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Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
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Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
1/18
Organization (S): EDF/AMA, DeltaCAD
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
Document: V3.03.502
SSLS502 - Orthotropic Cylindre subjected to a line
of load
Summary:
This test represents quasi-static calculation, of a short orthotropic cylinder and an orthotropic long cylinder
subjected to a line of load. Their ends, the cylinders rest on rigid diaphragms. This case
test makes it possible to validate modeling finite elements DST with meshs TRIA3 and QUAD4, a material
homogeneous orthotropic.
Displacements and the efforts obtained are compared with a reference solution experimental like to
an analytical solution.
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
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Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
2/18
1
Problem of reference
1.1 Geometry
Q
Y
Z
H
Diaphragm
rigid
X
R
Steel wire
L
Plastic
(ac
has rylic)
y
L = 0.560 m
H = 0.0061 m
roll short:
R = 0.13595 m
Q = 2357.143 NR/m
L = 2.465 m
H = 0.0061 m
roll long:
R = 0.13595 m
Q = 896.552 NR/m
1.2
Properties of material
The material constituting the cylinder is homogeneous orthotropic. The axes of orthotropism correspond
with the curvilinear directions X and Y.
[H
] = [hH; [H
= 0
H
= h3 H/12
membrane inflection] []
membrane
]
; [inflection]
[]
H11= 3.0644 X 109 NR/m ²; H12= 1.1048 X 109 NR/m ²; H13= 0
H22= 18.597 X 109 NR/m ²; H23= 0
; H33=1.250 X 109 NR/m ²
1.3
Boundary conditions and loadings
- CL: The ends of the cylinder rest on rigid diaphragms
- Modelings A and b: Force per unit of length: Q = - 2357.143 NR/m
- Modelings C and D: Force per unit of length: Q = - 896.552. NR/m
1.4 Conditions
initial
Without object
Handbook of Validation
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SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
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:
V3.03.502-A Page:
3/18
2
Reference solution
2.1
Method of calculation used for the reference solution
We will use for this test two reference solutions, one experimental, resulting from work from
Schwaighofer and Microys [bib2], the other drawn from work of Batoz in theory of the deep hulls
[bib1].
2.2
Results of reference
The results of reference are as follows:
Roll (A and B) short
Batoz [bib1]
Experiment [bib2]
Displacement W at the point F
0.35 104 m 0.6
104 m
Displacement W at the point C
0.7 103 m
0.6 103 m
Displacement W at the point D
0.25 104 m
0.1 103 m
Constraint xx at the point F
0.35 MPa
0.325 MPa
Constraint yy at the point F
0.50 MPa
0.60 MPa
Roll long (C and D)
Batoz [bib1]
Experiment [bib2]
Displacement W at the point F
1.32 103 m
1.35 103 m
Displacement W at the point C
2.45 103 m
2.46 103 m
Displacement W at the point D
0.35 103 m
0.51 103 m
Constraint xx at the point F
1.68 MPa
1.9 MPa
Constraint yy at the point F
1.8 MPa
1.55 MPa
2.3
Uncertainties on the solution
~ 5% with regard to the solution of Batoz, undoubtedly much more - ~30% - for the solution
experimental.
2.4 References
bibliographical
[1]
BATOZ J.L., DHATT G.: Modeling of the structures by finite elements, Vol 3, Coques,
HERMES.
[2]
SCHWAIGHOFER J., MICROYS H.F.: Orthotropic Cylindrical shells under line load, Journal
off applied Mechanics, June 1979, Vol 46.
[3]
GEOFFROY P., Développement and evaluation of a finite element for the non-linear analysis
statics and dynamics of thin hulls, Thčse de Docteur Ingénieur, Université of
Technology of Compiegne, 27/04/83.
