Code_Aster
®
Version
4.0
Titrate:
SSLP100 Stick in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B
Page:
1/8
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
Document: V3.02.100
SSLP100 - Stick in static substructure
Summary:
static Under-structuring: condensation of the matrices of rigidity and the loadings.
Linear behavior.
Plane model.
2 Modelings:
·
Model a: “ordinary” plan: it is the reference solution.
·
B: models with substructures.
Interest:
·
under-structuring on two levels,
·
rotation of the macronutrients and the loadings (following or not),
·
calculation of the fields inside the macronutrients.
The results of B are identical to those of A with 10
5
near.
Code_Aster
®
Version
4.0
Titrate:
SSLP100 Stick in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B
Page:
2/8
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
1
Problem of reference
1.1 Geometry
E
With
C
H
I
J
P4
G
N25
N11
N19
N27
N33
F
P1
B
y
X
4
N17
P2
4
3
1
N8
P3
45°
D
45°
45°
O
1.2
Material properties
E = 15. AP
= 0.3
1.3
Boundary conditions and loadings
·
[GH]: U + v = 0; N8, N17 and N25: U = v = 0; J: U = 2.0
·
loading case 1: pressure distributed on ADFH p = 10.0
·
loading case 2: N11, N19, N27, N33, P1: Fy = - 20.0
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
4.0
Titrate:
SSLP100 Stick in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B
Page:
3/8
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
This problem does not have a reference solution.
Modeling A is used as reference for modeling B.
2.2
Results of reference
Displacements U and v at the points P1, P2, P3, P4.
2.3
Uncertainty on the solution
The solution of “reference” depends on the space discretization of the model; this is why mesh
is drawn in [§1.1].
Modeling B must respect this mesh to lead to the same results as A.
Code_Aster
®
Version
4.0
Titrate:
SSLP100 Stick in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B
Page:
4/8
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
24 elements QUAD4, modeling:
“D_PLAN”
E
With
C
H
J
B
G
O
19
10
P1
7
4
5
8
6
9
30
11
12
28
24
26
25
27
22
23
21
15
17
13
16
18
20
14
P2
P3
1
3
2
33
32
31
29
35
36
34
P4
I
D
F
3.2
Characteristics of the mesh
A number of nodes: 36.
A number of meshs and types: 24 QUAD4
Code_Aster
®
Version
4.0
Titrate:
SSLP100 Stick in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B
Page:
5/8
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
P1 U
1.88327
P1 v
2.59224 10
2
P2 U
8.27372 10
2
case of
P2 v
8.27372 10
2
charge
P3 U
2.70375 10
1
n° 1
P3 v
5.69552 10
1
P4 U
5.17703 10
1
P4 v
5.43387 10
1
P1 U
1.71883
P1 v
6.04367
P2 U
4.60196 10
2
case of
P2 v
4.60196 10
2
charge
P3 U
2.26903 10
1
n° 2
P3 v
6.14296 10
1
P4 U
9.57110 10
1
P4 v
2.53878
4.2
Contents of the file results
Displacements
4.3 Parameters
of execution
Version:
3.02
Machine:
CRAY C90
System:
8.0 UNICOS
Overall dimension memory:
8 megawords
Time CPU To use:
4 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLP100 Stick in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B
Page:
6/8
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
E
With
C
H
J
B
G
O
P1
P2
P3
P4
I
D
F
Initial mesh
my
(level - 2 of the under-structuring) only the 12 QUAD4 contain of
IJBA
and
ABCD
.
macr_elem_stat
(
S_1
) is defined starting from the elements of
ABCD
. It
macr_elem_stat
is
digest on the nodes of
AB
and
CD
(level - 2).
With
B
my
I
J
D
C
With
B
C
D
S_1
Code_Aster
®
Version
4.0
Titrate:
SSLP100 Stick in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B
Page:
7/8
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
Mesh
ma_123
of level - 1 is defined while making turn 2 times
S_1
to represent the crown
ABCEGHFDA
.
With
B
H
G
ma_123
With
B
H
G
S_123
E
C
F
D
macr_elem_stat S_123
is defined starting from the substructures
ABCD
,
DCEF
and
FEGH
. It
macr_elem_stat
is condensed on the nodes of
AB
and
GH
.
Mesh
mag0
is defined by
macr_elem_stat S_123
.
Final mesh
mag
(level 0) is defined by the mesh
mag0
that one assembles (
ASSE_MAILLAGE
)
with the initial mesh
my
to recover the meshs of
IJBA
.
The resolution is then made on this final mesh, then one calculates displacements inside
macr_elem_stat
using the operator
DEPL_INTERN
.
With
B
H
G
mag0
With
B
H
G
mag
I
J
5.2
Characteristics of the mesh
A number of nodes: 20.
A number of meshs and types: 12 QUAD4
5.3 Functionalities
tested
Controls
Keys
MARCR_ELEM_STAT
DEFINITION
OUTSIDE
RIGI_MECA
[U4.44.01]
DEFI_MAILLAGE
DEFI_MAILLE
RECO_GLOBAL
DEFI_NOEUD
[U4.12.04]
AFFE_MODELE
AFFE_SOUS_STRUC
[U4.22.01]
ASSE_MAILLAGE
[U4.12.02]
DEPL_INTERN
[U4.65.01]
CALC_VECT_ELEM
SOUS_STRUC
[U4.41.02]
Code_Aster
®
Version
4.0
Titrate:
SSLP100 Stick in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B
Page:
8/8
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
P1 U
1.88327
1.88327
² 10
5
P1 v
2.59224 10
2
2.59224 10
2
² 10
5
P2 U
8.27372 10
2
8.27372 10
2
² 10
5
P2 v
8.27372 10
2
8.27372 10
2
² 10
5
P3 U
2.70375 10
1
2.70375 10
1
² 10
5
P3 v
5.69552 10
1
5.69552 10
1
² 10
5
P4 U
5.17703 10
1
5.17703 10
1
² 10
5
P4 v
5.43387 10
1
5.43387 10
1
² 10
5
P1 U
1.71883
1.71883
² 10
5
P1 v
6.04367
6.04367
² 10
5
P2 U
4.60196 10
2
4.60196 10
2
² 10
5
P2 v
4.60196 10
2
4.60196 10
2
² 10
5
P3 U
2.26903 10
1
2.26903 10
1
² 10
5
P3 v
6.14296 10
1
6.14296 10
1
² 10
5
P4 U
9.57110 10
1
9.57110 10
1
² 10
5
P4 v
2.53878
2.53878
² 10
5
6.2
Contents of the file results
Displacements.
6.3 Parameters
of execution
Version:
3.02
Machine:
CRAY C90
System:
8.0 UNICOS
Overall dimension memory:
8 megawords
Time CPU To use:
9 seconds
7
Summary of the results
Precision of the results obtained (error ² 10
5
) is natural because the static under-structuring is one
“exact” method (in infinite numerical precision).