Code_Aster
®
Version
7.2
Titrate:
SSLV139 - Buckling of a circular plate subjected to a force
Date:
12/05/04
Author (S):
X. DESROCHES, C. REZETTE
Key
:
V3.04.139-A
Page:
1/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA, DeltaCAD
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
Document: V3.04.139
SSLV139 - Buckling of a circular plate
subjected to a compressive force uniformly
distributed on its contour
Summary:
This test represents a calculation of stability of a circular plate subjected to a compressive force
uniformly distributed on its contour. We determine the critical load leading to buckling
rubber band of Euler as well as the associated modal deformation.
This test validates modeling
AXIS_FOURIER
for linear buckling with meshs
QUAD8
and
TRIA6
(circumferential mode equal to zero), and modeling
AXIS
with meshs
QUAD8
.
The critical load obtained is compared with an analytical reference solution.
Code_Aster
®
Version
7.2
Titrate:
SSLV139 - Buckling of a circular plate subjected to a force
Date:
12/05/04
Author (S):
X. DESROCHES, C. REZETTE
Key
:
V3.04.139-A
Page:
2/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
·
Thickness of the plate: H = 0.0005 m
·
Radius of the plate: R = 0.115 m
1.2
Properties of material
The properties of material constituting the plate are:
11
10
1
.
2
=
E
AP
Young modulus
3
.
0
=
Poisson's ratio
1.3
Boundary conditions and loadings
Boundary conditions:
·
on the contour of the plate (not B): displacement following Y=0 and rotation around Z = 0
Loading: one applies a compressive force uniformly distributed F to external contour
plate.
1.4 Conditions
initial
Without object.
X
Z
F
Cr
Z
X
Y
B
With
Y
.
Code_Aster
®
Version
7.2
Titrate:
SSLV139 - Buckling of a circular plate subjected to a force
Date:
12/05/04
Author (S):
X. DESROCHES, C. REZETTE
Key
:
V3.04.139-A
Page:
3/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
2
Reference solution
2.1
Method of calculation
The value of the critical load is given in [bib1] by the following expression:
2
68
.
14
R
D
F
Cr
=
with:
D
the bending stiffness of the plate (in N.m) defined by the following expression:
)
1
(
12
2
3
-
=
Eh
D
This critical load is associated a circumferential mode equal to 0.
2.2
Sizes and results of reference
For the characteristics given, the critical load is worth:
Cr
F
= 2668.315 NR/m
2.3
Uncertainties on the solution
Analytical solution
2.4 References
bibliographical
[1]
S.P. TIMOSHENKO, J.M. MANAGES: Theory of elastic stability, second edition, DUNOD
(1966)
Code_Aster
®
Version
7.2
Titrate:
SSLV139 - Buckling of a circular plate subjected to a force
Date:
12/05/04
Author (S):
X. DESROCHES, C. REZETTE
Key
:
V3.04.139-A
Page:
4/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling AXIS_FOURIER (QUAD8): 3 degrees of freedom per node (DX, DY, DZ)
Limiting conditions:
·
group meshs AD: DX = 0, DZ = 0
·
group meshs BC: DY = 0, DZ = 0
Characteristics of the discretization
·
Sides AB and CD: 460 elements
·
Sides AD and BC: 4 elements
3.2
Characteristics of the mesh
A number of nodes: 6449
A number of meshs: 1840 (QUAD8)
3.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
MODELING = “AXIS_FOURIER”
AFFE_CHAR_MECA DDL_IMPO
GROUP_MA
FORCE_CONTOUR
FX
MACRO_ELAS_MULT
CAS_CHARGE
MODE_FOURIER = 0
CALC_MATR_ELEM
OPTION = “RIGI_MECA”
OPTION = “RIGI_GEOM”
MODE_FOURIER = 0
MODE_ITER_SIMULT
METHOD = “SORENSEN”
TYPE_RESU = “MODE_FLAMB”
CALC_FREQ
OPTION = “SMALLER”
NORM_MODE
= “TRAN NORMALIZES”
3.4
Sizes tested and results
Identification
Reference
Aster %
Difference
Pressure criticizes (n=0)
8.4935 10
5
AP
8.4847 10
5
AP
0.104
Displacement
DY
with the node D
1 9.99985
10
1
0.001
With
B
C
D
Z
X
Code_Aster
®
Version
7.2
Titrate:
SSLV139 - Buckling of a circular plate subjected to a force
Date:
12/05/04
Author (S):
X. DESROCHES, C. REZETTE
Key
:
V3.04.139-A
Page:
5/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
3.5 Remarks
·
The pressure criticizes P
Cr
from reference, used in the command file, was obtained with
2
/
94
.
849350
2
m
NR
H
F
P
Cr
Cr
=
=
·
The standardization of the clean mode for largest of the components of translation
imply a value of reference equal to 1 for displacement DY to node D.
