Code_Aster
®
Version
4.0
Titrate:
SSLV120 Stretching of an orthotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.120-C
Page:
1/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
Document: V3.04.120
SSLV120 - Stretching of a parallelepiped
orthotropic under its own weight
Summary:
This test of mechanics of the structures allows the evaluation of displacements and the stresses 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).
Variations of the results obtained by
Aster
range between 0,00 and 0,5% of the calculated reference
analytically.
Code_Aster
®
Version
4.0
Titrate:
SSLV120 Stretching of an orthotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.120-C
Page:
2/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
1
Problem of reference
1.1 Geometry
Height: L = 3 m
Width: has = 1 m
Thickness: B = 1 m
L
has
B
With
B
C
D
Z
X
y
E
X
.
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. 10
11
AP,
E_T
= 5. 10
11
AP,
E_N
= 2. 10
11
AP.
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 10
10
AP,
G_LN
= 7.69231 10
10
AP,
G_TN
= 7.69231 10
10
AP.
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 stress with traction for the higher face:
Z
=
gL = + 229.554. AP
Code_Aster
®
Version
4.0
Titrate:
SSLV120 Stretching of an orthotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.120-C
Page:
3/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
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:
(
)
U
xz
G X Z
E Z
v
yz
G y Z
E Z
W
G Z
E Z
G
E Z
xz X
yzy
G L
E Z
= -
= -
= -
+
+
-
_
_
_
_
_
_
_
_
_
2
2
2
2
2
2
2
Stresses:
zz
xx
yy
xy
yz
zx
G Z
=
=
=
=
=
=
0
W
X
U
B
B'
C
It
E
With
D
Of
L/2
L
Z
W
B
X
.
2.2
Results of reference
Displacement of the points B, C, D, E and X.
Stresses
zz
in A and E
2.3
Uncertainty on the solution
Exact analytical results.
2.4 References
bibliographical
[1]
TIMOSHENKO (S.P) Theory of elasticity - Paris - Polytechnic Bookstore CH. Béranger,
p.279 to 282 (1961)
[2]
S.W. TSAI, H.T. HAHN - Introduction to composite materials. Technomic Publishing Company
(1980).
Code_Aster
®
Version
4.0
Titrate:
SSLV120 Stretching of an orthotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.120-C
Page:
4/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
3D meshs hexa20
L
has
B
With
C
D
Z
X
y
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
(NODE:WITH DX=0., DY=0., DZ=0. )
(NODE:D DY=0.)
Names of the nodes:
With = N59
B = N53
C = N12
D = N18
E = N56
X = N70
3.2
Characteristics of the mesh
A number of nodes: 111
A number of meshs and types: 12 HEXA20
3.3 Functionalities
tested
Controls
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
GRAVITY
FORCE_FACE
GROUP_MA
AFFE_MODELE
“MECHANICAL”
“3D”
ALL
[U4.22.01]
DEFI_MATERIAU
ELAS_ORTH
Code_Aster
®
Version
4.0
Titrate:
SSLV120 Stretching of an orthotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.120-C
Page:
5/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
U
B
0.
10
22
-
V
B
0.
10
22
-
W
B
1.72165510
6
1.72167410
6
0.01
U
C
0.
= 10
14
-
V
C
0.
= 10
19
-
W
C
1.707308 10
6
1.707326 10
6
0.01
U
D
1.721655 10
7
1.721652 10
7
0.01
V
D
0.
= 10
23
-
W
D
1.434713 10
8
1.432400 10
8
0.2
U
E
0.
= 10
22
V
E
0.
= 10
22
W
E
1.291241 10
6
1.291260 10
6
0.01
(AP)
zz
(A)
2.29554 10
5
2.2956 10
5
< 0.01
zz
(E)
1.14777 10
5
1.14777 10
5
< 0.01
zz
(X)
2.29554 10
5
2.29549 10
5
< 0.01
U
X
0.
10
20
-
V
X
5.738850 10
8
5.738740 10
8
0.01
W
X
4.782375 10
9
4.759220 10
9
0.5
4.2 Remarks
Modeling in HEXA20 is completely acceptable for this coarse mesh.
4.3 Parameters
of execution
Version: 3.04.00
Machine: CRAY C90
System:
UNICOS 8.0
Overall dimension memory:
8 MW
Time CPU To use:
4.99 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLV120 Stretching of an orthotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.120-C
Page:
6/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
5
Summary of the results
The results concerning displacements and the stresses are very close to the solution
analytical with adopted modeling (< 0.2% for displacements, < 0.5% for the stresses).
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 (about 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.