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Note of use of the elements
TUYAU_ *
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EDF/AMA, DeltaCAD
Instruction manual
U2.02 booklet: Elements of structure
Document: U2.02.02
Note of use of the elements
TUYAU_ *
Summary:
This document is a note of use for modelings
TUYAU_3M
and
TUYAU_6M
.
Finite elements
TUYAU_3M
and
TUYAU_6M
correspond to linear elements of right piping or
curve. The kinematics of the elements PIPE combines at the same time a kinematics of beam, which describes it
overall movement of the line of piping, and a kinematics of hull, which brings the description of
swelling, of the ovalization and the roll of the cross section.
These modelings are usable for problems of relatively thick three-dimensional pipings,
in linear mechanical analysis or not linear and small displacements.
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Count
matters
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1 Introduction
Finite elements
TUYAU_3M
and
TUYAU_6M
correspond to linear elements of piping
straight line or curve. They are based on a kinematics of beam of Timoshenko for displacements
and rotations of average fiber and on a kinematics of hull for the deformations of
transverse section (ovalization, roll, swelling). These transverse deformations are
broken up into Fourier series. Modeling
TUYAU_3M
takes into account 3 modes with
maximum, while modeling
TUYAU_6M
takes into account 6 modes of Fourier.
These modelings are usable for problems of three-dimensional pipings relatively
thick, only in linear mechanical analysis or not linear and small displacements.
Currently, no calculation of thermics or accoustics is possible.
This document presents the possibilities of modeling PIPE available in version 6 of
Code_Aster. One initially presents the possibilities of this type of modeling, then
one briefly points out the formulation of the finite elements and their differences with modelings
beam. One also gives the list of the options available for each element. One finishes
by the presentation of some academic case-tests and finally one gives some consultings
of use.
The right or curved pipe sections are gathered under modelings TUYAU_3M and
TUYAU_6M. The options of calculations are defined in this document. Current possibilities of these
elements pipes are as follows:
·
right or curved lines of piping,
·
linear element with 3 nodes (SEG3) or 4 nodes (SEG4),
·
relatively thick pipe: E/R<0.2 where E represents the thickness and R the radius of the section
transverse,
·
internal pressure, cross-bendings and anti-plane, torsion and extension,
·
small displacements,
·
elastoplastic in plane stresses, or not linear behavior incremental
unspecified,
·
the transverse section can become deformed by:
-
swelling due to the internal pressure or the effect Poisson,
-
ovalization due to the bending,
-
roll due to the bendings combined in the plan and except plan.
Compared with modeling TUYAU_3M, modeling TUYAU_6M allows the best
approximation of the behavior of the cross section if the aforementioned becomes deformed according to
a mode raised, for example in the case of thin tubes where the thickness report/ratio on radius of
cross section is < 0.1, and in the case of plasticity.
Modeling TUYAU_3M has 21 DDL per node (6 DDL of beam and 15 DDL of hull), tandis
that modeling TUYAU_6M has 39 DDL per node (6 DDL of beam and 33 DDL of hull).
For modeling TUYAU_3M, one can use meshs SEG3 and SEG4.
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2
Capacities of modeling
2.1
Recall of the formulation
2.1.1 Geometry of the elements pipes
We point out here the methods and the modelings implemented for the elements pipes and which
are presented in the reference document [R3.08.06].
For the elements pipes one defines an average, right fiber or curve (X defines the co-ordinate
curvilinear) and a section digs of circular type. This section must be small compared to
length of piping. The figure [Figure 2.1.1-a] illustrates the two various configurations. One
identify local oxyz is associated average fiber.
X
y
Z
L
H
R
R << L
X
y
Z
Average fiber
O
O
Appear 2.1.1-a: right Pipe or curve
2.1.2 Formulation of the elements pipes
The kinematics of the pipe [Figure 2.1.2-a] is composed of a kinematics of hull which brings
description of ovalization, swelling and the roll, and a kinematics of beam which
described the overall movement of the line of piping. Displacement U [Figure 2.1.2-b] of one
not material of the pipe of a macroscopic part beam (U is composed
P
) and of a part
additional local hull (U
S
): U = U
P
+ U
S
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M
M
bending-torsion of a right beam
In theory of the beams
theory of the hulls
Cross
Transverse section
Transverse section
ovalization
Cross
roll
U
W
v
increased
W
v
Appear 2.1.2-a: Decomposition of displacement in fields of beam and hull
The formulation of the elements rests on:
The theory of the beams for the kinematics of average fiber. If one makes the complete assumption of
theory of the beams: cross-sections associated displacements of beam (U
P
), which is
perpendiculars with average fiber of reference [Figure 2.1.2-b] remain perpendicular to fiber
average after deformation. The cross-section does not become deformed. This will be true on average in
the element PIPE. One uses the theory of the beams only to describe the movement of fiber
average: the average fiber of the pipe is equivalent to average fiber of a beam. This
kinematics makes it possible to describe the overall movement of the line of piping.
The theory of the hulls to describe the transverse deformation of the sections around fiber
average. Kinematics of the transverse sections: the cross-sections which are perpendicular to
surface average reference remain right. Material points located on the normal at surface
not deformed average remain on a line in the deformed configuration. The formulation used
is a formulation of the type LOVE_KIRCHHOFF without transverse shearing for the description of
behavior of the transverse sections. The thickness of the hull remains constant. Surface
average
pipe, located at mid thickness, is equivalent to the average surface of a hull. This
kinematics of hull brings the description of swelling, the ovalization and the roll of
cross section.
X
y
Z
O
o'
Section
L
Z
y
E
R
ext.
+
X
y
Z
X, U
S
, v
S
, W
S
O
o'
X, U
p
y, v
p
Z, W
p
xp
YP
zp
Average fiber
Surface average
Appear 2.1.2-b: Fiber and average surface in the case of a right pipe
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Additional displacements (U
S
) of the surface of the pipe are approximated by a series of
Fourier until the command M (M=3 for modeling TUYAU_3M and M=6 for modeling
TUYAU_6M).
=
=
+
=
M
m
m
M
m
I
m
S
m
X
U
m
X
U
X
U
2
0
2
sin
)
(
cos
)
(
)
,
(
=
-
+
=
M
m
I
m
I
S
m
X
v
X
W
X
v
2
1
sin
)
(
sin
)
(
)
,
(
=
+
M
m
m
m
X
v
X
W
2
0
0
1
cos
)
(
cos
)
(
=
=
+
+
=
M
m
m
M
m
I
m
S
m
X
W
m
X
W
W
X
W
2
0
2
0
sin
)
(
cos
)
(
)
,
(
Where
U
S
: represent the axial displacement of average surface in the local reference mark X
v
S
: represent orthoradial displacement average surface in the local reference mark X
W
S
: represent the radial displacement of average surface in the local reference mark X
W
0
: represent swelling
These elements thus utilize locally:
·
6 variables kinematics for the beam formulation: displacements U
p
, v
p
and W
p
according to
fiber of reference and rotations around the local axes,
·
3 variables kinematics for the hull formulation: additional displacements custom,
vs and ws in the reference mark of average surface,
·
4 stresses in the thickness of pipe noted SIXX (sxx), SIYY (sff), SIXY (sxf), and SIXZ
(sxz). Stress SIZZ (szz) is null (assumption of plane stresses). Stresses of
shearing transverses are null (assumption of Coils Kirchoff),
·
4 deformations in the thickness of pipe noted EPXX (exx), EPYY (EFF), EPXY (exf), and
EPXZ (sxz). Deformation EPZZ (ezz) is null for the beam part.
