Code_Aster
®
Version
8.2
Titrate:
SSNL102 - Non-linear behavior of an assembly of angles
Date:
02/11/05
Author (S):
G. DEVESA
Key
:
V6.02.102-B
Page:
1/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/05/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.102
SSNL102 - Non-linear behavior of one
assembly of angles
Summary:
One considers in this test a discrete element with 2 nodes subjected to a two-dimensional loading of traction and
from moment requesting the degrees of freedom in translation and rotation.
The analysis is static with a nonlinear relation of behavior incrémentable expressed by one
adimensional internal variable combining the two-dimensional efforts and generalized displacements.
The relation of behavior includes/understands 2 mechanisms respectively associated with 2 curves being connected
between them by a dishing.
The interest of the test is to simulate in an exhaustive way the possible ways of loading in load and
discharge and in particular the transition between mechanisms.
The results correspond to the numerical solution in displacements of the problem with 1 unknown factor (the variable of
mechanism running) obtained by the inversion of the curve of the relation of behavior in each one of
2 mechanisms compared to an imposed force.
Code_Aster
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Version
8.2
Titrate:
SSNL102 - Non-linear behavior of an assembly of angles
Date:
02/11/05
Author (S):
G. DEVESA
Key
:
V6.02.102-B
Page:
2/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
1 discrete element of null size to 2 nodes.
Identify local = total reference mark.
1 matrix of rigidity
“K_TR_D_L'
affected by defect (partner to 1 element
DIS_TR_L
)
1.6 NR/mm in translation, 1.9 NR/mm in rotation.
Characteristics of rigidity according to local directions'
X
and rotation around
y
are modified
by a relation of behavior of the type
“ASSE_CORN”
introduced by a characteristic material.
1.2
Material properties
Dependant on an incremental behavior
“ASSE_CORN”
including/understanding 2 mechanisms requiring each one
5 characteristic parameters (see [1.2-a] and [1.2-b]):
NR
1
= 10.050 NR,
M
1
= 150.000 N.mm,
U
1
= 1 mm,
1
= 6,7 10
- 2
,
C
1
= 0,95
NR
2
= 50.000 NR,
M
2
= 750.000 N.mm,
U
2
= 10 mm,
2
= 0,01,
C
2
= 0,95
0
0
U
1
U
2
Normal effort
mechanism 1
butted
SLF
SLU
mechanism 2
Displacement
0
0
Moment/y
mechanism 1
butted
SLF
SLU
mechanism 2
Rotation
2
1
Appear 1.2-a: Mechanisms of assembly in normal effort and moment
()
()
R p
N
m
p
N
m
R p
U
R
R
=
+
=
2
2
&
&
&
Code_Aster
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Version
8.2
Titrate:
SSNL102 - Non-linear behavior of an assembly of angles
Date:
02/11/05
Author (S):
G. DEVESA
Key
:
V6.02.102-B
Page:
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Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/05/005/A
N m
m
N
1
criterion
kinematics
1
U
R
R
N
= Nx/NR
m
= My/M
U
R
= U/U
R
=
/
Appear 1.2-b: Relation of behavior of assembly
()
()
&
&
&
'
'
'
'
p
U
p
R
p
H p
C
C
p
p
R
R
=
+
=
=
=
- -
-
2
2
1
2
2
1
1
1.3
Boundary conditions and loadings
Embedding in one of the 2 nodes.
Force imposed in the direction
X
by unit of 1.000 NR and Moment imposed around the axis
Z
by
unit of 3.000 NR. the whole on the second node, by increments of load.
1.4 Conditions
initial
Internal displacements, efforts and variables null.
Code_Aster
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Version
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Titrate:
SSNL102 - Non-linear behavior of an assembly of angles
Date:
02/11/05
Author (S):
G. DEVESA
Key
:
V6.02.102-B
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Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/05/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
One reproduces on an element a course of loading (growing and in discharge) in each one of
2 mechanisms of assembly of the bidirectional relation of behavior (effort according to the direction
X
and moment around the axis
y
). The aforementioned expresses the displacements reduced compared to the efforts
reduced. The mechanisms and the law of behavior of assembly are described on the figures
[Figure 1.2-a] and [Figure 1.2-b].
