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Titrate:
SSLS120 - Thin hull under hydrostatic pressure
Date:
12/12/02
Author (S):
J. Mr. PROIX
Key
:
V3.03.120-A
Page:
1/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and the hulls
HT-66/02/001/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V3.03 booklet: Linear statics of the plates and the hulls
Document: V3.03.120
SSLS120 - Cylindrical thin hull under pressure
hydrostatic
Summary:
This test represents a static calculation of thin cylindrical tank filled with water. It makes it possible to validate the maid
taking into account of the pressures function of the geometry, as well as the orthotropic materials rubber band. 3
modelings finite elements are used:
AXIS
,
COQUE_3D
with meshs
QUAD9
,
COQUE_3D
with
meshs
TRIA7
and DKT with meshs
QUAD4
. Displacements and the stresses obtained are compared with
an analytical reference solution.
Code_Aster
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Titrate:
SSLS120 - Thin hull under hydrostatic pressure
Date:
12/12/02
Author (S):
J. Mr. PROIX
Key
:
V3.03.120-A
Page:
2/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and the hulls
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Cylindrical reserve of average radius R = 5.7 m, thickness E = 0.04 m and height L = 16 m,
simply supported at its base (rotation is free), and subjected to an internal hydrostatic pressure.
Average radius: R
= 5.7 m
Thickness:
E = 0.04 m
Height:
L = 16 m
1.2
Material properties
The properties of materials constituting the plate are:
Material 1: isotropic rubber band:
Young modulus
E
= 2.1 10
11
AP
Poisson's ratio
= 0.3
Material 2: orthotropic rubber band:
E_L = 1.E10 AP
E_T = 2.1E11 AP
G_LT = 0.45E10 AP
G_TN = 0.35E10 AP
NU_LT = 0.075
The axis L is confused with axis Z.
1.3
Boundary conditions and loadings
Base Z = 0 simply supported
internal pressure varying linearly according to Z: p (Z) = P0.(L-z)/L
with P0 = 15000 AP.
1.4 Conditions
initial
Without object.
Code_Aster
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Titrate:
SSLS120 - Thin hull under hydrostatic pressure
Date:
12/12/02
Author (S):
J. Mr. PROIX
Key
:
V3.03.120-A
Page:
3/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and the hulls
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
·
Isotropic material: Analytical solution [bib1], obtained with the mean assumption of hull:
zz
=
0
(
)
=
-
PoR L Z
U
PoR
Ee
Z
L
R
=
-
2
1
U
PoRLvz
Ee
Z
L
Z
=
-
1 2
Radial displacement at the base of the cylinder:
U Z
PoR
Ee
R
(
)
=
=
0
2
Vertical displacement in top of the cylinder:
U Z
L
PoRLv
Ee
Z
(
)
=
= -
2
Circumferential stress in bottom of the cylinder
(
)
Z
PoR
=
=
0
·
Orthotropic material: The solution can be deduced from the preceding one: stresses being
statically determined, it is enough to amend the law of behavior, and to integrate them
deformations.
Raidal displacement at the base of the cylinder:
U Z
PoR
E E
R
T
(
)
=
=
0
2
Vertical displacement in top of the cylinder:
U Z
L
PoRLv
E E
Z
LT
T
(
)
=
= -
2
Circumferential stress in bottom of the cylinder
(
)
Z
PoR
=
=
0
Code_Aster
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Version
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Titrate:
SSLS120 - Thin hull under hydrostatic pressure
Date:
12/12/02
Author (S):
J. Mr. PROIX
Key
:
V3.03.120-A
Page:
4/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and the hulls
HT-66/02/001/A
2.2
Results of reference
Isotropic material:
Radial displacement at the base of the cylinder:
Ur (A1) = 5.8017857E05 m
Vertical displacement in top of the cylinder:
Uz (A3) = 2.442857E05 m
Circumferential stress in bottom of the cylinder:
STT (A1) = 2.1375E+06 AP
Orthotropic material:
Radial displacement at the base of the cylinder:
Ur (A1) = 5.8017857E05 m
Vertical displacement in top of the cylinder:
Uz (A3) = 6.107143E06 m
Circumferential stress in bottom of the cylinder:
STT (A1) = 2.1375E+06 AP
2.3
Uncertainty on the solution
·
Analytical solution.
2.4 References
bibliographical
[1]
PILKEY W.D.: “Formulated for stress, Strain and Structural Matrices”. Wiley & Idiots,
New York, 1994.
Code_Aster
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Titrate:
SSLS120 - Thin hull under hydrostatic pressure
Date:
12/12/02
Author (S):
J. Mr. PROIX
Key
:
V3.03.120-A
Page:
5/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and the hulls
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling AXIS. One nets only one generator of the cylinder. 2 meshs QUAD8 in
the thickness and 400 on the height.
