Code_Aster ®
Version
4.0
Titrate:
SDLS100 Etude of grids on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C Page:
1/10
Organization (S): EDF/IMA/MN
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
V2.03.100 document
SDLS100 - Etude of grids on a plate
square thin
Summary:
This three-dimensional problem consists in seeking the frequencies of vibration of a mechanical structure
composed of a thin square plate embedded on a side. One studies the influence of the distortion of the grid
on the results. This test of Mécanique of Structures corresponds to a dynamic analysis of a model
surface having a linear behavior. It comprises three modelings.
This problem makes it possible to test the element of plate DKT in transverse inflection and the calculation of the frequencies
clean, either by the method of Lanczos, or by the method of Bathe and Wilson. The first modeling
consist in netting finely and regularly the plate by triangles. For the second modeling, it
grid is coarser while for the third, it coarse and is distorted.
The first modeling is used as results of reference.
The results obtained are in concord between them and with those of a card NAFEMS. The effect of distortion of
grid does not appear on the first frequencies of vibration.
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SDLS100 Etude of grids on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C Page:
2/10
1
Problem of reference
1.1 Geometry
y
8
7
6
has
9
5
1
1
2
3
4
has
Test 1
Test 2
Test 3
Test 4
Square plate:
side has = 10. m
thickness T = 0.05 m
Co-ordinates of the points (in m):
Test 2
Test 4
Node
X
y
Node
X
y
1
4.0
4.0
1
4.0
4.0
2
2.25
2.25
3
4.75
2.5
4
7.25
2.75
5
7.5
4.75
6
7.75
7.25
7
5.25
7.25
8
2.25
7.25
9
2.5
4.75
1.2
Properties of materials
E = 2.1011 Pa
= 0.3
= 8.000. kg/m3
1.3
Boundary conditions and loadings
Any point P such as xp = 0: (U = v = W = 0, y = 0).
1.4 Conditions
initial
Without object for the modal analysis.
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SDLS100 Etude of grids on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C Page:
3/10
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is that given in the card “Test 16” of the tests of reference published by
NAFEMS.
Card NAFEMS gives the results of reference as well as computation results carried out in
using elements of the mean hull type of Kirchoff based on a formulation of displacement
isoparametric quadratic (ddl of rotation and normal translation to the plate).
2.2
Results of reference
the first 6 clean modes.
2.3 References
bibliographical
[1]
F.
ABASSIAN, D.J.
DAWSWELL, N.C.
KNOWLES. Selected Benchmarks for Natural
Frequency Analysis. NAFEMS (1987).
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SDLS100 Etude of grids on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C Page:
4/10
3 Modeling
With
3.1
Characteristics of modeling
Fine grid for validation of the reference solution
y
Test 0
121
111
89
67
has
45
23
1
3
5
7
9
11
X
has
Cutting:
10 on each side of the rhombus 200 meshs TRIA3.
has
Twinge of the element
= 20.
10 T
Limiting conditions:
in all the nodes P on the Xp side = 0. :
DDL_IMPO: (GROUP_NO: DIMENSION DX:0., DY:0., DZ: 0., DRY: 0. )
Name of the nodes:
Point 1 = N1
Point 121 = N121
3.2
Characteristics of the grid
A number of nodes:
121
A number of meshs and types:
200 TRIA3
3.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM
COQUE
TOUT
[U4.24.01]
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“DKT”
TOUT
[U4.22.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
MODE_ITER_SIMULT
METHODE
“TRI_DIAG”
[U4.52.02]
CALC_FREQ
OPTION
“PLUS_PETITE”
NMAX_FREQ
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SDLS100 Etude of grids on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C Page:
5/10
4
Results of modeling A
4.1 Values
tested
Command of the mode
Reference
Aster
% difference
clean
Frequency (Hz)
Frequency (Hz)
1
0.421
0.4178
0.8
2
1.029
1.0255
0.3
3
2.582
2.5669
0.6
4
3.306
3.2733
1.
5
3.753
3.7347
0.5
6
6.555
6.5236
0.5
7
7.3756
8
7.7332
9
8.5567
10
11.1199
11
11.6474
12
14.3551
4.2 Remarks
Calculations carried out by:
MODE_ITER_SIMULT
METHODE: “TRI_DIAG”
OPTION:“PLUS_PETITE”
NMAX_FREQ: 12
4.3
Contents of the file results
the first 12 Eigen frequencies, clean vectors and modal parameters.
4.4 Parameters
of execution
Version: 3.03.25
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
7.2 seconds
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SDLS100 Etude of grids on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C Page:
6/10
5 Modeling
B
5.1
Characteristics of modeling
Element DKT coarser grid
y
Test 1
21
20
19
18
22
8
7
6
23
17
9
1
5
24
16
has
2
3
4
25
15
10
11
12
13
14
X
has
Twinge of the elements:
= 50.
