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Titrate:
SSNS501 - Grands displacements of a cylindrical panel
Date:
03/05/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.05.501-A Page:
1/10
Organization (S): EDF/AMA, DeltaCAD
Handbook of Validation
V6.05 booklet: Non-linear statics of the hulls and the plates
Document: V6.05.501
SSNS501 - Grands displacements of a panel
cylindrical simply supported
Summary:
This test represents a calculation of stability of a cylindrical panel simply supported subjected to an effort
concentrate in its center. The behavior of the panel changes completely and shows points clearly
of return in load and displacement “snap-through/snap-back”. In this case a control in displacement
diverge and a control in length of arc must be selected.
It makes it possible to validate modeling finite elements COQUE_3D with meshs TRIA7 and QUAD9 in
geometrical non-linear quasi-static field in the presence of strong instabilities.
Displacements and the critical load are compared with a numerical reference solution.
Handbook of Validation
V6.05 booklet: Non-linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNS501 - Grands displacements of a cylindrical panel
Date:
03/05/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.05.501-A Page:
2/10
1
Problem of reference
1.1 Geometry
Z, W
Z
P
E
F
With
D
H
B
2L
G
C
L = 0.254 m
R = 2.54 m
R
H = 0.00635 m
y, v
= 0.1 rd
y
X, U
X
1.2
Properties of material
The properties of material constituting the plate are:
E = 3. 10275 X 109 Pa
Young modulus
= 0.3
Poisson's ratio
1.3
Boundary conditions and loadings
- C.L panel simply supported on sides EC and GF (null displacements, free rotations)
- One seeks the successive states of balance under a load P imposed on point A.
1.4 Conditions
initial
Without object
Handbook of Validation
V6.05 booklet: Non-linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNS501 - Grands displacements of a cylindrical panel
Date:
03/05/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.05.501-A Page:
3/10
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution was obtained with a finite element of hull DKT24 (grid 4x6) with
4 nodes with 6 degrees of freedom per node in Formulation Lagrangienne Totale. This solution is
described in details in [bib2].
2.2
Results of reference
WA
Charge P Charges
WA
Charge P
Charge
WA
Charge P
Charge
(x103m)
(KN)
P/Pmax
(x103m)
(KN)
P/Pmax
(x103m)
(KN)
P/Pmax
0.0 0.000
0.0000
16.4 0.480 0.8000 14.0 0.295 0.4916
1.7 0.150
0.2500
16.7 0.415 0.6916 14.3 0.345 0.5750
3.5 0.265
0.4416
16.9 0.350 0.5833 15.0 0.370 0.6166
4.9 0.345
0.5750
17.0 0.290 0.4833 16.1 0.380 0.6333
6.8 0.410
0.6833
17.1 0.225 0.3750 17.3 0.375 0.6250
8.4 0.475
0.7916
17.1 0.150 0.2500 18.7 0.350 0.5833
9.8 0.520
0.8666
17.0 0.090 0.1500 20.3 0.305 0.5083
11.1 0.555 0.9250
16.8 0.020 0.0333 21.8 0.230 0.3833
12.2 0.580 0.9666
16.4 0.035 0.0583 23.5 0.120 0.2000
13.1 0.595 0.9916
16.0 0.085 0.1416 25.2 0.025 0.0416
14.0 0.600 1.0000
15.3 0.130 0.2166 26.8 0.210 0.3500
14.9 0.585 0.9750
14.8 0.155 0.2583 28.5 0.445 0.7416
15.5 0.565 0.9416
14.2 0.195
0.3250
16.1 0.525 0.8750
14.0 0.240
0.4000
Not limits 1
0,7
Charge |P| (KN)
0,6
0,5
0,4
Not limits 2
0,3
0,2
0,1
0,0
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30
- 0,1
Displacement |W | (mm)
With
- 0,2
Not limits 3
- 0,3
- 0,4
Not limits 4
- 0,5
2.3
Uncertainties on the solution
< 2% numerical solution
2.4 References
bibliographical
[1]
HAMMADI Fodil: Formulation and evaluation of finite elements with C° continuity of the geometry
for the linear and non-linear analysis of the hulls.
