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Titrate:
SSLV303 - Roll embedded under actual weight and pressure
Date
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X. DESROCHES
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Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA















Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
Document: V3.04.303



SSLV303 - Roll embedded under actual weight and
pressure


Summary:

The goal of the test is to validate a load of gravity as well as a pressure, starting from an analysis 2D with
decomposition in Fourier series of the load.

Two modelings are adopted for this analysis; they differ from the key word used to define
gravity:
·
modeling a: to validate the key word
GRAVITY
,
·
modeling b: to validate the key word
FORCE_INTERN
.

Gravity is calculated in mode 1, and the pressure applied is given in mode 1.

The two loading cases are combined and compared with a numerical calculation in modeling 3D (model C).

The fourth modeling (D) is built with an aim of validating the key word
FORCE_INTERN
defined to leave
of a function.
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Titrate:
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Key
:
V3.04.303-A
Page:
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V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
1
Problem of reference
1.1 Geometry

Length
: L
= 0.240 m
Radius
: R
= 0.006 m

1.2
Material properties
E = 2.1 X 10
11
NR/m
2
= 0.3
= 7800 kg/m
3

1.3
Boundary conditions and loadings
·
Sections AB, CD embedded
·
Gravity according to R
: G = 9.81 m/s
2
·
Pressure given by: p = p
O
cos
, p
O
= 10.000 NR/m
2

1.4 Conditions
initial
Without object for the static analysis.
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Titrate:
SSLV303 - Roll embedded under actual weight and pressure
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V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
2
Reference solution
2.1
Method of calculation used for the reference solution
In the case of load of gravity alone:
The value of the field of radial displacement, according to Z, is given by:




+
-
=
2
2
3
4
2
2
12
Z
L
Lz
Z
I.E.(internal excitation)
Q
ur
Maximum displacement, in the median section, is worth:
()
roll
clean
weight
:
,
384
3
P
I.E.(internal excitation)
PL
ur
E
=
In the case of load of pressure, one carries out a comparison with the results of
modeling C.
2.2
Results of reference
·
Displacement in the median section,
()
E
ur
= 0.3566 X 10
­ 6
m
·
Stresses of embedding at point b:
zz
= ­ 0.2496 X 10
6
AP

2.3
Uncertainty on the solution
Analytical solution for gravity.

2.4 Reference
bibliographical
[1]
S. TIMOSHENKO: Resistance of materials, 1ère left. Polytechnic bookstore
CH. Béranger, Paris, 1947
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V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling A
AXIS_FOURIER, T6 mesh



Cutting:
80 elements according to the length
2 elements according to the radius
Loadings:
C1:
vertical gravity (Ug field) (G
2
)
C2:
pressure (Up field) p
O
= 10.000 NR/m
2
Components of displacements: U
R
(radial), U
Z
(axial), U
(circumferential)
Names of the nodes:
With = N1
B = N2
C = N3
D = N4
E = N249
F = N87

3.2
Characteristics of the mesh
A number of nodes: 805
A number of meshs and types: 320 TRIA6
R
B
With
E
F
C
D
Z
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Date
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X. DESROCHES
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V3.04.303-A
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V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
3.3 Functionalities
tested
Controls
“MECHANICAL” AFFE_MODELE “AXIS_FOURIER”
ALL
AFFE_CHAR_MECA DDL_IMPO
GRAVITY
GROUP_NO
CALC_CHAM_ELEM OPTION
MODE_FOURIER
“SIGM_ELNO_DEPL”
AFFE_CHAR_MECA_F PRES_REP
GROUP_MA
COMB_CHAM_NO
COMB_CHAM_ELEM
COMB_FOURIER
COMB_FOURIER
MACRO_ELAS_MULT CHAR_MECA_GLOBAL
CAS_CHARGE
MODE_FOURIER
TYPE_MODE
CHAR_MECA
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Titrate:
SSLV303 - Roll embedded under actual weight and pressure
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Key
:
V3.04.303-A
Page:
6/16
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
4
Results of modeling A
4.1 Values
tested
Values provided for
= 0.

