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Titrate:
Modelings POU_D_T, POU_D_E, POU_C_T, BARS


Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER Key
:
U3.11.01-E Page
: 1/6

Organization (S): EDF-R & D/AMA, DeltaCAD
Handbook of Utilization
U3.11 booklet: Mechanical elements of structure 1D
Document: U3.11.01
Modelings POU_D_T, POU_D_E, POU_C_T,
BARRE

Summary:

Four modelings POU_D_T, POU_D_E, POU_C_T and BARRE correspond to the traditional formulations
elements of beams and bars, inspired of Résistance of Matériaux.

They are usable for three-dimensional problems in linear mechanical analysis or not linear
isotropic.

Handbook of Utilization
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Modelings POU_D_T, POU_D_E, POU_C_T, BARS


Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER Key
:
U3.11.01-E Page
: 2/6

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.

BARRE
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

BARRE
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
Principal characteristics of modelings

Modeling POU_D_E (Poutre Droite d' 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 (Poutre Droite de Timoshenko) takes into account the effects of shearing
transverse.

Modeling POU_C_T is similar to POU_D_T with a curvature (Poutre Courbe of
Timoshenko).

Modeling BARRE treats only the efforts and axial deformations.

The beam with warping is treated in [U3.11.04].
Handbook of Utilization
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Modelings POU_D_T, POU_D_E, POU_C_T, BARS


Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER Key
:
U3.11.01-E Page
: 3/6

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 grid. The definition of these data is carried out with
order AFFE_CARA_ELEM associated with the key words following factors:

· POUTRE
Allows to define and affect the characteristics of the cross section and the orientation of
principal axes of inertia around neutral fiber.
Supported modelings: POUT_D_T, POU_D_E, POU_C_T

· BARRE
Allows to define and affect the characteristics of the cross section.
Supported modeling: BARRE

· 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 principal 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 grid 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 element POU_D_E (for
POU_D_T the terms of transverse shearing improve a little conditioning). With
resolution, one then loses 8 decimals for the POU_D_E.
Handbook of Utilization
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Modelings POU_D_T, POU_D_E, POU_C_T, BARS


Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER Key
:
U3.11.01-E Page
: 4/6

3 Loadings
supported

The loadings available are as follows:

· “CONTACT”
Allows to define the zones 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 principal 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, BARS

· “INTE_ELEC”
Allows to apply the force of LAPLACE acting on a principal 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

· “PESANTEUR”
Allows to apply a loading of the gravity type.
Supported modelings: POU_D_T, POU_D_E, POU_C_T, BARS

· “TEMP_CALCULEE”
Allows to apply a thermal loading.
Supported modelings: POU_D_T, POU_D_E, POU_C_T, BARS

Note:

Possible contact between beam and surface [R5.03.50].

Handbook of Utilization
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A

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Titrate:
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Author (S):
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:
U3.11.01-E Page
: 5/6

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: BARRE

/“VMIS_ASYM_LINE”
Supported modeling: BARRE

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 key word ALGO_1D (METHODE=
“DEBORST”).

4.2 Deformations

Only the linearized deformations key word “PETIT” under DEFORMATION are available in
relations of behavior (Cf. [U4.51.11]):

5
Examples of implementation: case-tests

· POU_D_T
­ Statique
linear
DEMO004A: Analyze of a lattice 3D without reinforcement, under weight actual and subjected to a force
specific.
FORMA01A: Analyze 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 inflection.
­ 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.

Handbook of Utilization
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Modelings POU_D_T, POU_D_E, POU_C_T, BARS


Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER Key
:
U3.11.01-E Page
: 6/6

· 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 inflection.
­ Dynamique
linear
Modal FORMA12A: Analyze 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: Calcul of the linear temporal response of a piping.

· BARRE
­ 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.

Handbook of Utilization
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A

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