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Code_Aster
®
Version
7.4
Titrate:
Modelings
TUYAU_3M
and
TUYAU_6M
Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.06-C
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: U3.11.06



Modelings
TUYAU_3M
and
TUYAU_6M



Summary:

This document describes for modelings
TUYAU_3M
and
TUYAU_6M
:
·
degrees of freedom carried by the finite elements which support modeling,
·
the related meshs supports,
·
supported loadings,
·
non-linear possibilities,
·
case-tests implementing modelings.

Modelings
TUYAU_3M
and
TUYAU_6M
correspond to a formulation of linear elements of piping
straight line or curve, which are based on a kinematics of beam of Timoshenko for displacements and them
rotations of average fiber and on a kinematics of hull for the deformations of the transverse section
(ovalization, roll, swelling). These transverse deformations are broken up into series of
Fourier. Modeling
TUYAU_3M
takes into account 3 modes to the maximum, while modeling
TUYAU_6M
takes into account 6 modes of Fourier.

These modelings are usable for problems of three-dimensional pipings in mechanical analysis
linear or not linear and in small displacements.
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Code_Aster
®
Version
7.4
Titrate:
Modelings
TUYAU_3M
and
TUYAU_6M
Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.06-C
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:
·
six components of displacement of average fiber (three translations and three rotations),
·
three degrees of freedom corresponding to modes 0 and 1,
·
for each mode of Fourier 6 degrees of freedom (U corresponds to the roll, V with
orthoradial displacement, W with radial displacement).
Finite element
Degrees of freedom (with each node node) Remarks
TUYAU_3M DX
DY
DZ
DRX
DRY
DRZ
W0
WI1
WO1
UI2
VI2
WI2
UO2
VO2
WO2
mode 2
UI3
VI3
WI3
UO3
VO3
WO3
mode 3
TUYAU_6M DX
DY
DZ
DRX
DRY
DRZ
W0
WI1
WO1
UI2
VI2
WI2
UO2
VO2
WO2
mode 2
UI3
VI3
WI3
UO3
VO3
WO3
mode 3
UI4
VI4
WI4
UO4
VO4
WO4
mode 4
UI5
VI5
WI5
UO5
VO5
WO5
mode 5
UI6
VI6
WI6
UO6
VO6
WO6
mode 6
1.2
Net support of the matrices of rigidity
The meshs support of the finite elements, in displacement formulation, are segments with 3 or 4
nodes.
Modeling Nets Element
finished
Remarks
TUYAU_3M SEG3 MET3SEG3
SEG4
MET3SEG4
TUYAU_6M SEG3 MET6SEG3

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Code_Aster
®
Version
7.4
Titrate:
Modelings
TUYAU_3M
and
TUYAU_6M
Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.06-C
Page
:
3/4
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.
Supported modelings:
TUYAU_3M
,
TUYAU_6M
·
ORIENTATION
Allows to define and affect a generator.
Supported modelings:
TUYAU_3M
,
TUYAU_6M
·
SOLID MASS
Optional, allows to define and affect a direction of growth (necessary
only in the case of a law of behavior
ASSE_COMBU)
.
Supported modelings:
TUYAU_3M
,
TUYAU_6M

3 Loadings
supported
The loadings available are as follows:
·
“FORCE_POUTRE”
Allows to apply linear forces
Supported modelings:
TUYAU_3M
,
TUYAU_6M
·
“FORCE_TUYAU”
Allows to apply a pressure in the pipe.
Supported modelings:
TUYAU_3M
,
TUYAU_6M
·
“GRAVITY”
Allows to apply a loading of the gravity type.
Supported modelings:
TUYAU_3M
,
TUYAU_6M
·
“TEMP_CALCULEE”
Allows to apply a thermal loading.
Supported modelings:
TUYAU_3M
,
TUYAU_6M
background image
Code_Aster
®
Version
7.4
Titrate:
Modelings
TUYAU_3M
and
TUYAU_6M
Date:
01/06/05
Author (S):
J.L. FLEJOU, F. LEBOUVIER
Key
:
U3.11.06-C
Page
:
4/4
Instruction manual
U3.11 booklet: Mechanical elements of structure 1D
HT-66/05/004/A
4 Possibilities
non-linear
4.1
Law of behaviors
All the laws of behaviors available in C_PLAN are usable under
COMP_INCR
in
STAT_NON_LINE
and
DYNA_NON_LINE
(Cf [U4.51.11]).

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
·
TUYAU_3M
­ Statique
linear
FORMA01E [V7.15.100]: Analyze of a piping comprising an elbow embedded with one
end and subjected to a force at the other end.
SSLL106A [V3.01.106]: Quasi-static analysis of a pipe right embedded at an end and
subjected to a traction, 2 efforts sharp, 2 bending moments and a torsion with the other
end. One applies moreover one internal pressure, a linear force distributed and one
thermal dilation.
­ Statique
non-linear
SSNL117A [V6.02.117]: Elastoplastic analysis of an elbow embedded at an end and
subjected to a loading of bending in its plan at the other end.
­ Dynamique
linear
SDLL14A [V2.02.014]: Seek Eigen frequencies and modes associated with one
bent piping.
­ Dynamique
non-linear
Elastoplastic SDNL113A: Dynamic response of a piping in the shape of subjected quadrant
with a seismic loading.
·
TUYAU_6M
­ Statique
linear
SSLL106C [V3.01.106]: Quasi-static analysis of a pipe right embedded at an end and
subjected to a traction, 2 efforts sharp, 2 bending moments and a torsion with the other
end. One applies moreover one internal pressure, a linear force distributed and one
thermal dilation.
­ Statique
non-linear
HSNV100D [V7.22.100]: Analyze thermoplastic in simple traction of a right pipe.
­ Dynamique
linear
SDLL14B [V2.02.014]: Seek Eigen frequencies and modes associated with one
bent piping.