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
4/18
3 Modeling
With
3.1
Characteristics of modeling
Z
DST modeling (one models a half rolls)
Y
C
Z
- 8 elements in the circumferential direction
y
- 12 elements in the longitudinal direction
B
Z
F
R, W
X
- Boundary conditions: Side AB:
U = W = y=0
- Conditions of symmetry: Sides AD and BC: U =
E
y= z= 0
X
Side cd.:
v = x= z= 0
D
- Force per unit of length side BC: Q/2 = 1178.5715 NR/m
With
L/2
3.2
Characteristics of the grid
A number of nodes: 224
A number of meshs and type: 192 QUAD4
3.3 Functionalities
tested
Commands Key word
factor
Key word
AFFE_MODELE
AFFE
“DST”
DEFI_MATERIAU
ELAS_COQUE
MEMB_L
MEMB_LT
MEMB_T
MEMB_G_LT
FLEX_L
FLEX_LT
FLEX_T
FLEX_G_LT
CISA_L
CISA_T
AFFE_CARA_ELEM
COQUE
EPAIS
ANGL_REP
AFFE_CHAR_MECA
FORCE_ARETE
FZ
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
5/18
4
Results of modeling A
4.1 Values
tested
Identification Reference Reference
Aster %
differences
numerical
expériementale
[bib1]
[bib2]
Displacement W at the point F
0.35x104m 0.6
104m 0.373
104m 6.703 [bib1]
37.757 [bib2]
Displacement W at the point C
0.7 103 m
0.6 103 m
0.721 x103
3.033 [bib1]
20.205 [bib2]
Displacement W at the point D
0.25 104 m
0.1 103 m
0.369 104
47.689 [bib1]
- 63.078 [bib2]
Constraint SIXX at the point F
0.350 MPa
0.325 MPa
0.480 MPa
37.339 [bib1]
47.904 [bib2]
Constraint SIYY at the point F
0.500 MPa
0.600 MPa
0.490 MPa
- 1.901 [bib1]
- 18.259 [bib2]
4.2
Value of normal displacement W along CD
EDF
Department Mecanique and Modeles Numeriques
Electricity
W according to the angle along CD
from France
0.6
ROLL SHORT ORTHOTROPIC
DKT 8 X 12 QUAD4
0.4
0.2
0.0
mm)
T (
L
acemen
W (total reference mark)
E
p
D
- 0.2
W normal Batoz reference
W normal
W normal experimental
- 0.4
- 0.6
- 0.8
0
20
40
60
80
100
120
140
160
180
angle (deg)
agraf 19/04/2001 (c) EDF/DER 1992-1999
One can note that beyond the variations observed on the points tested C, F, D, normal displacement
calculated along CD is close to the solution in theory “deep hulls” adopted by Batoz
[bib1]. One can charge the errors relating to the points F and D to the low value of the displacement (of
the command of 105 m).
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
6/18
4.3
Value of the constraints along CD
EDF
Department Mecanique and Modeles Numeriques
Electricity
Sigma XX along CD
from France
2
ROLL SHORT ORTHOTROPIC
DKT 8 X 12 QUAD4
1
0
- 1
has
)
P
- 2
M
(
your
T
R
has
in
N
sigma XX
Co
- 3
Experimental ref. Schwaighofer/Microys
Ref. Batoz
- 4
- 5
- 6
- 7
0
20
40
60
80
100
120
140
160
180
angle (deg)
agraf 05/06/2001 (c) EDF/DER 1992-1999
EDF
Department Mecanique and Modeles Numeriques
Electricity
sigma YY along CD
from France
3
ROLL SHORT ORTHOTROPIC
DKT 8 X 12 QUAD4
2
1
0
has
)
P
- 1
M
(
your
T
R
has
in
N
sigma YY
Co
- 2
Experimental ref. Schwaighofer/Microys
Ref. Batoz
- 3
- 4
- 5
- 6
0
20
40
60
80
100
120
140
160
180
angle (deg)
agraf 05/06/2001 (c) EDF/DER 1992-1999
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
7/18
One can note that the constraints calculated along CD are overall in agreement with the solution
in theory “deep hulls” adopted by Batoz [bib1].
4.4 Remarks
· The values of coefficients CISA_L and CISA_T are not available. Like the structure
is thin (H/R=0.045), one supposes that the effects of transverse shearing are negligible,
we thus imposed CISA_L=CISA_T=1010.
· Displacement W normal (figure of [§4.2]) is expressed in the local cylindrical reference mark (R, Z), it
acts of normal displacement to the element of hull. Displacement W tested with [§4.1] is as for
he expressed in the total reference mark (displacement following Z).
