Code_Aster
®
Version
7.2
Titrate:
SSNS102 Flambage of a cylindrical hull with stiffener
Date:
18/12/03
Author (S):
J.M. PROIX, S. BAGUET, A. COMBESCURE
Key
:
V6.05.102-A
Page:
1/8
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA, INSA LYON
Manual of Validation
V6.05 booklet: Nonlinear statics
Document: V6.05.102
SSNS102 Flambage of a cylindrical hull with
stiffener
Summary:
This test of nonlinear quasi-static mechanics makes it possible to validate elements SHB8 into nonlinear
geometrical, with or without taking into account of the following pressures and buckling of Euler. He shows them
capacities of this element to deal with problems of thin hulls with stiffener.
Code_Aster
®
Version
7.2
Titrate:
SSNS102 Flambage of a cylindrical hull with stiffener
Date:
18/12/03
Author (S):
J.M. PROIX, S. BAGUET, A. COMBESCURE
Key
:
V6.05.102-A
Page:
2/8
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/03/008/A
1
Problem of reference
1.1 Geometry
Cylindrical hull (which one will be able to represent a quarter), comprising a stiffener surfaces intern of it.
The section (axisymmetric) is following form:
Geometry: Radius R = 2.488m
Height L = 600m
Thickness H = 0.024m
Core la=0.156m, H = 0.01m
Stiffener Lr = 0.120m, H = 0.024m
1.2
Properties of material
Material:
E = 2.1011Pa
= 0.3
1.3
Boundary conditions and loadings
Boundary conditions of symmetry: with SU90: DX = 0
SU0:
DY = 0
on
SUINF: DZ = 0
Loading:
External pressure uniform P = 1Pa regarded as nonfollowing pressure then
following
SU0
Lr
L
R
SUINF
SU90
Z
y
X
Code_Aster
®
Version
7.2
Titrate:
SSNS102 Flambage of a cylindrical hull with stiffener
Date:
18/12/03
Author (S):
J.M. PROIX, S. BAGUET, A. COMBESCURE
Key
:
V6.05.102-A
Page:
3/8
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/03/008/A
2
Reference solution
2.1
Method of calculation
Numerical solution [bib1]: values of the moment (thus of the external pressure) according to
radial displacement of the P2 point (with nonfollowing pressure).
2.2
Sizes and results of reference
The critical loads of Euler found by INCA [bib1] are:
Mode Size Unit
Reference
:
(INCA)
1 Pcr
(AP) 1.27522
2 Pcr
(AP) 2.70735
3 Pcr
(AP) 2.81099
4 Pcr
(AP) 2.83234
5 Pcr
(AP) 3.11185
6 Pcr
(AP) 3.25732
7 Pcr
(AP) 3.61713
8 Pcr
(AP) 3.99700
9 Pcr
(AP) 4.07395
10 Pcr
(AP) 4.10499
In great displacements, without following pressure, the solution found by INCA is:
Moment = pressure
Radial displacement point
1.000E-01 6.414E-04
2.000E-01 1.288E-03
3.001E-01 1.942E-03
4.000E-01 2.604E-03
4.999E-01 3.279E-03
5.996E-01 3.971E-03
6.987E-01 4.688E-03
7.964E-01 5.443E-03
8.909E-01 6.256E-03
9.768E-01 7.142E-03
1.056E+00 8.254E-03
1.103E+00 9.278E-03
1.130E+00 1.020E-02
1.148E+00 1.106E-02
1.160E+00 1.189E-02
1.169E+00 1.271E-02
1.175E+00 1.351E-02
1.181E+00 1.430E-02
1.185E+00 1.509E-02
1.188E+00 1.587E-02
1.191E+00 1.681E-02
1.194E+00 1.774E-02
1.196E+00 1.866E-02
1.197E+00 1.959E-02
1.199E+00 2.051E-02
1.200E+00 2.144E-02
1.201E+00 2.236E-02
1.201E+00 2.328E-02
1.202E+00 2.420E-02
Code_Aster
®
Version
7.2
Titrate:
SSNS102 Flambage of a cylindrical hull with stiffener
Date:
18/12/03
Author (S):
J.M. PROIX, S. BAGUET, A. COMBESCURE
Key
:
V6.05.102-A
Page:
4/8
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/03/008/A
1.202E+00 2.512E-02
1.203E+00 2.622E-02
1.203E+00 2.732E-02
1.203E+00 2.843E-02