Important remark:
The kinematics of beam is based on the assumption of Timoshenko [R3.08.03]. The element pipe
is not “exact” with the nodes for loadings or torques concentrated at the ends, it
is necessary to net with several elements to obtain correct results.
According to average fiber, these elements are of isoparametric type. It results from it that them
displacements vary like polynomials of command 2 following X for the elements with 3 nodes and
of command 3 per 4 nodes.
2.2
Comparison with other elements
2.2.1 Differences between the elements pipes
The elements pipes TUYAU_3M and TUYAU_6M are linear elements:
·
TUYAU_3M with three or four nodes
·
TUYAU_6M with four nodes
These elements are different only on the level from the approximation from the field from displacement
additional HULL, which is made by a decomposition in Fourier series:
·
TUYAU_3M until command 3
·
TUYAU_6M until command 6
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Consequently the number of DDL is different:
·
TUYAU_3M 21 per node (6 DDL of beam and 15 DDL of hull)
·
TUYAU_6M 39 per node (6 DDL of beam and 33 DDL of HULL)
Compared with modeling TUYAU_3M, modeling TUYAU_6M allows the best
approximation of the behavior of the cross section if the aforementioned becomes deformed according to
a mode raised, for example in the case of thin tubes where the thickness report/ratio on radius of
cross section is < 0.1, and in certain cases in plasticity.
2.2.2 Differences between the elements pipes and the elements beams
Like the finite elements PIPE, the finite elements BEAM also form part of the class of
linear finite elements. One compares in this part the applicable formulations and loadings
for these two classes of elements.
On the level of the formulation:
·
Element BEAM:
The formulation is based on an exact resolution of the equations of the continuous model carried out
for each element of the mesh. Several types of elements of beam are available:
-
POU_D_E: transverse shearing is neglected, as well as the inertia of rotation. This
assumption is checked for strong twinges (Assumption of Euler),
-
POU_D_T, POU_C_T: transverse shearing and all the terms of inertia are taken in
count. This assumption is to be used for weak twinges (Assumption of
Timoshenko).
These elements use meshs of the type SEG2 with 6 DDL by nodes, 3 displacements and
three rotations. The formulation of these elements is presented in the reference document
[R3.08.01]. The section is constant, the only possible behavior of the transverse sections
is the translation and rotation for the whole of the points of the section. The section perhaps
of an unspecified form constant or variable over the length.
·
Element PIPE:
The formulation combines at the same time a beam formulation based on the assumption of Timoshenko
and a hull formulation based on the assumption of Love_Kirchhoff allowing to modelize
phenomena of swelling, ovalization and roll. The hollow section, of
form circular, is constant over the entire length of the element. The element is not
“exact” for the nodes for loadings or torques concentrated at the ends, it is necessary
thus to net with several elements to obtain correct results.
These elements use meshs of the type SEG3 or SEG4 with, for the kinematics of beam
6 DDL by nodes, 3 displacements and three rotations, and for the kinematics from hull, 15 or
33 DDL to typify displacement.
On the level of the applicable loadings:
·
Element BEAM:
The possible loadings are the loadings of extension, bending and torsion.
internal loading of pressure for the hollow sections does not exist (the section is
indeformable).
·
Element PIPE:
The element PIPE admits the conventional loadings of beam as well as the application of one
internal pressure.
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3
Description of the command sets
3.1
Assignment of a modeling and space discretization
In this part, one describes the choice and the assignment of one of two modelings PIPE as well as
degrees of freedom and associated meshs. The majority of described information are extracted from
documentation of use [U3.11.06]: Modelings TUYAU_3M and TUYAU_6M.
3.1.1 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 and W with
ovalization: V with displacement orthoradial, W with radial displacement, I means “in plane” and O
mean “out off planes”).
Element
Degrees of freedom to each node node
Remarks
TUYAU_3M DX DY DZ
Value of the component of
displacement in imposed translation
on the specified nodes
DRX
DRY
DRZ
Value of the component of
displacement in rotation imposed on
specified nodes
W0
WI1
WO1
DDL of swelling and mode 1 on W
UI2 VI2 WI2 UO2 VO2 WO2
DDL related to mode 2
UI3 VI3 WI3 UO3 VO3 WO3
DDL related to mode 3
TUYAU_6M DX DY DZ
Value of the component of
displacement in imposed translation
DRX
DRY
DRZ
Value of the component of
displacement in imposed rotation
W0
WI1
WO1
DDL of swelling and mode 1 on W
UI2 VI2 WI2 UO2 VO2 WO2
DDL related to mode 2
UI3 VI3 WI3 UO3 VO3 WO3
DDL related to mode 3
UI4 VI4 WI4 UO4 VO4 WO4
DDL related to mode 4
UI5 VI5 WI5 UO5 VO5 WO5
DDL related to mode 5
UI6 VI6 WI6 UO6 VO6 WO6
DDL related to mode 6
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3.1.2 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 METUSEG3
Linear mesh
SEG4
MET3SEG4
Linear mesh
TUYAU_6M SEG3 MET6SEG3
Linear mesh
The meshs SEG4, which have cubic functions of forms, were developed to solve one
simple problem of beam in bending. For this simple example, the exact solution is obtained with aid
of only one element with mesh SEG4.
For more complex problems, the experiment shows that one can net much more
coarsely with meshs SEG4. For example one needs about fifteen elements SEG3 to obtain
a correct solution for an elbow in bending whereas one needs of it half with elements SEG4.
Note:
One can use operator MODI_MAILLAGE to build meshs SEG4 from
meshs SEG3.
3.1.3 Net support of the loadings
All the loadings applicable to the elements used are treated by direct discretization on
net support of the element in displacement formulation. Linear pressure and other forces
as well as gravity are examples of loadings applying directly to the element.
No special mesh of loading is thus necessary.
3.1.4 Model
:
AFFE_MODELE
The assignment of modeling passes through operator AFFE_MODELE [U4.41.01]. It is reminded the meeting that only
the mechanical phenomenon is available with the element PIPE.
AFFE_MODELE
TUYAU_3M
TUYAU_6M
Remarks
AFFE
·
PHENOMENON:
“MECHANICAL”
·
MODELING “TUYAU_3M'
·
MODELING “TUYAU_6M'
·
On the level of the choice of modeling PIPE, one can note that the use of a decomposition in
Fourier series to command 6 (element TUYAU_6M) improve the approximation of the behavior of
cross section if the aforementioned becomes deformed according to a raised mode, for example in
mean cases of tubes where the thickness report/ratio on radius of the cross section is < 0.1, and in
case of plasticity
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3.2
Elementary characteristics: AFFE_CARA_ELEM
In this part, the operands characteristic of the element pipe are described. Documentation
of use of operator AFFE_CARA_ELEM is [U4.42.01].
