Code_Aster
®
Version
7.2
Titrate:
SSLS125 - Buckling of a free cylinder under external pressure
Date:
28/10/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.125-A
Page:
1/6
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA, INSA LYON
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.125
SSLS125 - Buckling of a free cylinder under
external pressure
Summary:
This test represents a calculation of stability of a free thin cylindrical envelope at its ends subjected to
an external pressure. One calculates the critical loads leading to the elastic buckling of Euler. The matrix
of geometrical rigidity used in the resolution of the problem to the eigenvalues is that which is due to
initial stresses.
He makes it possible to validate modeling finite elements SHB8.
The critical load and the clean mode obtained are compared with an analytical reference solution.
Code_Aster
®
Version
7.2
Titrate:
SSLS125 - Buckling of a free cylinder under external pressure
Date:
28/10/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.125-A
Page:
2/6
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
1
Problem of reference
1.1 Geometry
=
Z, W
y, v
X, U
L/2
Free cylinder at the ends
B
O
With
Z
X
y
O'
C
D
The symmetry of the problem makes it possible to modelize a quarter of cylinder length L, with conditions
of symmetry specific to the lower edge.
L = 2m
Average radius R = 2m
Thickness E = 0.02m
1.2
Properties of material
The properties of material constituting the plate are:
E
= 2. 10
11
AP
Young modulus
= 0.3
Poisson's ratio
1.3
Boundary conditions and loadings
·
Loading:
- pressure uniformly distributed of p
Cr
= 1. AP on the cylindrical part.
- Conditions of symmetry:
- on AB: DZ = 0
- on BC: DX=0
- on DA: DY=0
1.4 Conditions
initial
Without object
Code_Aster
®
Version
7.2
Titrate:
SSLS125 - Buckling of a free cylinder under external pressure
Date:
28/10/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.125-A
Page:
3/6
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The critical pressure is given in [bib1] or [bib2] by the following expression:
Pcr = E/12/(1-naked ²) .n ².(E/R)
3
with N number of the mode (here N = 2,4,6)
2.2
Results of reference
The pressures criticize (out of AP) are:
Mode (N)
Reference
2 73260
4 293040
6 659340
2.3
Uncertainties on the solution
Analytical solution
2.4 References
bibliographical
[1]
S.P. TIMOSHENKO, J.M. MANAGES: Theory of elastic stability, page 500, second
edition, DUNOD 1966.
[2]
BO O. ALMROTH, D.O. BRUSH: Buckling off bars, punts and shells, page 173, Mc Graw-
Hill, New York, 1975.
Code_Aster
®
Version
7.2
Titrate:
SSLS125 - Buckling of a free cylinder under external pressure
Date:
28/10/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.125-A
Page:
4/6
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
Z, W
y, v
X, U
48
4
L/2
Modeling SHB8
B
C
O
P1,
P12
Z
X
y
O'
D
F
G
E
H
3.2
Characteristics of the mesh
A number of nodes: 882
A number of meshs and types: 400 HEXA8
3.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE AFFE
MODELISATION=SHB8
AFFE_CHAR_MECA PRES_REP NEAR
CALC_MATR_ELEM OPTION
“RIGI_MECA”
“RIGI_GEOM”
MODE_ITER_SIMULT METHOD
OPTION
“SORENSEN”
“PLUS_PETITE”
4
Results of modeling A
4.1 Values
tested
Identification Mode
(N)
Reference
Aster %
difference
Pressure criticizes (AP)
2
73260
72492
1
4
293040
293481
0.2
6
659340
673600
2
Code_Aster
®
Version
7.2
Titrate:
SSLS125 - Buckling of a free cylinder under external pressure
Date:
28/10/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.125-A
Page:
5/6
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
5
Summary of the results
The results obtained are satisfactory. Uncertainties on the critical pressure do not exceed
2%.
The modal deformation obtained corresponds well to the awaited circumferential mode: n=2 for both
modelings.
This test made it possible to test modeling SHB8 in linear buckling of Euler of a mean structure
subjected to an external pressure.
Code_Aster
®
Version
7.2
Titrate:
SSLS125 - Buckling of a free cylinder under external pressure
Date:
28/10/03
Author (S):
J.M. PROIX, S. BAGUET
Key
:
V3.03.125-A
Page:
6/6
Manual of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A
Intentionally white left page.