1.204E+00 2.953E-02
1.204E+00 3.063E-02
1.204E+00 3.172E-02
1.204E+00 3.282E-02
1.203E+00 3.391E-02
1.203E+00 3.500E-02
1.203E+00 3.608E-02
1.203E+00 3.737E-02
1.203E+00 3.866E-02
1.202E+00 3.992E-02
1.202E+00 4.115E-02
1.202E+00 4.234E-02
1.202E+00 4.347E-02
1.201E+00 4.450E-02
1.201E+00 4.540E-02
1.201E+00 4.609E-02
1.202E+00 4.644E-02
2.3
Uncertainties on the solution
Without object
2.4 References
[1]
“Elastoplastic Stability analysis oh shells using the physically stabilized finite element
SHB8PS " A. Legay, A. Combescure, International Newspaper for Numerical Methods in
Engineering, 20 1-6, 2000,
Code_Aster
®
Version
7.2
Titrate:
SSNS102 Flambage of a cylindrical hull with stiffener
Date:
18/12/03
Author (S):
J.M. PROIX, S. BAGUET, A. COMBESCURE
Key
:
V6.05.102-A
Page:
5/8
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
1/4 of the stiffened cylinder:
3.2
Characteristics of the mesh
966 nodes, 440 SHB8,
180 QUAD4 (external skin)
3.3 Functionalities
tested
Controls
AFFE_MODELE MODELING
SHB8
CALC_MATR_EE % OPTION
RIGI_GEOM
STAT_NON_LINE COMP_ELAS DEFORMATION
GREEN
STAT_NON_LINE EXCIT
TYPE_CHARGE
SUIV
Code_Aster
®
Version
7.2
Titrate:
SSNS102 Flambage of a cylindrical hull with stiffener
Date:
18/12/03
Author (S):
J.M. PROIX, S. BAGUET, A. COMBESCURE
Key
:
V6.05.102-A
Page:
6/8
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/03/008/A
4
Results of modeling A
4.1
Sizes tested and results
The 1
era
critical load of Euler calculated in “linear elasticity (small displacements) is worth:
Size mode
Reference
:
(INCA)
Aster % difference
1 Pcr
(AP)
1.27522 1.24 2.8%
In great displacements, without and with following pressure, the curve pressure-displacement calculated
is as follows:
The reference solution (INCA calculation without following pressure) is compared with the Aster solution in
the following table:
Dx moment
reference Aster % difference
1.00000E01 6.4140000000000D04 6.3028161362598D04 1.733
2.00000E01 1.2880000000000D03 1.2633755411986D03 1.912
3.00100E01 1.9420000000000D03 1.9008128106875D03 2.121
4.00000E01 2.6040000000000D03 2.5419377905484D03 2.383
4.99900E01 3.2790000000000D03 3.1900306901409D03 2.713
5.99600E01 3.9710000000000D03 3.8469948518654D03 3.123
6.98700E01 4.6880000000000D03 4.5156706481172D03 3.676
7.96400E01 5.4430000000000D03 5.2005667509131D03 4.454
8.90900E01 6.2560000000000D03 5.9087504926846D06 5.551
Code_Aster
®
Version
7.2
Titrate:
SSNS102 Flambage of a cylindrical hull with stiffener
Date:
18/12/03
Author (S):
J.M. PROIX, S. BAGUET, A. COMBESCURE
Key
:
V6.05.102-A
Page:
7/8
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/03/008/A
5
Summary of the results
The results obtained by Code_Aster with modeling SHB8 show the capacity of this element
to deal with problems of thin hulls with nongeometrical linearities.
The results with nonfollowing pressure are close to those of the reference.
The results with following pressure, for which one does not have a reference solution, show all
in the same way the good taking into account of this assumption in calculations.
Code_Aster
®
Version
7.2
Titrate:
SSNS102 Flambage of a cylindrical hull with stiffener
Date:
18/12/03
Author (S):
J.M. PROIX, S. BAGUET, A. COMBESCURE
Key
:
V6.05.102-A
Page:
8/8
Manual of Validation
V6.05 booklet: Nonlinear statics
HT-66/03/008/A
Intentionally white left page.