre subjected to an effort
Date:
01/03/04
Author (S):
J.L. FLEJOU
Key
:
V6.02.122-B
Page:
3/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
2
Reference solution
2.1
Sizes and results of reference
Arrow out of B following Z
Arrow out of B following Y
y
Z
Z
I
E
L
F
.
.
3
.
3
=
Z
y
y
I
E
L
F
.
.
3
.
3
=
Stress in a point C of co-ordinates (v
y
, v
Z
) of the section of the beam
y
Z
Z
Z
y
y
I
M
I
M
S
NR
v
.
v
.
-
+
=
with
Lo
F
M
Lo
F
M
Z
y
y
Z
.
.
-
=
+
=
from where:
(
)
Z
Z
y
y
L
ELo
S
NR
v
.
v
.
.
.
3
3
+
-
=
éq
2.1-1
2.2 Reference
bibliographical
[1]
“M7-01-72 Project. Elastoplastic behavior of the beams. New approach.” Note
HM77/01/140/A.
Code_Aster
®
Version
7.2
Titrate:
SSNL122 - Beam cantilever Multifibre subjected to an effort
Date:
01/03/04
Author (S):
J.L. FLEJOU
Key
:
V6.02.122-B
Page:
4/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
3 Modeling
With
3.1
Characteristics of modeling and the mesh
Linear element: POU_D_TGM.
S001: 1m
S002: 2m
E00200
E00201
E00202
E00203
E00204
E00100
E00101
E00102
Mechanical characteristics of the section (homogeneous units with [m]):
WITH IY
IZ AY AZ JX JG
8.0e-04 2.666667e-08 1.066667e-07 1.191790e+0
0
1.172840e+0
0
7.093682e-08 1.438125e-12
Loading at the point B.
Fx Fy Fz
Moment 1
80.000N
150N
200N
Moment 2
80.000N
280N
400N
At moment 1 the section remains elastic, at moment 2 the section is partially plasticized.
3.2
Classification of fibers
The main reference mark of inertia (Y0, Z0) of the beam must be turned of 90° so that the strongest inertia
“IZ” is along the axis “Y” of the total reference mark. The goal is to test the key word ORIENTATION of
order AFFE_CARA_ELEM.
In the local reference mark of the beam
In the total reference mark of study
1
2
3
4
5
6
32
31
30
Z0
Y0
33
34
35
36
37
38
39
40
41
48
49
29
52
53
60
1
2
3
4
5
6
32
31
30
Z0
Y0
33
34
35
36
37
38
39
40
41
48
49
29
52
53
60
Z
Y
Code_Aster
®
Version
7.2
Titrate:
SSNL122 - Beam cantilever Multifibre subjected to an effort
Date:
01/03/04
Author (S):
J.L. FLEJOU
Key
:
V6.02.122-B
Page:
5/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
Several “types” of fibers are used:
·
fibers whose numbers go from 1 to 32. They are affected of a nonnull surface in
command file,
·
fibers whose numbers are 33, 34, 35, 36. They are located at the 4 corners of the section. These
fibers, in the command file, are affected of a section equal to zero. They
are useful that with postprocessing,
·
fibers whose numbers go from 37 to 60. They are located on the edge external of the section.
These fibers, in the command file, are affected of a section equal to zero. They
are used that for postprocessing.
3.3 Functionalities
tested
Controls
DEFI_MODELE POU_D_TGM
AFFE_CARA_ELEM BEAM
AFFE_FIBER
ORIENTATION
IMPR_RESU
SIEF_ELGA
SIEF_ELNO_ELGA
Code_Aster
®
Version
7.2
Titrate:
SSNL122 - Beam cantilever Multifibre subjected to an effort
Date:
01/03/04
Author (S):
J.L. FLEJOU
Key
:
V6.02.122-B
Page:
6/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
4
Results of modeling A
4.1
Sizes tested and results
The sizes tested and analyzed are them:
· SIEF_ELGA, at the first point of Gauss of the E00200 element. It is the point of Gauss it
more close to embedding, Lo = 2.95491933m.
· SIEF_ELNO_ELGA, with the 2 nodes of the E00200 element. The G00202 node is the point
of embedding (Lo = 3.0m), the I00200 node is in Lo = 2.6m.
4.1.1 Behavior
rubber band
Stresses at the point of Gauss: SIEF_ELGA
The stresses calculated by the equation [éq 2.1-1] and by Code_Aster are given in both
tables below (values in MPa). The provision of the tables takes again the diagram of provision
fibers in the total reference mark. The most requested fiber is the n°36 with a stress of 390 MPa
Stresses calculated in
fibers by the equation [éq 2.1-1]
Stresses calculated in
fibers by Code_Aster.