AFFE_CARA_ELEM
TUYAU_3M
TUYAU_6M
Remarks
BEAM
·
SECTION:
“CIRCLE”
·
% constant section
·
% section Variable
·
MODI_METRIQUE
·
TUYAU_NCOU tncouch
·
TUYAU_NSEC tnsec
·
ORIENTATION
“GENE_TUYAU”
·
Definition of a generator. By
defect, a generator is created
PRECISION
·
CRITERION
·
The characteristics which it is possible to affect on the elements PIPE, are:
·
SECTION: “CIRCLE”
The section is defined by its radius “R” external and its thickness “EP”, on each mesh
since the mesh is represented by average fiber of the pipe.
·
TUYAU_NCOU: tncouch
It is the number of layers to be used for the integration of the relations of behavior not
linear in the thickness of the right pipe sections. In linear elasticity, one to two
layers are enough, into nonlinear one advises to put between 3 and 5 layers. The number of
not Gauss is equal to twice the number of layers plus one (2 * tncouch + 1), which makes
that time CPU increases quickly with the number of the layers.
·
TUYAU_NSEC: tnsec
It is the number of angular sectors to use for the integration of the relations of
nonlinear behavior in the circumference of the right pipe sections. By defect it
a many sectors are worth 16. One advises to put 32 sectors into nonlinear for
precise results (attention with the increase in time CPU with the number of sectors).
·
ORIENTATION (“GENE_TUYAU”)
One defines from one of the nodes ends of the line of piping a continuous line
traced on the pipe. The operands PRECISION and CRITERION make it possible to define the precision
for the construction of the generator and the limit enters a right pipe section and one
curved element.
Note:
The directing vector of the line thus defined should not be colinéaire with average fiber of
bend with the node end considered, by using the key word INFORMATION:2 one can check if it
definite vector is correct.
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3.2.1 Operand
MODI_METRIQUE
Operand MODI_METRIQUE makes it possible to define for the elements PIPE the type of integration in
the thickness:
·
MODI_METRIQUE: “NOT” resulted in assimilating in integrations the radius to the radius
means. This is thus valid for the pipes low thickness (relative with the radius),
·
MODI_METRIQUE: “YES” implies a complete integration, more precise for
thick pipings, but being able in certain cases to lead to oscillations of
solution.
3.2.2 Generator and concept of local reference mark: key word ORIENTATION
The generator traced throughout piping makes it possible to define the origin of the angles
[Figure 2.1.2-b]. This is used:
·
to interpret the degrees of freedom of ovalization;
·
to choose the place of extraction of the stresses (option SIGM_ELNO_TUYO) and the variables
interns (option VARI_ELNO_TUYO).
·
·
·
·
· ·
1
2
Generating line
Appear 3.2.2-a: Representation of two noncoplanar elbows connected by a right pipe.
For a transverse section end of the line of piping [Figure 3.2.2-b], the user defines in
AFFE_CARA_ELEM
under the key word
ORIENTATION
a vector of which projection on the section
transverse end defines a vector origin Z
1
unit.
Syntax is as follows:
AFFE_CARA_ELEM (…
ORIENTATION: (GROUP_NO: END
CARA: “GENE_TUYAU”
VALE: (X, y, Z)));
where:
END
centers transverse section end is the node;
(X, y, Z)
contains the 3 components of the vector directing the generator of the pipe, to project on
the transverse section end. This vector must be defined in a node or a group_no
end of the pipe. The geometry is then built automatically for all the elements
related of PIPE.
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The intersection between the direction of this vector and the average surface of the elbow determines the trace of
generator on this section. X is called
1
, y
1
, Z
1
the direct trihedron associated this section where X
1
is it
unit vector perpendicular to the transverse section. The intersection enters the transverse section and
straight line resulting from the center of this section directed by Z
K
is the trace of a generator represented Ci
below. For the whole of the other transverse sections, trihedron X
K
, y
K
, Z
K
is obtained either by
rotation of the trihedron
X
k-1
, y
k-1
, Z
k-1
in the case of the bent parts, is by translation of trihedron X
k-1
, y
k-1
,
Z
k-1
for the right parts of piping.
X
1
Z
1
y
1
X
2
Z
2
y
2
Appear 3.2.2-b: Representation of the generator of reference
The origin of
commune with all the elements is defined compared to the trace of this generator on
the transverse section. The angle enters the trace of the generator and the current position on the section
transverse is identified by the angle
. The local reference mark of the right and bent pipe is thus defined by the option
ORIENTATION
(
“GENE_TUYAU”
) of the control
AFFE_CARA_ELEM
who allows to define the first
vector Z
K
at an end.
X
y
Z
Surface average
Trace
the generator
Appear 3.2.2-c: Identify local element XYZ
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3.2.3 Example
of assignment of characteristic
This example is a piping comprising two elbows (problem of Hoovgaard resulting from the test
SSLL101C).
Z
y
X
With
B
10
4
5
5
4
Modeling PIPE (SEG3)
C
H
G
F
E
D
Boundary conditions: Points C and H
- DDL of Beam: DX = DY = DZ = DRX = DRY = DRZ
= 0
- DDL of Hull: UIm = VIm = Wim = 0 (m=2,3)
UOm = VOm = WOm = 0 (m=2,3)
WI1 = WO1 = WO = 0
·
diameter external of the pipe: 0.185 m
·
thickness of the pipe: 6.12 m
·
radius of curvature of the elbows: 0.922 m
MODELE=AFFE_MODELE (MAILLAGE=MAILLAGE,
AFFE=_F (ALL = “YES”,
PHENOMENON = “MECHANICAL”,
MODELING = “TUYAU_3M')
)
CARELEM=AFFE_CARA_ELEM (MODELE=MODELE,
POUTRE=_F (GROUP_MA = “TOUT_ELT”,
SECTION = “CIRCLE”,
CARA = (“R”, “EP”,),
VALE = (0.0925, 0.00612,)),
ORIENTATION=_F (GROUP_NO = “It,
CARA = “GENE_TUYAU”,
VALE = (1., 0., 0.,))
)
3.3 Materials
:
DEFI_MATERIAU
The definition of the behavior of a material is carried out using operator DEFI_MATERIAU
[U4.43.01]. There is no particular stress which had with the use of the elements PIPE.
The materials used with the whole of modelings can have elastic behaviors
in plane stresses whose linear characteristics are constant or function of the temperature.
The nonlinear behaviors in plane stresses are available for modelings
pipes. For more information on these nonlinearities one can refer to [§ 2.6].
DEFI_MATERIAU
TUYAU_3M TUYAU_6M
Remarks
ELAS, ELAS_FO,
ECRO_LINE,
TRACTION,…
·
·
all them
materials
available in
C_PLAN
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3.4 Limiting loadings and conditions
: AFFE_CHAR_MECA and
AFFE_CHAR_MECA_F
One points out that it is not possible to carry out thermal calculations, however the assignment of
temperature is possible, using operator CREA_CHAMP. (see paragraph [§3.4.4]).
