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Code_Aster
®
Version
7.4
Titrate:
Modelings
POU_D_T
,
POU_D_E
,
POU_C_T
,
BAR
Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.01-E
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: U3.11.01



Modelings
POU_D_T
,
POU_D_E
,
POU_C_T
,
BAR




Summary:

Four modelings
POU_D_T
,
POU_D_E
,
POU_C_T
and
BAR
correspond to the conventional formulations
elements of beams and bars, inspired of the Resistance of Materials.

They are usable for three-dimensional problems in linear mechanical analysis or not linear
isotropic.
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Code_Aster
®
Version
7.4
Titrate:
Modelings
POU_D_T
,
POU_D_E
,
POU_C_T
,
BAR
Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.01-E
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 three modelings of 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_T
DX
DY
DZ
DRX
DRY
DRZ
POU_D_E
DX
DY
DZ
DRX
DRY
DRZ
POU_C_T
DX
DY
DZ
DRX
DRY
DRZ
For the modeling of bar into three-dimensional the degrees of freedom of discretization are, in
each node of the mesh support, three components of displacement in translation.
BAR
DX
DY
DZ
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_T SEG2
MECA_POU_D_T
POU_D_E SEG2
MECA_POU_D_E
POU_C_T SEG2
MECA_POU_C_T
BAR
SEG2 MECA_BARRE
1.3
Net support of the loadings
All the loadings applicable to the elements of beam and bar are treated by discretization
direct 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 modelings
Modeling
POU_D_E
(Right Beam of Euler) corresponds to the assumption of Euler-Bernouilli,
i.e. the sections remain right and perpendicular to average fiber (assumption of
great twinge).
Modeling
POU_D_T
(Right Beam of Timoshenko) takes into account the effects of shearing
transverse.
Modeling
POU_C_T
is similar to
POU_D_T
with a curvature (Beam Curves
Timoshenko).
Modeling
BAR
treat only the efforts and axial deformations.
The beam with roll is treated in [U3.11.04].
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Code_Aster
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Version
7.4
Titrate:
Modelings
POU_D_T
,
POU_D_E
,
POU_C_T
,
BAR
Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.01-E
Page
:
3/6
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A
2
Assignment of the characteristics
For these elements 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:
·
BEAM
Allows to define and affect the characteristics of the cross section and the orientation of
main axes of inertia around neutral fiber.
Supported modelings:
POUT_D_T
,
POU_D_E
,
POU_C_T
·
BAR
Allows to define and affect the characteristics of the cross section.
Supported modeling:
BAR
·
DEFI_ARC
Allows to define and assign to curved beams characteristics related to the curvature of
the element (radius of curvature and orientation of the plan of the arc).
Supported modelings:
POU_C_T
·
ORIENTATION
Allows to define and affect the main axes of the cross sections of the elements of the type
beam.
Supported modelings:
POUT_D_T
,
POU_D_E
,
POU_C_T

Notice on the discretization:
With regard to the mesh of the beams in meshs
SEG2
, it is useless to refine
excessively these elements whose integrated formulation makes it possible to obtain solutions
exact with the nodes in linear statics [R3.08.01]. In modal analysis and dynamics, one
will take care to net sufficiently to represent the awaited modes, but without excess: it is necessary
that the elements remain a sufficient length, according to dimensions of the section,
so that the assumption of beam is valid.