[2]
JAAMEI S.: Study of various Lagrangian formulations for the nonlinear analysis of
plates and thin hulls elastoplastic in great displacements and great rotations,
Thesis of doctorate, Université de Technologie of Compiegne 1986.
Handbook of Validation
V6.05 booklet: Non-linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNS501 - Grands displacements of a cylindrical panel
Date:
03/05/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.05.501-A Page:
4/10
3 Modeling
With
3.1
Characteristics of modeling
With
Modeling COQUE_3D (TRIA7)
Boundary conditions:
6
D
- Side CD: U = v = W = 0
Conditions of symmetry:
B
- Side AB:
U = = = 0
y
Z
- Side AD: v = = = 0
X
Z
6
A quarter of the plate is modelled.
C
The successive states of balance are
obtained thanks to a method of
control by length of arc.
p
In this case, ETA_PILOTAGE = pmax
3.2
Characteristics of the grid
A number of nodes: 241
A number of meshs and type: 72 TRIA7
3.3 Functionalities
tested
Commands Key word
factor
Key word
AFFE_MODELE AFFE
MODELISATION=' COQUE_3D'
AFFE_CARA_ELEM HULL
EPAIS
A_CIS=0.833
COEF_RIGI_DRZ = 0.001
AFFE_CHAR_MECA FORCE_NODALE FZ
STAT_NON_LINE CONTROL
TYPE=' LONG_ARC'
4
Results of modeling A
4.1 Values
tested
Identification Moments
Reference
Aster %
difference
Not limits n°1
DZ
1.03
0.0140
0.01322
5.573
Eta_PILOTAGE 1.03
1.0
0.9729
2.471
Not limits n°2
DZ
1.78
0.0171
0.01696
0.847
Eta_PILOTAGE 1.78
0.375
0.07513 75.96
0.250
Not limits n°3
DZ
2.3
0.0140
0.01458
4.176
Eta_PILOTAGE 2.3
0.400
0.533 19.67
0.492
Not limits n°4
DZ
2.48
0.0161
0.01617
0.452
Eta_PILOTAGE 2.48
0.633
0.6442
1.717
Handbook of Validation
V6.05 booklet: Non-linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSNS501 - Grands displacements of a cylindrical panel
Date:
03/05/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.05.501-A Page:
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4.2 Remarks
The strategy of calculation used breaks up into two stages:
·
calculation in loading imposed to P = 582.N correspondent on 97% of the critical load,
·
calculation in “imposed displacement”: then, one imposes a displacement imposed while using
technique length of arc imposed on all the structure (option LONG_ARC in
STAT_NON_LINE).
The use of the technique length of arc makes difficult the definition of the value of reference to
to introduce into command TEST_RESU, since these values cannot be imposed. For
to define the values of reference, we sought the values of the closest possible DZ
those listed in the table of [§2.2] and we deferred the values of the parameter of control
that one was to obtain for the values of DZ in question.