The assignment of the loadings and the boundary conditions on a mechanical model is carried out with
the aid of operators AFFE_CHAR_MECA, if loadings and boundary conditions mechanical
on a system are actual values depending on no parameter, or
AFFE_CHAR_MECA_F, if these values are functions of the position or the increment of loading.
The documentation of use of AFFE_CHAR_MECA and AFFE_CHAR_MECA_F is [U4.44.01].
3.4.1 List key words factors of AFFE_CHAR_MECA and AFFE_CHAR_MECA_F
The key words factors available for these two operators are gathered in the two tables
following.
AFFE_CHAR_MECA TUYAU_3M
TUYAU_6M
Drank, remarks and examples
DDL_IMPO
·
Drank: to impose, with nodes or groups of nodes, one
or of the values of displacement
Mode 0 (swelling) and:
-
modes 1 to 3 for TUYAU_3M
-
modes 1 to 6 for TUYAU_6M
Example: SDLL14, SSLL101, SSLX102, SSNL106,…
LIAISON_DDL
·
Drank: to define a linear relation between degrees of freedom
from two or several nodes
LIAISON_OBLIQUE
·
Drank: to apply, with nodes or groups of nodes,
even component value of displacement definite by
component in an unspecified oblique reference mark
LIAISON_GROUP
·
Drank: to define linear relations between certain degrees of
freedom of couples of nodes, these couples of nodes being
obtained while putting in opposite two lists of meshs or of
nodes
LIAISON_UNIF
·
Drank: to impose the same value (unknown) on degrees of
freedom of a whole of nodes
Example: ELSA01B, ELSA01C and ELSA01D
LIAISON_SOLIDE
·
Drank: to modelize an indeformable part of a structure
Example: ELSA01B, ELSA01C and ELSA01D
LIAISON_ELEM
·
Drank: to modelize the connections of a massive part 3D with
a pipe part or of a hull part with a pipe part
Example: SSLX101B, SSLX102A and SSLX102F
LIAISON_CHAMNO
·
Drank: to define a linear relation between all ddls present
in a concept
CHAM_NO
TEMP_CALCULEE
·
Drank
: to recover a thermal loading (temperature
affected by CREA_CHAMP)
Example: HSNS101D, HSNV100C, SSLL101C,…
GRAVITY
·
Drank: to apply an effect of gravity
Example: SSLL101, SSLL106
FORCE_POUTRE
·
Drank: to apply linear forces, to elements of the type
beam
Example: SSLL106
FORCE_NODALE
·
Drank: to apply, with nodes or groups of nodes,
nodal forces, definite component by component in
identify
TOTAL
or in an oblique reference mark defined by 3 angles
nautical
Example: SSLL106,…
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FORCE_TUYAU
·
Drank: to apply, with elements or groups of elements
of pipe type an internal pressure
Example: SSLL106, SSNL117, SSNL503
AFFE_CHAR_MECA_F
TUYAU_3M
TUYAU_6M
Remarks
DDL_IMPO
· See
above
LIAISON_DDL
· See
above
LIAISON_OBLIQUE
· See
above
LIAISON_GROUP
· See
above
LIAISON_UNIF
· See
above
LIAISON_SOLIDE
· See
above
FORCE_POUTRE
· See
above
FORCE_NODALE
· See
above
FORCE_TUYAU
· See
above
3.4.2 Application of an internal pressure: key word FORCE_TUYAU
This key word factor is usable to apply an internal pressure to elements pipe, definite
by one or more meshs or groups of meshs. The pressure is applied to the level of the radius
intern, as in 3D.
Syntax to apply this loading is pointed out below:
·
AFFE_CHAR_MECA:
|
FORCE_TUYAU
:
(
/ALL: “YES”
/
NET
:
lma
[l_maille]
/
GROUP_MA
:
lgma [l_gr_maille]
NEAR:
p
[R]
)
·
AFFE_CHAR_MECA_F:
|
FORCE_TUYAU
:
(
/ALL: “YES”
/
NET
:
lma
[l_maille]
/
GROUP_MA
:
lgma [l_gr_maille]
NEAR:
PF
[function]
)
The operand available is:
NEAR:
p (PF)
Value of the imposed pressure (real or function of time or the geometry).
p is positive according to the contrary direction of the normal to the element.
This loading applies to the types of meshs and following modelings:
Net Modélisation
SEG3, SEG4
SEG3
“TUYAU_3M'
“TUYAU_6M'
Examples of use are available in the base of tests: case-tests ELSA01B, SSLL106A,
SSNL117A and SSNL503A.
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3.4.3 Application of a force distributed: key word FORCE_POUTRE
This key word factor is usable to apply linear, constant forces according to X, to
elements of the beam type defined on all the mesh or one or more meshs or of
groups of meshs. The forces are definite component by component, that is to say in the reference mark
TOTAL
, that is to say in the local reference mark of the element defined by the operator
AFFE_CARA_ELEM
[U4.42.01].
Syntax is available in the documentation of
AFFE_CHAR_MECA
/
AFFE_CHAR_MECA_F
[U4.44.01].
This loading applies to the types of meshs and following modelings:
Net Modélisation
SEG3, SEG4
SEG3
TUYAU_3M
TUYAU_6M
An example of use is available in the base of tests: case-test SSLL106.
3.4.4 Application of a thermal dilation: key word TEMP_CALCULEE
No thermal calculation is available with modeling PIPE, it is nevertheless possible
to apply a dilation (thermal loading of origin), in the shape of a field of temperature
with the nodes in the thickness of the tubes.
This field will have been beforehand creates using operator CREA_CHAMP (documentation
[U4.72.04]).
CREA_CHAMP
TUYAU_3M
TUYAU_6M
Remarks
TYPE_CHAM “NOEU_TEMP_R”
“NOEU_TEMP_F”
·
Field result of the temperature type
OPERATION
MESH
MODEL
AFFE
ALL: “YES”
GROUP_MA
NET
NODE
GROUP_NO
·
The field is manufactured by
assignment of values on
nodes or of the meshs
NOM_CMP “TEMP”
·
Names of the components that
one wants to affect: temperature
“TEMP_INF”
·
Lower temperature
“TEMP_SUP”
·
Temperature superior
The assignment of thermal dilation is carried out using operator AFFE_CHAR_MECA
(documentation [U4.44.01]).
AFFE_CHAR_MECA
TUYAU_3M
TUYAU_6M
Remarks
MODEL
·
TEMP_CALCULEE temple
·
temple is the field creates by
CREA_CHAMP
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The following example is extracted from case-test SSLL101C.