35
80.168.257
346
390 35
80
168
257 346
390
21
66.154.243
331
376 21
66
154
243 331
376
- 7
37.126.215
303
348 - 7
37
126
215 303
348
- 35
9 98 187
275
320 - 35
9
98
187 275
320
- 63
- 19 70 158
247
291 - 63
- 19
70
158 247
291
- 91
- 47 42 130
219
263 - 91
- 47
42
130 219
263
- 120
- 75 13 102
191
235 - 120
- 75
13
102 191
235
- 148
- 103 - 15 74
163
207 - 148
- 103
- 15
74 163
207
- 176
- 131 - 43 46
134
179 - 176
- 131
- 43
46 134
179
- 190
- 146 - 57 32
120
165 - 190
- 146
- 57
32 120
165
The relative error between two calculations is given in the table below. Whatever the fiber,
it remains lower than 0.1%.
- 0.022%
- 0.013% - 0.009% - 0.008% - 0.007%
- 0.007%
- 0.026%
- 0.012% - 0.009% - 0.008% - 0.007%
- 0.007%
0.014%
- 0.010% - 0.007% - 0.006% - 0.006%
- 0.006%
- 0.010%
0.010% - 0.004% - 0.005% - 0.005%
- 0.005%
- 0.013%
- 0.029% 0.000% - 0.003% - 0.004%
- 0.004%
- 0.014%
- 0.021% 0.012% 0.000% - 0.002%
- 0.003%
- 0.014%
- 0.019% 0.069% 0.004% - 0.001%
- 0.002%
- 0.015%
- 0.018% - 0.094% 0.012% 0.002%
0.000%
- 0.015%
- 0.018% - 0.043% 0.029% 0.006%
0.003%
- 0.015%
- 0.018% - 0.036% 0.049% 0.009%
0.005%
Code_Aster
®
Version
7.2
Titrate:
SSNL122 - Beam cantilever Multifibre subjected to an effort
Date:
01/03/04
Author (S):
J.L. FLEJOU
Key
:
V6.02.122-B
Page:
7/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
Stresses with the nodes: SIEF_ELNO_ELGA
The stresses calculated by the equation [éq 2.1-1] and by Code_Aster are given in the table
below (values in MPa)
Analytical node Code_Aster
Relative error
G00202
SIMAX = 394.307
SIMAX = 394.276
- 0.008%
SIMIN = - 194.307
SIMIN = - 194.276
- 0.016%
I00200
SIMAX = 355.066
SIMAX = 355.057
- 0.002%
SIMIN = - 155.066
SIMIN = - 155.057
- 0.006%
4.1.2 Behavior
plastic
Stresses at the point of Gauss: SIEF_ELGA
The table below gives the values of the stresses, after plasticization partial of the section,
obtained with Code_Aster. The behavior of material is elastoplastic “almost perfect”,
slope of work hardening is weak. The maximum stress, which is beyond the yield stress, remains
thus very close to the elastic threshold of 400MPa.
8
79
223
366
400
400
- 16
55
199
342
400
400
- 64
7
151
294
400
400
- 112
- 41
103
246
390
400
- 160
- 89
55
198
342
400
- 208
- 137
7
150
294
365
- 256
- 185
- 41
102
246
317
- 305
- 233
- 89
54
198
269
- 353
- 281 - 137
6
150
221
- 377
- 305 - 161
- 18
126
197
This calculation is carried out for the test of nonregression of Code_Aster.
Stresses with the nodes: SIEF_ELNO_ELGA
The table below gives the values of the stresses to the nodes, after plasticization partial of
section, obtained with Code_Aster. These values are interpolated by Code_Aster from
SIEF
_
ELGA
. The behavior of material is elastoplastic “almost perfect”, the slope
of work hardening is weak. The maximum stress, which is beyond the yield stress, thus remains very
neighbor of the elastic threshold of 400MPa.
Node
Code_Aster
G00202
SIMAX = 400.091
SIMIN = - 385.441
I00200
SIMAX = 400.053
SIMIN = - 306.905
This calculation is carried out for the test of nonregression of Code_Aster.
Code_Aster
®
Version
7.2
Titrate:
SSNL122 - Beam cantilever Multifibre subjected to an effort
Date:
01/03/04
Author (S):
J.L. FLEJOU
Key
:
V6.02.122-B
Page:
8/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
5
Summary of the results
This case test shows the correct operation of a modeling of the behavior of the beams by one
approach multifibre. The postprocessing of the beams does not require any more, with this modeling, of
to calculate the SIGM_ELNO_SIEF or the SIPO_ELNO_SIEF.