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Code_Aster
®
Version
4.0
Titrate:
SSLV121 Stretching of a transverse isotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.121-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: V3.04.121
SSLV121 - Stretching of an isotropic parallelepiped
transverse 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 isotropic transverse.
modeling is three-dimensional. The model is similar to test VPCS SSLV07 (but in this case the material
is isotropic) and with test SSLV120 (in this case the material is orthotropic.).
Variations of the results obtained by
Aster
range between 0,00 and 0,2% of the calculated reference
analytically.
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Code_Aster
®
Version
4.0
Titrate:
SSLV121 Stretching of a transverse isotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.121-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 the xy plan and direction Z:
E_L
= 5. 1011 AP,
E_N
= 2. 1011 AP.
Poisson's ratios relating to the xy plan and direction Z:
_LT
= 0.1,
_LN
= 0.3.
Modulus of rigidity relating to direction Z:
G_LN
= 7.69231 1010 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
background image
Code_Aster
®
Version
4.0
Titrate:
SSLV121 Stretching of a transverse isotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.121-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 transverse isotropic elastic matrix). The analytical expression of the solution
is as follows:
Displacements:
(
)
U
Z
G X Z
E Z
v
Z
G y Z
E Z
W
G Z
E Z
G
E Z
Z X
zy
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).
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Code_Aster
®
Version
4.0
Titrate:
SSLV121 Stretching of a transverse isotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.121-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
L
has
B
With
C
D
Z
X
y
Cutting:
3 in height
2 in width and thickness
meshs hexa20
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_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“3D”
ALL
[U4.22.01]
DEFI_MATERIAU
ELAS_ISTR_FO
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Code_Aster
®
Version
4.0
Titrate:
SSLV121 Stretching of a transverse isotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.121-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
­ 1.72167210
­ 6
0.01
U
C
0.
= 10
­
14
-
V
C
0.
= 10
­
19
-
W
C
­ 1.707308 10
­ 6
­ 1.707325 10
­ 6
0.01
U
D
­ 1.721655 10
­ 7
­ 1.721649 10
­ 7
0.01
V
D
0.
= 10
­
23
-
W
D
1.434713 10
­ 8
1.432587 10
­ 8
0.2
U
E
0.
= 10
­ 22
V
E
0.
= 10
­ 23
W
E
­ 1.291241 10
­ 6
­ 1.291259 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
­ 1.721655 10
­ 7
­ 1.721649 10
­ 7
-
W
X
1.434712 10
­ 8
1.432587 10
­ 8
0.15
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:
4.25 seconds
background image
Code_Aster
®
Version
4.0
Titrate:
SSLV121 Stretching of a transverse isotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.121-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 fact that there is only one component of the stresses (
zz) in the problem only allows
to test 2 elastic coefficients (E_Z and NU_Z).
Although these coefficients are constant, they were introduced in the form of functions to test
functionality
ELAS_GITR_FO
.
The elastic coefficients in plan XY and direction Z 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 SSLV07) or orthotropic (test SSLV120). Numerically, these values are very close
those of these tests at the points considered (about 10
- 6
) the difference resulting from the mode of
construction of the matrices of stiffness in the various cases. As in point X, these values differ but
correspond well to the reference solution.