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Code_Aster
®
Version
7.4
Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
1/18
Manual of Reference
R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
Organization (S):
EDF-R & D/AMA, LME















Manual of Reference
R5.03 booklet: Nonlinear mechanics
Document: R5.03.32



Law of behavior of the assembly
ASSE_CORN


Summary:


This document describes the nonlinear behavior of the nonlinear assemblies of angles of pylons
modelized by discrete elements
DIS_TR
. This law of behavior is affected on the discrete elements
by means of the relation
ASSE_CORN
called by the operators of resolution of nonlinear problems
STAT_NON_LINE
[R5.03.01] or
DYNA_NON_LINE
[R5.05.05].

The law represents at the same time behavior in traction of the assembly and the relation moment-rotation around
the axis of the bolts perpendicular to the assembly. The other directions of loading present one
linear elastic behavior describes by conventional characteristics of rigidity.

One distinguishes in the law from behavior two phases associated with two mechanisms: the first
representing the friction and the slip of the bolts until the stop, and the second representing
plasticization of the assembly until the ruin. The laws of the plastic type describing each one of these phases have
even pace and have a dishing at their connection which makes convergence problematic and
require a particular digital processing in the options of calculation to which the method appeals
iterative of Newton.

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Code_Aster
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Version
7.4
Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
2/18
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R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
Count
matters
1
Notations ................................................................................................................................................ 3
2
Physical model of the one-way behavior of the assembly ................................................... 5
3
Relation of behavior of the mechanisms ......................................................................................... 7
3.1
One-way behavior ......................................................................................................... 7
3.2
Incremental two-dimensional behavior .................................................................................... 8
4
Establishment in Code_Aster ......................................................................................................... 11
4.1
Formulation in sizes reduced in loading ....................................................................... 12
4.1.1
Operator K
NR
........................................................................................................................ 12
4.1.2
Operator K
however
........................................................................................................................ 13
4.2
Formulation in sizes reduced in unloading .................................................................. 14
4.3
Tangent operators K
N
and K
O
......................................................................................................... 14
4.4
Digital processing of connection enters the mechanisms of the law of assembly .............. 15
5
Variables and parameters of the law of behavior ............................................................................ 17
5.1
Variables of the law .......................................................................................................................... 17
5.2
parameters of the law ....................................................................................................................... 17
6
Bibliographical references ............................................................................................................... 18
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Code_Aster
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Version
7.4
Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
3/18
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R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
1 Notations
SLF
Surface Limite of Friction
y
M
Moment in the assembly around the axis y
1
NR
Effort limits slip of the assembly on axis X
1
M
Moment limits slip of the assembly on the axis y
SLU
Surface Ultimate Limite
2
NR
Ultimate limiting effort of the assembly on axis X
2
M
Ultimate limiting moment of the assembly on the axis y
NR
Limiting effort
M
Limiting moment
1
U
Displacement limits mechanism 1 on axis X
1
Rotation limits mechanism 1 on the axis y
2
U
Displacement limits mechanism 2 on axis X
2
Rotation limits mechanism 2 on the axis y
U
Displacement of the assembly on axis X
Rotation of the assembly on the axis y
N
Reduced effort
NR
Nx
N
/
=
m
Reduced moment
M
My
m
/
=
R
U
Reduced displacement
U
U
Ur
/
=
R
Reduced rotation
/
=
R
U
Displacement limits on axis X
Rotation limits on the axis y
()
X
H
Scalar function
has
Parameter of nonlinearity
D
Constant scalar
D
Vector reduced generalized displacement
F
Vector reduced generalized effort
p
Variable interns scalar
feq
Effort generalized equivalent reduces scalar
F
Surface loading
()
X
R
Scalar function
()
()
X
H
X
R
1
-
=
D
Vector generalized displacement
F
Vector generalized effort
[]
D
Stamp displacement generalized limit
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Version
7.4
Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
4/18
Manual of Reference
R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
[]
F
Stamp effort generalized limit
+
X
Value of
X
at the moment
T
+
dt
-
X
Value of
X
at the moment
T
E
Eccentricity of loading
X
y
NR
M
E
/
=
R
E
Reduced eccentricity of loading
N
m
E
R
/
=
Sign
N
[]
Stamp
{}
Vector column
>
<
Vector line
O
K
Tangent operator at the moment
T
N
K
Tangent operator at the moment
T
+
dt
NR
however
K
K,
Reduced tangent operators

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Code_Aster
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Version
7.4
Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
5/18
Manual of Reference
R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
2 Physical model of the one-way behavior of
assembly
Assembly of an angle on the wing of another or a plate (bracket or splice plate) by
bolts is schematized by [Figure 2-a].
Appear 2-a: identifies local connection; axis X is confused with the axis of the bar
and centers it is confused there with the axis of the bolts

The one-way behavior of the assembly is modelized for the loading in traction or in
bending.
The modeling selected of the one-way behavior in loading of the assembly subjected to one
normal effort or a moment around is represented there by [Figure 2-b].