TEMP = CREA_CHAMP (MESH = MESH,
TYPE_CHAM = “NOEU_TEMP_R”,
OPERATION = “AFFE”, AFFE= (
_F (ALL = “YES”,
NOM_CMP = “TEMP”,
VALE = 472.22),
_F (ALL = “YES”,
NOM_CMP = “TEMP_INF”,
VALE = 472.22),
_F (ALL = “YES”,
NOM_CMP = “TEMP_SUP”,
VALE = 472.22))
)
DILATA=AFFE_CHAR_MECA (MODELE=MODELE,
TEMP_CALCULEE=TEMP
)
Note:
If one wants to apply a temperature defined by a function, one can use
operator CREA_RESU (TYPE_RESU=' EVOL_THER',…) (see the document [U4.44.12])
to create a concept of the type EVOL_THER usable in AFFE_CHAR_MECA. An example
is available in the form of case-test HSNS101D.
Examples of use are available in the base of tests: case-tests ELSA01B, SSLL106A,
SSNL117A and SSNL503A.
3.4.5 Application of gravity: key word GRAVITY (AFFE_CHAR_MECA only)
This key word is used for applied the effect of gravity on piping.
AFFE_CHAR_MECA
TUYAU_3M
TUYAU_6M
Remarks
GRAVITY
(G, ap, LP, CP)
·
Acceleration and direction of
gravity
Example of use of the operand GRAVITY:
POI_PROP = AFFE_CHAR_MECA (MODELE=MODELE,
PESANTEUR= (9.81, 0., 0., - 1.,)
)
3.4.6 Connections hull-pipes, 3D-pipe and pipe-beams: key word LIAISON_ELEM
It is a question of establishing the connection between a node end of a pipe section and a group of mesh of
edge of elements of hulls or elements 3D. This makes it possible to net part of piping (by
example an elbow) in hulls or elements 3D and the remainder in right pipes. The formulation of the connection
hull-pipes and of the connection 3D-Pipe is presented in the reference document [R3.08.06]. It
connection makes it possible to transmit the roll and ovalization means of the mesh hull or 3D to
ddl agent of the pipe.
The connection:
·
Hull - pipe: it makes it possible to connect elements of edge (SEG2, SEG3) of the hull part to
node of the pipe to be connected. This connection is currently realizable for pipes of which
neutral fiber is perpendicular to the normals with the breakages of the plates or the hulls.
connection is usable by using key word LIAISON_ELEM: (OPTION: “COQ_TUYAU”)
AFFE_CHAR_MECA.
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·
Pipe - 3D: it makes it possible to connect elements of edge (TRIA3, QUAD4, TRIA6,…) part
3D with the node of the pipe to be connected. The connection is usable by using the key word
LIAISON_ELEM: (OPTION: “3d_TUYAU”) of AFFE_CHAR_MECA.
Appear 3.4.6-a: Example of connection between a mesh COQUE_3D and PIPE
The case-tests which test the connections are presented on the following table.
NAME
MODELING ELEMENT
Remarks
SSLX101B
Doc. V:
[V3.05.101]
DKT
PIPE
DIS_TR
MEDKQU4
METUSEG3
POI1
Connection COQ_TUYAU:
Pipe right modelized in hulls and beams.
This test aims to test the connection
hull pipe “COQ_TUYAU” in the presence of
unit loadings: traction, bending and of
torsion.
SSLX102A
Doc. V:
[V3.05.102]
DKT
PIPE
MEDKQU4
METUSEG3
MEDKQU4
METUSEG3
Connection COQ_TUYAU:
Piping bent in bending.
SSLX102F
Doc. V:
[V3.05.102]
3D
PIPE
HEXA20
METUSEG3 Connection 3d_TUYAU:
Piping bent in bending: modeling
3D-PIPE, relations linear 3d_TUYAU.
elbow is modelized with elements 3D.
In all these case-tests, the results are satisfactory given that part of the variations
noted is ascribable with the fusion of the mesh 3D or hulls.
Note:
Connections pipe-beams.
It is a question of establishing a connection between a node end of a pipe section and a node end of one
element of beam. The pipe formulation comprises a kinematics of the beam type identical to
kinematics of the elements beams. There is thus no cut between displacements of the type
beam (3 displacements and 3 rotations). The average fiber of the beam and the pipe are the same ones. By
count, the kinematics of the elements of beam does not include/understand kinematics of hull (the section
is indeformable) like in the case of the elements pipes, there is thus a cut on the level of
deformation of the transverse section.
There does not exist in specific Code_Aster of connection pipe-beam, the connection between these two
elements is automatically assured, without intervention of the user, by the node common to
the element pipe and with the element beam. Nevertheless, some care are to be taken, it is necessary that
transition between the beam and pipe sections is sufficiently distant from all areas “pipe” or
the deformation of the transverse section is significant, i.e. that one should connect only when
ovalization is deadened.
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3.4.7 Limiting conditions: key words DDL_IMPO and LIAISON_ *
The key word factor DDL_IMPO makes it possible to impose, with nodes introduced by one (at least) of the words
keys: ALL, NODE, GROUP_NO, MESH, GROUP_MA, one or more values of displacement (or of
certain associated sizes). According to the name of the operator called, the values are provided
directly (AFFE_CHAR_MECA) or via a concept function (AFFE_CHAR_MECA_F).
The operands available for DDL_IMPO, are listed below:
·
DX DY DZ
Blocking on the component of displacement in translation
·
DRX DRY DRZ
Blocking on the component of displacement in rotation
If the specified nodes belong to elements “TUYAU_3M' (these elements have 15 DDL of
hull):
U: roll
V, W: ovalization
I: “in plane”
O: “out off planes”
That is to say:
·
UI2 VI2 WI2 UO2 VO2 WO2
DDL related to mode 2
·
UI3 VI3 WI3 UO3 VO3 WO3
DDL related to mode 3
·
WO WI1 WO1
DDL of swelling and mode 1 on W
If the specified nodes belong to elements “TUYAU_6M' (these elements have 33 DDL of
hull), one adds the following DDL:
·
UI4 VI4 WI4 UO4 VO4 WO4
DDL related to mode 4
·
UI5 VI5 WI5 UO5 VO5 WO5
DDL related to mode 5
·
UI6 VI6 WI6 UO6 VO6 WO6
DDL related to mode 6
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4 Resolution
4.1
Linear calculations: Linear MECA_STATIQUE and other operators
Linear calculations are carried out in small deformations. Several linear operators of resolution
are available:
·
MECA_STATIQUE: resolution of a problem of static mechanics linear ([U4.51.01]),
·
MACRO_ELAS_MULT: calculate linear static answers for various loading cases
or modes of Fourier. ([U4.51.02]),
·
MODE_ITER_SIMULT: calculation of the values and vectors clean by methods of under
spaces. ([U4.52.03]),
·
MODE_ITER_INV: calculation of the values and vectors clean by the method of iterations opposite
([U4.52.04]),
·
MODE_ITER_CYCL
: calculation of the clean modes of a structure with cyclic symmetry
([U4.52.05]),
·
DYNA_LINE_TRAN: calculation of the transitory dynamic response to a temporal excitation
unspecified ([U4/U4.53.02]).
Concerning the operator of resolution of static mechanics linear, following information is
extracted the documentation of use of operator MECA_STATIQUE: [U4.51.01].
