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Titrate:
SSLS07 - Thin Cylindre under uniform axial loading

Date
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01/10/03
Author (S):
X. DESROCHES Key
:
V3.03.007-A Page:
1/8

Organization (S): EDF-R & D/AMA
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.007
SSLS07 - Thin Cylindre under axial loading
uniform

Summary:

The purpose of this test from guide VPCS (SSLS 07/89) is to validate a linear loading (FORCE_POUTRE) in
axisymmetric modeling.

One will use for that the 2 commands: AFFE_CHAR_MECA (modeling A) and AFFE_CHAR_MECA_F
(modeling B).
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

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Titrate:
SSLS07 - Thin Cylindre under uniform axial loading

Date
:
01/10/03
Author (S):
X. DESROCHES Key
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1
Problem of reference

1.1 Geometry

Average radius: Ro =
1m
Thickness
: H
= 0.02 m
Height
: L
= 4 m
Internal radius: IH =
Ro ­ H/2

1.2
Material properties

Young modulus
: E = 2.1 X 1011 Pa
Poisson's ratio: = 0.3

1.3
Boundary conditions and loadings

·
Axial displacement no one at the low end (U = 0) + conditions of symmetry
·
Uniform axial loading per unit of length Q = 10000 NR/m, applied at the high end



1.4 Conditions
initial

Without object for the static analysis.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

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SSLS07 - Thin Cylindre under uniform axial loading

Date
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X. DESROCHES Key
:
V3.03.007-A Page:
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2
Reference solution

2.1
Method of calculation used for the reference solution

Q
Axial stress:
=
11

H
Circumferential constraint:
0
22 =

qL
Lengthening of the cylinder: U X =

Eh
Q R

Radial displacement: U
O
R = -

Eh

2.2
Results of reference

11 = 5 X 105 Pa
U X = 9.52 X 10­6 m
U R = ­ 7.14 X 10­7 m

2.3
Uncertainty on the solution

Analytical solution.

2.4 Reference
bibliographical

[1]
Guide VPCS ­ Edition 1990 (SSLS 07/89)
[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-66/03/008/A

Code_Aster ®
Version
6.5
Titrate:
SSLS07 - Thin Cylindre under uniform axial loading

Date
:
01/10/03
Author (S):
X. DESROCHES Key
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V3.03.007-A Page:
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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 Ro of the axis

Cutting:
100 elements according to the height

1 element in the thickness


Limiting conditions: DY = 0
on AB



Loading:
Force distributed = 500 000
on CD


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_CONTOUR
GROUP_MA
CALC_CHAM_ELEM OPTION
“SIGM_ELNO_DEPL”

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
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Titrate:
SSLS07 - Thin Cylindre under uniform axial loading

Date
:
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4
Results of modeling A

4.1 Values
tested

Standard localization
of
value Référence Aster
% difference
Points G, H, I
ur (m)
­ 7.14 10­7
­ 7.14 10­7 0.
Points C, D, I
ux (m)
9.52 10­6
9.52 10­6 0.
Points A, B, C, D, E,
22 (Pa)
0.
10­6
-
F, G, H, I
Points A, B, C, D, E,
11 (Pa)
5. 10­5
5.00 105 0.
F, G, H, I

4.2 Notice

The Fy value provided corresponds to the pressure p = Q/h.

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

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Titrate:
SSLS07 - Thin Cylindre under uniform axial loading

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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 Ro of the axis

Cutting: 100 elements according to the height

1 element in the thickness

The load is broken up in the following way:

·
charge q1 varying linearly of 0 in D with 10000 NR/m out of C field of U1 displacements
·
charge q2 varying linearly of 10000 NR/m in D with 0 out of C field of U2 displacements

The results are given separately for each field U1 and U2.

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: 557
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_F FORCE_CONTOUR
GROUP_MA

AFFE_CHAR_MECA DDL_IMPO
GROUP_NO

CALC_CHAM_ELEM OPTION
“SIGM_ELNO_DEPL”

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
6.5
Titrate:
SSLS07 - Thin Cylindre under uniform axial loading

Date
:
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Author (S):
X. DESROCHES Key
:
V3.03.007-A Page:
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6
Results of modeling B

6.1 Values
tested

Fields Standard Localization
of Référence
Aster
% difference
value
U1
Not G (N51)
ur (m)
­ 3,583. 10­7
­ 3,5833. 10­7
0,009
Not H (N202)
­ 3,583. 10­7
­ 3,5833. 10­7
0,009
Not I (N503)
­ 1,012. 10­6
­ 1,0116. 10­7
­ 0,036

Not C (N452)
ux (m)
4,896. 10­6
4,8963. 10­6
0,007
Not D (N504)
4,658. 10­6
4,6583. 10­6
0,006
Not I (N503)
4,777. 10­6
4,7774. 10­6
0,009
U2
Not G
ur (m)
­ 3,559. 10­7
­ 3,5595. 10­7
0,015
Not H
­ 3,559. 10­7
­ 3,5595. 10­7
0,015
Not I
2,973. 10­7
2,9735. 10­7
0,017

Not C (N452)

4,627. 10­6
4,6275. 10­6
0,001
Not D (N504)
4,865. 10­6
4,8655. 10­6
0,011
Not I (N503)
4,746. 10­6
4,7464. 10­6
0,008

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
6.5
Titrate:
SSLS07 - Thin Cylindre under uniform axial loading

Date
:
01/10/03
Author (S):
X. DESROCHES Key
:
V3.03.007-A Page:
8/8

7
Summary of the results

Key word FORCE_CONTOUR used starting from 2 commands AFFE_CHAR_MECA and
AFFE_CHAR_MECA_F provides right results.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

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