Standard localization
of
value
Reference
Aster
% difference
Ug field
(for
= 0.)
Not E, F
U
R
(m)
U
(m)
3.566 X 10
­ 7
0.
3.541 X 10
­ 7
3.94 10
­ 14
­ 0.701
Not B
zz
(AP)
­ 2.496 X 10
5
­ 2.598 X 10
5
+
4.09
Up field
(for
= 0.)
Not E
U
R
(m)
­ 7.82 X 10
­ 6
­ 7.71 X 10
­ 6
­ 1.4
Not F
­ 7.82 X 10
­ 6
­ 7.70 X 10
­ 6
­ 1.5
Not B
rr
(AP)
zz
(AP)
(AP)
1.63 X 10
6
5.51 X 10
6
1.65 X 10
6
1.41 X 10
6
5.65 X 10
6
1.89 X 10
6
­ 13.4
2.7
14.7
Up field + Ug
(for
= 0.)
Not E
U
R
(m)
­ 7.46 X 10
­ 6
­ 7.358 X 10
­ 6
­ 1.3
Not F
U
R
(m)
­ 7.44 X 10
­ 6
­ 7.348 X 10
­ 6
­ 1.2
Not B
rr
(AP)
zz
(AP)
(AP)
1.56 X 10
6
5.25 X 10
6
1.57 X 10
6
1.34 X 10
6
5.398 X 10
6
1.80 X 10
6
­ 13.7
2.8
15.0

4.2 Remarks
·
The values of reference for the pressure (Up field) are obtained in modeling C, with
to start from a mesh 3D.
·
For gravity, it should be stressed that the command of the components in
GRAVITY
is: R,
,
Z (whereas in
FORCE_INTERN
the command is R, Z,
).

4.3
Contents of the file results
Displacements, stresses.
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Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
5 Modeling
B
5.1
Characteristics of modeling B
AXIS_FOURIER, T6 meshs



Cutting:
80 elements according to the length
2 elements according to the radius
Loadings:
C1: vertical gravity (Ug field) in the form of voluminal density of forces
G
= 76.518 AP
C2: pressure (Up field)
Components of displacements: U
R
(radial), U
Z
(axial), U
(circumferential)
Names of the nodes:
With = N1
B = N2
C = N3
D = N4
E = N249
F = N87

5.2
Characteristics of the mesh
A number of nodes: 805
A number of meshs and types: 320 TRIA6
R
B
With
E
F
C
D
Z
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V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
5.3 Functionalities
tested
Controls
“MECHANICAL” AFFE_MODELE “AXIS_FOURIER”
ALL
AFFE_CHAR_MECA DDL_IMPO
FORCE_INTERN
GROUP_NO
CALC_CHAM_ELEM OPTION
MODE_FOURIER
“SIGM_ELNO_DEPL”
AFFE_CHAR_MECA_F PRES_REP
GROUP_MA
COMB_CHAM_NO
COMB_CHAM_ELEM
COMB_FOURIER
COMB_FOURIER
MACRO_ELAS_MULT CHAR_MECA_GLOBAL
CAS_CHARGE
MODE_FOURIER
TYPE_MODE
CHAR_MECA
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Code_Aster
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Titrate:
SSLV303 - Roll embedded under actual weight and pressure
Date
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X. DESROCHES
Key
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V3.04.303-A
Page:
9/16
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
6
Results of modeling B
6.1 Values
tested

Standard localization
of
value
Reference
Aster
% difference
Ug field
(for
= 0.)
Not E, F
U
R
(m)
U
(m)
3.566 X 10
­ 7
0.
3.541 X 10
­ 7
0.
­ 0.70
Not B
zz
(AP)
­ 2.496 X 10
5
­ 2.60 X 10
5
+
4.1
Up field
(for
= 0.)
Not E
U
R
(m)
­ 7.82 X 10
­ 6
­ 7.71 X 10
­ 6
­ 1.4
Not F
­ 7.82 X 10
­ 6
­ 7.70 X 10
­ 6
­ 1.5
Not B
rr
(AP)
zz
(AP)
(AP)
1.63 X 10
6
5.51 X 10
6
1.65 X 10
6
1.41 X 10
6
5.65 X 10
6
1.89 X 10
6
­ 13.4
2.7
14.7
Up field + Ug
(for
= 0.)
Not E
U
R
(m)
­ 7.46 X 10
­ 6
­ 7.358 X 10
­ 6
­ 1.3
Not F
U
R
(m)
­ 7.46 X 10
­ 6
­ 7.348 X 10
­ 6
­ 1.5
Not B
rr
(AP)
zz
(AP)
(AP)
1.56 X 10
6
5.25 X 10
6
1.57 X 10
6
1.34 X 10
6
5.398 X 10
6
1.80 X 10
6
­ 13.7
2.8
15.0

