Code_Aster ®
Version
4.0
Titrate:
SSLP100 Crosse in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B Page:
1/8
Organization (S): EDF/IMA/MN
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
Document: V3.02.100
SSLP100 - Crosse 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 except for 10­5.
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLP100 Crosse in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B Page:
2/8
1
Problem of reference
1.1 Geometry
y
E
N27
N19
G
N25
N17
C
P2
4
N11
N8
F
P3
D
H
45° 45°
P4
45°
O
X
With
B
4
I
P1
N33
J
1
3
1.2
Material properties
E = 15. Pa
= 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.
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLP100 Crosse in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B Page:
3/8
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 grid
is drawn in [§1.1].
Modeling B must respect this grid to lead to the same results as A.
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLP100 Crosse in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B Page:
4/8
3 Modeling
With
3.1
Characteristics of modeling
24 elements QUAD4, modeling: “D_PLAN”
E
20
19
27
18
P2
17
C
G
12
28
25
9
16
26
15
23
11
6
8
24
13
14
21
3
5
F P3
H 22
2
D
1
4
7
10 P4
O
With
B
30
32
34
36
29
31
33
35
I
P1
J
3.2
Characteristics of the grid
A number of nodes: 36.
A number of meshs and types: 24 QUAD4
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLP100 Crosse in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B Page:
5/8
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
P1 U
1.88327
P1 v
2.59224 10­2
P2 U
­ 8.27372 10­2
case of
P2 v
8.27372 10­2
charge
P3 U
2.70375 10­1
n° 1
P3 v
5.69552 10­1
P4 U
5.17703 10­1
P4 v
5.43387 10­1
P1 U
1.71883
P1 v
­ 6.04367
P2 U
­ 4.60196 10­2
case of
P2 v
4.60196 10­2
charge
P3 U
2.26903 10­1
n° 2
P3 v
­ 6.14296 10­1
P4 U
­ 9.57110 10­1
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
Obstruction memory:
8 megawords
Time CPU To use:
4 seconds
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLP100 Crosse in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B Page:
6/8
5 Modeling
B
5.1
Characteristics of modeling
E
G
C
P2
F
H
P 3D
B
O
With
P4
I
J
P1
The initial grid my (level - 2 of the under-structuring) contains only the 12 QUAD4 of IJBA and
ABCD.
The macr_elem_stat (S_1) is defined starting from the elements of ABCD. This macr_elem_stat is
digest on the nodes of AB and CD (level - 2).
C
D
C
With
B
D
I
my
J
With
B
S_1
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLP100 Crosse in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B Page:
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The grid ma_123 of level - 1 is defined while making turn 2 S_1 times to represent the crown
ABCEGHFDA.
E
C
G
G
F
D
H
H
With
B
With
B
ma_123
S_123
The macr_elem_stat S_123 is defined starting from substructures ABCD, DCEF and FEGH. It
macr_elem_stat is condensed on the nodes of AB and GH.
The grid mag0 is defined by the macr_elem_stat S_123.
The final grid mag (level 0) is defined by the grid mag0 which one assembles (ASSE_MAILLAGE)
with the initial grid my to recover the meshs of IJBA.
The resolution is then made on this final grid, then one calculates displacements inside
macr_elem_stat using operator DEPL_INTERN.
G
H
With
B
G
mag
H
With
B
mag0
I
J
5.2
Characteristics of the grid
A number of nodes: 20.
A number of meshs and types: 12 QUAD4
5.3 Functionalities
tested
Commands
Keys
MARCR_ELEM_STAT
DEFINITION
EXTERIEUR
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]
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLP100 Crosse in static substructure
Date:
19/01/98
Author (S):
J. PELLET
Key:
V3.02.100-B Page:
8/8
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
P1 U
1.88327
1.88327
² 10­5
P1 v
2.59224 10­2
2.59224 10­2
² 10­5
P2 U
­ 8.27372 10­2
­ 8.27372 10­2
² 10­5
P2 v
8.27372 10­2
8.27372 10­2
² 10­5
P3 U
2.70375 10­1
2.70375 10­1
² 10­5
P3 v
5.69552 10­1
5.69552 10­1
² 10­5
P4 U
5.17703 10­1
5.17703 10­1
² 10­5
P4 v
5.43387 10­1
5.43387 10­1
² 10­5
P1 U
1.71883
1.71883
² 10­5
P1 v
­ 6.04367
­ 6.04367
² 10­5
P2 U
­ 4.60196 10­2
­ 4.60196 10­2
² 10­5
P2 v
4.60196 10­2
4.60196 10­2
² 10­5
P3 U
2.26903 10­1
2.26903 10­1
² 10­5
P3 v
­ 6.14296 10­1
­ 6.14296 10­1
² 10­5
P4 U
­ 9.57110 10­1
­ 9.57110 10­1
² 10­5
P4 v
­ 2.53878
­ 2.53878
² 10­5
6.2
Contents of the file results
Displacements.
6.3 Parameters
of execution
Version:
3.02
Machine:
CRAY C90
System:
8.0 UNICOS
Obstruction memory:
8 megawords
Time CPU To use:
9 seconds
7
Summary of the results
The precision of the results obtained (error ² 10­5) is natural because the static under-structuring is one
“exact” method (in infinite numerical precision).
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A