3.2
Characteristics of the mesh
A number of nodes: 3206
A number of meshs and types: 800 QUAD8
3.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = `AXIS `
MASSIVE AFFE_CARA_ELEM
ANGL_REP
AFFE_CHAR_MECA_F FORCE_CONTOUR
FX
DEFI_MATERIAU ELAS_ORTH
3.4 Values
tested
Isotropic material
Value Identification
Reference
Aster %
difference
Ur (z=0)
DX (PM)
5.8018E05
5.7875E05
0.25
Uz (z=L)
DY (A3)
2.4429E05
2.433E05
0.4
Uz (z=L)
DY (A4)
2.4429E05
2.4185E05
1
SigmaTT (z=0)
SIZZ (PM)
2.1375E+06
2.13 E6
0.4
Orthotropic material
Value Identification
Reference
Aster %
difference
Ur (z=0)
DX (A1)
5.8018E05
5.7828E05
0.33
Uz (z=L)
DY (A3)
6.10714E06
5.992E06
1.9
Uz (z=L)
DY (A4)
2.4429E05
6.1367E06
0.5
SigmaTT (z=0)
SIZZ (PM)
2.1375E+06
2.13E6
0.4
Code_Aster
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Version
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Titrate:
SSLS120 - Thin hull under hydrostatic pressure
Date:
12/12/02
Author (S):
J. Mr. PROIX
Key
:
V3.03.120-A
Page:
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Manual of Validation
V3.03 booklet: Linear statics of the plates and the hulls
HT-66/02/001/A
4 Modeling
B
4.1
Characteristics of modeling
Modeling COQUE_3D. One nets only half of the cylinder (symmetry compared to the y=0 plan)
10 meshs QUAD9 in the height and 20 on the semicircumference.
4.2
Characteristics of the mesh
A number of nodes: 664
A number of meshs and type: 200 QUAD9
4.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = COQUE_3D
AFFE_CARA_ELEM HULL
ANGL_REP
AFFE_CHAR_MECA_F FORCE_COQUE
NEAR
DEFI_MATERIAU ELAS_ORTH
Code_Aster
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Version
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Titrate:
SSLS120 - Thin hull under hydrostatic pressure
Date:
12/12/02
Author (S):
J. Mr. PROIX
Key
:
V3.03.120-A
Page:
7/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and the hulls
HT-66/02/001/A
4.4 Values
tested
Isotropic material
Value Identification
Reference
Aster %
difference
Ur (z=0)
DX (PM)
5.8018E05
5.7982E05
0.06
Ur (z=0)
DX (A1)
5.8018E05
5.7982E05
0.06
Ur (z=0)
DX (A2)
5.8018E05
5.7982E05
0.06
Uz (z=L)
DZ (A3)
2.4429E05 2.4429E05
2.E4
Uz (z=L)
DZ (A4)
2.4429E05 2.4429E05
2.E4
SigmaTT (z=0)
SIZZ (PM) 2.1375E+06
2.1371E+06 0.02
Orthotropic material
Value Identification
Reference
Aster %
difference
Ur (z=0)
DX (PM)
5.8018E05 5.8018E05 2.E5
Ur (z=0)
DX (A1)
5.8018E05 5.8018E05
2.E5
Ur (z=0)
DX (A2)
5.8018E05 5.8018E05
2.E5
Uz (z=L)
DZ (A3)
6.10714E06 6.10716E06
3.E4
Uz (z=L)
DZ (A4)
6.10714E06 6.10716E06
3.E4
SigmaTT (z=0)
SIZZ (PM) 2.1375E+06
2.1371E+06 0.02
Code_Aster
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Version
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Titrate:
SSLS120 - Thin hull under hydrostatic pressure
Date:
12/12/02
Author (S):
J. Mr. PROIX
Key
:
V3.03.120-A
Page:
8/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and the hulls
HT-66/02/001/A
5 Modeling
C
5.1
Characteristics of modeling
Modeling COQUE_3D. One nets only half of the cylinder (symmetry compared to the y=0 plan)
10 meshs TRIA7 in the height and 20 on the semicircumference.