6.2 Remarks
·
The values of reference for the pressure (Up field) are obtained in modeling C, with
to start from a mesh 3D.
·
The results obtained are rigorously identical to those of modeling A with
GRAVITY
.

6.3
Contents of the file results
Displacements, stresses.
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Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
7 Modeling
C
7.1
Characteristics of modeling C
3D, H20 Meshs and P15




Position of the points: With, B in the section Z = 0
E, F in the median section Z = L/2
Cutting:
20 elements according to the length
2 elements according to the radius, 8 elements according to the circumference.
The loading being symmetrical, the half only of the cylinder is modelized.
X, U
B, F
WITH, E
X
y
B
F
Z
y, v
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V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
Boundary conditions:
·
section embedded ends (U = v = W = 0)
·
conditions of symmetry in the xz plan: v = 0
1)
Pressure on the circumference (Up field)
The surface of the cylinder is divided into 8 lines of elements according to the circumference (1 line
elements represents a sector of
/8 radians.
Pressure being in “Cos
“, it is supposed to be uniform on each line. For any point of
the surface of angle
, (including enters
1
and
2
,
1
= (N ­ 1)
8
,
2
= N
8
, 1 N 8, the value of
pressure assigned to the line of elements containing this point is taken equalizes with:
2
0
p
(cos
1
+ cos
2
).
2)
Vertical gravity according to X (Ug field)
Names of the nodes:
With = N845
B = N965
E = N865
F = N995

7.2
Characteristics of the mesh
A number of nodes: 1285
A number of meshs and types: 160 HEXA20, 80 PENTA15

7.3 Functionalities
tested
Controls
“MECHANICAL” AFFE_MODELE “AXIS_FOURIER”
ALL
AFFE_CHAR_MECA DDL_IMPO
FORCE_INTERN
GRAVITY
GROUP_NO
GROUP_MA
AFFE_CHAR_MECA_F PRES_REP
GROUP_MA
CALC_CHAM_ELEM OPTION
SIGM_ELNO_DEPL
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Titrate:
SSLV303 - Roll embedded under actual weight and pressure
Date
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15/07/03
Author (S):
X. DESROCHES
Key
:
V3.04.303-A
Page:
12/16
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
8
Results of modeling C
8.1 Values
tested

Standard localization
of
value
Reference
Aster
% difference
Up field
Not E
U (m)
v (m)
0.
­ 7.82 X 10
­ 6
10
­ 21
Not F
U (m)
v (m)
0.
­ 7.816 X 10
­ 6
10
­ 21
Not B
xx
(AP)
yy
(AP)
zz
(AP)
1.63 X 10
6
1.65 X 10
6
5.51 X 10
6
Up field + Ug
Not E
U (m)
v (m)
0.
­ 7.46 X 10
­ 6
10
­ 21
Not F
U (m)
v (m)
0.
­ 7.44 X 10
­ 6
10
­ 21
Not B
xx
(AP)
yy
(AP)
zz
(AP)
1.56 X 10
6
1.57 X 10
6
5.25 X 10
6

8.2 Remarks
·
There are no values of reference for this modeling. The results are to be compared with
those of modelings AXIS_FOURIER (A, B, D).
·
At the point B (located in the symmetry plane), one a:
rr
=
xx
,
=
yy
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SSLV303 - Roll embedded under actual weight and pressure
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Page:
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Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
9 Modeling
D
9.1
Characteristics of modeling D
AXIS_FOURIER, T6 meshs



