Code_Aster
®
Version
5.0
Titrate:
SSLS110 Stability of a compressed square plate
Date:
03/01/00
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V3.03.110-A
Page:
1/8
Manual of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Organization (S):
EDF/IMA/MN,
SAMTECH
Manual of Validation
V3.03 booklet: Linear statics of the hulls and the plates
Document: V3.03.110
SSLS110 - Stability of a compressed square plate
Summary:
A homogeneous isotropic linear plate square elastic simply pressed on its four sides is subjected
with a linear compressive force acting on two on its sides.
One calculates the critical loads leading to the elastic buckling of the plate. The matrix of rigidity
geometrical used in the resolution of the problem to the eigenvalues is that which is due to the stresses
initial.
·
linear elastic mechanics,
·
buckling of a hull,
·
interest of the test: calculation of the geometrical matrix of rigidity of the elements
COQUE_3D
,
·
2 modelings.
Code_Aster
®
Version
5.0
Titrate:
SSLS110 Stability of a compressed square plate
Date:
03/01/00
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V3.03.110-A
Page:
2/8
Manual of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
1
Problem of reference
1.1 Geometry
Because of the geometrical and physical symmetry of the problem, only the quarter of the plate is
modelized. By taking account the conditions of symmetry, one can collect only the only modes of
buckling symmetrical.
X
y
Z
5 mm
=
H
250 mm
2
=
L
2
L
Q
1
P
2
P
3
P
4
P
1.2
Material properties
E = 2.1 10
+5
Mpa.
= 0.3
The transverse coefficient of shearing for the plate is worth A_CIS = 5/6.
Code_Aster
®
Version
5.0
Titrate:
SSLS110 Stability of a compressed square plate
Date:
03/01/00
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V3.03.110-A
Page:
3/8
Manual of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
1.3
Boundary conditions and loadings
C.L. :
P2P3:
DZ = 0.
P3P4:
DZ = 0.
Symmetry
P1P2:
DY = 0.
DRX=0.
DRZ=0.
P4P1:
DX=0.
DRY=0. DRZ=0.
Loading:
Linear compressive force
Q
on P2P3
1.4 Remarks
It is not possible to solve the problem of deformation of compression without introducing them
conditions of symmetry. Indeed, to impose boundary conditions of symmetry for a quarter of
plate amounts eliminating the modes from rigid body for the complete plate.
2
Reference solution
2.1
Reference solution
The analytical solution obtained with a thin theory of section in homogeneous linear elasticity
isotropic [bib1] without taking into account of the transverse energy of shearing determines
I
ème load
critical:
2
2
2
)
1
(
I
I
L
D
Q
I
Cr
+
=
with:
)
1
(
12
2
3
-
=
Eh
D
: the coefficient of rigidity of bending of the hull
H
: the thickness
L
: the length on the side of the square plate.
2.2
Results of reference
Certain modes corresponding to the critical loads of the analytical solution are not
symmetrical and cannot be collected with the conditions of symmetry for a quarter of plate.
The Values of the critical loads obtained thus correspond to the first 3 symmetrical modes
of buckling:
·
Mode 1 of the quarter of the plate = Mode 1 of all the plate
·
Mode 2 of the quarter of the plate = Mode 3 of all the plate
·
Mode 3 of the quarter of the plate = Mode 5 of all the plate
2.3
Uncertainty on the solution
Exact solution for a theory of plate without transverse shearing.
2.4 References
bibliographical
[1]
J.G. EISLEY “Mechanics off Elastic Structures: Classical years Finite Methods Element”.
Prentice Hall, Englewood Cliffs N.J. 07632 (19XX).
[2]
“Stability off Public garden Punt Biaxial Under Loading”. The the SAMCEF software User' S Manuals V7.1. (1998).
Code_Aster
®
Version
5.0
Titrate:
SSLS110 Stability of a compressed square plate
Date:
03/01/00
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V3.03.110-A
Page:
4/8
Manual of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
3 Modeling
With
3.1
Characteristics of modeling
MEC3QU9H (hull 3D)
3
4
1
2
modeling
COQUE_3D
3.2
Characteristics of the mesh
A number of nodes: 121
A number of meshs and types: 25 QUAD9
3.3 Functionalities
tested
Controls
Keys
AFFE_MODELE
“MECHANICAL”
“COQUE_3D”
ALL
[U4.22.01]
AFFE_CARA_ELEM
HULL
A_CIS
[U4.24.01]
THICK
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_ARETE
GROUP_MA
CALC_MATR_ELEM
“RIGI_GEOM”
[U4.41.01]
MODE_ITER_SIMULT
“PLUS_PETITE”
[U4.52.02]
Code_Aster
®
Version
5.0
Titrate:
SSLS110 Stability of a compressed square plate
Date:
03/01/00
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V3.03.110-A
Page:
5/8
Manual of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
4
Results of modeling A
4.1 Values
tested
Identification Reference Aster %
difference
mode 1
3.79600E+02 3.78520E+02 0.987
mode 2
1.05444E+03 1.04904E+03 0.512
mode 3
2.56609E+03 2.57466E+03 +0.334
4.2 Remarks
Energy due to transverse shearing is not neglected.
4.3 Parameters
of execution
Version: 5.02.20
Machine: SGI - ORIGIN 2000
Overall dimension memory:
32 Mo
Time CPU To use: 13.30 seconds
Code_Aster
®
Version
5.0
Titrate:
SSLS110 Stability of a compressed square plate
Date:
03/01/00
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V3.03.110-A
Page:
6/8
Manual of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
5 Modeling
B
5.1
Characteristics of modeling
MEC3TR7H (
COQUE_3D
)
3
4
1
2
modeling
COQUE_3D
5.2
Characteristics of the mesh
A number of nodes: 641
A number of meshs and types: 200 TRIA7
5.3 Functionalities
tested
Controls
Keys
AFFE_MODELE
“MECHANICAL”
“COQUE_3D”
ALL
[U4.22.01]
AFFE_CARA_ELEM
HULL
A_CIS
[U4.24.01]
THICK
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_ARETE
GROUP_MA
CALC_MATR_ELEM
“RIGI_GEOM”
[U4.41.01]
MODE_ITER_SIMULT
“PLUS_PETITE”
[U4.52.02]
Code_Aster
®
Version
5.0
Titrate:
SSLS110 Stability of a compressed square plate
Date:
03/01/00
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V3.03.110-A
Page:
7/8
Manual of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
6
Results of modeling B
6.1 Values
tested
Identification Reference Aster %
difference
Mode 1
3.79600E+02 3.77689E+02 0.503
Mode 2
1.05444E+03 1.05744E+03 +0.284
mode 3
2.56609E+03 2.58295E+03 +0.657
6.2 Remarks
Energy due to transverse shearing is not neglected.
6.3 Parameters
of execution
Version: 5.02.20
Machine: SGI - ORIGIN 2000
Overall dimension memory:
32 Mo
Time CPU To use: 48.06 seconds
Code_Aster
®
Version
5.0
Titrate:
SSLS110 Stability of a compressed square plate
Date:
03/01/00
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V3.03.110-A
Page:
8/8
Manual of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
7
Summary of the results
The results obtained are very satisfactory for the two types of elements, QUAD9 and TRIA7, even
if it is necessary to employ a greater number of elements triangles.