Code_Aster
®
Version
7.4
Titrate:
Modelings
POU_D_TG
,
POU_D_TGM
Date:
17/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.04-F
Page
:
1/4
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: U3.11.04
Modelings
POU_D_TG
,
POU_D_TGM
Summary:
This document describes for modelings
POU_D_TG
and
POU_D_TGM
·
degrees of freedom carried by the finite elements which support modeling,
·
the related meshs supports,
·
supported loadings,
·
nonlinear possibilities,
·
case-tests implementing modelings
Modeling
POU_D_TG
corresponds to a formulation of elements of beams of fascinating Timoshenko in
count a modeling of the roll of the section (cf [R3.08.03]).
Modeling
POU_D_TGM
be based on the same formulation and allows to take into account one
nonlinear behavior of multifibre type.
They are usable for problems of beams in isotropic linear mechanical analysis and in
elastoplasiticity.
Code_Aster
®
Version
7.4
Titrate:
Modelings
POU_D_TG
,
POU_D_TGM
Date:
17/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.04-F
Page
:
2/4
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A
1 Discretization
1.1
Degrees of freedom
The degrees of freedom are, in each node of the mesh support, the six components of displacement
(three translations and three rotations) more one component
(GRX)
relating to the roll of
section compared to neutral fiber (cf [R3.08.03]).
Finite element
Degrees of freedom (with each node node)
POU_D_TG DX
DY
DZ
DRX
DRY
DRZ
GRX
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_TG SEG2
MECA_POU_D_TG
POU_D_TGM SEG2
MECA_POU_D_TGM
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.
Supported modelings:
POU_D_TG
,
POU_D_TGM
·
ORIENTATION
Allows to lay down and affect the orientation of the main axes of inertia around fiber
neutral.
Supported modelings:
POU_D_TG
,
POU_D_TGM
3 Loadings
supported
Loadings specific, available in
AFFE_CHAR_MECA
are as follows:
·
“CONTACT”
Allows to define the areas subjected to conditions of contact.
Supported modelings:
POU_D_TG
,
POU_D_TGM
·
“EPSI_INIT”
Allows to apply a loading of initial deformation.
Supported modeling:
POU_D_TG
Code_Aster
®
Version
7.4
Titrate:
Modelings
POU_D_TG
,
POU_D_TGM
Date:
17/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.04-F
Page
:
3/4
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A
·
“FORCE_POUTRE”
Allows to apply linear forces
Supported modelings:
POU_D_TG
,
POU_D_TGM
·
“GRAVITY”
Allows to apply a loading of the gravity type.
Supported modelings:
POU_D_TG
,
POU_D_TGM
·
“TEMP_CALCULEE”
Allows to apply a thermal loading.
Supported modelings:
POU_D_TG
,
POU_D_TGM
4 Possibilities
non-linear
4.1
Laws 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]):
/“VMIS_POU_LINE”
Supported modeling:
POU_D_TG
/“VMIS_CINE_LINE”
Supported modeling:
POU_D_TGM
/“VMIS_POU_FLEJOU”
Supported modeling:
POU_D_TG
/“VMIS_ISOT_LINE”
Supported modeling:
POU_D_TGM
/“VMIS_ISOT_TRAC”
Supported modeling:
POU_D_TGM
/“GRAN_IRRA_LOG”
Supported modeling:
POU_D_TGM
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
Deformations available, used in the relations of behavior under the key word
DEFORMATION
for the operators
STAT_NON_LINE
and
DYNA_NON_LINE
are (cf [U4.51.11]):
/“SMALL”
The deformations used for the relation of behavior are the linearized deformations.
/“PETIT_REAC”
The increments of deformations used in the incremental relation of behavior are them
linearized deformations of the increment of displacement in the reactualized geometry.
Note:
Attention, the calculation of the deformations using
PETIT_REAC
is only one approximation of
the assumption of great displacements. It requires to carry out very small increments of
loading. To correctly take into account great displacements, and especially them
great rotations, it is recommended to use modeling
POU_D_T_GD
.
Code_Aster
®
Version
7.4
Titrate:
Modelings
POU_D_TG
,
POU_D_TGM
Date:
17/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.04-F
Page
:
4/4
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A
5
Examples of implementation: case-test
·
POU_D_TG
Statique
linear
SSLL102D [V3.01.102]: Analyze of a beam fixed at an end and subjected to
unit efforts at the other end.
Statique
non-linear
SSNL106A [V6.02.106]: Analyze of a right beam embedded at an end and subjected to
a displacement in traction and bending at the other end, with a law of behavior
elastoplastic or linear work hardening.
Dynamique
linear
SDLL01B [V2.02.01]: Seek frequencies of vibration and modes associated with one
short beam on simple supports.
Dynamique
non-linear
SSNL106I [V6.02.106]: Analyze of a right beam embedded at an end and subjected to one
displacement in traction and bending at the other end, with a law of behavior
elastoplastic or linear work hardening. The analysis was carried out with the operator of
nonlinear dynamics.
·
POU_D_TGM
Statique
non-linear
SSNL122A [V6.01.122]: Analyze of a beam multifibre embedded at an end and
subjected to a force at the other end.
Dynamique
linear
SDLL132A [V2.02.132]: Seek frequencies of vibration and clean modes
associated of a frame.