5.2
Characteristics of the mesh
A number of nodes: 864
A number of meshs and types: 400 TRIA7
5.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = COQUE_3D
AFFE_CARA_ELEM HULL
ANGL_REP
AFFE_CHAR_MECA_F FORCE_COQUE
NEAR
DEFI_MATERIAU ELAS_ORTH
Code_Aster
®
Version
6.0
Titrate:
SSLS120 - Thin hull under hydrostatic pressure
Date:
12/12/02
Author (S):
J. Mr. PROIX
Key
:
V3.03.120-A
Page:
9/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and the hulls
HT-66/02/001/A
5.4 Values
tested
Isotropic material
Value Identification Reference
Aster %
difference
Ur (z=0)
DY (PM)
5.8018E05
5.799E05
0.4
Ur (z=0)
DX (A1)
5.8018E05
5.793E05
0.15
Ur (z=0)
DX (A2)
5.8018E05
5.806E05
0.06
Uz (z=L)
DZ (A3)
2.4429E05
2.4428E05
0.004
Uz (z=L)
DZ (A4)
2.4429E05
2.4428E05
0.004
SigmaTT (z=0)
SIZZ (PM) 2.1375E+06
2.1377E+06 0.008
Orthotropic material
Value Identification Reference
Aster %
difference
Ur (z=0)
DX (PM)
5.8018E05
5.8013E05
0.008
Ur (z=0)
DX (A1)
5.8018E05
5.7904E05
0.2
Ur (z=0)
DX (A2)
5.8018E05
5.8122E05
0.18
Uz (z=L)
DZ (A3)
6.10714E06
6.1044E06
0.045
Uz (z=L)
DZ (A4)
6.10714E06
6.1070E06
0.002
SigmaTT (z=0)
SIZZ (PM) 2.1375E+06
2.1377E+06 0.008
Code_Aster
®
Version
6.0
Titrate:
SSLS120 - Thin hull under hydrostatic pressure
Date:
12/12/02
Author (S):
J. Mr. PROIX
Key
:
V3.03.120-A
Page:
10/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and the hulls
HT-66/02/001/A
6 Modeling
D
6.1
Characteristics of modeling
Modeling DKT. One nets only half of the cylinder (symmetry compared to the y=0 plan) 30
meshs QUAD4 in the height and 60 on the semicircumference.
6.2
Characteristics of the mesh
A number of nodes: 1894
A number of meshs and types: 1800 QUAD4
6.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = DKT
AFFE_CARA_ELEM HULL
ANGL_REP
AFFE_CHAR_MECA_F FORCE_COQUE
NEAR
DEFI_MATERIAU ELAS_ORTH
DEFI_COQU_MULT SLEEP
ANGL_REP
Code_Aster
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Version
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Titrate:
SSLS120 - Thin hull under hydrostatic pressure
Date:
12/12/02
Author (S):
J. Mr. PROIX
Key
:
V3.03.120-A
Page:
11/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and the hulls
HT-66/02/001/A
6.4 Values
tested
Isotropic material
Value Identification
Reference
Aster %
difference
Ur (z=0)
DY (PM)
5.8018E05
5.7916E05
0.18
Ur (z=0)
DX (A1)
5.8018E05
5.7916E05
0.18
Ur (z=0)
DX (A2)
5.8018E05
5.7916E05
0.18
Uz (z=L)
DZ (A3)
2.4429E05
2.4420E05
0.03
Uz (z=L)
DZ (A4)
2.4429E05
2.4420E05
0.03
SigmaTT (z=0)
SIZZ (PM) 2.1375E+06 2.1371E+06 0.02
Orthotropic material
Value Identification
Reference
Aster %
difference
Ur (z=0)
DY (PM)
5.8018E05
5.798E05
0.06
Ur (z=0)
DX (A1)
5.8018E05
5.798E05
0.06
Ur (z=0)
DX (A2)
5.8018E05
5.798E05
0.06
Uz (z=L)
DZ (A3)
6.10714E06
6.105E06
0.03
Uz (z=L)
DZ (A4)
6.10714E06
6.105E06
0.03
SigmaTT (z=0)
SIZZ (PM) 2.1375E+06 2.1371E+06 0.02
6.5 Remarks
To obtain a correct result, it is necessary to take guard with the convention adopted for NU_LT for
hulls multi layers (
DEFI_COQU_MULT
), which is different from that used for
ELAS_ORTH
:
Here, it is necessary to take Nu_LT such as NuTL=ET/EL * NuLT, that is to say NU_LT = 0.014285714).
Code_Aster
®
Version
6.0
Titrate:
SSLS120 - Thin hull under hydrostatic pressure
Date:
12/12/02
Author (S):
J. Mr. PROIX
Key
:
V3.03.120-A
Page:
12/12
Manual of Validation
V3.03 booklet: Linear statics of the plates and the hulls
HT-66/02/001/A
7
Summary of the results
The results of four modelings are very close to the analytical solution: to the maximum 0.4%
variation for modelings COQUE_3D and DKT, and less than 2% of variation for modeling
axisymmetric, which is explained by the fact why the analytical solution is a mean solution hull.
This test thus validates on the one hand the efforts of pressure varying linearly with the geometry, for
thin hulls, and in addition the taking into account of orthotropic elasticity.