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Code_Aster
®
Version
7.4
Titrate:
Modeling
POU_D_EM
Date:
17/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.07-B
Page
:
1/6
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A
Organization (S):
EDF-R & D/AMA, DeltaCAD















Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
Document: U3.11.07



Modeling
POU_D_EM




Summary:

Modeling
POU_D_EM
corresponds to the formulation of elements of multifibre beam (beam of section
heterogeneous divided into several fibers).

They are usable for three-dimensional problems in linear and nonlinear mechanical analysis.

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Code_Aster
®
Version
7.4
Titrate:
Modeling
POU_D_EM
Date:
17/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.07-B
Page
:
2/6
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A
1 Discretization
1.1
Degrees of freedom
For the modeling of multifibre beam into three-dimensional the degrees of freedom of discretization are,
in each node of the mesh support, six components of displacement (three translations and three
rotations). These nodes are supposed to describe a segment of average fiber of the beam.
Finite element
Degrees of freedom (with each node node)
POU_D_EM
DX
DY
DZ
DRX
DRY
DRZ
1.2
Net support of the matrices of rigidity
The meshs support of the finite elements, in displacement formulation, are segments with two nodes
SEG2
:
Modeling Nets Element
finished
Remarks
POU_D_EM SEG2
MECA_POU_D_EM
1.3
Net support of the loadings
As for the conventional elements of beam (
POU_D_E
), all loadings applicable to
elements of multifibre beam are treated by direct discretization on the mesh support of the element in
displacement formulation.
No mesh support of loading is thus necessary for the edge of the elements of beam or
of bar.
1.4
Main characteristics of modeling
Modeling
POU_D_EM
is based on the resolution of a problem of beam for which each
definite section is divided into several fibers.
Each fiber behaves then like a beam of Euler, i.e. the sections remain right
and perpendicular to average fiber (assumption of great twinge).
The section can be of an unspecified form.
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Code_Aster
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Version
7.4
Titrate:
Modeling
POU_D_EM
Date:
17/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.07-B
Page
:
3/6
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A
2
Assignment of the characteristics
For this element of structures 1D, it is necessary to affect geometrical characteristics which
are complementary to the data of mesh. The definition of these data is carried out with
order
AFFE_CARA_ELEM
associated the key words following factors:
·
AFFE_SECT
Allows to associate a plane mesh of section an element beam.
·
AFFE_FIBER
Allows to associate a section made up of one or more specific fibers an element
beam.
·
BEAM
Allows to associate a geometrical characteristic of torsion an element beam.
·
ORIENTATION
Allows “to turn” the plane mesh of the section around the axis of the beam.
Remarks on the characteristics of modeling:
1) Within the framework of modeling of a multifibre type, there are two “levels” of modeling. It
y with the modeling known as “longitudinal” which will be represented by a beam (support
geometrical
SEG2
) and a modeling planes section (perpendicular to
SEG2
).
The operand
AFFE_SECT
allows to associate a plane mesh of section an element beam.
The operand
AFFE_FIBER
allows to associate a section made up of one or more
specific fibers (defined by their position and surfaces) with an element beam.
2) In general in the plane modeling of the section, several materials cohabit. By
example, in a section concrete reinforced, there are at the same time concrete and reinforcements. In it
case there, the operator
CREA_MAILLAGE
allows to duplicate support E.F so that there is not
that only one material by support.
3) The operand
BEAM
is used to affect a geometrical characteristic of torsion (
JX
)
who cannot be calculated starting from the plane mesh of the section. If the value is used
GENERAL
for the key word
SECTION
operand
BEAM
, the characteristics should be given
(
CARA
)
With
,
IY
and
IZ
in addition to
JX
because the operator
AFFE_CARA_ELEM
waits at least these
four characteristics for a conventional beam.
Values (
VALE
) given to
With
,
IY
and
IZ
are not used by the element
POU_D_EM
, because
they are calculated starting from the plane mesh of the section. On the other hand a checking of
coherence of information (
SURFACE
and
INERTIA
) provided on the one hand by
With
,
IY
,
IZ
and of other
leaves by the key words
AFFE_SECT
and
AFFE_FIBER
is realized. The criterion of error is based
on the error relating and is compared either with the default value or to that given by
the user via the key words
PREC_AIRE
and
PREC_INERTIE
. (Cf orders
AFFE_CARA_ELEM
key words
PREC_AIRE
and
PREC_INERTIE
operand
BEAM
).
4) The operand
ORIENTATION
is used in general “to turn” the plane mesh of the section
around the axis of the beam (
CARA “ANGL_VRIL”
). Indeed, by defect, axis X (horizontal)
plane mesh of the section is confused with the axis there beam (see [Figure 3-a]).
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Code_Aster
®
Version
7.4
Titrate:
Modeling
POU_D_EM
Date:
17/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.07-B
Page
:
4/6
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A












Appear 3-a: Orientation by defect of the plane mesh compared to the element beam

3 Loadings
supported
The loadings available are as follows:
·
“FORCE_POUTRE”
Allows to apply linear forces.
·
“GRAVITY”
Allows to apply a loading of the gravity type.
·
“ROTATION”
Allows to define the rotational speed and the vector of rotation.
·
“TEMP_CALCULEE”
Allows to apply a thermal loading.

4 Possibilities
non-linear
4.1
Law of behaviors
Laws of behaviors specific to this modeling, usable under
COMP_INCR
in
STAT_NON_LINE
and
DYNA_NON_LINE
are as follows (cf [U4.51.11]):
/“CORR_ACIER”
/“LABORD_1D'
/“PINTO_MENEGOTTO”
/“VMIS_CINE_LINE”
/“VMIS_ISOT_LINE”
/“VMIS_ISOT_TRAC”
/“GRAN_IRRA_LOG”
Moreover, it is possible for this modeling, which uses a monodimensional state of stresses
to use the behaviors 3D by using the key word
ALGO_1D (METHOD = DEBORST)
.
4.2 Deformations
Only linearized deformations key word
“SMALL”
under
DEFORMATION
are available in
relations of behavior (cf [U4.51.11]).
Mesh section
X
y
X
p
Y
p
Z
p
Element beam
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Code_Aster
®
Version
7.4
Titrate:
Modeling
POU_D_EM
Date:
17/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.07-B
Page
:
5/6
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A
5
Examples of implementation: case-tests
·
Linear statics
SSLL111A [V3.01.111]: Static response of a concrete beam reinforced (section in T) with one
linear behavior subjected to three successive loading cases: a specific force, the weight
clean and a rise in temperature.
·
Non-linear statics
SSNL119A [V6.02.119]: Deflection test 3 points, static response of a reinforced concrete beam
(rectangular section) with a nonlinear behavior of Borderie.
·
Linear dynamics
SDLL130B [V2.02.130]: Seismic response of a reinforced concrete beam (rectangular section) to
linear behavior.
·
Non-linear dynamics
SDNL130A [V5.02.130]: Seismic response of a reinforced concrete beam (rectangular section) to
nonlinear behavior.
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Code_Aster
®
Version
7.4
Titrate:
Modeling
POU_D_EM
Date:
17/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.07-B
Page
:
6/6
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A

























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