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SSLS117 - Excentrement of nonsymmetrical plates
Date:
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P. Key MASSIN, D. NUNEZ-GUAJARDO
:
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Organization (S): EDF/AMA, CS IF
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.117
SSLS117 - Excentrement of plates
nonsymmetrical
Summary:
This test validates the offsetting of nonsymmetrical simple plates compared to the plan of the grid or plan
of diagram (key word EXCENTREMENT of command AFFE_CARA_ELEM).
The reference is given by a first resolution where one models double-layered made up of two layers
various thicknesses and of two materials.
It is used to validate the second calculation where one models two layers offset compared to the plan of the grid.
It differs from test SSLS111 only by the fact that the 2 layers are different thicknesses.
Four modelings implement elements DKT, DKQ, DST, DSQ.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
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Titrate:
SSLS117 - Excentrement of nonsymmetrical plates
Date:
19/08/02
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P. Key MASSIN, D. NUNEZ-GUAJARDO
:
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1
Problem of reference
1.1 Geometry
10 m
0.4 m
5 m
A4
A3
0.2 m
A1
A2
m1 m2 m3
Z
y
X
1.2
Properties of materials
The material constituting the first layer is orthotropic and is characterized by the data
following:
EL=20000. 106 Pa
ET=20000. 106 Pa
LT = 0.3
GLT=2000. 106 Pa
The material constituting the second layer is also orthotropic and has the following characteristics:
EL=15000. 106 Pa
ET=15000. 106 Pa
LT = 0.3
GLT=1500. 106 Pa
1.3
Boundary conditions and loadings
The A1 node is embedded
DX=DY=DZ=0.
DRX=DRY=DRZ=0.
The A2 node is blocked according to following ddls: DX=DY=0.
One applies nodal forces FZ=1000 NR to the A3 node, and one applies the loading distributed
(key word FORCE_COQUE) on the meshs m1, m2 and m3:
FX=200 NR
FX=500. NR/m2 FZ=500.
NR/m2
MX=100. NR/m
MY=40. NR/m
The selected loading utilizes stresses out of membrane and inflection.
Handbook of Validation
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SSLS117 - Excentrement of nonsymmetrical plates
Date:
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2
Reference solution
2.1
Method of calculation used for the reference solution
Calculation with double-layered material (command DEFI_COQU_MULT) is used as reference. Not
regression compared to the results obtained by this first calculation is checked. Two plates of
the second modeling are offset compared to the average plan of the double-layered one.
2.2
Results of reference
They are consisted of the values of the field of displacement DX, DY, DZ, DRX, DRY at the A3 point and A4,
efforts at the A1 point and of the first 4 Eigen frequencies.
2.3
Uncertainty on the solution
Uncertainty is null since it is about the same calculation carried out by two different ways.
2.4 Bibliography
[1]
[R3.07.03]: Elements of plate DKT, DST, DKQ, DSQ and Q4.
[2]
[R3.07.06]: Processing of offsetting for the elements of plate DKT, DST, DKQ, DSQ
and Q4G.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
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SSLS117 - Excentrement of nonsymmetrical plates
Date:
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:
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3 Modeling
With
3.1
Characteristics of modeling
The model consists of two plates corresponding to the average plan of each of both
layers of the model of reference. To represent these two plates, one leaves the grid of the plan
of diagram which one offsets distances 0.1 and 0.2.
Plan average Plaq2
d=0.1 m
d= - 0.2 m
Plan of diagram
Plan average Plaq1
The elements used are elements of plate DKT.
3.2
Characteristics of the grid
Co-ordinates of the nodes:
Node Coor_X Coor_Y Coor_Z
A1 0. 0. 0.
A2 10.
0.
0.
A3 10.
5.
0.
A4 0. 5. 0.
94 Nodes
100 meshs DKT (TRIA3)
3.3 Functionalities
tested
Commands Key word
factor Word-key
AFFE_CARA_ELEM
EXCENTREMENT
AFFE_CHAR_MECA
FORCE_COQUE
PLAN
DEFI_COQU_MULT
Handbook of Validation
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Titrate:
SSLS117 - Excentrement of nonsymmetrical plates
Date:
19/08/02
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:
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4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
Displacement
DX (A4)
1.9426 106 1.93937
106 0.166
DY (A4)
1.1438 106 1.138746
106 0.442
DZ (A4)
2.1832 104 2.169149 104 0.644
DRX (A4)
6.0633 105 6.03126
105 0.528
DRY (A4) 1.2815
104 1.28078
104 0.056
DX (A3)
2.4225 106 2.419616
106 0.119
DY (A3)
2.3106 107 2.3104
107 0.04
DZ (A3)
1.5584 103 1.5563
103 0.133
DRX (A3)
1.2578 104 1.2543
104 0.276
DRY (A3) 1.3909 104 1.3903 104 0.038
Eigen frequencies
Frequency 1st mode
1.5303
1.53038
0.006
Frequency 2nd mode
6.41979
6.41979
1.07 E-04
Frequency 3rd mode
1.269898 101 1.269898
101 2.81
E-05
Frequency 4th mode
2.61597 101 2.61597
101 1.23
E-04
Efforts
NXX
N6
1.12134 E+04
1.11996 E+04
0.124
NYY
N6
7.52699 E+03
7.48953 E+03
0.498
NXY
N6
1.89850 E+03
1.89286 E+03
0.297
MXX
N6
2.33596 E+04
2.33480 E+04
0.050
MYY
N6
1.67905 E+04
1.66988 E+04
0.546
MXY
N6
5.43976 E+03
5.42402 E+03
0.289
QX
N6
4.60472 E+03
4.63427 E+03
0.642
QY
N6
1.58798 E+03
1.61207 E+03
1.517
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SSLS117 - Excentrement of nonsymmetrical plates
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5 Modeling
B
5.1
Characteristics of modeling
The model consists of two plates corresponding to the average plan of each of both
layers of the model of reference. To represent these two plates, one leaves the grid of the plan
of diagram which one offsets distances 0.1 and 0.2
Plan average Plaq2
d=0.1 m
d= - 0.2 m
Plan of diagram
Plan average Plaq1
The elements used are elements of plate DKQ.