Code_Aster
®
Version
7.2
Titrate:
SSLV139 - Buckling of a circular plate subjected to a force
Date:
12/05/04
Author (S):
X. DESROCHES, C. REZETTE
Key
:
V3.04.139-A
Page:
6/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
4 Modeling
B
4.1
Characteristics of modeling
Modeling AXIS (QUAD8): 2 degrees of freedom per node (DX, DY)
Limiting conditions:
·
group meshs AD: DX = 0
·
group meshs BC: DY = 0
Characteristics of the discretization
·
Sides AB and CD: 460 elements
·
Sides AD and BC: 4 elements
4.2
Characteristics of the mesh
A number of nodes: 6449
A number of meshs: 1840 (QUAD8)
4.3 Functionalities
tested
.
Controls
AFFE_MODELE
AFFE
MODELING = “AXIS”
AFFE_CHAR_MECA DDL_IMPO
GROUP_MA
FORCE_CONTOUR
FX
MACRO_ELAS_MULT CAS_CHARGE
CALC_MATR_ELEM
OPTION = “RIGI_MECA”
OPTION = “RIGI_GEOM”
MODE_ITER_SIMULT
METHOD = “SORENSEN”
TYPE_RESU = “MODE_FLAMB”
CALC_FREQ
OPTION = “SMALLER”
NORM_MODE
= “TRAN NORMALIZES”
4.4
Sizes tested and results
Identification
Reference
Aster %
Difference
Pressure criticizes (n=0)
8.4935 10
5
AP
8.4847 10
5
AP
0.104
Displacement
DY
with the node D
1 9.99985
10
1
0.001
With
B
C
D
Z
X
Code_Aster
®
Version
7.2
Titrate:
SSLV139 - Buckling of a circular plate subjected to a force
Date:
12/05/04
Author (S):
X. DESROCHES, C. REZETTE
Key
:
V3.04.139-A
Page:
7/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
4.5 Remarks
·
The pressure criticizes P
Cr
from reference, used in the command file, was obtained with
2
/
94
.
849350
2
m
NR
H
F
P
Cr
Cr
=
=
·
The standardization of the clean mode for largest of the components of translation
imply a value of reference equal to 1 for displacement DY to node D.
Code_Aster
®
Version
7.2
Titrate:
SSLV139 - Buckling of a circular plate subjected to a force
Date:
12/05/04
Author (S):
X. DESROCHES, C. REZETTE
Key
:
V3.04.139-A
Page:
8/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
5 Modeling
C
5.1
Characteristics of modeling
Modeling AXIS_FOURIER (TRIA6): 3 degrees of freedom per node (DX, DY, DZ)
Limiting conditions:
·
group meshs AD: DX = 0, DZ = 0.
·
group meshs BC: DY = 0, DZ = 0.
Characteristic of the discretization
·
Sides AB and CD: 690 elements
·
Sides AD and BC: 6 elements
5.2
Characteristics of the mesh
A number of nodes: 17 964
A number of meshs: 8.280 (TRIA6)
5.3 Functionalities
tested
.
Controls
AFFE_MODELE
AFFE
MODELING = “AXIS_FOURIER”
AFFE_CHAR_MECA DDL_IMPO
GROUP_MA
FORCE_CONTOUR
FX
MACRO_ELAS_MULT
CAS_CHARGE
MODE_FOURIER = 0
CALC_MATR_ELEM
OPTION = “RIGI_MECA”
OPTION = “RIGI_GEOM”
MODE_FOURIER = 0
MODE_ITER_SIMULT
METHOD = “SORENSEN”
TYPE_RESU = “MODE_FLAMB”
CALC_FREQ
OPTION = “SMALLER”
NORM_MODE
= “TRAN NORMALIZES”
5.4
Sizes tested and results
Identification
Reference
Aster %
Difference
Pressure criticizes (n=0)
8.4935 10
5
AP
8.6943 10
5
AP
2.364
Displacement
DY
with the node D
1 9.99986
10
1
0.001
With
B
C
D
Z
X
Code_Aster
®
Version
7.2
Titrate:
SSLV139 - Buckling of a circular plate subjected to a force
Date:
12/05/04
Author (S):
X. DESROCHES, C. REZETTE
Key
:
V3.04.139-A
Page:
9/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
5.5 Remarks
·
The pressure criticizes P
Cr
from reference, used in the command file, was obtained with
2
/
94
.
849350
2
m
NR
H
F
P
Cr
Cr
=
=
·
The standardization of the clean mode for largest of the components of translation
imply a value of reference equal to 1 for displacement DY to node D.
Code_Aster
®
Version
7.2
Titrate:
SSLV139 - Buckling of a circular plate subjected to a force
Date:
12/05/04
Author (S):
X. DESROCHES, C. REZETTE
Key
:
V3.04.139-A
Page:
10/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
6
Summary of the results
The results obtained are very satisfactory for the meshs
QUAD8
independently of
modeling used (
AXIS
or
AXIS_FOURIER)
: uncertainties on the critical pressure
0.104% do not exceed.
However, it will be noted that modeling
AXIS_FOURIER
is definitely less precise with
meshs
TRIA6
that with meshs
QUAD8
.
This test with license to test and compare modelings
AXIS
and
AXIS_FOURIER
in buckling
linear of Euler of a circular mean structure subjected to an external force of compression
uniformly distributed on its contour.