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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
Date
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15/07/03
Author (S):
X. DESROCHES Key
:
V3.04.303-A Page:
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Organization (S): EDF-R & D/AMA
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
Document: V3.04.303
SSLV303 - Cylindre 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 key word PESANTEUR,
· modeling b: to validate 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 key word FORCE_INTERN defined to leave
of a function.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
Date
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Author (S):
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:
V3.04.303-A Page:
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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 1011 NR/m2
= 0.3
= 7800 kg/m3

1.3
Boundary conditions and loadings

· Sections AB, CD embedded
· Gravity according to R
: G = 9.81 m/s2
· Pressure given by: p = Po cos, Po = 10.000 NR/m2

1.4 Conditions
initial

Without object for the static analysis.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

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SSLV303 - Cylindre embedded under actual weight and pressure
Date
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:
V3.04.303-A Page:
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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:

Q 4
2
Z
L

ur =

- 3
Lz +
2
Z


12EI 2
2


Maximum displacement, in the median section, is worth:

3
PL
(
ur E) =
, P:
roll



clean

weight

384EI

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, (
ur E) = 0.3566 X 10­6 m
· Constraints of embedding at point b: zz = ­ 0.2496 X 106 Pa

2.3
Uncertainty on the solution

Analytical solution for gravity.

2.4 Reference
bibliographical

[1]
S. TIMOSHENKO: Resistance of materials, 1čre left. Polytechnic bookstore
CH. Béranger, Paris, 1947
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

Code_Aster ®
Version
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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
Date
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Author (S):
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:
V3.04.303-A Page:
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3 Modeling
With

3.1
Characteristics of modeling A

AXIS_FOURIER, T6 mesh

With
E
D
B
F
C
Z


R

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) Po = 10.000 NR/m2

Components of displacements: ur (radial), uz (axial), U (circumferential)

Names of the nodes:

With = N1
B = N2
C = N3
D = N4
E = N249
F = N87

3.2
Characteristics of the grid

A number of nodes: 805
A number of meshs and types: 320 TRIA6
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
Date
:

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:
V3.04.303-A Page:
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3.3 Functionalities
tested

Commands


“MECHANICAL” AFFE_MODELE “AXIS_FOURIER”
TOUT
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
PESANTEUR
CALC_CHAM_ELEM OPTION
“SIGM_ELNO_DEPL”
MODE_FOURIER
AFFE_CHAR_MECA_F PRES_REP
GROUP_MA

COMB_CHAM_NO
COMB_FOURIER


COMB_CHAM_ELEM
COMB_FOURIER
MACRO_ELAS_MULT CHAR_MECA_GLOBAL
MODE_FOURIER

CAS_CHARGE
TYPE_MODE
CHAR_MECA
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
Date
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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
ur (m)
3.566 X 10­7
3.541 X 10­7
­ 0.701
U (m)
0.
3.94 10­14
Not B
zz (Pa)
­ 2.496 X 105
­ 2.598 X 105 +
4.09
Up field




(for = 0.)
Not E
ur (m)
­ 7.82 X 10­6
­ 7.71 X 10­6 ­ 1.4
Not F

­ 7.82 X 10­6
­ 7.70 X 10­6 ­ 1.5
Not B
rr (Pa)
1.63 X 106
1.41 X 106
­ 13.4

5.51 X 106
5.65 X 106
2.7
zz (Pa)

1.65 X 106
1.89 X 106
14.7
(Pa)
Up field + Ug




(for = 0.)
Not E
ur (m)
­ 7.46 X 10­6
­ 7.358 X 10­6 ­ 1.3
Not F
ur (m)
­ 7.44 X 10­6
­ 7.348 X 10­6 ­ 1.2
Not B
rr (Pa)
1.56 X 106
1.34 X 106
­ 13.7

5.25 X 106
5.398 X 106
2.8
zz (Pa)

1.57 X 106
1.80 X 106
15.0
(Pa)

4.2 Remarks

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

4.3
Contents of the file results

Displacements, constraints.

Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

Code_Aster ®
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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
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5 Modeling
B

5.1
Characteristics of modeling B

AXIS_FOURIER, T6 meshs

With
E
D
B
F
C
Z


R

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 Pa
C2: pressure (Up field)

Components of displacements: ur (radial), uz (axial), U (circumferential)

Names of the nodes:

With = N1
B = N2
C = N3
D = N4
E = N249
F = N87

5.2
Characteristics of the grid

A number of nodes: 805
A number of meshs and types: 320 TRIA6
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
Date
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15/07/03
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V3.04.303-A Page:
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5.3 Functionalities
tested

Commands


“MECHANICAL” AFFE_MODELE “AXIS_FOURIER”
TOUT
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FORCE_INTERN
CALC_CHAM_ELEM OPTION
“SIGM_ELNO_DEPL”
MODE_FOURIER
AFFE_CHAR_MECA_F PRES_REP
GROUP_MA

COMB_CHAM_NO
COMB_FOURIER


COMB_CHAM_ELEM
COMB_FOURIER
MACRO_ELAS_MULT CHAR_MECA_GLOBAL
MODE_FOURIER

CAS_CHARGE
TYPE_MODE
CHAR_MECA
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

Code_Aster ®
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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
Date
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V3.04.303-A Page:
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6
Results of modeling B

6.1 Values
tested

Standard localization
of
value
Reference
Aster
% difference
Ug field




(for = 0.)
Not E, F
ur (m)
3.566 X 10­7
3.541 X 10­7
­ 0.70
U (m)
0.
0.
Not B
zz (Pa)
­ 2.496 X 105
­ 2.60 X 105 +
4.1
Up field




(for = 0.)
Not E
ur (m)
­ 7.82 X 10­6
­ 7.71 X 10­6 ­ 1.4
Not F

­ 7.82 X 10­6
­ 7.70 X 10­6 ­ 1.5
Not B
rr (Pa)
1.63 X 106
1.41 X 106
­ 13.4

5.51 X 106
5.65 X 106
2.7
zz (Pa)

1.65 X 106
1.89 X 106
14.7
(Pa)
Up field + Ug




(for = 0.)
Not E
ur (m)
­ 7.46 X 10­6
­ 7.358 X 10­6 ­ 1.3
Not F
ur (m)
­ 7.46 X 10­6
­ 7.348 X 10­6 ­ 1.5
Not B
rr (Pa)
1.56 X 106
1.34 X 106
­ 13.7

5.25 X 106
5.398 X 106
2.8
zz (Pa)

1.57 X 106
1.80 X 106
15.0
(Pa)

6.2 Remarks

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

6.3
Contents of the file results

Displacements, constraints.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

Code_Aster ®
Version
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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
Date
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:
V3.04.303-A Page:
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7 Modeling
C

7.1
Characteristics of modeling C

3D, Mailles H20 and P15
Z
F
WITH, E
y, v
B
B, F
X
y

X, U

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 modelled.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

Code_Aster ®
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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
Date
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Author (S):
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:
V3.04.303-A Page:
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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.
The pressure being in “Cos”, it is supposed to be uniform on each line. For any point of


the surface of angle, (ranging between 1 and 2, 1 = (N ­ 1)
,
, 1 N 8, the value of
8
2 = N 8
pressure assigned to the line of elements containing this point is taken equalizes with:
p0 (cos
2
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 grid

A number of nodes: 1285
A number of meshs and types: 160 HEXA20, 80 PENTA15

7.3 Functionalities
tested

Commands


“MECHANICAL” AFFE_MODELE “AXIS_FOURIER”
TOUT
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO

FORCE_INTERN
GROUP_MA
PESANTEUR
AFFE_CHAR_MECA_F PRES_REP
GROUP_MA

CALC_CHAM_ELEM OPTION
SIGM_ELNO_DEPL
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

