Code_Aster
®
Version
4.0
Titrate:
SDLS02 Plates mean rhombus embedded at the edge
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.002-C
Page:
1/6
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
V2.03.002 document
SDLS02 - Plate mean rhombus embedded at the edge
Summary:
This three-dimensional problem consists in seeking the frequencies of vibration of a mechanical structure
composed of a parallelepipedic plate (nonrectangular), embedded on only one side. This test of
mechanics of the structures corresponds to a dynamic analysis of a surface model having one
linear behavior. It comprises only one modeling.
This problem makes it possible to test the element of plate
DKT
and the calculation of frequencies of vibration by the method of
Lanczos.
The results obtained on the first two Eigen frequencies are in concord with those of the guide
VPCS.
Code_Aster
®
Version
4.0
Titrate:
SDLS02 Plates mean rhombus embedded at the edge
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.002-C
Page:
2/6
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
T
With
Z, W
y, v
has
C
B
has
X, U
D
O
has
has
X
y
side has = 1. m, thickness T = 0.01 m,
= 30°
Co-ordinates of the points (in m):
With
B
C
D
X
0.
has
(1 + sin has
)
sin has
y
0.
0.
cos has
cos has
Z
0.
0.
0.
0.
1.2
Properties of materials
E = 2.1 10
11
AP
= 0.3
= 7.800. kg/m
3
1.3
Boundary conditions and loadings
Embedded side AB:
for any point P such as
y
p
=
0.
U
=
v
=
W
=
0.
X
=
y
=
Z
=
0.
1.4 Conditions
initial
Without object for the modal analysis.
Code_Aster
®
Version
4.0
Titrate:
SDLS02 Plates mean rhombus embedded at the edge
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.002-C
Page:
3/6
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 formula of reference is that given in card SDLS02/89 of the guide VPCS which presents
method of calculation in the following way:
The formulation of Mr. V. BARTON, for a plate on side, led to:
(
)
F
has
E T
I
I
I
=
-
=
1
2
12
1
1 2
2
2
2
2
,….
where:
I
2
=
G
()
with, for a Poisson's ratio
= 0.3 and
= 30°:
=
30
°
1
2
3.961
2
2
10.19
·
Mr. V. Barton mentions the sensitivity of the result to the command of the mode and the angle
.
·
This reference solution applies to the thin sections such as: T/has < 0.1.
·
Coefficients
I
were established with a limited development of an insufficient nature.
2.2
Results of reference
The first two clean modes given by:
·
the formula of Mr. V. Barton,
·
the average of 5 software packages of calculation by the finite element method.
2.3
Uncertainty on the solution
Semi-analytical solution < 2%.
2.4 References
bibliographical
[1]
Mr. V. BARTON, Vibrations off rectangular and skew cantilever punts. Newspaper off Applied
Mechanics, vol. 18, p. 129-134 (1951).
Code_Aster
®
Version
4.0
Titrate:
SDLS02 Plates mean rhombus embedded at the edge
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.002-C
Page:
4/6
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
DKT
y
X
1
2
3
4
5
6
7
8
9
10
11
111
100
89
78
67
56
45
34
23
12
121
110
99
88
77
66
55
44
33
22
Cutting: 10 on each side of the rhombus
200 meshs TRIA3.
Limiting conditions:
in all the nodes on the side AB:
DDL_IMPO: (GROUP_NO: AB DX:0., DY:0., DZ: 0., DRX: 0., DRY: 0., DRZ: 0.)
Name of the nodes:
Not A = N1
Not C: N121
Bridge B = N11
Not D = N111
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
[U4.21.01]
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:
SDLS02 Plates mean rhombus embedded at the edge
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.002-C
Page:
5/6
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
Frequency (Hz)
proper I
Reference
(Barton)
Reference
(average of
5 codes)
Aster
% difference/
average codes
1
9.8987
9.7355
9.8402
1.08
2
25.4651
23.2745
23.5790
1.31
4.2 Remarks
Calculations carried out by:
MODE_ITER_SIMULT
METHOD: 'TRI_DIAG
OPTION:“PLUS_PETITE”
NMAX_FREQ: 2
4.3
Contents of the file results
the first 2 Eigen frequencies, clean vectors and modal parameters.
4.4 Parameters
of execution
Version: NEW 3.4
Machine: CRAY C90
System:
UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use:
4.5 seconds
Code_Aster
®
Version
4.0
Titrate:
SDLS02 Plates mean rhombus embedded at the edge
Date:
08/01/98
Author (S):
B. QUINNEZ
Key:
V2.03.002-C
Page:
6/6
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and the plates
HI-75/96/013 - Ind A
5
Summary of the results
Results given by
Code_Aster
are comparable with the results given by other codes of
using calculation of the formulations different for this plate in form from parallélélogramme.