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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:
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
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:
2/8
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
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:
3/8
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
:
V3.03.007-A Page:
4/8
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
6.5
Titrate:
SSLS07 - Thin Cylindre under uniform axial loading
Date
:
01/10/03
Author (S):
X. DESROCHES Key
:
V3.03.007-A Page:
5/8
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
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:
6/8
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
:
01/10/03
Author (S):
X. DESROCHES Key
:
V3.03.007-A Page:
7/8
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
Outline document