MECA_STATIQUE
TUYAU_3M
TUYAU_6M
ANGLE
ndegré
·
This word is used only for the postprocessings required on
pipe sections. It is the angle (in degrees)
not compared to the generator of the circuit of
piping. It is worth 0 per defect
NUME_COUCHE nume
·
This word is used only for the postprocessings required on
pipe sections. It is the angle (in degrees)
not compared to the generator of the circuit of
piping. L is worth 0 per defect
NIVE_COUCHE “INF”
“SUP”
“MOY”
·
This word is used only for the postprocessings required on
pipe sections. It is the angle (in degrees)
not compared to the generator of the circuit of
piping. L is worth 0 per defect
By defect, the only computed field is the fields of displacement DEPL. Other fields are
available by the operand OPTION (see the options available in the paragraph [§5.2] bearing on
the use of CALC_ELEM).
·
ANGLE: /delta (0. per defect)
·
NUME_COUCHE: /nume (standard entirety, 1 per defect)
·
NIVE_COUCHE: /“INF”, “SUP” or “MOY” (“MOY” by defect)
with:
·
delta: angle in degrees counted starting from the position of the generator of the element pipe,
·
nume: number of layer (number 1 corresponds to the internal layer). Must be
inferior or equal to the total number of layers given in STAT_NON_LINE (key word
TUYAU_NCOU),
·
NIVE_COUCHE indicates the position of the point of integration in layer (INF corresponds to
not more the intern).
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4.2
Nonlinear calculations: STAT_NON_LINE and DYNA_NON_LINE
4.2.1 Behaviors and assumptions of deformations available
Following information is extracted from the documentation of use of the operator
STAT_NON_LINE: [U4.51.03].
STAT_NON_LINE
DYNA_NON_LINE
TUYAU_3M
TUYAU_6M
COMP_INCR RELATION
·
all behaviors available
in C_PLAN
DEFORMATION SMALL
·
Incremental relations of behavior (key word factor COMP_INCR) according to the assumption of
small displacements and small deformations (key word DEFORMATION: “SMALL”) are only
mechanical nonlinear relations of behavior available for modeling PIPE. These
relations of behavior connect the rates of deformation to the rates of stresses. Behaviors
nonlinear supported are those already existing in plane stresses defined in the operators
STAT_NON_LINE and DYNA_NON_LINE. Moreover, with ALGO_C_PLAN: `DEBORST `all them
behaviors 2D (D_PLAN, AXIS) in small deformations are usable.
The options specific to modeling PIPE are:
The concept RESULT of STAT_NON_LINE contains displacement, stress fields and
variables intern at the points of integration always calculated at the points of gauss:
·
SIEF_ELGA: Tensor of the stresses by element at the points of integration in the reference mark
room of the element,
·
VARI_ELGA: Field of variables intern by element at the points of integration in
identify local element,
·
DEPL: fields of displacements.
Moreover, one call to operator CALC_ELEM or CALC_NO, gives access other fields.
In particular, one can carry out the passage of the stresses and internal variables of the points of Gauss
with the nodes to form fields SIEF_ELNO_ELGA and VARI_ELNO_ELGA (see the paragraph
[§5.2]).
A field VARI_… can have several types of components. For example, components of
field VARI_ELNO_ELGA are, for the elements PIPE:
·
K time: (V1, V2, ..... Vn)
Where:
K is the number of points of integration total: K= (2 * NCOU+1) * (2 * NSEC+1);
NR is the number of variables intern and depends on the behavior.
4.2.2 Details on the points of integration
For linear and non-linear calculations, numerical integration is carried out with a method of:
·
Gauss along average fiber.
The number of points of integration is fixed at 3. For a mesh whose nodes are 1 and 2
and numbered from 1 to 2, the 3 points of gauss are such as first is close to 1, it
second is at equal distance from 1 and 2 and the third is closer to 2. It is thus necessary to make
attention with the orientation of the meshs when one looks at the results at the points of gauss 1 and
3. Indeed if the orientation of the mesh is changed and that one numbers it from 2 to 1, the first
not gauss is closer to 2.
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·
Simpson in the thickness and on the circumference:
-
Integration in the thickness is an integration of Simpson at 3 points per layer.
a number of points of integration per layer is fixed at 3, in the middle of the layer, in skin
higher and in lower skin of the layer, the two points ends being common
with the close layers.
-
Integration according to the circumference is an integration of Simpson per sector, each
sector being of angle 2
/NSEC. is the angle between the generator and the center of the sector.
The number of points of integration per sector is fixed at 3, in the middle of the sector, partly
higher (
+/NSEC) and lower (-/NSEC) of the sector, two points
ends being common with the close sectors.
The number of layers and the number of sectors must be defined by the user starting from the key words:
TUYAU_NCOU, TUYAU_NSEC of operator AFFE_CARA_ELEM.
For example, with 3 layers and 16 sectors, the number of points of integration per element is
(2 * NCOU+1) * (2 * NSEC+1) * NPG what gives 693 points of integration. For each point of gauss on
the length of the element, one stores information on the layers and for each layer on all
sectors. If one wants information at the point of gauss NG, on layer NC level NCN (NCN
= 1 so lower, NCN = 0 if medium, NCN = + 1 so higher), on the sector NS, level NSN (NSN =
1 so lower, NSN = 0 if medium, NSN = +1 so higher), then one looks at the values sought with
not integration:
NP = (NG-1) * (2NCOU+1) * (2NSEC+1) + (2 * NC+NCN-1) * (2NSEC+1) + (2 * NS+NSN).
In practice, it is more convenient to observe:
·
that is to say values extracted in a thickness and a sector: * _TUYO;
·
maybe of the total values, for example SIEF_ELNO_ELGA.
4.3 Calculations
dynamic
Concerning dynamic calculations, no specificity due to the finite element PIPE exists.
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5
Additional calculations and postprocessings
5.1
Elementary calculations of matrices: operator CALC_MATR_ELEM
Operator CALC_MATR_ELEM (documentation [U4.61.01]) allows to calculate matrices
elementary compilable by control ASSE_MATRICE (documentation [U4.61.22]).
The only calculable matrices with the elements pipe are the matrices of rigidity and mass of
elements of the model:
CALC_MATR_ELEM
TUYAU_3M TUYAU_6M
Remarks
“RIGI_MECA”
· ·
“MASS_MECA”
· ·
These calculations of elementary matrices for example are used for the determination of the frequencies
clean of a thick cylindrical ring, in case-test SDLS109G.
5.2
Calculations by elements: operator CALC_ELEM
Operator CALC_ELEM (documentation [U4.81.01]) carries out the calculation of the fields to the elements:
·
stresses, deformations, variables intern with the nodes;
·
equivalent values (nonavailable for modeling PIPE).
One presents hereafter the options of postprocessing for the pipe sections. For the structures
modelized by pipe sections, it is particularly important to know how are
presented results of the stresses: the approach adopted in Code_Aster consists in observing
stresses in a particular reference mark related to the element whose reference axis was defined in
paragraph [§3.2.2]. This approach seems most physical because, for a cylindrical structure, them
the stresses easiest to interpret are not the stresses in Cartesian reference mark but them
stresses in cylindrical co-ordinates. Moreover this approach allows a greater flexibility
of use.
