Code_Aster ®
Version
7.2
Titrate:
SSLS125 - Flambement of a free cylinder under external pressure
Date:
28/10/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.125-A Page:
1/6

Organization (S): EDF-R & D/AMA, INSA LYON

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.125

SSLS125 - Flambement 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 constraints.

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.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS125 - Flambement of a free cylinder under external pressure
Date:
28/10/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.125-A Page:
2/6

1
Problem of reference

1.1 Geometry

=
Z, W
Free cylinder at the ends
Z
O'
C
D
L/2
O
B
y
With
y, v
X
X, U


The symmetry of the problem makes it possible to model 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. 1011 Pa
Young modulus
= 0.3
Poisson's ratio

1.3
Boundary conditions and loadings

·
Loading:
- pressure uniformly distributed of pcr= 1. Pa 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
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS125 - Flambement of a free cylinder under external pressure
Date:
28/10/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.125-A Page:
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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 Pa) 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.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS125 - Flambement of a free cylinder under external pressure
Date:
28/10/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.125-A Page:
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3 Modeling
With

3.1
Characteristics of modeling


Z, W
Modeling SHB8
Z
G
48
H
O'
F

E
4
L/2
C
D
O
B
y
P1,
y, v
P12
X
X, U


3.2
Characteristics of the grid

A number of nodes: 882
A number of meshs and types: 400 HEXA8

3.3 Functionalities
tested

Commands 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
“SORENSEN”

OPTION
“PLUS_PETITE”

4
Results of modeling A

4.1 Values
tested

Identification Mode
(N)
Reference
Aster %
difference
Pressure criticizes (Pa)
2
73260
72492
1
4
293040
293481
0.2
6
659340
673600
2
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS125 - Flambement of a free cylinder under external pressure
Date:
28/10/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.125-A Page:
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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.

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS125 - Flambement of a free cylinder under external pressure
Date:
28/10/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.125-A Page:
6/6

Intentionally white left page.

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

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