For example, for a beam length 1, and a circular section of external radius 0.05
and thickness 0.01, 10 elements are enough to apprehend the 10 first correctly
modes. But if one refines enormously, for example with 1000 elements, then each
element of beam is very short: length 0.001 for an external radius of 0.05. Matrices
elementary are very badly conditioned, in particular for the element
POU_D_E
(for
POU_D_T
the terms of transverse shearing improve a little conditioning). With
resolution, one loses then 8 decimals for
POU_D_E
.
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Code_Aster
®
Version
7.4
Titrate:
Modelings
POU_D_T
,
POU_D_E
,
POU_C_T
,
BAR
Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.01-E
Page
:
4/6
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A
3 Loadings
supported
The loadings available are as follows:
·
“CONTACT”
Allows to define the areas subjected to conditions of contact.
Supported modelings:
POU_D_T
,
POU_D_E
·
“EPSI_INIT”
Allows to apply a loading of initial deformation.
Supported modelings:
POU_D_T
,
POU_D_E
·
“FORCE_ELEC”
Allows to apply the force of LAPLACE acting on a main conductor, due to
presence of a secondary conductor right.
Supported modelings:
POU_D_T
,
POU_D_E
·
“FORCE_POUTRE”
Allows to apply linear forces
Supported modelings:
POU_D_T
,
POU_D_E
,
POU_C_T
,
BAR
·
“INTE_ELEC”
Allows to apply the force of LAPLACE acting on a main conductor, due to
presence of a secondary conductor not necessarily right compared to this conductor
the main thing.
Supported modelings:
POU_D_T
,
POU_D_E
·
“GRAVITY”
Allows to apply a loading of the gravity type.
Supported modelings:
POU_D_T
,
POU_D_E
,
POU_C_T
,
BAR
·
“TEMP_CALCULEE”
Allows to apply a thermal loading.
Supported modelings:
POU_D_T
,
POU_D_E
,
POU_C_T
,
BAR
Note:
Possible contact between beam and surface [R5.03.50].
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Code_Aster
®
Version
7.4
Titrate:
Modelings
POU_D_T
,
POU_D_E
,
POU_C_T
,
BAR
Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.01-E
Page
:
5/6
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A
4 Possibilities
non-linear
4.1
Law of behaviors
Laws of behaviors specific to these modelings, usable under
COMP_INCR
in
STAT_NON_LINE
,
DYNA_NON_LINE
and
DYNA_TRAN_EXPLI
are as follows (cf [U4.51.11]):
/“ASSE_COMBU”
Supported modelings:
POU_D_T
,
POU_D_E
/“VMIS_POU_LINE”
Supported modelings:
POU_D_T
,
POU_D_E
,
POU_C_T
/“VMIS_POU_FLEJOU”
Supported modelings:
POU_D_T
,
POU_D_E
,
POU_C_T
/“PINTO_MENEGOTTO”
Supported modeling:
BAR
/“VMIS_ASYM_LINE”
Supported modeling:
BAR
Note:
It is possible for these modelings using a monodimensional state of stresses
to use the behaviors 3D, for that it is necessary to use the key word
ALGO_1D
(
METHODE=
“DEBORST”
).
4.2 Deformations
Only linearized deformations key word
“SMALL”
under
DEFORMATION
are available in
relations of behavior (cf [U4.51.11]):

5
Examples of implementation: case-tests
·
POU_D_T
­ Statique
linear
DEMO004A: Analyzes of a lattice 3D without reinforcement, under weight actual and subjected to a force
specific.
FORMA01A: Analyzes of a piping comprising an elbow subjected to a specific force.
­ Statique
non-linear
SSNL106B [V6.02.106]: Elastoplastic analysis of a right beam in traction and bending.
­ Dynamique
linear
SDLL01A [V2.02.01]: Seek Eigen frequencies of a short beam on supports
simple.
­ Dynamique
non-linear
SDNL103A [V5.02.103]: Calculation of the response of a post subjected to a seismic loading
unspecified.
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Code_Aster
®
Version
7.4
Titrate:
Modelings
POU_D_T
,
POU_D_E
,
POU_C_T
,
BAR
Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.01-E
Page
:
6/6
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A
·
POU_D_E
­ Statique
linear
SSLL102A [V3.01.102]: Analyze of a fixed beam subjected to unit efforts.
­ Statique
non-linear
SSNL106C [V6.02.106]: Elastoplastic analysis of a right beam in traction and bending.
­ Dynamique
linear
FORMA12A: Analyzes modal of a beam (multiple modes).
­ Dynamique
non-linear
SDNL105A [V5.02.105]: Shock of 3 beams between-they - calculation of the transitory answer by
under structuring in the case of taken into account of nonlinearity of the type shock enters
mobile structures.
·
POU_C_T
­ Statique
linear
FORMA01A [V5.02.105]: Analyze of a piping comprising an elbow subjected to a force
specific.
­ Dynamique
linear
SDLL 11th: Calculation of the Eigen frequencies of a thin circular ring.
­ Dynamique
non-linear
SDNX300A: Calculation of the linear temporal response of a piping.
·
BAR
­ Statique
linear
SSLS110A [V3.01.110]: Analyze of a system of 3 bars out of U under actual weight.
­ Statique
non-linear
SSLS111B [V6.02.111]: Analyze of three elastoplastic bars perfect Von Mises.