The way of load expressed in
()
(
)
p
R p
1
1
,
comprise 12 stages thus definite:
8
7
6
5
4
Mechanism 2
R p 1
(
)
3
2
1
Mechanism 1
p1
= 1
p 1
11
12
10
9
2.2
Results of reference
To find the correspondence variable-criterion of the limiting curve of the relation of behavior.
2.3
Uncertainty on the solution
Numerical solution of the inversion of a non-linear relation. There is an unknown factor at the same time: the variable
intern of the mechanism. The other values result some. Calculation is direct for the 1st mechanism,
incremental for the second (discussion in the synthesis in [§5]).
2.4 References
bibliographical
[1]
P. PENSERINI: “Modeling of the assemblies bolted in the webmasts”. Note
HM-77/93/287
Code_Aster
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Version
8.2
Titrate:
SSNL102 - Non-linear behavior of an assembly of angles
Date:
02/11/05
Author (S):
G. DEVESA
Key
:
V6.02.102-B
Page:
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Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/05/005/A
3 Modeling
With
3.1
Characteristics of modeling
An element
DIS_TR_L
with 2 nodes of null size (idem 1.1).
A node N2: all is locked.
A N3 node: one imposes
F
X
by pitches of 1.000 NR and
M
y
by pitches of 3.000 N.mm with the card of
time:
T 0. 1. 2. 3. 4. 6. 8. 10.
11. 12.
0. 6. 7 17. 40. 20. 42 0. - 6
.
- 17.
3.2
Characteristics of the mesh
1 SEG2.
2 nodes.
3.3 Functionalities
tested
Controls Key word
factor
Key word
DEFI_MATERIAU ASSE_CORN
STAT_NON_LINE COMP_INCR
RELATION
=
ASSE_CORN
Code_Aster
®
Version
8.2
Titrate:
SSNL102 - Non-linear behavior of an assembly of angles
Date:
02/11/05
Author (S):
G. DEVESA
Key
:
V6.02.102-B
Page:
6/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/05/005/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
Displacement UX, N3 Node, Command 2
9.468
10
2
9.468
10
2
(Direct Calculation and
Displacement DRY, N3 Node, Command 2
1.275
10
3
1.275
10
3
exact)
Displacement UX, N3 Node, Command 8
3.7366
3.7366
Incremental calculation
Displacement DRY, N3 Node, Command 8
1.3754
10
2
1.3754
10
2
exact
Displacement UX, N3 Node, Command 12
2.6799
2.6799
Incremental calculation
Displacement DRY, N3 Node, Command 12
5.3598
10
4
5.3598
10
4
exact
Variable interns 1, Noeud N3, Ordre 2
9.6574
10
2
9.6574
10
2
Exact direct calculation
Variable interns 1, Noeud N3, Ordre 3
1.07417
1.07417
Incremental calculation
exact
Variable interns 1, Noeud N3, Ordre 11
9.6574 10
2
9.6574
10
2
Incremental calculation
exact
Variable interns 1, Noeud N3, Ordre 12
1.07417
1.07417
Incremental calculation
exact
4.2 Notice
The reference solution is the numerical solution of a problem to an unknown factor determined by
Code_Aster.
5
Summary of the results
The interest of the test is to represent the exhaustiveness of the possible ways of loadings with
multiple factors of change of incline: load-discharge, transition from mechanism.
On the other hand, the dimension of the problem makes it possible to have only one unknown factor (the internal variable
current), solution of the inversion of the curve of the law of behavior: direct solution for 1st
mechanism and incremental for the second.
The reduction of the problem makes it possible (if one converges) to trust Aster like “slide rule” and
to regard the result as a numerical solution “exact”.