square Plate “solid”

Transcription

Code_Aster
Titre : SDLS502 - Plaque carrée « solide » simplement supp[...]
Responsable : KUDAWOO Ayaovi-Dzifa
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SDLS502- Square plate «solid» simply supported
Summary:
This test represents a computation in dynamic modal analysis of a thick square plate simply supported. This
test validates:
•
•
modelizations finite elements DST, DKT, COQUE_3D with meshes QUAD4 and TRIA3, QUAD8 and
TRIA6, and 3d with meshes HEXA20,
the taking into account of transverse shear rigidity.
The frequencies and the modes obtained are compared with a reference solution, suggested by NAFEMS,
obtained with a computation finite elements of volume type.
Warning : The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is
provided as a convenience.
Licensed under the terms of the GNU FDL (http://www.gnu.org/copyleft/fdl.html)
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1
Reference problem
1.1
Geometry
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C
B
h
z, w
L
y, v
D
A
1.2
L = 10.0 m
h = 1.0m
x, u
Material properties
The material properties constituting the plate are:
E=2. 1011
 =0.3
3
=8000. kg / m
1.3
Pa Modulus of Young
Poisson ratio's
Density
Boundary conditions and loadings
Plate simply supported on its edges.
1.4
Initial conditions
Aimless
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2
Reference solution
2.1
Computation method used for the reference solution
the reference solution suggested by NAFEMS [bib1] was obtained to leave a computation finite
elements 3D with elements bricks with 20 nodes and meshed 4×4 (plane xy ) and 1 element
following the thickness.
2.2
Reference results
the first 7 non-zero frequencies and the associated eigen modes, the first three modes are those of
body rigid:
•
•
•
•
•
Frequency (mode 4 except plane)
Frequency (modes 5 & 6 except
plane)
Frequency (mode 7 except plane)
Frequency (Mode 8 in the plane)
Frequency (mode 9 & 10 in the plane)
:
:
44.762 hz
110.52 hz
:
:
:
169.08 hz
193.93 hz
206.64 hz
mode 4 except plane
5 & 6 mode except plane
mode 7 except plane
mode 8 in the plane
9 & 10 mode in the plane
2.3
Uncertainties on the solution
< 2% for a mesh identical to that of [§ 2.1], i.e. with few elements.
2.4
Bibliographical references
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1. NAFEMS: Standard The NAFEMS Benchmarks, TNSB, Rev. 3, October 5th, 1990.
3
Modelization A
3.1
Characteristics of modelization
C
Y
Modélisation DST (TRIA3)
- La plaque est située dans le plan Z= 2.3
- Point O : (0. ;0. ;2.3)
B
Conditions aux limites :
O
15°5
X
- Cotés AB, BC, CD, DA : w=0
D
A
To validate modelization in a reference different from the global system, the plate is turned of
This should not change the Eigen frequencies obtained.
3.2
15,5 ° .
Characteristics of the mesh
Number of nodes: 122
Number of meshes and types: 200 TRIA3
3.3
Quantities tested and results
Identification
Frequency
(mode 4 except plane)
Frequency
(modes 5 & 6 except plane)
Frequency
Frequency
(Mode 8 in the plane)
Frequency
(mode 9 & 10 in the plane)
Moments
Reference
44,762
Aster
44,989
% difference
0,507
110.52
169.08
107,608
107,880
165,454
- 2,634
- 2,388
- 2,144
193.93
196,089
1,114
206.64
211,658
212,000
2,428
2,594
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3.4
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Remarks
•
•
In Aster, the computed modes are those of rigid body: the fourth mode of reference is the first
mode computed by Code_Aster.
Appearance of two modes of bending between modes 8 and 9 of reference: these modes are
modes 6 and 7 of Code_Aster.
In the table below we put the first 14 found Eigen frequencies.
N ° mode
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Frequency (Hz)
44.98
107.61
107.88
165.45
196.09
202.80
203.54
211.66
212.00
222.53
254.74
255.62
264.73
289.85
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4
Modelization B
4.1
Y
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C
Modélisation DST (QUAD4)
- Point O : (0. ;0. ;2.3)
B
O
15°5
X
D
A
4.2
15,5 ° .
Number of meshes and types: 100 QUAD4
4.3
Identification
Frequency
Frequency
Frequency
Frequency
Frequency
Moment
s
Reference
Aster
% difference
44,762
44.64
110.52
108.04
- 2,247
108.26
- 2,041
169.08
162.86
- 3,681
193.93
195.70
0,912
206.64
208.89
1,088
- 0,273
208.89
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4.4
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Remarks
•
•
In Code_Aster, the computed modes are those of rigid body: the fourth mode of reference is the
first mode computed by Code_Aster.
Appearance of two modes of bending between modes 8 and 9 of reference: these modes are
modes 6 and 7 of Code_Aster.
N ° mode
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Frequency (
Hz )
44.64
108.04
108.26
162.86
195.70
203.97
206.08
208.89
208.89
220.92
248.12
250.10
252.49
289.79
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5
Modelization C
5.1
Y
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C
Modélisation DKT (TRIA6)
- Point O : (0. ;0. ;2.3)
B
O
15°5
X
D
A
5.2
15,5 ° .
5.3
Identification
Frequency
Frequency
Frequency
Frequency
Frequency
Moment
s
Reference
Aster
% difference
44,762
47,358
5,799
110.52
169.08
118,029
118,059
187,504
6,795
6,822