Handbook of Validation
V6.05 booklet: Non-linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNS501 - Grands displacements of a cylindrical panel
Date:
03/05/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.05.501-A Page:
6/10
5 Modeling
B
5.1
Characteristics of modeling
With
Modeling COQUE_3D (QUAD9)
Boundary conditions:
6
D
- Side CD: U = v = W = 0
Conditions of symmetry:
B
- Side AB:
U = = = 0
y
Z
- Side AD: v = = = 0
X
Z
6
C
5.2
Characteristics of the grid
A number of nodes: 169
A number of meshs and type: 36 QUAD9
5.3 Functionalities
tested
Commands Key word
factor
Key word
AFFE_MODELE AFFE
MODELISATION=' COQUE_3D'
AFFE_CARA_ELEM HULL
EPAIS
A_CIS=0.833
COEF_RIGI_DRZ = 0.001
AFFE_CHAR_MECA FORCE_NODALE FZ
STAT_NON_LINE CONTROL
TYPE=' LONG_ARC'
6
Results of modeling B
6.1 Values
tested
Identification Moments
Reference
Aster %
difference
Not limits n°1
DZ
1.03
0.0140
0.01318
5.886
Eta_PILOTAGE 1.03
1.0
0.9724
2.760
Not limits n°2
DZ
0.0171
0.01702
0.462
Eta_PILOTAGE
0.375
0.101 67.69
0.250
Not limits n°3
DZ
0.0140
0.01446
3.269
Eta_PILOTAGE
0.400
0.558 25.177
0.492
Not limits n°4
DZ
0.0161
0.0161
0.007
Eta_PILOTAGE
0.633
0.640
1.120
Handbook of Validation
V6.05 booklet: Non-linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNS501 - Grands displacements of a cylindrical panel
Date:
03/05/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.05.501-A Page:
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6.2 Remarks
The strategy of calculation used breaks up into two stages:
·
calculation in loading imposed to P = 582.N correspondent on 97% of the critical load,
·
calculation in imposed displacement: then, one imposes a displacement imposed while using
technique length of arc imposed (option LONG_ARC in STAT_NON_LINE).
The use of the technique length of arc makes difficult the definition of the value of reference to
to introduce into command TEST_RESU, since these values cannot be imposed. For
to define the values of reference, we sought the values of the closest possible DZ
those listed in the table of [§2.2] and we deferred the values of the parameter of control
that one was to obtain for the values of DZ in question.
Handbook of Validation
V6.05 booklet: Non-linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNS501 - Grands displacements of a cylindrical panel
Date:
03/05/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.05.501-A Page:
8/10
7
Summary of the results
Normal displacement at the top of the panel according to the force
800
600
400
200
0
Charge (NR)
0
0,005
0,01
0,015
0,02
- 200
- 400
- 600
Displacement W (m)
Appear 7-a: normal Déplacement in the node of the panel according to the force applied.
Enlarging around the point limits 1
Appear 7-b: normal Déplacement in the node of the panel according to the force applied
standardized by its maximum value
The results for the two loads limit 1 and 4 are correct. The maximum error is 2.5% for
mesh TRIA3 and of 2.8% for mesh QUAD9. On the other hand, the error on vertical displacement is
more important. It is 5.6% for mesh TRIA7 and 5.9% for mesh QUAD9.
Handbook of Validation
V6.05 booklet: Non-linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSNS501 - Grands displacements of a cylindrical panel
Date:
03/05/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.05.501-A Page:
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The results between the two loads limit 1 and 4 are qualitatively correct. They well are detected
points limit 2 and 3. Quantitatively the values of displacements for these points are good with
less than 1% for the point limits 2 and to less than 5% for the point limits 3. On the level of the loads
corresponding, the load at the point limits 2 is very strongly underestimated (about 70%) and
that at the point limits 3 strongly over-estimated (about 20%).
Whatever the mesh, the behavior pre-buckling is correctly evaluated. Pace in
postbuckling makes it possible to determine displacements at the points correctly limit 2 and 3.
loads obtained are further away from the reference solution. From the point limits 4, one
find a good agreement between the reference and our solution.
The coefficient of correction of transverse shearing A_CIS was put at 0.833, corresponding to
thick hulls. The value (2500=106xH/L) which should have been taken into account does not allow
to carry out calculations, because of a bad conditioning of the matrices of rigidity.
Handbook of Validation
V6.05 booklet: Non-linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSNS501 - Grands displacements of a cylindrical panel
Date:
03/05/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V6.05.501-A Page:
10/10
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Handbook of Validation
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