CALC_ELEM
TUYAU_3M TUYAU_6M Remarks
“SIEF_ELGA_DEPL”
· ·
“EFGE_ELNO_DEPL”
· ·
“EPSI_ELGA_DEPL”
· ·
“SIGM_ELNO_TUYO”
· ·
“SIEF_ELNO_ELGA”
· ·
“VARI_ELNO_ELGA”
· ·
“VARI_ELNO_TUYO”
· ·
·
SIEF_ELGA_DEPL: calculation of the stresses by element at the points of integration of the element with
to leave displacements (Use only in elasticity), in the local reference mark of
the element.
·
EFGE_ELNO_DEPL: calculation of the generalized efforts of conventional beam per element with
nodes starting from displacements, in the local reference mark of the element (only in elasticity
linear).
·
EPSI_ELGA_DEPL: calculation of the deformations by element at the points of integration of the element
starting from displacements, in the local reference mark with the element (small deformations).
·
SIEF_ELNO_ELGA: calculation of the torque of the efforts generalized by element with the nodes, in
identify local element (calculated by integration starting from SIEF_ELGA).
Code_Aster
®
Version
6.3
Titrate:
Note of use of the elements
TUYAU_ *
Date:
24/05/02
Author (S):
A. ASSIRE, P. MASSIN, F. LEBOUVIER
Key
:
U2.02.02-A
Page
:
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Instruction manual
U2.02 booklet: Elements of structure
HT-66/02/003/A
·
VARI_ELNO_ELGA: calculation of the field of variables intern by element with the nodes to leave
points of Gauss, for all the layers (in thickness SUP/MOY/INF) and for all
sectors in the local reference mark of the element.
·
SIGM_ELNO_TUYO: calculation of the local stresses by elements with the nodes from
points of integration, in the local reference mark of the element. Calculations provide the stresses
at the point defined by options NUME_COUCHE, NIVE_COUCHE and ANGLE.
·
VARI_ELNO_TUYO: calculation of the variables intern in a layer and for a sector
angular of elements pipe (key words
NUME_COUCHE, NIVE_COUCHE
and
ANGLE
affected by
AFFE_CARA_ELEM, to see paragraph [§3.2]).
One obtains then by node of each tensor only one element of stresses (or only one whole of
variables intern), which allows the graphic examination (evolution of a component,…).
5.3
Calculations with the nodes: operator CALC_NO
CALC_NO
TUYAU_3M TUYAU_6M
Remarks
“FORC_NODA”
· ·
“REAC_NODA”
· ·
“EFGE_NOEU_DEPL”
· ·
“SIEF_NOEU_ELGA”
· ·
“VARI_NOEU_ELGA”
· ·
Operator CALC_NO (documentation [U4.81.02]) carries out the calculation of the fields to the nodes by
moyennation and the calculation of the forces and reactions:
·
fields with the nodes: internal stresses, deformations, variables, equivalent values;
-
Name of option: to replace _ELNO_ by _NOEU_
-
One can calculate the fields with the nodes by CALC_NO
SIEF_NOEU_ELGA, VARI_NOEU_ELGA
·
forces and reactions:
-
starting from the stresses, balance: FORC_NODA (calculation of the nodal forces from
stresses at the points of integration, element by element),
-
then by removing the loading applied: REAC_NODA (calculation of the nodal forces of
reaction to the nodes, the stresses at the points of integration, element by
element):
REAC_NODA = FORC_NODA - loadings applied,
-
useful for checking of the loading and calculations of resultants, moments, etc
Code_Aster
®
Version
6.3
Titrate:
Note of use of the elements
TUYAU_ *
Date:
24/05/02
Author (S):
A. ASSIRE, P. MASSIN, F. LEBOUVIER
Key
:
U2.02.02-A
Page
:
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Instruction manual
U2.02 booklet: Elements of structure
HT-66/02/003/A
5.4
Calculations of the elementary fields: operator CALC_CHAM_ELEM
Operator CALC_CHAM_ELEM (documentation [U4.81.03]) allows to calculate fields
elementary starting from already calculated fields of type CHAM_NO_ * or CHAM_ELEM_ *.
TUYAU_3M TUYAU_6M Remarks
“EFGE_ELNO_DEPL”
· ·
For modeling PIPE, only the efforts generalized for a field of displacement are
available.
5.5 Calculations of quantities on whole or part of the structure: operator
POST_ELEM
Operator POST_ELEM (documentation [U4.81.22]) allows to calculate quantities on all or
part of the structure. The calculated quantities correspond to particular options of calculation of
affected modeling.
TUYAU_3M TUYAU_6M
Remarks
“MASS_INER”
· ·
For modeling PIPE, the only currently available option is calculation, on each
element, of the mass, inertias and the position of the center of gravity (option “MASS_INER”).
5.6 Values of components of fields of sizes: operator
POST_RELEVE_T
For modeling PIPE, operator POST_RELEVE_T (documentation [U4.81.21]) can be
used for, on a line, to extract from the values (for example SIEF_ELNO_ELGA or
SIGM_ELNO_TUYO). The produced concept is of type counts.
Important remark:
If one comes from an interface with a maillor (PRE_GIBI, PRE_IDEAS, PRE_GMSH), the nodes
of a groupno are arranged by numerical command. It is necessary to reorder the nodes along
line of examination. The solution is to use operator DEFI_GROUP with the option
NOEU_ORDO. This option makes it possible to create an ordered GROUP_NO containing the nodes of one
together of meshs made of segments (SEG2, SEG3 or SEG4).
An example of extraction of component is given in case-test SSNL503 (see description with
paragraph [§6.2]):
TAB_DRZ=POST_RELEVE_T (ACTION=_F (
GROUP_NO = “Of,
ENTITLE = “TB_DRZ”,
RESULT = RESUL,
NOM_CHAM = “DEPL”,
NOM_CMP = “DRZ”,
TOUT_ORDRE = “YES”,
OPERATION = “EXTRACTION”
)
)
Code_Aster
®
Version
6.3
Titrate:
Note of use of the elements
TUYAU_ *
Date:
24/05/02
Author (S):
A. ASSIRE, P. MASSIN, F. LEBOUVIER
Key
:
U2.02.02-A
Page
:
27/32
Instruction manual
U2.02 booklet: Elements of structure
HT-66/02/003/A
The purpose of this syntax is:
·
to extract:
OPERATION = “EXTRACTION”
·
on the line (the group of nodes) D: GROUP_NO = “Of
·
component DRZ of displacement: NOM_CHAM = “DEPL”, NOM_CMP = “DRZ”,
·
for every moment of calculation:
TOUT_ORDRE = “YES”
5.7
Impression of the results: operator IMPR_RESU
Operator IMPR_RESU allows to write the mesh and/or the results of a calculation on listing with the format
“RESULT” or on a file in a displayable format by external tools for postprocessing with
Aster: format RESULT and ASTER (documentation [U4.91.01]), format CASTEM (documentation
[U7.05.11]), format ENSIGHT documentation [U7.05.31]), format IDEAS (documentation [U7.05.01]),
format MED (documentation [U7.05.21]) or format GMSH (documentation [Ux.xx.xx]).
