Code_Aster ®
Version
5.0
Titrate:
SSLS110 Stabilité of a compressed square plate


Date:
03/01/00
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V3.03.110-A Page:
1/8

Organization (S): EDF/IMA/MN, SAMTECH

Handbook 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 constraints
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.
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLS110 Stabilité of a compressed square plate


Date:
03/01/00
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V3.03.110-A Page:
2/8

1
Problem of reference

1.1 Geometry

Because of the geometrical and physical symmetry of the problem, only the quarter of the plate is
modelled. By taking account the conditions of symmetry, one can collect only the only modes of
buckling symmetrical.

L
L = 250 mm
2
2
P3
Q
P4
P2
H = 5 mm
1
P
Z
y
X


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.
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLS110 Stabilité of a compressed square plate


Date:
03/01/00
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V3.03.110-A Page:
3/8

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 I čme load determines
critical:

2
D
1 2
Q
= (I +)
Cr I
2
L
I

with:

3
=
Eh
D
: the coefficient of rigidity of inflection of the hull
12 1
(
2
-)

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.
Valeurs 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 Element Methods”.
Prentice Hall, Englewood Cliffs N.J. 07632 (19XX).
[2]
“Stability off Square Plate Under Biaxial Loading”. The the SAMCEF software User' S Manuals V7.1. (1998).
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLS110 Stabilité of a compressed square plate


Date:
03/01/00
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V3.03.110-A Page:
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3 Modeling
With

3.1
Characteristics of modeling

MEC3QU9H (hull 3D)

4
3
1
2

modeling COQUE_3D

3.2
Characteristics of the grid

A number of nodes: 121

A number of meshs and types: 25 QUAD9

3.3 Functionalities
tested

Commands



Keys
AFFE_MODELE
“MECANIQUE”
“COQUE_3D”
TOUT
[U4.22.01]
AFFE_CARA_ELEM
COQUE
A_CIS
[U4.24.01]
EPAIS

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]

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLS110 Stabilité of a compressed square plate


Date:
03/01/00
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V3.03.110-A Page:
5/8

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


Obstruction memory:
32 Mo
Time CPU To use: 13.30 seconds

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLS110 Stabilité of a compressed square plate


Date:
03/01/00
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V3.03.110-A Page:
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5 Modeling
B

5.1
Characteristics of modeling

MEC3TR7H (COQUE_3D)

4
3
1
2

modeling COQUE_3D

5.2
Characteristics of the grid

A number of nodes: 641

A number of meshs and types: 200 TRIA7

5.3 Functionalities
tested

Commands



Keys
AFFE_MODELE
“MECANIQUE”
“COQUE_3D”
TOUT
[U4.22.01]
AFFE_CARA_ELEM
COQUE
A_CIS
[U4.24.01]
EPAIS

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]

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLS110 Stabilité of a compressed square plate


Date:
03/01/00
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V3.03.110-A Page:
7/8

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


Obstruction memory:
32 Mo
Time CPU To use: 48.06 seconds

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSLS110 Stabilité of a compressed square plate


Date:
03/01/00
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V3.03.110-A Page:
8/8

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.

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A

Outline document