10,897
193.93
196,089
1,114
206.64
211,658
212,000
2,428
2,594
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5.4
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Remarks
•
•
Appearance of two modes of bending after mode 11 of reference (mode 8 of Code_Aster), same
form as those appeared in DST modelization between modes 8 and 9 of reference (modes 6 and
7 of Code_Aster).
N ° mode
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Frequency (Hz)
47,358
118.03
118.06
187.50
196.09
211.66
212.00
222.53
235.41
235.56
264.73
289.85
302.84
303.15
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6
Modelization D
6.1
Y
C
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Modélisation DKT (QUAD4)
- Point O : (0. ;0. ;2.3)
B
15°5
O
X
D
A
6.2
15,5 ° .
6.3
Identification
Frequency
Frequency
Frequency
Frequency
Frequency
Moment
s
Reference
Aster
% difference
44,762
47,182
5,408
110.52
117,463
6,283
169.08
184,746
9,266
193.93
195,699
0,912
206.64
208,887
1,088
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6.4
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Remarks
•
•
Appearance of two modes of bending after mode 11 of reference (mode 8 of Code_Aster), same
form as those appeared in model DST between modes 8 and 9 of reference (modes 6 and 7 of
Code_Aster).
N ° mode
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Frequency (Hz)
47,183
117.46
117.46
184.75
195.70
208.89
208.89
220.92
234.74
234.74
252.49
289.79
297.27
297.27
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7
Modelization E
7.1
Y
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C
Modélisation COQUE_3D (TRIA6)
- Point O : (0. ;0. ;2.3)
B
O
15°5
X
D
A
7.2
15,5 ° .
7.3
Identification
Frequency
Frequency
Frequency
Frequency
Frequency
Moment
s
Reference
Aster
% difference
44,762
43,867
2.00
110.52
169.08
106,058
106,066
160,010
- 4,037
- 4,029
- 5,305
193.93
193,600
- 0,170
206.64
206,209
206,211
0,208
0,207
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7.4
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Remarks
•
•
Appearance of two modes of bending between modes 8 and 9 of reference: they are modes 6 and
7 of Code_Aster.
N ° mode
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Frequency (
Hz )
43.867
106.06
106.07
160.11
186.72
193.60
199.76
200.23
206.21
206.21
219.28
245.91
245.94
249.27
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8
Modelling F
8.1
Y
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C
Modélisation COQUE_3D (QUAD8)
- Point O : (0. ;0. ;2.3)
B
O
15°5
X
D
A
8.2
15,5 ° .
8.3
Identification
Frequency
Frequency
Frequency
Frequency
Frequency
Moment
s
Reference
Aster
% difference
44,762
43,870
- 1,993
110.52
106,041
- 4,052
169.08
160,055
- 5,337
193.93
193,588
- 0,176
206.64
206,192
- 0,216
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8.4
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Remarks
•
•
7 of Code_Aster.
N ° mode
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Frequency (
Hz )
43.87
106.04
106.04
160.06
193.59
199.64
200.13
206.19
206.19
219.26
245.68
245.68
249.20
287.99
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9
Modelization G
9.1
Y
C
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Modélisation 3D (HEXA20)
- Le plan moyen de la plaque est situé dans le plan Z= 2.3
- Point O : (0. ;0. ;2.3)
B
O
15°5
X
Z
D
X
O
A
9.2
Number of meshes and types: 200 HEXA20
9.3
Identification
Frequency
Frequency
Frequency
Frequency
Frequency
Moment
s
Reference
Aster
% difference
44,762
43,862
- 2,009
110.52
105,953
- 4,132
169.08
159,749
- 5,518
193.93
193,590
- 0,175
206.64
199,410
199,903
- 3,498
- 3,260
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9.4
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Remarks
•
•
7 of Code_Aster.
N ° mode
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Frequency (
Hz )
43.86
105.95
105.95
159.75
193.59
199.41
199.90
206.16
206.16
219.27
245.07
245.07
249.13
287.75
Code_Aster
10
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Summary of results
Taking into account the nature of the numerical solution (volumic finite elements), the results obtained are
satisfactory for:
•
•
•
•
modelization A and B (DST) the maximum gap is of less 4% for the first 5 modes,
modelization E and F (COQUE_3D), the maximum gap is of approximately 5% for the first 5
modes,
modelization G (3d), the maximum gap is of approximately 5% for the first 5 modes,
the modes of reference 5 and 6 except plane have symmetry different from those met in
modelizations E, F and G, but they are equivalent because they are modal recombinations.
Modelizations C and D (DKT) are less satisfactory with relative variations reaching 10% on mode 7 except
plane, this due to is not taken into account transverse shear for this relatively thick plate.
Moreover one observes the appearance of modes of bending and membrane for all these modelizations,
including modelization 3d volumic G. Lorsque one refines sufficiently the meshes, this tendency is confirmed
and the relative variations regress. Computation 3d in addition showed that in on this side mesh 6×6 in the
plane ( XY ), the modes of bending and membrane were not detected.

square Plate “solid”

Transcription

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