Code_Aster
®
Version
4.0
Titrate:
SDLS100 Study of mesh on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C
Page:
1/10
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
V2.03.100 document
SDLS100 - Study of mesh 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 mesh
on the results. This test of Mechanics of the 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 bending 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
mesh 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
mesh does not appear on the first frequencies of vibration.
Code_Aster
®
Version
4.0
Titrate:
SDLS100 Study of mesh on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C
Page:
2/10
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
1
Problem of reference
1.1 Geometry
has
y
has
8
7
6
9 1
5
2
3
4
1
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 = 2.10
11
AP
= 0.3
= 8.000. kg/m
3
1.3
Boundary conditions and loadings
Any point P such as X
p
= 0: (U = v = W = 0,
y = 0).
1.4 Conditions
initial
Without object for the modal analysis.
Code_Aster
®
Version
4.0
Titrate:
SDLS100 Study of mesh on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C
Page:
3/10
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
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).
Code_Aster
®
Version
4.0
Titrate:
SDLS100 Study of mesh on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C
Page:
4/10
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
Fine mesh for validation of the reference solution
121
has
y
111
89
67
45
23
1
3
5
7
9
11
has
Test 0
X
Cutting:
10 on each side of the rhombus
200 meshs TRIA3.
Twinge of the element
has
10 T
=
20
.
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 mesh
A number of nodes:
121
A number of meshs and types:
200 TRIA3
3.3 Functionalities
tested
Controls
Keys
AFFE_CARA_ELEM
HULL
ALL
[U4.24.01]
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“DKT”
ALL
[U4.22.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
MODE_ITER_SIMULT
METHOD
“TRI_DIAG”
[U4.52.02]
CALC_FREQ
OPTION
“PLUS_PETITE”
NMAX_FREQ
Code_Aster
®
Version
4.0
Titrate:
SDLS100 Study of mesh on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C
Page:
5/10
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
4
Results of modeling A
4.1 Values
tested
Command of the mode
clean
Reference
Frequency (Hz)
Aster
Frequency (Hz)
% difference
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
METHOD: “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
Overall dimension memory:
8 megawords
Time CPU To use:
7.2 seconds
Code_Aster
®
Version
4.0
Titrate:
SDLS100 Study of mesh on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C
Page:
6/10
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
Element DKT coarser mesh
has
y
22
23
24
25
10
11
12
13
14
Test 1
X
2
3
4
9
1
5
8
7
6
21
20
19
18
17
16
15
Twinge of the elements:
has
4 T
=
50
.
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 mesh
A number of nodes:
25
A number of meshs and types:
32 TRIA3
5.3 Functionalities
tested
Controls
Keys
AFFE_CARA_ELEM
HULL
ALL
[U4.24.01]
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“DKT”
ALL
[U4.22.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
MODE_ITER_SIMULT
METHOD
“JACOBI”
[U4.52.02]
CALC_FREQ
OPTION
“PLUS_PETITE”
NMAX_FREQ
Code_Aster
®
Version
4.0
Titrate:
SDLS100 Study of mesh on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C
Page:
7/10
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
6
Results of modeling B
6.1 Values
tested
Frequency (Hz)
Command of the mode
clean
Reference
Test NAFEMS
Aster
% difference
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
METHOD: “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
Overall dimension memory:
8 megawords
Time CPU To use:
5.36 seconds
Code_Aster
®
Version
4.0
Titrate:
SDLS100 Study of mesh on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C
Page:
8/10
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
7 Modeling
C
7.1
Characteristics of modeling
Element DKT with distorted mesh
y
22
23
24
25
10
11
12
13
14
Test 2
X
2
4
9
1
5
8
7
6
21
20
19
18
17
16
15
3
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 mesh
A number of nodes:
25
A number of meshs and types:
32 TRIA3
7.3 Functionalities
tested
Controls
Keys
AFFE_CARA_ELEM
HULL
ALL
[U4.24.01]
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“DKT”
ALL
[U4.22.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
MODE_ITER_SIMULT
METHOD
“TRI_DIAG”
[U4.52.02]
CALC_FREQ
OPTION
“PLUS_PETITE”
NMAX_FREQ
Code_Aster
®
Version
4.0
Titrate:
SDLS100 Study of mesh on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C
Page:
9/10
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
8
Results of modeling C
8.1 Values
tested
Frequency (Hz)
Command of the mode
clean
Reference
Test NAFEMS
Aster
% difference
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
METHOD: “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
Overall dimension memory:
8 megawords
Time CPU To use:
5.2 seconds
Code_Aster
®
Version
4.0
Titrate:
SDLS100 Study of mesh on a thin square plate
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.100-C
Page:
10/10
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
9
Summary of the results
% differences/reference
Command of
mode
clean
Reference
NAFEMS
Aster
Test 0
Aster
Test 1
Aster
Test 2
% diff.
Test 0
% diff.
Test 1
% diff.
Test 2
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
mode
clean
Reference
NAFEMS
Aster
Test 0
Aster
Test 1
Aster
Test 2
% diff.
Test 0
% diff.
Test 1
% diff.
Test 2
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 of quadratic element of hull).
·
Until the 9th mode, the error on the frequency is ² 2.5%.
·
The effect of distortion of the mesh appears really only on modes 7 and 12.