Code_Aster ®
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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
Date
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:
V3.04.303-A Page:
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8
Results of modeling C

8.1 Values
tested

Standard localization
of
value
Reference
Aster
% difference
Up field




Not E
U (m)

­ 7.82 X 10­6

v (m)
0.
10­21
Not F
U (m)

­ 7.816 X 10­6

v (m)
0.
10­21
Not B
xx (Pa)

1.63 X 106


1.65 X 106
yy (Pa)

5.51 X 106
zz (Pa)
Up field + Ug




Not E
U (m)

­ 7.46 X 10­6

v (m)
0.
10­21
Not F
U (m)

­ 7.44 X 10­6

v (m)
0.
10­21
Not B
xx (Pa)

1.56 X 106


1.57 X 106
yy (Pa)

5.25 X 106
zz (Pa)

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

Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

Code_Aster ®
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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
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9 Modeling
D

9.1
Characteristics of modeling D

AXIS_FOURIER, T6 meshs

With
E
D
B
F
C
Z


R

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: ur (radial), uz (axial), U (circumferential)

Names of the nodes:

With = N1
B = N2
C = N3
D = N4
E = N249
F = N87

9.2
Characteristics of the grid

A number of nodes: 805
A number of meshs and types: 320 TRIA6
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

Code_Aster ®
Version
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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
Date
:

15/07/03
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9.3 Functionalities
tested

Commands


“MECHANICAL” AFFE_MODELE “AXIS_FOURIER”
TOUT
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO

AFFE_CHAR_MECA_F FORCE_INTERN


CALC_CHAM_ELEM OPTION
“SIGM_ELNO_DEPL”
MODE_FOURIER
AFFE_CHAR_MECA_F PRES_REP
GROUP_MA

COMB_CHAM_NO
COMB_FOURIER


COMB_CHAM_ELEM
COMB_FOURIER
MACRO_ELAS_MULT CHAR_MECA_GLOBAL
MODE_FOURIER

CAS_CHARGE
TYPE_MODE
CHAR_MECA
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

Code_Aster ®
Version
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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
Date
:

15/07/03
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:
V3.04.303-A Page:
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10 Results of modeling D

10.1 Values
tested

Standard localization
of
value
Reference
Aster
% difference
Ug field




(for = 0.)
Not E, F
ur (m)
3.566 X 10­7
3.535 X 10­7
­ 0.84
U (m)
0.
0.
Not B
zz (Pa)
­ 2.496 X 105
­ 2.60 X 105 +
4.1
Up field




(for = 0.)
Not E
ur (m)
­ 7.82 X 10­6
­ 7.71 X 10­6 1.4
Not F

­ 7.82 X 10­6
­ 7.70 X 10­6 1.5
Not B
rr (Pa)
1.63 X 106
1.41 X 106
­ 13.4

5.51 X 106
5.65 X 106
2.7
zz (Pa)

1.65 X 106
1.89 X 106
14.7
(Pa)

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, constraints.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

Code_Aster ®
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Titrate:
SSLV303 - Cylindre embedded under actual weight and pressure
Date
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:
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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:
NOT F
1.5
= U in 3D
= ur in AXI
Constraints zz
NOT B
2.8
Constraints xx (3D)
NOT B
­ 14.1
= rr (AXI)
Constraints yy (3D)
NOT B
14.6
= (AXI)

· 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 involves:


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 constraints is approximately 25%.

· The second calculation on model AXIS_FOURIER was carried out with a finer grid:
4 elements in the thickness instead of 2, denser grid in the vicinity of embedding AB
(total 800 TRIA6).
The variation observed on the constraints rr and at point AB remains: rr = 1.51 X 106, = 2.08 X 106
(loading case combined).
The relation of embedding xx = yy thus is checked much better on the model 3D, with one
grid in the thickness however coarse.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A

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