Code_Aster
®
Version
4.0
Titrate:
SDLS101 Plates rectangular thin on elastic mattress
Date:
01/12/98
Author (S):
B. QUINNEZ, L. VIVAN
Key:
V2.03.101-A
Page:
1/6
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
Organization (S):
EDF/IMA/MN, CISI
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
Document: V2.03.101
SDLS101 - Thin rectangular plate on mattress
rubber band
Summary:
This test makes it possible to validate modeling
“APPUI_REP”
[U4.22.01] for elements of hull. It corresponds
with calculations of frequency of bending of a thin rectangular plate which rests on an elastic mattress. By
report/ratio with test SDLS03 [V2.03.003], which validates the frequencies of vibrations of a plate pressed on its edge,
this test validates modeling
“APPUI_REP”
and orders it
CREA_MAILLAGE
[U4.12.06]. The plate is
with a grid with triangles and quadrangles.
Code_Aster
®
Version
4.0
Titrate:
SDLS101 Plates rectangular thin on elastic mattress
Date:
01/12/98
Author (S):
B. QUINNEZ, L. VIVAN
Key:
V2.03.101-A
Page:
2/6
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
C
B
y, v
has
B
X, U
D
Z, W
With
T
Rectangular plate:
length
= 1.5 m have
width
B = 1. m
thickness
T = 0.01 m
Co-ordinates of the points (in m)
With
B
C
D
X
0.
0.
1.
1.
y
0.
1.5
1.5
0.
Z
0.
0.
0.
0.
Z
1.2
Properties of materials
E = 2.1 E11 AP
= 0.3
= 7800 kg/m
3
E
F
= 7th + 5 NR/m
3
1.3
Boundary conditions and loadings
Simple support on all the sides.
Any point P such as:
X
p
= 0 or X
p
= 1 W = 0
y
p
= 0 or y
p
= 1 W = 0
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
4.0
Titrate:
SDLS101 Plates rectangular thin on elastic mattress
Date:
01/12/98
Author (S):
B. QUINNEZ, L. VIVAN
Key:
V2.03.101-A
Page:
3/6
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
The formulation for a rectangular plate thickness
T
posed on the four sides leads to:
(
)
F
I
has
J
B
And
ij
=
+
-
2
12 1
2
2
2
2
with:
I
= a number of half-lengths of wave according to y
J
= a number of half-lengths of wave according to X
The formulation for the plate posed on the four sides and resting on a led elastic mattress
with:
F
F
E
T
ij
ij
F
=
+
/
/
without mattress
2
2
1 2
4
with
E
F
: density of stiffness per unit of area.
2.2
Results of reference
the first 6 clean modes of nonnull frequency (the system comprises 3 modes of rigid body).
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
D. BLEVINS: Formulated for natural frequency and mode shape page 238-239.
Code_Aster
®
Version
4.0
Titrate:
SDLS101 Plates rectangular thin on elastic mattress
Date:
01/12/98
Author (S):
B. QUINNEZ, L. VIVAN
Key:
V2.03.101-A
Page:
4/6
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
Modeling DKT
With
B
C
D
X
y
Z
Limiting conditions:
in all the nodes located on the edges
DDL_IMPO: (GROUP_NO: EDGE DZ = 0.)
3.2
Characteristics of the mesh
A number of nodes: 176
A number of meshs and types: 150 TRIA3, 75 QUAD4
3.3 Functionalities
tested
Controls
Keys
DEFI_GROUP
CREA_GROUP_NO
GROUP_MA
[U4.12.03]
CREA_MAILLAGE
CREA_GROUP_MA
GROUP_MA
[U4.12.06]
DEFI_MATERIAU
APPUI_ELAS
[U4.23.01]
AFFE_MODELE
MODELING: “DKT”
[U4.22.01]
MODELING: “APPUI_REP”
MODELING:“DIS_T'
MODE_ITER_SIMULT
OPTION: “TAPE”
[U4.52.02]
METHOD: “TRI_DIAG”
Code_Aster
®
Version
4.0
Titrate:
SDLS101 Plates rectangular thin on elastic mattress
Date:
01/12/98
Author (S):
B. QUINNEZ, L. VIVAN
Key:
V2.03.101-A
Page:
5/6
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
4
Results of modeling A
4.1 Values
tested
Modeling
DKT
Identification
Reference
Aster
% difference
Frequency 4
35.62638
35.5056
0.339
Frequency 5
68.51227
68.0411
0.688
Frequency 6
109.61964
109.0087
0.557
Frequency 7
123.32210
122.1914
0.917
Frequency 8
142.50554
140.6399
1.309
Frequency 9
197.31535
193.3111
2.029
Modeling
DKT
and
APPUI_REP
Identification
Reference
Aster
% difference
Frequency 4
38.68542
38.8710
0.480
Frequency 5
70.15165
69.6943
0.652
Frequency 6
110.65166
110.0539
0.540
Frequency 7
124.24034
123.1200
0.902
Frequency 8
143.30092
141.4473
1.293
Frequency 9
197.89056
193.9004
2.016
Modeling
DKT
and
DIS_T_N
(to be able to make comparisons, the mattress was replaced
rubber band by discrete springs positioned in each node of the mesh).
Identification
Reference
Aster
% difference
Frequency 4
38.68542
38.1366
1.419
Frequency 5
70.15165
69.4507
0.999
Frequency 6
110.65166
109.8944
0.684
Frequency 7
124.24034
122.9824
1.012
Frequency 8
143.30092
141.3281
1.377
Frequency 9
197.89056
193.8133
2.060
4.2 Parameters
of execution
Version: 3.06.04
Machine: CRAY C90
System:
Overall dimension memory:
8 MW
Time CPU To use:
22 seconds
Code_Aster
®
Version
4.0
Titrate:
SDLS101 Plates rectangular thin on elastic mattress
Date:
01/12/98
Author (S):
B. QUINNEZ, L. VIVAN
Key:
V2.03.101-A
Page:
6/6
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/98/040 - Ind A
5
Summary of the results
The results obtained are correct compared to the results of reference.