Cutting:
80 elements according to the length
2 elements according to the radius
Loadings:
C1:
vertical gravity (Ug field)
C2:
pressure (Up field)
Components of displacements: U
R
(radial), U
Z
(axial), U
(circumferential)
Names of the nodes:
With = N1
B = N2
C = N3
D = N4
E = N249
F = N87

9.2
Characteristics of the mesh
A number of nodes: 805
A number of meshs and types: 320 TRIA6
R
B
With
E
F
C
D
Z
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V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
9.3 Functionalities
tested
Controls
“MECHANICAL” AFFE_MODELE “AXIS_FOURIER”
ALL
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
AFFE_CHAR_MECA_F FORCE_INTERN
CALC_CHAM_ELEM OPTION
MODE_FOURIER
“SIGM_ELNO_DEPL”
AFFE_CHAR_MECA_F PRES_REP
GROUP_MA
COMB_CHAM_NO
COMB_CHAM_ELEM
COMB_FOURIER
COMB_FOURIER
MACRO_ELAS_MULT CHAR_MECA_GLOBAL
CAS_CHARGE
MODE_FOURIER
TYPE_MODE
CHAR_MECA
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Titrate:
SSLV303 - Roll embedded under actual weight and pressure
Date
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15/07/03
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X. DESROCHES
Key
:
V3.04.303-A
Page:
15/16
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
10 Results of modeling D
10.1 Values
tested

Standard localization
of
value
Reference
Aster
% difference
Ug field
(for
= 0.)
Not E, F
U
R
(m)
U
(m)
3.566 X 10
­ 7
0.
3.535 X 10
­ 7
0.
­ 0.84
Not B
zz
(AP)
­ 2.496 X 10
5
­ 2.60 X 10
5
+
4.1
Up field
(for
= 0.)
Not E
U
R
(m)
­ 7.82 X 10
­ 6
­ 7.71 X 10
­ 6
1.4
Not F
­ 7.82 X 10
­ 6
­ 7.70 X 10
­ 6
1.5
Not B
rr
(AP)
zz
(AP)
(AP)
1.63 X 10
6
5.51 X 10
6
1.65 X 10
6
1.41 X 10
6
5.65 X 10
6
1.89 X 10
6
­ 13.4
2.7
14.7

10.2 Remarks
·
The values of reference for the pressure (Up field) are obtained in modeling C, with
to start from a model 3D.
·
The results obtained are identical to those of modelings A and B.

10.3 Contents of the file results
Displacements, stresses.
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Titrate:
SSLV303 - Roll embedded under actual weight and pressure
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15/07/03
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X. DESROCHES
Key
:
V3.04.303-A
Page:
16/16
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
11 Summary of the results
Maximum differences (in %) between modelings AXIS_FOURIER and modeling 3D, observed at the points E, F,
B (in the plan
= 0°), on the combined loading cases.

Localization
Variation
AXIS_FOURIER/3D
In (%)
Displacements U:
= U in 3D
= U
R
in AXI
NOT F
1.5
Stresses
zz
NOT B
2.8
Stresses
xx (3D)
=
rr (AXI)
NOT B
­ 14.1
Stresses
yy (3D)
=
(AXI)
NOT B
14.6

·
The results between modelings 3D on the one hand and AXIS_FOURIER on the other hand, are
concordant with regard to displacements (variation of 1.5%) and the bending stress
zz
(variation of 2.8%).
·
With embedding, the relation
xx
=
yy
= 0 involve:
xx
=
yy
=
-
1
zz
The relation of embedding is well checked at the point B, in modeling 3D.
·
In addition, at the point B, one has moreover:
xx
=
rr
yy
=
In modeling AXIS_FOURIER, the difference between the two stresses is approximately 25%.
·
The second calculation on model AXIS_FOURIER was carried out with a finer mesh:
4 elements in the thickness instead of 2, denser mesh in the vicinity of embedding AB
(total 800 TRIA6).
The variation observed on the stresses
rr
and
at point AB remains:
rr
= 1.51 X 10
6
,
= 2.08 X 10
6
(loading case combined).
The relation of embedding
xx
=
yy
thus is checked much better on the model 3D, with one
mesh in the thickness however coarse.