Code_Aster ®
Version
4.0
Titrate:
SSLV121 Etirement of a transverse isotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.121-C Page:
1/6
Organization (S): EDF/IMA/MN
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
Document: V3.04.121
SSLV121 - Etirement of an isotropic parallelepiped
transverse 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 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.).
The variations of the results obtained by Aster range between 0,00 and 0,2% 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:
SSLV121 Etirement of a transverse isotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.121-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 the xy plan and direction Z:
E_L = 5. 1011 Pa, E_N = 2. 1011 Pa.
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 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:
SSLV121 Etirement of a transverse isotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.121-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 transverse isotropic elastic matrix). The analytical expression of the solution
is as follows:
Displacements:
_ Z G X Z
_ Z G y Z
G z2 G
G L2
U = -
v = -
W = -
+
(_zx2 +_zy2) -
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:
SSLV121 Etirement of a transverse isotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.121-C Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
3D
Z
B
With
D
y
L
X
C
has
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
(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_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“3D”
TOUT
[U4.22.01]
DEFI_MATERIAU
ELAS_ISTR_FO
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLV121 Etirement of a transverse isotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.121-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
­ 1.72167210­6
0.01
CPU
0.
= 10­14
-
VC
0.
= 10­19
-
WC
­ 1.707308 10­6
­ 1.707325 10­6
0.01
UD
­ 1.721655 10­7
­ 1.721649 10­7
0.01
VD
0.
= 10­23
-
WD
1.434713 10­8
1.432587 10­8
0.2
EU
0.
= 10­22
VE
0.
= 10­23
WE
­ 1.291241 10­6
­ 1.291259 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
­ 1.721655 10­7
­ 1.721649 10­7
-
WX
1.434712 10­8
1.432587 10­8
0.15
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:
4.25 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:
SSLV121 Etirement of a transverse isotropic parallelepiped
Date:
26/01/98
Author (S):
G. DEBRUYNE
Key:
V3.04.121-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 fact that there is only one component of the constraints (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 (of about a 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.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A