4 T
Limiting conditions:
in all the nodes P on the Xp side = 0. :
DDL_IMPO: (GROUP_NO: DIMENSION DX:0., DY:0., DZ: 0., DRY: 0. )
Name of the nodes:
Point 1 = N1
Point 25 = N25
5.2
Characteristics of the grid
A number of nodes:
25
A number of meshs and types:
32 TRIA3
5.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM
COQUE
TOUT
[U4.24.01]
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“DKT”
TOUT
[U4.22.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
MODE_ITER_SIMULT
METHODE
“JACOBI”
[U4.52.02]
CALC_FREQ
OPTION
“PLUS_PETITE”
NMAX_FREQ
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SDLS100 Etude of grids on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C Page:
7/10
6
Results of modeling B
6.1 Values
tested
Frequency (Hz)
Command of the mode
Reference
Test NAFEMS
Aster
% difference
clean
NAFEMS
1
0.421
0.4174
0.4165
1.07
2
1.029
1.020
1.0301
0.11
3
2.582
2.564
2.5793
0.10
4
3.306
3.302
3.2572
1.47
5
3.753
3.769
3.7397
0.35
6
6.555
6.805
6.4544
1.54
Test 0
7
7.3756
7.2821
1.27
8
7.7332
7.6852
0.62
9
8.5567
8.3764
2.11
10
11.1199
10.7209
3.59
11
11.6474
11.2904
3.06
12
14.3531
13.7573
4.16
6.2 Remarks
Calculations carried out by:
MODE_ITER_SIMULT
METHODE: “JACOBI”
OPTION:“PLUS_PETITE”
NMAX_FREQ: 12
6.3
Contents of the file results
the first 12 Eigen frequencies, clean vectors and modal parameters.
6.4 Parameters
of execution
Version: 3.03.25
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
5.36 seconds
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SDLS100 Etude of grids on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C Page:
8/10
7 Modeling
C
7.1
Characteristics of modeling
Element DKT with distorted grid
y
Test 2
21
20
19
18
22
8
23
7
6
17
5
24
1
16
9
3
4
25
15
2
10
11
12
13
14
X
Twinge of the element: between 50 and 75.
Limiting conditions:
in all the nodes P on the Xp side = 0. :
DDL_IMPO: (GROUP_NO: DIMENSION DX:0., DY:0., DZ: 0., DRY: 0. )
Name of the nodes:
Point 1 = N1
Point 25 = N25
7.2
Characteristics of the grid
A number of nodes:
25
A number of meshs and types:
32 TRIA3
7.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM
COQUE
TOUT
[U4.24.01]
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“DKT”
TOUT
[U4.22.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
MODE_ITER_SIMULT
METHODE
“TRI_DIAG”
[U4.52.02]
CALC_FREQ
OPTION
“PLUS_PETITE”
NMAX_FREQ
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SDLS100 Etude of grids on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C Page:
9/10
8
Results of modeling C
8.1 Values
tested
Frequency (Hz)
Command of the mode
Reference
Test NAFEMS
Aster
% difference
clean
NAFEMS
1
0.421
0.4174
0.4163
1.12
2
1.029
1.020
1.0340
0.49
3
2.582
2.571
2.5644
0.68
4
3.306
3.317
3.2539
1.58
5
3.753
3.780
3.7433
0.26
6
6.555
6.883
6.4898
0.99
Test 0
7
7.3756
7.2119
2.22
8
7.7332
7.6026
1.69
9
8.5567
8.3232
2.73
10
11.1199
10.7735
3.12
11
11.6474
11.2607
3.32
12
14.3531
13.3008
7.34
8.2 Remarks
Calculations carried out by:
MODE_ITER_SIMULT
METHODE: “TRI_DIAG”
OPTION:“PLUS_PETITE”
NMAX_FREQ: 12
8.3
Contents of the file results
the first 12 Eigen frequencies, clean vectors and modal parameters.
8.4 Parameters
of execution
Version: 3.03.25
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
5.2 seconds
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SDLS100 Etude of grids on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C Page:
10/10
9
Summary of the results
% differences/reference
Command of
Reference
Aster
Aster
Aster
% diff.
% diff.
% diff.
mode
NAFEMS
Test 0
Test 1
Test 2
Test 0
Test 1
Test 2
clean
1
0.421
0.4178
0.4165
0.4163
0.76
1.07
1.12
2
1.029
1.0255
1.0301
1.0340
0.34
0.11
0.49
3
2.582
2.5669
2.5793
2.5644
0.58
0.10
0.68
4
3.306
3.2733
3.2572
3.2539
0.99
1.47
1.58
5
3.753
3.7347
3.7397
3.7433
0.49
0.35
0.26
6
6.555
6.5236
6.4544
6.4898
0.48
1.54
0.99
% differences/reference
Command of
Reference
Aster
Aster
Aster
% diff.
% diff.
% diff.
mode
NAFEMS
Test 0
Test 1
Test 2
Test 0
Test 1
Test 2
clean
7
7.3756
7.2821
7.2119
1.27
2.22
8
7.7332
7.6852
7.6026
0.62
1.69
9
8.5567
8.3764
8.3232
2.11
2.73
10
11.1199
10.7209
10.7735
3.59
3.12
11
11.6474
11.2904
11.2607
3.07
3.32
12
14.3551
13.7573
13.3008
4.16
7.34
· For tests 1 and 2, the quadrangles of card NAFEMS were cut out in triangles.
· Tests 3 and 4 can be carried out by Aster (not quadratic element of hull).
· Until the 9th mode, the error on the frequency is ² 2.5%.
· The effect of distortion of the grid appears really only on modes 7 and 12.
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A