Handbook of Validation
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Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
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:
V3.03.502-A Page:
8/18
5 Modeling
B
5.1
Characteristics of modeling
Z
DST modeling (one models a half rolls)
Y
C
Z
- 8 elements in the circumferential direction
y
- 12 elements in the longitudinal direction
B
Z
F
R, W
X
- Boundary conditions: Side AB:
U = W = y=0
- Conditions of symmetry: Sides AD and BC: U =
E
y= z= 0
X
Side cd.:
v = x= z= 0
D
- Force per unit of length side BC: Q/2 = 1178.5715 NR/m
With
L/2
5.2
Characteristics of the grid
A number of nodes: 224
A number of meshs and type: 384 TRIA3
5.3 Functionalities
tested
Commands Key word
factor
Key word
AFFE_MODELE
AFFE
“DST”
DEFI_MATERIAU
ELAS_COQUE
MEMB_L
MEMB_LT
MEMB_T
MEMB_G_LT
FLEX_L
FLEX_LT
FLEX_T
FLEX_G_LT
CISA_L
CISA_T
AFFE_CARA_ELEM
COQUE
EPAIS
ANGL_REP
AFFE_CHAR_MECA
FORCE_ARETE
FZ
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
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Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
9/18
6
Results of modeling B
6.1 Values
tested
Identification Reference
Reference
Aster %
differences
[bib1]
[bib2]
Displacement W at the point F
0.35 10-4m 0.6
104m 0.383
104
9.571 [bib1]
36.084 [bib2]
Displacement W at the point C
0.7 10-3m 0.6
103 m
7.138 104
1.985 [bib1]
18.982 [bib2]
Displacement W at the point D
0.25 10-4m 0.1
103 m
0.350 104
40.368 [bib1]
64.908 [bib2]
Constraint SIXX at the point F
0.350 MPa
0.325 MPa
0.470 MPa
34.348 [bib1]
44.682 [bib2]
Constraint SIYY at the point F
0.500 MPa
0.600 MPa
0.400 MPa
19.929 [bib1]
33.274 [bib2]
6.2 Remarks
· The values of coefficients CISA_L and CISA_T are not available. Like the structure
is thin (H/R=0.045), one supposes that the effects of transverse shearing are negligible,
we thus imposed CISA_L=CISA_T=1010.
· Displacement W normal is expressed in the local cylindrical reference mark (R, Z), it acts of
normal displacement with the element of hull.
6.3
Value of normal displacement along CD
The results obtained with a grid TRIA3 are very close to those obtained by the grid
QUAD4.
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
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Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
10/18
6.4
Value of the constraints along CD
EDF
Department Mecanique and Modeles Numeriques
Electricity
Sigma XX along CD
from France
2
ROLL SHORT ORTHOTROPIC
DKT 8 X 12 TRIA3
1
0
- 1
has
)
P
- 2
M
(
your
T
R
has
in
N
sigma XX
Co
- 3
Experimental ref. Schwaighofer/Microys
Ref. Batoz
- 4
- 5
- 6
- 7
0
20
40
60
80
100
120
140
160
180
angle (deg)
agraf 05/06/2001 (c) EDF/DER 1992-1999
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
11/18
EDF
Department Mecanique and Modeles Numeriques
Electricity
sigma YY along CD
from France
3
ROLL SHORT ORTHOTROPIC
DKT 8 X 12 TRIA3
2
1
0
has
)
P
- 1
M
(
your
T
R
has
in
N
sigma YY
Co
- 2
Experimental ref. Schwaighofer/Microys
Ref. Batoz
- 3
- 4
- 5
- 6
0
20
40
60
80
100
120
140
160
180
angle (deg)
agraf 05/06/2001 (c) EDF/DER 1992-1999
The profiles of the constraints obtained by modeling B with TRIA3 are as a whole
near to the solutions of Batoz.