5.2
Characteristics of the grid
Co-ordinates of the nodes:
Node Coor_X Coor_Y Coor_Z
A1 0. 0. 0.
A2 10.
0.
0.
A3 10.
5.
0.
A4 0. 5. 0.
67 Nodes
50 meshs DKQ (QUAD4)
5.3 Functionalities
tested
Commands Key word
factor Word-key
AFFE_CARA_ELEM
EXCENTREMENT
AFFE_CHAR_MECA
FORCE_COQUE
PLAN
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
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Titrate:
SSLS117 - Excentrement of nonsymmetrical plates
Date:
19/08/02
Author (S):
P. Key MASSIN, D. NUNEZ-GUAJARDO
:
V3.03.117-A Page:
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6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster %
difference
Displacement
DX (A4)
2.354 106 2.341
106 0.520
DY (A4)
2.059 106 2.039
106 0.940
DZ (A4)
2.50 104 2.45
104 1.924
DRX (A4)
6.93 105 6.823
105 1.538
DRY (A4) 1.541
104 1.541
104 0.005
DX (A3)
2.9951 106 2.9835
106 0.384
DY (A3)
4.4646 107 4.4648
107 0.006
DZ (A3)
1.8604 103 1.8550
103 0.287
DRX (A3)
1.3346 104 1.3217
104 0.963
DRY (A3) 1.6649
104 1.6649
104 0.002
Eigen frequencies
Frequency 1st mode
1.4362
1.4362
0.
Frequency 2nd mode
5.57419
5.57419
0.
Frequency 3rd mode
1.23524 101 1.23524
101 0.
Frequency 4th mode
2.52573 101 2.52573
101 0.
Efforts
NXX
N60
1.30762 E+04
1.31749 E+04
0.755
NYY
N60
2.68634 E+03
2.82116 E+03
5.019
NXY
N60
4.33581 E+02
4.32313 E+02
0.292
MXX
N60
4.17329 E+04
4.19250 E+04
0.460
MYY
N60
1.84443 E+04
1.79620 E+04
2.615
MXY
N60
6.33337 E+03
6.29774 E+03
0.563
QX
N60
3.19128 E+04
3.20627 E+04
0.470
QY
N60
1.43089 E+04
1.39373 E+04
2.597
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SSLS117 - Excentrement of nonsymmetrical plates
Date:
19/08/02
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7 Modeling
C
7.1
Characteristics of modeling
The model consists of two plates corresponding to the average plan of each of both
layers of the model of reference. To represent these two plates, one leaves the grid of the plan
of diagram which one offsets distances 0.1 and 0.2
Plan average Plaq2
d=0.1 m
d= - 0.2 m
Plan of diagram
Plan average Plaq1
The elements used are elements of DST plate.
7.2
Characteristics of the grid
Co-ordinates of the nodes:
Node Coor_X Coor_Y Coor_Z
A1 0. 0. 0.
A2 10.
0.
0.
A3 10.
5.
0.
A4 0. 5. 0.