Currently this procedure makes it possible to write with the choice:
·
a mesh,
·
fields with the nodes (of displacements, temperatures, clean modes, modes
statics,…),
·
fields by elements with the nodes or the points of GAUSS (of stresses, efforts
generalized, of variables intern…).
The element PIPE being treated same manner that the other finite elements, we return it
reader with the notes use corresponding to the format of exit which it wishes to use.
Code_Aster
®
Version
6.3
Titrate:
Note of use of the elements
TUYAU_ *
Date:
24/05/02
Author (S):
A. ASSIRE, P. MASSIN, F. LEBOUVIER
Key
:
U2.02.02-A
Page
:
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Instruction manual
U2.02 booklet: Elements of structure
HT-66/02/003/A
6 Examples
The tables according to describe some case-tests using the element PIPE.
6.1
Analyze static linear
SSLL101
Z
y
X
With
B
C
H
G
F
E
D
Titrate: Problem of Hovgaard. Analyze static of a piping
three-dimensional comprising elbows
Documentation V: [V3.01.101]
Modelings:
SSLL101D TUYAU_6M SEG3
SSLL101C TUYAU_3M SEG3
SSLL101E TUYAU_3M SEG4
ssll106 Title
:
Tube right subjected to several loadings.
Documentation V: [V3.01.106]
Modelings:
SSLL106B TUYAU_3M SEG3
SSLL106E TUYAU_3M SEG4
SSLL106D TUYAU_6M SEG3
Loadings: a traction, 2 efforts sharp, 2 moments of
bending, a torsion and a pressure. It makes it possible to test them
displacements, efforts with the nodes and stresses and
deformations at the points of Gauss, compared to a solution of
analytical reference. The mesh used is the same one for
four modelings. Modelings A and C use
MECA_STATIQUE, while modelings B and D use
STAT_NON_LINE for the resolution.
sslx102 Title
:
Piping bent in bending.
Documentation V: [V3.05.102]
Modelings:
SSLX102B TUYAU_3M SEG3
SSLX102C TUYAU_6M SEG3
Code_Aster
®
Version
6.3
Titrate:
Note of use of the elements
TUYAU_ *
Date:
24/05/02
Author (S):
A. ASSIRE, P. MASSIN, F. LEBOUVIER
Key
:
U2.02.02-A
Page
:
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Instruction manual
U2.02 booklet: Elements of structure
HT-66/02/003/A
6.2
Analyze static nonlinear material
SSNL503
1,83
0.61m
M
0.407m
0.0104m
R= 0.61m
X
y
p
With
B
C
D
Titrate: Elastoplastic ruin of a thin bent pipe.
Documentation V: [V2.05.002]
Modelings:
SSNL503A TUYAU_3M SEG3
Loading: thin bent pipe subjected to a bending in sound
plan and has an internal pressure with basic effect.
ssNl106 Title
:
Fixed beam has an end and charged by one
traction with linear work hardening or a moment in plasticity
perfect.
Documentation V: [X]
Modelings:
SSNL106E TUYAU_3M SEG3
SSNL106F TUYAU_3M SEG4
SSNL106G TUYAU_6M SEG3
Loadings: a traction, 2 efforts sharp, 2 moments of
bending, a torsion and a pressure. Modelings A and C
use MECA_STATIQUE, while modelings B and D
use STAT_NON_LINE for the resolution.
HSNV100 Titrates
:
Thermo plasticity in simple traction of a pipe.
Documentation V: [V7.22.100]
Modelings:
HSNV100C TUYAU_3M SEG3
HSNV100D TUYAU_6M SEG3
6.3
Modal analysis in dynamics
SDLX02
Z
y
X
With
B
C
H
G
F
E
D
Titrate::Problem of Hovgaard. Analyze dynamic of one
three-dimensional piping comprising of the elbows.
Documentation V: [V2.05.002]
Modelings:
SDLX02D TUYAU_3M SEG3
SDLX02F TUYAU_3M SEG4
SDLX02E TUYAU_6M SEG3
Code_Aster
®
Version
6.3
Titrate:
Note of use of the elements
TUYAU_ *
Date:
24/05/02
Author (S):
A. ASSIRE, P. MASSIN, F. LEBOUVIER
Key
:
U2.02.02-A
Page
:
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Instruction manual
U2.02 booklet: Elements of structure
HT-66/02/003/A
sDll14 Title
:
Mode of vibration of a thin elbow of piping.
Documentation V: [V2.02.014]
Modelings:
SDLL14A TUYAU_3M SEG3
SDLL14C TUYAU_3M SEG4
SDLL14B TUYAU_6M SEG3
6.4
Analyze dynamic nonlinear
ELSA
Titrate: Nonlinear seismic analysis of a line of piping.
Documentation V: [V1.10.119]
Modelings:
ELSA01B TUYAU_3M SEG3
ELSA01C TUYAU_3M SEG4
Loadings: a seismic excitation is imposed on the line.
The aforementioned involves a partial plasticization (1%) elbows
only.
Code_Aster
®
Version
6.3
Titrate:
Note of use of the elements
TUYAU_ *
Date:
24/05/02
Author (S):
A. ASSIRE, P. MASSIN, F. LEBOUVIER
Key
:
U2.02.02-A
Page
:
31/32
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U2.02 booklet: Elements of structure
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7 References
bibliographical
[1]
P. MASSIN, J.M. PROIX, A. BEN HAJ YEDDER: Finite elements of right pipe and curve with
ovalization, swelling and roll in elastoplasticity, Code_Aster Documentation,
Manual of Reference [R3.08.06], EDF, 2001.
[2]
J. Mr. PROIX, Modelings PIPE and TUYAU_6M, Code_Aster Documentation, Manual
of Use [U3.11.06], EDF, 2000.
[3]
E. CHAMPAIN, ELSA01: Nonlinear seismic analysis of piping, Documentation
Code_Aster, Manual of Validation [V1.10.119], EDF, 2001.
[4]
P. MASSIN, J.M. PROIX, F. WAECKEL, E. CHAMPAIN: Modeling of the behavior
non-linear hardware of the pipings right and bent in statics and dynamics, Note
HI-74/99/013/A, EDF/MTI, 1999.
[5]
E. CHAMPAIN, Project CACIP: Validation of the developments relating to the taking into account
plasticity in the pipes, HP-52/99 * 029/B, EDF/AMV, 2000.
Code_Aster
®
Version
6.3
Titrate:
Note of use of the elements
TUYAU_ *
Date:
24/05/02
Author (S):
A. ASSIRE, P. MASSIN, F. LEBOUVIER
Key
:
U2.02.02-A
Page
:
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Instruction manual
U2.02 booklet: Elements of structure
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Intentionally white left page.