Code_Aster ®
Version
4.0
Titrate:
SSLV120 Etirement of an orthotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.120-C Page:
1/6
Organization (S): EDF/IMA/MN
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
Document: V3.04.120
SSLV120 - Etirement of a parallelepiped
orthotropic under its own weight
Summary:
This test of mechanics of the structures allows the evaluation of displacements and the constraints of one
parallelepiped becoming deformed under its own weight. The material is elastic linear orthotropic.
modeling is three-dimensional. The model is similar to test VPCS SSLV07 (but in this case the material
is isotropic) and with test SSLV121 (in this case the material is isotropic transverse).
The variations of the results obtained by Aster range between 0,00 and 0,5% of the calculated reference
analytically.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV120 Etirement of an orthotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.120-C Page:
2/6
1
Problem of reference
1.1 Geometry
Z
X
.
B
With
D
y
E
L
B
X
C
has
Height: L = 3 m
Width: has = 1 m
Thickness: B = 1 m
Co-ordinates of the points (in meters):
With
B
C
D
E
X
X
0.
0.
0.5
0.5
0.
0.
y
0.
0.
0.
0.
0.
0.5
Z
3.
0.
0.
3.
1.5
3.
1.2
Material properties
YOUNG moduli in directions X, y and Z:
E_L = 5. 1011 Pa, E_T = 5. 1011 Pa, E_N = 2. 1011 Pa.
Poisson's ratios in the xy plans, xz and yz:
_LT = 0.1, _LN = 0.3, _TN = 0.1.
Moduli of rigidity in the xy plans, xz and yz:
G_LT = 7.69231 1010 Pa, G_LN = 7.69231 1010 Pa,
G_TN = 7.69231 1010 Pa.
Density: = 7800 kg/m3.
1.3
Boundary conditions and loadings
Not a: (U = v = W = 0, X = y = Z = 0)
Actual weight following axis Z
Uniform constraint with traction for the higher face:
Z = gL = + 229.554. Pa
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV120 Etirement of an orthotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.120-C Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution results from that given in card SSLV07/89 of guide VPCS (in
considering in more one orthotropic elastic matrix). The analytical expression of the solution is
following:
Displacements:
_ xz G X Z
_ yz G y Z
G z2 G
G L2
U = -
v = -
W = -
+
(_xzx2 +_yzy2) -
E_ Z
E_ Z
2e_ Z
2e_ Z
2e_ Z
Constraints:
=
=
=
=
=
=
zz
G Z
xx yy xy yz zx 0
Z
X U
.
With
Of
D
L/2
E
L
B
C
X
It
W wB
B'
2.2
Results of reference
Displacement of the points B, C, D, E and X.
Constraints zz of A and E
2.3
Uncertainty on the solution
Exact analytical results.
2.4 References
bibliographical
[1]
TIMOSHENKO (S.P) Théorie of elasticity - Paris - Librairie Polytechnique CH. Béranger,
p.279 to 282 (1961)
[2]
S.W. TSAI, H.T. HAHN - Introduction to composite materials. Technomic Publishing Company
(1980).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV120 Etirement of an orthotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.120-C Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
3D meshs hexa20
Z
B
With
D
y
L
C
X
has
Cutting:
3 in height
2 in width and thickness
Limiting conditions:
on axis AB
DDL_IMPO: (GROUP_NO:ABsansA DX=0., DY=0. )
in A and D
(NOEUD:WITH DX=0., DY=0., DZ=0. )
(NOEUD:D DY=0.)
Names of the nodes:
With = N59
B = N53
C = N12
D = N18
E = N56
X = N70
3.2
Characteristics of the grid
A number of nodes: 111
A number of meshs and types: 12 HEXA20
3.3 Functionalities
tested
Commands
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
PESANTEUR
FORCE_FACE
GROUP_MA
AFFE_MODELE
“MECANIQUE”
“3D”
TOUT
[U4.22.01]
DEFI_MATERIAU
ELAS_ORTH
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV120 Etirement of an orthotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.120-C Page:
5/6
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
UB
0.
1022
-
VB
0.
1022
-
WB
1.721655106
1.721674106
0.01
CPU
0.
= 1014
-
VC
0.
= 1019
-
WC
1.707308 106
1.707326 106
0.01
UD
1.721655 107
1.721652 107
0.01
VD
0.
= 1023
-
WD
1.434713 108
1.432400 108
0.2
EU
0.
= 1022
VE
0.
= 1022
WE
1.291241 106
1.291260 106
0.01
(Pa)
zz (A)
2.29554 105
2.2956 105
< 0.01
zz (E)
1.14777 105
1.14777 105
< 0.01
zz (X)
2.29554 105
2.29549 105
< 0.01
UX
0.
1020
-
VX
5.738850 108
5.738740 108
0.01
WX
4.782375 109
4.759220 109
0.5
4.2 Remarks
Modeling in HEXA20 is completely acceptable for this coarse grid.
4.3 Parameters
of execution
Version: 3.04.00
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 MW
Time CPU To use:
4.99 seconds
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV120 Etirement of an orthotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.120-C Page:
6/6
5
Summary of the results
The results concerning displacements and the constraints are very close to the solution
analytical with adopted modeling (< 0.2% for displacements, < 0.5% for the constraints).
The elastic coefficients in the 3 directions of orthotropism were selected so as to obtain them
same values of displacements at the points B, C, D and E that those calculated for a material
isotropic (test SSLV007) or isotropic transverse (test SSLV121). Numerically, these values are very
close relations of those of these tests at the points considered (of about a 10-6) the difference resulting from
method of construction of the matrices of rigidity in the various cases. As in point X, these values differ
but correspond well to the reference solution.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A