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
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Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
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P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
12/18
7 Modeling
C
7.1
Characteristics of modeling
Z
DST modeling (one models a half rolls)
Y
C
Z
- 8 elements in the circumferential direction
y
- 12 elements in the longitudinal direction
B
Z
F
R, W
X
- Boundary conditions: Side AB:
U = W = y=0
- Conditions of symmetry: Sides AD and BC: U =
E
y= z= 0
X
Side cd.:
v = x= z= 0
D
- Force per unit of length side BC: Q/2 = 448.276 NR/m
With
L/2
7.2
Characteristics of the grid
A number of nodes: 224
A number of meshs and type: 384 TRIA3
7.3 Functionalities
tested
Commands Key word
factor
Key word
AFFE_MODELE
AFFE
“DST”
DEFI_MATERIAU
ELAS_COQUE
MEMB_L
MEMB_LT
MEMB_T
MEMB_G_LT
FLEX_L
FLEX_LT
FLEX_T
FLEX_G_LT
CISA_L
CISA_T
AFFE_CARA_ELEM
COQUE
EPAIS
ANGL_REP
AFFE_CHAR_MECA
FORCE_ARETE
FZ
8
Results of modeling C
8.1 Values
tested
Identification Reference
Reference
Aster %
difference
numerical
experimental
[bib1]
[bib2]
Displacement W at the point F
1.325 103 m
1.35 103 m
1.327 103 m
0.154 [bib1]
1.701 [bib2]
Displacement W at the point C
2.45 103 m
2.46 103 m
2.379 103 m
2.881 [bib1]
3.275 [bib2]
Displacement W at the point D
0.51 103 m
0.35 103 m
0.529 103 m
3.859 [bib1]
51.337 [bib2]
Constraint SIXX at the point F
1.68 MPa
1.9 MPa
1.643 MPa
2.155 [bib1]
13.484 [bib2]
Constraint SIYY at the point F
1.8 MPa
1.55 MPa
1.782 MPa
0.986 [bib1]
14.984 [bib2]
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
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Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
13/18
8.2 Remarks
· The value of coefficients CISA_L and CISA_T are not available. As the structure is
thin (H/R=0.045), that the effects of transverse shearing are negligible, us are supposed
thus imposed CISA_L=CISA_T=1010.
· Displacement W normal is expressed in the local cylindrical reference mark (R, Z), it acts of
normal displacement with the element of hull.
8.3
Value of normal displacement along CD
EDF
Department Mecanique and Modeles Numeriques
Electricity
W according to the angle along CD
from France
1.5
ROLL LONG ORTHOTROPIC
DKT 8 X 12 TRIA3
1.0
0.5
0.0
mm)
T (
- 0.5
L
acemen
W normal
E
p
D
W normal Batoz reference
W normal experimental
- 1.0
- 1.5
- 2.0
- 2.5
0
20
40
60
80
100
120
140
160
180
angle (deg)
agraf 19/04/2001 (c) EDF/DER 1992-1999
One can note that beyond the variation observed on the experimental value at the point D, displacement
normal calculated along CD is very close to the solution in adopted theory “deep hulls”
by Batoz [bib1].
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
14/18
8.4
Value of the constraints along CD
EDF
Department Mecanique and Modeles Numeriques
Electricity
Sigma XX along CD
from France
3
ROLL LONG ORTHOTROPIC
DKT 12 X 8 TRIA3
2
1
0
has
)
P
M
(
your
- 1
T
R
has
in
N
Experimental ref. Schwaighofer/Microys
Co
Ref. Batoz
sigma XX
- 2
- 3
- 4
- 5
0
20
40
60
80
100
120
140
160
180
angle (deg)
agraf 05/06/2001 (c) EDF/DER 1992-1999
EDF
Department Mecanique and Modeles Numeriques
Electricity
sigma YY along CD
from France
3
ROLL LONG ORTHOTROPIC
DKT 12 X 8 TRIA3
2
1
0
has
)
P
M
(
your
- 1
T
R
has
in
N
Experimental ref. Schwaighofer/Microys
Co
Batoz theory “deep hulls”
sigma YY
- 2
- 3
- 4
- 5
0
20
40
60
80
100
120
140
160
180
angle (deg)
agraf 05/06/2001 (c) EDF/DER 1992-1999
The profiles of the constraints calculated by the code are overall in agreement with work of
Batoz.