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 2-b: mechanisms of assembly in normal effort and moment
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Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
6/18
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R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
One distinguishes two phases of the behavior associated with two mechanisms:
·
mechanism 1: friction and slip until the stop (beginning of the shearing of
bolts).
·
mechanism 2: plasticization of the assembly until the ruin by shearing of the bolts
or ripping of the grips.
The limiting surface of friction (SLF) is the curve corresponding to the appearance of the slip in
space
X
NR
­
y
M
. Friction is described by the law of Coulomb.
Ultimate limiting surface (SLU) is the curve corresponding to the ruin of the assembly in space
X
NR
­
y
M
. The ruin can be due, according to the design of the assembly, with the shearing of the bolts
or with the ripping of the grips.
Tests on the same geometry but with tightening torques of the different bolts
show that the tangent stiffness of mechanism 2 at the point of stop decreases when the SLF
bring closer the SLU.
This justifies the physical modeling retained for the assembly of the two mechanisms [Figure 2-b].
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Code_Aster
®
Version
7.4
Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
7/18
Manual of Reference
R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
3
Relation of behavior of the mechanisms
The behavior of mechanisms 1 and 2 is similar. It is nonlinear between a behavior
initial tangent rigid and an asymptotic limiting behavior.
It is described by two essential parameters: the parameter of nonlinearity and the parameter surface
limit.
The stop (mechanism 1) or ruins it (mechanism 2) are described by an associated kinematic criterion.

3.1 Behavior
one-way
We said to [§2] that one-way behaviors in normal effort and moment around
are similar there [Figure 2-b].
They can be described consequently relation if the adimensional sizes are used:
·
reduced forces:
M
M
m
NR
NR
N
y
X
=
=
and
·
reduced displacements:
=
=
R
R
U
U
U
and
[Figure 3.1-a] represents in adimensional form the one-way behavior.
Analytically, it can be written (it is a choice):
()
()
()
has
has
has
has
R
R
N
N
D
X
X
D
X
H
m
H
N
H
U
-
=
-
=
=
=
+
+
1
1
1
with
or
1
1
has
is the scalar parameter of nonlinearity.
N
and
has
are identified on the one-way tests.
N
who takes into account the variability of the tests generally takes value 0.95.
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Version
7.4
Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
8/18
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R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
N m
m
N
1
criterion
kinematics
1
U
R
R
N
=
Nx/NR
m
=
My/M
U
R
=
U/U
R
=
/
Appear 3.1-a: relation of behavior of assembly

It is noticed that
()
1
=
N
H
or
()
1
=
m
H
, i.e.:
1
=
R
U
or
1
=
R
, or:
U
U
=
or
=
.
The one-way kinematic criterion is thus checked for
N
N
=
or
m
m
=
.
3.2
Incremental two-dimensional behavior
The coupling in extreme cases is defined by limiting surface:
1
2
2
=




+


M
M
NR
NR
y
X
The one-way behavior in reduced variables is described by the relation of [§3.1]:
()
F
H
D
=

where
D
is the vector reduced displacements




R
R
U
F
is the vector reduced forces




m
N
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Code_Aster
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Version
7.4
Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
9/18
Manual of Reference
R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
Into two-dimensional behavior, the isotropy is translated by a model with a variable interns scalar
p
such as:
()
loading
in
feq
H
p
=
where
feq
is the equivalent reduced force (scalar).
feq
is defined such as:
*
F
F
feq
=
where
F
is the point running of loading




y
X
M
NR
*
F
is the limiting loading associated
F




*
*
y
X
M
NR
The expression of
feq
results from the expression of limiting surface. Membership of
*
F
with
surface limit is written:
1
2
*
2
*
=


