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SSLS09 - Thin Cylindre under actual weight
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:
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Organization (S): EDF-R & D/AMA
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.009
SSLS09 - Thin Cylindre under actual weight

Summary:

This test from guide VPCS (SSLS 09/89) aims to test a voluminal loading (here the weight
clean), in axisymmetric analysis, by using key word FORCE_INTERN.

One will use for that the two commands: AFFE_CHAR_MECA (modeling A) and AFFE_CHAR_MECA_F
(modeling B).

Modeling C tests the incompressible elements by using key word PESANTEUR on a loading
equivalent.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A

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SSLS09 - Thin Cylindre under actual weight
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1
Problem of reference

1.1 Geometry

Average radius: R
= 1m
Thickness
: H
= 0.02 m
Height
: L
= 4 m

1.2
Material properties

Young modulus
: E = 2.1 X 1011 Pa
Poisson's ratio: = 0.3
Voluminal weight
: = 7.85 X 104 NR/m3

1.3
Boundary conditions and loadings

·
Axial displacement no one at the low end (U = 0) + conditions of symmetry
·
Actual weight, according to the axis, direction + X

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A

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2
Reference solution

2.1
Method of calculation used for the reference solution

In a point of co-ordinate X:

- X-ray

· radial displacement: U R =

E
x2

· axial displacement: U X =

2nd
R

· rotation of a generator:
-
=

E
· axial stress:
= X

11

· circumferential constraint:
0
22 =


2.2
Results of reference

· Axial displacement high end: U X = 2.99 X 10­6 m
· Radial displacement low end: U R = ­ 4.49 X 10­7 m
· = ­ 1.12 X 10­7 rad
· 11 = 3.14 X 105 Pa, at the low end
·
0
22 =
. everywhere

2.3
Uncertainty on the solution

Analytical solution.

2.4 Reference
bibliographical

[1]
Guide VPCS ­ Edition 1990 (SSLS 09/89)
[2]
R.J. ROARK and W.C. YOUNG: Formulated for stress and strain, 5th edition, New York,
Mc Graw-Hill, 1975
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A

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3 Modeling
With

3.1
Characteristics of modeling

AXIS, T6 meshs and Q8


Position of the points:

·
E, F with middle height
·
G, H, I remote R of the axis

Cutting:
100 elements according to the height

1 element in the thickness


Limiting conditions: DY = 0 on AB


Loading:
Constant voluminal force equalizes with ­ 78500.

Name of the nodes:

Not A = N1
Not C = N452
Not E = N201
Not G = N51
Not I = N503
Not B = N101
Not D = N504
Not F = N203
Not H = N202


3.2
Characteristics of the grid

A number of nodes: 553
A number of meshs and types: 50 QUAD8, 100 TRIA6, 204 SEG3

3.3 Functionalities
tested

Commands


“MECHANICAL” AFFE_MODELE “AXIS”
TOUT
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
FORCE_INTERN
CALC_CHAM_ELEM OPTION
“SIGM_ELNO_DEPL”

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A

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4
Results of modeling A

4.1 Values
tested

Standard localization
of
value Référence Aster
% difference
Points C, D, I
ux (m)
2.99 10­6
2.99 10­6 0.
Not G
ur (m)
­ 4.49 10­7
­ 4.42 10­7 ­ 1.5
Not G
11 (Pa)
­ 3.14 105
­ 3.14 105 0.
Points A, B, G
22 (Pa)
0. <
40
-

4.2 Remarks

· The values of 22 data are not significant.
· Taking into account the grid (1 element in the thickness), the results are completely satisfactory.

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A

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5 Modeling
B

5.1
Characteristics of modeling

AXIS, T6 meshs and Q8


Position of the points:

·
E, F with middle height
·
G, H, I remote R of the axis

Cutting:
100 elements according to the height

1 element in the thickness


Limiting conditions: DY = 0 on AB


Loading:
Voluminal force in the form of a constant function defined in y = 0, 3, 6.

Name of the nodes:

Not A = N1
Not C = N452
Not E = N201
Not G = N51
Not I = N503
Not B = N101
Not D = N504
Not F = N203
Not H = N202


5.2
Characteristics of the grid

A number of nodes: 553
A number of meshs and types: 50 QUAD8, 100 TRIA6, 204 SEG3

5.3 Functionalities
tested

Commands


“MECHANICAL” AFFE_MODELE “AXIS”
TOUT
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO

AFFE_CHAR_MECA_F FORCE_INTERN


CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A

Code_Aster ®
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SSLS09 - Thin Cylindre under actual weight
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6
Results of modeling B

6.1 Values
tested

Standard localization
of
value Référence Aster
% difference
Points C, D, I
ux (m)
2.99 10­6
2.99 10­6 0.
Not G
ur (m)
­ 4.49 10­7
­ 4.42 10­7 ­ 1.5
Not G
11 (Pa)
­ 3.14 105
­ 3.14 105 0.
Points A, B, G
22 (Pa)
0. <
40
-

6.2 Remarks

· The values of 22 data are not significant.
· The results are identical to those of modeling A.

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A

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7 Modeling
C

7.1
Characteristics of modeling

AXIS_INCO, T6 meshs and Q8


Position of the points:

·
E, F with middle height
·
G, H, I remote R of the axis

Cutting:
100 elements according to the height

1 element in the thickness


Limiting conditions: DY = 0 on AB


Loading:
Gravity

Name of the nodes:

Not A = N1
Not C = N452
Not E = N201
Not G = N51
Not I = N503
Not B = N101
Not D = N504
Not F = N203
Not H = N202


7.2
Characteristics of the grid

A number of nodes: 553
A number of meshs and types: 50 QUAD8, 100 TRIA6, 204 SEG3

7.3 Functionalities
tested

Commands


“MECHANICAL” AFFE_MODELE “AXIS_INCO” ALL
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO

AFFE_CHAR_MECA GRAVITY


STAT_NON_LINE
COMP_ELAS
RELATION = “ELAS”

CALC_ELEM OPTION
“SIEF_ELNO_ELGA”

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A

Code_Aster ®
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Titrate:
SSLS09 - Thin Cylindre under actual weight
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8
Results of modeling C

8.1 Values
tested

Standard localization
of
value Référence Aster
% difference
Points C, D, I
ux (m)
2.99 10­6
2.99 10­6 0.
Not G
ur (m)
­ 4.49 10­7
­ 4.42 10­7 ­ 1.5
Not G
11 (Pa)
­ 3.14 105
­ 3.14 105 0.
Points A, B, G
22 (Pa)
0. <
40
-

8.2 Remarks

· The found values of 22 are not significant.
· The results are identical to those of modeling A and B.

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A

Code_Aster ®
Version
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Titrate:
SSLS09 - Thin Cylindre under actual weight
Date
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02/11/05
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X. DESROCHES Key
:
V3.03.009-B Page:
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9
Summary of the results

The use of a function for the definition of a constant density of volume charge is valid: results
are identical, whether one uses one or the other of 2 commands AFFE_CHAR_MECA or
AFFE_CHAR_MECA_F. An equivalent loading gravity gives the same results.
Moreover, the incompressible elements give the same results (modeling C).
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A

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