Code_Aster ®
Version
4.0
Titrate:
SSLV07 Etirement of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D Page:
1/10
Organization (S): EDF/IMA/MN
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
Document: V3.04.007
SSLV07 - Etirement of a parallelepiped
under its own weight
Summary:
This static test 3D makes it possible to validate the following functionalities:
· loading in actual weight (gravity or internal force) and in uniform pressure,
· calculation of the potential energy of the structure,
· estimator of error in residue (modeling B).
It includes/understands 3 modelings. Its interest lies in the description of the effect of the Poisson's ratio
(of contraction).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV07 Etirement of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D Page:
2/10
1
Problem of reference
1.1 Geometry
Z
B
With
D
y
E
L
B
C
X
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
0.
0.
0.5
0.5
0.
y
0.
0.
0.
0.
0.
Z
3.
0.
0.
3.
1.5
1.2
Material properties
E = 2 1011 MPa
= 0.3
= 7.800 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
1.4 Conditions
initial
Without object for the static analysis.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV07 Etirement of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D Page:
3/10
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is that given in card SSLV07/89 of the guide VPCS which presents
method of calculation in the following way:
Displacements:
G X Z
G y Z
G z2 G
G L2
U
= -
v
= -
W
=
+
(x2 + y2) -
E
E
2nd
2nd
2nd
Constraints:
=
=
=
=
=
=
zz
G Z
xx
yy
xy
yz
zx
0
Z
U
With
Of
D
L/2
E
L
B
C
It
X
W
wB
B'
2.2
Results of reference
Displacement of the points B, C, D and E.
Constraints zz of A and E.
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
S.P. TIMOSHENKO. Theory of elasticity. Paris. Polytechnic bookstore. CH. Béranger,
p.279 to 282 (1961).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV07 Etirement of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D Page:
4/10
3 Modeling
With
3.1
Characteristics of modeling
3D
Z
B
With
D
y
L
C
X
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:
Not A = N59
Not B = N53
Not C = N12
Not D = N18
Not E = N56
3.2
Characteristics of the grid
A number of nodes: 111
A number of meshs and types: 12 HEXA20
Files:
Aster: yes
IDEAS: not
ALI-BABA: not
3.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
“MECANIQUE”
“3D”
TOUT
[U4.22.01]
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
PESANTEUR
FORCE_FACE
GROUP_MA
CALC_CHAM_ELEM
OPTION
“SIGM_ELNO_DEPL”
[U4.61.01]
“EPOT_ELEM_DEPL”
POST_ELEM
ENER_POT
[U4.61.04]
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV07 Etirement of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D Page:
5/10
4
Results of modeling A
4.1 Values
tested
Localization
Type of value
Reference
Aster
% difference
(m)
Not B
UB
0.
< 1014
-
VB
0.
< 1014
-
WB
1.721655 106
1.7217 106
< 0.1
Not C
CPU
0.
= 1014
-
VC
0.
< 1014
-
WC
1.707308 106
1.7073 106
< 0.1
Not D
UD
1.721655 107
1.7216 107
< 0.1
VD
0.
< 1014
-
WD
1.434713 108
1.4324 108
0.2
Not E
EU
0.
< 1014
VE
0.
< 1014
WE
1.291241 106
1.2913 106
< 0.1
(Pa)
Not A
2.29554 105
2.2956 105
< 0.1
zz
Not E
1.14777 105
1.14777 105
< 0.1
zz
4.2 Remarks
Modeling in HEXA20 is completely acceptable for this coarse grid.
4.3
Contents of the file results
Displacements and constraints. Potential energy by element.
4.4 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
4.26 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:
SSLV07 Etirement of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D Page:
6/10
5 Modeling
B
5.1
Characteristics of modeling
3D
Cutting:
12 in height
8 in width and thickness
meshs HEXA8
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:
Not A = N533
Not B = N521
Not C = N989
Not D = N1001
Not E = N527
5.2
Characteristics of the grid
A number of nodes: 1053
A number of meshs and types: 768 HEXA8
5.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
“MECANIQUE”
“3D”
TOUT
[U4.22.01]
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_INTERN
PESANTEUR
AFFE_CHAR_MECA_F
FORCE_FACE
GROUP_MA
MECA_STATIQUE
OPTION
“SIGM_ELNO_DEPL”
[U4.31.01]
“EPOT_ELEM_DEPL”
CALC_ELEM
OPTION
“ERRE_ELGA_NORE”
[U4.61.02]
5.4 Remarks
This modeling makes it possible to test the estimator of error in residue in 3D.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV07 Etirement of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D Page:
7/10
6
Results of modeling B
6.1 Values
tested
Localization
Type of value
Reference
Aster
% difference
(m)
Not B
UB
0.