+




M
M
NR
NR
y
X
By the definition of
feq
, one can write:
1
2
2
=




+




M
feq
M
NR
feq
NR
y
X
i.e. according to the reduced forces
N
and
m
:
1
2
2
=




+




feq
m
feq
N
from where
2
2
m
N
feq
+
=
The surface of loading then is defined
F
, homothetic on limiting surface, by:
()
()
()
p
H
p
R
p
R
feq
1
where
0
:
-
=
=
-
F
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Code_Aster
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Version
7.4
Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
10/18
Manual of Reference
R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
For a formalism similar to that of plasticity with isotropic work hardening [bib2], one obtains the relation
of behavior continues expressed in reduced sizes:
()
()
()
0
if
'
0
if
0
=
-
=
<
-
=
=
=
·
·
·
·
·
·
p
R
feq
eq
F
feq
H
p
p
R
feq
p
feq
F
p
F
p
D
F
The relation of behavior of the rigid type - plastic without elasticity is written finally:
[] []
[]
[]




=




=




=




=
=
-
·
·
M
NR
F
U
D
M
NR
F
U
D
F
F
D
feq
p
D
y
X
0
0
and
0
0
and
where
1
The relation of incremental behavior in reduced sizes is obtained by integration of the relation
continue between
T
(variables -) and
T
+
dt
(variables +).
In loading,
p
check
F
= 0 with
T
+
dt
:
)
(
p
p
R
feq
+
=
-
+
éq
2.2-1
By introducing the relation of behavior,
+
+
=
feq
F
p
D
éq
2.2-2
one deduces the value from
p
,
2
2
.
R
R
U
D
D
p
+
=
=
and one calculates the value of
+
feq
by [éq 2.2-1]. The relation of behavior [éq 2.2-2] gives them
reduced efforts:
(
)
(
)
p
p
R
p
m
p
p
R
p
U
N
R
R
+
=
+
=
-
+
-
+
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Code_Aster
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Version
7.4
Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
11/18
Manual of Reference
R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
In unloading,
p
= 0 and one have by [éq 2.2-2]:
0
=
D


4
Establishment in Code_Aster
The relation of behavior
ASSE_CORN
is assigned to discrete elements of modeling
DIS_TR
with 2 confused nodes. This relation is called by the operators of resolution of
nonlinear problems
STAT_NON_LINE
[R5.03.01] or
DYNA_NON_LINE
[R5.05.05].

The local axes of these elements X, y, Z are defined as on [Figure 2-a].
The integration of this relation of behavior of the assemblies in the operator
STAT_NON_LINE
of Code_Aster the formulation of the tangent operators requires
O
K
and
N
K
[bib3].
·
O
K
is tangent rigidity at the beginning of the pitch of time, moment
T
.
·
N
K
is tangent rigidity at the end of the pitch of time, moment
T
+
dt
.
The illustration of the operators
O
K
and
N
K
is given by [Figure 4-a].
Appear 4-a: definition of the operators K
O
and K
N
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Version
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Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
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Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
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:
12/18
Manual of Reference
R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
4.1
Formulation in sizes reduced in loading
4.1.1 Operator
K
NR
We saw with [§3.2] that the relation of behavior is written:
(
)
2
2
.
R
R
U
D
D
p
p
p
R
p
D
F
+
=
=
+
=
-
+
with
The operator
NR
K
is defined by:
2
,
1




=
J
I
D
F
K
J
I
NR
It is written:
[]
{}
()
{}
()
p
p
R
D
p
D
p
R
p
D
p
D
Id
p
K
J
J
NR
>
<
·
+
>
<
·
-
=
+
+
+
+
'
2
Calculation gives then:
{}






=
>
<
·




=
>
<
+
+
p
p
U
p
U
p
U
D
p
D
p
p
U
D
p
R
R
R
R
R
R
J
R
R
J
2
2
;
and with
()
X
X
D
X
H
has
-
=
=
1
1
:
1
2
has
one
()
()
()
()
[
]
()
[
]
()
()
[
]
p
R
p
R
p
R
D
p
R
H
p
R
p
D
p
D
p
D
p
H
p
R
-
-
=
=




+
+
-
=
=
-
2
1
'
1
'
4
2
1
2
2
2
1
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Code_Aster
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Version
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Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
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:
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HT-66/05/002/A
4.1.2 Operator
K
however
For the elastoplastic behaviors, the operator
O
K
with
T
= 0 are equal to the rigidity of the structure
rubber band. In our case, the tangent initial behavior is rigid. The operator
however
K
is defined then
by the passage in extreme cases when
p
tends towards 0 of the operator
NR
K
. One obtains:
()
()
()
[]
Id
p
p
R
K
p
p
R
p
R
p
however
p
0
0
'
=
=
where
of
However
()
p
p
R
<
1
and if one supposes that the user gives, for the first pitch of loading, of
values such as
4
10
-
>
p
, one can retain in practice:




=
=
4
4
10
0
0
10
0
T
however
K
These remarks are illustrated by [Figure 4.1.2-a].
Appear 4.1.2-a: operator KB in T = 0

At the moment
T
running, the operator
however
K
is equal to the operator
NR
K
preceding pitch defined by
[§4.1.1].
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Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
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Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
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:
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R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
4.2
Formulation in sizes reduced in unloading
To avoid numerical problems, one describes the behavior (rigid) in unloading by:
0
=
=
=
T
however
NR
however
K
K
K
4.3
Tangent operators K
N
and K
O
·
The tangent operator
N
K
is written:
6
,
1




=
J
I
D
F
K
J
I
N
with
Z
X
Z
y
R
y
R
y
R
X
R
X
KR
D
F
KR
D
F
K
D
F
K
D
F
M
m
M
D
F
U
M
U
m
U
M
D
F
NR
N
NR
D
F
U
NR
U
N
U
NR
D
F
=
=
=
=
×
=
=
×
=
=
×
=
=
×
=
=
6
6
4
4
3
3
2
2
5
5
1
5
5
1
1
1
The other values are null.
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Version
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Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
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:
15/18
Manual of Reference
R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
·
The tangent operator
O
K
, with
T
= 0, are written:


















=
Rz
X-ray
Z
y
O
K
M
O
K
K
K
O
U
NR
K
4
4
10
10

4.4 Digital processing of connection enters the mechanisms of
law of assembly
During the resolution of each pitch of loading by the iterative method of Newton, one
must calculate with each iteration the tangent with the curve of balance force-displacement of the law of
behavior. The problem is that connection enters the mechanisms of the law of assembly, on
the law of behavior, has a dishing (cf [Figure 2-b]) which returns convergence
problems when, during a pitch of loading, one passes from one mechanism to the other.

In the subroutine TE0041 which calculates, for each increment of load, the elementary matrix of
tangential rigidity of a discrete finite element with 2 nodes having of the degrees of freedom in translation
and in rotation, it proved to be necessary to converge, to calculate a directed secant stiffness of the state
initial of null effort and displacement towards the state, at the end of the pitch of loading, consisted the effort
imposed and displacement corresponding on the curve of balance of the law of behavior. It was necessary
for that, which was unusual on the level of this option, to know the number of iteration interns
numerical process calculating the pitch of loading, then to consider the effort imposed on the element with the end of
this pitch.
Indeed, if one notes
+
F
effort imposed on the level of an element (a priori unknown since one does not know
that assembled efforts),
+
U
displacement corresponding on the curve of balance, and for
the iteration
I
, respective values
() ()
I
K
I
F
I
U
S
,
),
(
displacement, effort and matrix
secant ­ acting as tangent matrix ­ calculated at the end of the iteration, one knows only in
input of the above mentioned subroutine
I
U
, and values at the beginning of the pitch of load
()
0
F
and
()
0
U
, because one
the values with the preceding iteration I did not store - 1. In the expression of the residue calculated in end
of iteration I - 1:
()
()
()
(
)
1
)
(
.
1
1
-
-
-
=
-
-
+
I
U
I
U
I
K
I
F
F
S
, one thus does not know any more but
)
(I
U
with
the iteration
I
, except in the particular case
I
= 1 where one a:
()
() () ()
(
)
0
1
.
0
0
U
U
K
F
F
S
-
=
-
+
+
F
y is the only unknown value at the beginning and results from the others. One also deduces it
displacement
+
U
at the end of the pitch according to the relation of balance:
[]
()


