Code_Aster
®
Version
4.0
Titrate:
SSLV07 Stretching of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D
Page:
1/10
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: V3.04.007
SSLV07 - Stretching 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).
Code_Aster
®
Version
4.0
Titrate:
SSLV07 Stretching of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D
Page:
2/10
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
L
has
B
B
C
D
Z
X
y
E
With
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 10
11
MPa
= 0.3
= 7.800 kg/m
3
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
1.4 Conditions
initial
Without object for the static analysis.
Code_Aster
®
Version
4.0
Titrate:
SSLV07 Stretching of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D
Page:
3/10
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 is that given in card SSLV07/89 of the guide VPCS which presents
method of calculation in the following way:
Displacements:
(
)
U
G X Z
E
v
G y Z
E
W
G Z
E
G
E
X
y
G L
E
= -
= -
=
+
+
-
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
2.2
Results of reference
Displacement of the points B, C, D and E.
Stresses
zz
in 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).
Code_Aster
®
Version
4.0
Titrate:
SSLV07 Stretching of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D
Page:
4/10
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:
Not A = N59
Not B = N53
Not C = N12
Not D = N18
Not E = N56
3.2
Characteristics of the mesh
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
Controls
Keys
AFFE_MODELE
“MECHANICAL”
“3D”
ALL
[U4.22.01]
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
GRAVITY
FORCE_FACE
GROUP_MA
CALC_CHAM_ELEM
OPTION
“SIGM_ELNO_DEPL”
[U4.61.01]
“EPOT_ELEM_DEPL”
POST_ELEM
ENER_POT
[U4.61.04]
Code_Aster
®
Version
4.0
Titrate:
SSLV07 Stretching of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D
Page:
5/10
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
Localization
Type of value
(m)
Reference
Aster
% difference
Not B
U
B
0.
< 10
14
-
V
B
0.
< 10
14
-
W
B
1.721655 10
6
1.7217 10
6
< 0.1
Not C
U
C
0.
= 10
14
-
V
C
0.
< 10
14
-
W
C
1.707308 10
6
1.7073 10
6
< 0.1
Not D
U
D
1.721655 10
7
1.7216 10
7
< 0.1
V
D
0.
< 10
14
-
W
D
1.434713 10
8
1.4324 10
8
0.2
Not E
U
E
0.
< 10
14
V
E
0.
< 10
14
W
E
1.291241 10
6
1.2913 10
6
< 0.1
(AP)
Not A
zz
2.29554 10
5
2.2956 10
5
< 0.1
Not E
zz
1.14777 10
5
1.14777 10
5
< 0.1
4.2 Remarks
Modeling in HEXA20 is completely acceptable for this coarse mesh.
4.3
Contents of the file results
Displacements and stresses. Potential energy by element.
4.4 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
System:
UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use:
4.26 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLV07 Stretching of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D
Page:
6/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
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
(NODE: WITH DX=0., DY=0., DZ=0. ), (NODE: 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 mesh
A number of nodes: 1053
A number of meshs and types: 768 HEXA8
5.3 Functionalities
tested
Controls
Keys
AFFE_MODELE
“MECHANICAL”
“3D”
ALL
[U4.22.01]
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_INTERN
GRAVITY
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.
Code_Aster
®
Version
4.0
Titrate:
SSLV07 Stretching of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D
Page:
7/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
6
Results of modeling B
6.1 Values
tested
Localization
Type of value
(m)
Reference
Aster
% difference
Not B
U
B
0.
< 10
15
-
V
B
0.
< 10
15
-
W
B
1.721655 10
6
1.7217 10
6
< 0.1
Not C
U
C
0.
3.7081 10
9
-
V
C
0.
< 10
15
-
W
C
1.707308 10
6
1.7095 10
6
0.13
Not D
U
D
1.721655 10
7
1.6846 10
7
2.2
V
D
0.
< 10
15
-
W
D
1.434713 10
8
1.2118 10
8
15.5
Not E
U
E
0.
< 10
15
-
V
E
0.
< 10
15
-
W
E
1.291241 10
6
1.2917 10
6
< 0.1
(AP)
Not A
zz
2.29554 10
5
2.1739 10
5
5.3
HEX12
relative error
1.15
1.148
0.17
HEX600
relative error
1.30
1.301
0.07
6.2 Remarks
The mesh 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 stresses. 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
Overall dimension memory:
8 megawords
Time CPU To use:
36.42 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLV07 Stretching of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D
Page:
8/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
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
(NODE: WITH DX=0., DY=0., DZ=0. ), (NODE: 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 mesh
A number of nodes: 1053
A number of meshs and types: 768 HEXA8
7.3 Functionalities
tested
Controls
Keys
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
AFFE_CHAR_MECA_F
FORCE_INTERN
FORCE_FACE
GROUP_MA
AFFE_MATERIAU
ALL
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“3D”
ALL
[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 the key word
FORCE_INTERN
in
AFFE_CHAR_MECA_F
.
Code_Aster
®
Version
4.0
Titrate:
SSLV07 Stretching of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D
Page:
9/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
8
Results of modeling C
8.1 Values
tested
Locali-
sation
Type of value
(m)
Reference
ASTER
% difference
Not B
U
B
0.
< 10
15
-
V
B
0.
< 10
15
-
W
B
1.721655 10
6
1.7217 10
6
< 0.1
Not C
U
C
0.
3.7081 10
9
-
V
C
0.
< 10
15
-
W
C
1.707308 10
6
1.7095 10
6
+0.13
Not D
U
D
1.721655 10
7
1.6846 10
7
2.15
V
D
0.
< 10
15
-
W
D
1.434713 10
8
1.2118 10
8
15.5
Not E
U
E
0.
< 10
15
-
V
E
0.
< 10
15
-
W
E
1.291241 10
6
1.2917 10
6
< 0.1
(AP)
Not A
zz
2.29554 10
5
2.1739 10
5
5.3
8.2 Remarks
The mesh remains insufficient for a modeling in HEXA8.
8.3
Contents of the file results
Displacements and stresses.
8.4 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
System:
UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use:
11.61 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLV07 Stretching of a parallelepiped under its own weight
Date:
21/01/98
Author (S):
X. DESROCHES
Key:
V3.04.007-D
Page:
10/10
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
9
Summary of the results
Type of value
(m)
Reference
Aster
Hexa20
(A)
Aster
Hexa8
(B)
U
B
0.
V
B
0.
W
B
1.721655 10
6
< 0.1%
< 0.1%
U
C
0.
X
V
C
0.
W
C
1.707308 10
6
< 0.1%
0.1%
U
D
1.721655 10
7
< 0.1%
2.2%
V
D
0.
W
D
1.434713 10
8
0.2%
15.5%
U
E
0.
V
E
0.
W
E
1.291241 10
6
< 0.1%
< 0.1%
(AP)
With
zz
2.29554 10
5
< 0.1%
5.3%
E
zz
1.14777 10
5
< 0.1%
< 0.1%
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 mesh much finer.