< 1015
-
VB
0.
< 1015
-
WB
1.721655 106
1.7217 106
< 0.1
Not C
CPU
0.
3.7081 109
-
VC
0.
< 1015
-
WC
1.707308 106
1.7095 106
0.13
Not D
UD
1.721655 107
1.6846 107
2.2
VD
0.
< 1015
-
WD
1.434713 108
1.2118 108
15.5
Not E
EU
0.
< 1015
-
VE
0.
< 1015
-
WE
1.291241 106
1.2917 106
< 0.1
(Pa)
Not A
2.29554 105
2.1739 105
5.3
zz
HEX12
relative error
1.15
1.148
0.17
HEX600
relative error
1.30
1.301
0.07
6.2 Remarks
The grid remains insufficient for a modeling in HEXA8. The total relative error is weak (3%)
but 20% exceed on certain meshs.
6.3
Contents of the file results
Displacements and constraints. Relative and absolute errors total by the estimator in residue. Errors
by element. Potential energy by element.
6.4 Parameters
of execution
Version:
3.02.11
Machine:
CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
36.42 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:
SSLV07 Etirement of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D Page:
8/10
7 Modeling
C
7.1
Characteristics of modeling
3D
Cutting:
12 in height
8 in width and thickness
meshs hexa8
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:
Not A = N533
Not B = N521
Not C = N989
Not D = N1001
Not E = N527
7.2
Characteristics of the grid
A number of nodes: 1053
A number of meshs and types: 768 HEXA8
7.3 Functionalities
tested
Commands
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
AFFE_CHAR_MECA_F
FORCE_INTERN
FORCE_FACE
GROUP_MA
AFFE_MATERIAU
TOUT
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“3D”
TOUT
[U4.22.01]
DEFI_MATERIAU
ELAS
[U4.23.01]
CALC_CHAM_ELEM
OPTION
“SIGM_ELNO_DEPL”
[U4.61.01]
7.4 Remarks
This modeling makes it possible to test key word FORCE_INTERN in AFFE_CHAR_MECA_F.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLV07 Etirement of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D Page:
9/10
8
Results of modeling C
8.1 Values
tested
Locali-
Type of value
Reference
ASTER
% difference
sation
(m)
Not B
UB
0.
< 1015
-
VB
0.
< 1015
-
WB
1.721655 106
1.7217 106
< 0.1
Not C
CPU
0.
3.7081 109
-
VC
0.
< 1015
-
WC
1.707308 106
1.7095 106
+0.13
Not D
UD
1.721655 107
1.6846 107
2.15
VD
0.
< 1015
-
WD
1.434713 108
1.2118 108
15.5
Not E
EU
0.
< 1015
-
VE
0.
< 1015
-
WE
1.291241 106
1.2917 106
< 0.1
(Pa)
Not A
2.29554 105
2.1739 105
5.3
zz
8.2 Remarks
The grid remains insufficient for a modeling in HEXA8.
8.3
Contents of the file results
Displacements and constraints.
8.4 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
11.61 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:
SSLV07 Etirement of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D Page:
10/10
9
Summary of the results
Type of value
Reference
Aster
Aster
(m)
Hexa20
Hexa8
(A)
(B)
UB
0.
VB
0.
WB
1.721655 106
< 0.1%
< 0.1%
CPU
0.
X
VC
0.
WC
1.707308 106
< 0.1%
0.1%
UD
1.721655 107
< 0.1%
2.2%
VD
0.
WD
1.434713 108
0.2%
15.5%
EU
0.
VE
0.
WE
1.291241 106
< 0.1%
< 0.1%
(Pa)
With
2.29554 105
< 0.1%
5.3%
zz
E
1.14777 105
< 0.1%
< 0.1%
zz
Modeling:
With (HEXA20 cutting: 3 in Z, 2 in X and Y)
B (HEXA8 cutting: 12 in Z, 8 in X and Y)
Modeling in HEXA8 would require a grid much finer.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A