66 Nodes
100 meshs DST (TRIA3)
7.3 Functionalities
tested
Commands Key word
factor Word-key
AFFE_CARA_ELEM
EXCENTREMENT
AFFE_CHAR_MECA
FORCE_COQUE
PLAN
Handbook of Validation
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HT-66/02/001/A
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Titrate:
SSLS117 - Excentrement of nonsymmetrical plates
Date:
19/08/02
Author (S):
P. Key MASSIN, D. NUNEZ-GUAJARDO
:
V3.03.117-A Page:
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8
Results of modeling C
8.1 Values
tested
Identification Reference
Aster %
difference
Displacement
DX (A4)
1.939 106 1.93217
106 0.352
DY (A4)
1.149 106 1.1358
106 1.145
DZ (A4)
2.2091 104 2.199799
104 0.421
DRX (A4)
6.09302 105 6.06238
105 0.503
DRY (A4) 1.297279
104 1.30383
104 0.505
DX (A3)
2.4385 106 2.4305
106 0.328
DY (A3)
2.3382 107 2.4272
107 3.806
DZ (A3)
1.5864 103 1.5952
103 0.558
DRX (A3)
1.2639 104 1.2621
104 0.138
DRY (A3) 1.4127
104 1.4215
104 0.627
Eigen frequencies
Frequency 1st mode
1.512356
1.50555
0.450
Frequency 2nd mode
6.373398
6.343485
0.469
Frequency 3rd mode
1.25011 101 1.24249
101 0.610
Frequency 4th mode
2.546726 101 2.518863
101 1.094
Efforts
NXX
N1
9.85902 E+03
1.09606 E+04
11.173
NYY
N1
6.36055 E+03
7.04694 E+03
10.791
NXY
N1
2.07601 E+03
2.07850 E+03
0.120
MXX
N1
2.11639 E+04
2.10507 E+04
0.535
MYY
N1
1.49410 E+04
1.46867 E+04
1.701
MXY
N1
5.82623 E+03
5.86877 E+03
0.730
QX
N1
2.56538 E+03
2.35368 E+03
8.252
QY
N1
1.79286 E+03
1.81901 E+03
1.458
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SSLS117 - Excentrement of nonsymmetrical plates
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9 Modeling
D
9.1
Characteristics of modeling
The model consists of two plates corresponding to the average plan of each of both
layers of the model of reference. To represent these two plates, one leaves the grid of the plan
of diagram which one offsets distances 0.1 and 0.2
Plan average Plaq2
d=0.1 m
d= - 0.2 m
Plan of diagram
Plan average Plaq1
The elements used are elements of plate DSQ.
9.2
Characteristics of the grid
Co-ordinates of the nodes:
Node Coor_X Coor_Y Coor_Z
A1 0. 0. 0.
A2 10.
0.
0.
A3 10.
5.
0.
A4 0. 5. 0.
67 Nodes
50 meshs DSQ (QUAD4)
9.3 Functionalities
tested
Commands Key word
factor Word-key
AFFE_CARA_ELEM
EXCENTREMENT
AFFE_CHAR_MECA
FORCE_COQUE
PLAN
Handbook of Validation
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HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSLS117 - Excentrement of nonsymmetrical plates
Date:
19/08/02
Author (S):
P. Key MASSIN, D. NUNEZ-GUAJARDO
:
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10 Results of modeling D
10.1 Values
tested
Identification Reference
Aster %
difference
Displacement
DX (A4)
2.34539 106 2.3241
106 0.904
DY (A4)
1.9694 106 1.9363
106 1.680
DZ (A4)
2.2428 104 2.1154
104 5.680
DRX (A4)
6.2983 105 5.9831
105 5.003
DRY (A4) 1.5823
104 1.5991
104 1.062
DX (A3)
3.0023 106 2.9771
106 0.839
DY (A3)
4.6612 107 4.6487
107 0.267
DZ (A3)
1.8842 103 1.8923
103 0.430
DRX (A3)
1.2768 104 1.2478
104 2.264
DRY (A3) 1.7064
104 1.724
104 1.054
Eigen frequencies
Frequency 1st mode
1.4219
1.4155
0.445
Frequency 2nd mode
5.2995
5.21015
1.686
Frequency 3rd mode
1.215 101 1.206
101 0.723
Frequency 4th mode
2.4385 101 2.407
101 1.252
Efforts
NXX
N1
8.68372 E+03
1.64692 E+04
89.657
NYY
N1
4.10693 E+03
2.34359 E+03
42.936
NXY
N1
3.90190 E+02
4.54002 E+02
16.354
MXX
N1
3.47663 E+04
3.43655 E+04
1.153
MYY
N1
1.52451 E+04
1.45102 E+04
4.821
MXY
N1
6.34489 E+03
6.33555 E+03
0.147
QX
N1
1.70439 E+04
1.56565 E+04
8.140
QY
N1
9.82819 E+03
9.49952 E+03
3.344
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/02/001/A
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Titrate:
SSLS117 - Excentrement of nonsymmetrical plates
Date:
19/08/02
Author (S):
P. Key MASSIN, D. NUNEZ-GUAJARDO
:
V3.03.117-A Page:
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11 Summary of the results
With regard to displacements for the modelings DKT and DKQ, the results obtained with
2 offset hulls differ from to the more 2% compared to the reference solution. For the others
modelings, one obtains to the maximum of the errors of 4% for DST and 6% for the DSQ. For these
two last modelings, the error is more important because the calculation of transverse shearing is not
not are equivalent between the double-layered one and the two offset plates.
Indeed, transverse shearing is supposed to be constant in the thickness of each DST element or
DSQ; this transverse shearing is an average shearing. An average value is thus obtained
for each plate offset, overall different from average transverse shearing on
the double-layered plate.
This is marked even more for the efforts, where the differences remain lower than 5% for
modelings DKT (A and B) but reach 11% for modeling C and 89% for modeling
D. Etant given the nature of the test, one cannot know a priori if the problem comes from the hulls and plates
multi-layer or of offsetting. An anomaly is in the course of processing on this problem.
Handbook of Validation
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