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
15/18
9 Modeling
D
9.1
Characteristics of modeling
Z
DST modeling (one models a half rolls)
Y
C
Z
- 8 elements in the circumferential direction
y
- 12 elements in the longitudinal direction
B
Z
F
R, W
X
- Boundary conditions: Side AB:
U = W = y=0
- Conditions of symmetry: Sides AD and BC: U =
E
y= z= 0
X
Side cd.:
v = x= z= 0
D
- Force per unit of length side BC: Q/2 = 448.276 NR/m
With
L/2
9.2
Characteristics of the grid
A number of nodes: 224
A number of meshs and type: 192 QUAD4
9.3 Functionalities
tested
Commands Key word
factor
Key word
AFFE_MODELE
AFFE
“DST”
DEFI_MATERIAU
ELAS_COQUE
MEMB_L
MEMB_LT
MEMB_T
MEMB_G_LT
FLEX_L
FLEX_LT
FLEX_T
FLEX_G_LT
CISA_L
CISA_T
AFFE_CARA_ELEM
COQUE
EPAIS
ANGL_REP
AFFE_CHAR_MECA
FORCE_ARETE
FZ
10 Results of modeling D
10.1 Values
tested
Identification Reference
Reference
Aster %
difference
[bib1]
[bib2]
Displacement W at the point F
1.325 103 m
1.35 103 m
1.329 103 m
0.365 [bib1]
1.494 [bib2]
Displacement W at the point C
2.45 103 m
2.46 103 m
2.369 103 m
3.274 [bib1]
3.667 [bib2]
Displacement W at the point D
0.51 103 m
0.35 103 m
0.528 103 m
3.634 [bib1]
51.009 [bib2]
Constraint SIXX at the point F
1.68 MPa
1.9 MPa
1.79 MPa
6.616 [bib1]
5.729 [bib2]
Constraint SIYY at the point F
1.8 MPa
1.55 MPa
1.84 MPa
2.465 [bib1]
18.991 [bib2]
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
16/18
10.2 Remarks
· The value of coefficients CISA_L and CISA_T are not available. As the structure is
thin (H/R=0.045), that the effects of transverse shearing are negligible, us are supposed
thus imposed CISA_L=CISA_T=1010.
· Displacement W normal is expressed in the local cylindrical reference mark (R, Z), it acts of
normal displacement with the element of hull. Displacement W tested is that of the total reference mark
(displacement following Z).
10.3 Value of displacement along CD
EDF
Department Mecanique and Modeles Numeriques
Electricity
W according to the angle along CD
from France
1.5
ROLL LONG ORTHOTROPIC
DKT 8 X 12 QUAD4
1.0
0.5
0.0
mm)
T (
- 0.5
L
acemen
W normal Batoz reference
E
p
D
W normal
W normal experimental
- 1.0
- 1.5
- 2.0
- 2.5
0
20
40
60
80
100
120
140
160
180
angle (deg)
agraf 19/04/2001 (c) EDF/DER 1992-1999
One can note that beyond the variation observed on the experimental value at the point D, displacement
normal calculated along CD is very close to the solution in adopted theory “deep hulls”
by Batoz [bib1].
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
17/18
10.4 Values of the constraints along CD
EDF
Department Mecanique and Modeles Numeriques
Electricity
Sigma XX along CD
from France
3
ROLL LONG ORTHOTROPIC
DKT 12 X 8 QUAD4
2
1
0
has
)
P
M
(
your
- 1
T
R
has
in
N
sigma XX
Co
Experimental ref. Schwaighofer/Microys
Ref. Batoz
- 2
- 3
- 4
- 5
0
20
40
60
80
100
120
140
160
180
angle (deg)
agraf 05/06/2001 (c) EDF/DER 1992-1999
EDF
Department Mecanique and Modeles Numeriques
Electricity
sigma YY along CD
from France
3
ROLL LONG ORTHOTROPIC
DKT 12 X 8 QUAD4
2
1
0
has
)
P
M
(
your
- 1
T
R
has
in
N
sigma YY
Co
Experimental ref. Schwaighofer/Microys
Batoz theory “deep hulls”
- 2
- 3
- 4
- 5
0
20
40
60
80
100
120
140
160
180
angle (deg)
agraf 05/06/2001 (c) EDF/DER 1992-1999
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLS502 - Orthotropic Cylindre subjected to a line of load
Date:
19/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V3.03.502-A Page:
18/18
11 Summary of the results
The results are as a whole satisfactory. The specific variations which appear at the points
tested, in particular the point D, seem due to the experimental uncertainty, undoubtedly reinforced by
an uncertainty as for the graphic taking away.
A contrario, the solutions suggested by Batoz in theory “deep hulls” are well checked by
four modelings, with relative errors of less than 5% for the long cylinder.
It appears that:
· modelings TRIA3 and QUAD4 are appreciably equivalent for this problem,
· the relative errors are much weaker for the long cylinder (modelings C and D)
that for the cylinder runs (modelings A and B): at the point F, the error is reduced of a factor
10 compared to the reference solution of Batoz,
· the refinement of the grid does not minimize in a decisive way the relative variations, so much with
TRIA3 that with the QUAD4.
It is thus noted that the results are degraded when the report/ratio length on the diameter
decrease, indeed the geometrical effects become important with this type of modeling. It would be
desirable to be able to carry out a calculation in finite elements of hulls in orthotropic medium, in order to
to better take into account the curvature, the plates constituting a borderline case.
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/02/001/A
Outline document