=
·
·
·
R
R
U
p
R
m
N
p
,
.
,
.
, from where secant stiffness
()
+
+
=
U
F
K
S
/
1
.
background image
Code_Aster
®
Version
7.4
Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
16/18
Manual of Reference
R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
The problem is that in this first iteration, displacement
()
1
U
imposed is different from
final displacement to calculate
+
U
in balance with
+
F
from now on known (with the test of balance close to
no the preceding loading). Effort calculated at the end of this iteration
()
1
F
must thus be also
different from
+
F
and such as
()
() ()
1
.
1
1
U
K
F
S
=
so that starting from the couple
()
1
U
and
()
1
F
, one points
with the secant
()
1
S
K
on the couple
+
U
and
+
F
. One thus obtains at the beginning of iteration 2 one
displacement
()
2
U
very near to
+
U
and one can then calculate by the relation of balance
()
2
F
very
near also to
+
F
as well as the secant stiffness
()
() ()
2
/
2
2
U
F
K
S
=
.
If one converged exactly with the preceding pitch of load, 2 internal iterations are enough to converge
exactly, if not one needs some additional iterations to satisfy the test of balance on
residue.
The method known as of “directed secant” is schematized on [Figure 4.3-a] where one has them
following correspondences:
()
()
()
I
K
U
K
I
U
U
S
I
T
I
=
=
for a law of behavior
()
()
I
F
U
LLC
I
=
.
U0
U1
U+
F
F+
F (U1)
0
0
Elementary loop of Newton:
Inputs: U
0
U
i+1
Sig- VAr
Mater->LC
iter = i+1
If iter = 1:
F is estimated
+
= LLC (U
0
) + Kt (U
0
) (U
1
­ U
0
)
U is estimated
+
= LLC
- 1
(F
+
)
K (U
1
) = F
+
/U
+
, F (U
1
) = K (U
1
) * U
1
Exits: K (U
1
) F (U
1
) Sig+ Var+
If iter > 1:
Exits: Kt (U
i+1
) LLC (U
i+1
) Sig+ Var+
Appear 4.3-a: method of directed secant

One thus sees now why it was necessary in the option calculated by the above mentioned subroutine to know it
internal number of iteration
I
in order to distinguish the particular case
I
= 1.
background image
Code_Aster
®
Version
7.4
Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
17/18
Manual of Reference
R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
5
Variables and parameters of the law of behavior
5.1
Variables of the law
The law of behavior comprises 4 internal variables per point of calculation of which 3 only are
active:
·
V1 is displacement reduces equivalent p maximum reached out of mechanism 1,
·
V2 is displacement reduces equivalent p maximum reached out of mechanism 2,
·
V3 is an indicator which is worth 1 or 2 according to whether one is respectively on surface limits
mechanism 1 or 2, and 0 if one is under this limiting surface (after discharge for example),
·
V4 is inactive for the moment (thus remains to 0).
5.2
parameters of the law
The parameters of the law of behavior entered like data under the key word
ASSE_CORN
of
the control
DEFI_MATERIAU
[U4.43.01]:
·
NU_
: one enters behind this key word the value of the parameter
1
NR
mechanism 1,
·
MU_1
: one enters behind this key word the value of the parameter
1
M
mechanism 1,
·
DXU_1
: one enters behind this key word the value of the parameter
1
U
mechanism 1,
·
DRYU_1
: one enters behind this key word the value of the parameter
1
mechanism 1,
·
C_1
: one enters behind this key word the value common to the parameters
N
and
m
mechanism 1,
·
NU_2
: one enters behind this key word the value of the parameter
2
NR
mechanism 2,
·
MU_2
: one enters behind this key word the value of the parameter
2
M
mechanism 2,
·
DXU_2
: one enters behind this key word the value of the parameter
2
U
mechanism 2,
·
DRYU_2
: one enters behind this key word the value of the parameter
2
mechanism 2,
·
C_2
: one enters behind this key word the value common to the parameters
N
and
m
mechanism 2,
·
KY
,
KZ
,
KRX
,
KRZ
take the values of the characteristics of linear behavior in
local directions y, Z, X-ray, Rz respectively.

background image
Code_Aster
®
Version
7.4
Titrate:
Law of behavior of the assembly
ASSE_CORN
Date
:
14/04/05
Author (S):
G. DEVESA, J.L. FLEJOU, P. PENSERINI
Key
:
R5.03.32-A
Page
:
18/18
Manual of Reference
R5.03 booklet: Nonlinear mechanics
HT-66/05/002/A
6 References
bibliographical
[1]
P. PENSERINI: “Modeling of the assemblies bolted in the webmasts”
Note EDF/R & D HM-77/93/287
[2]
P. PENSERINI: “Characterization and modeling of the behavior of the connections structure
metal-foundation “Thesis of doctorate of the University Paris 6, 1991
[3]
J.P. LEFEBVRE, P. MIALON: “Quasi-static nonlinear Algorithm of Code_Aster”
Note EDF/R & D HI-75/7832