Code_Aster ®
Version
6.4

Titrate:
FORMA01 - TP of the basic training to the use of Code_Aster
Date:
16/05/03
Author (S):
J.M. PROIX, I. BAKER, E. BOYERE
Key: V7.15.100-B
Page:
1/28

Organization (S): EDF-R & D/AMA

Handbook of Validation
V7.15 booklet: Thermomechanical linear statics of the voluminal systems
(formation)
V7.15.100 document

FORMA01 - Travaux practice formation of
base with the use of Code_Aster

Summary:

This test corresponds to practical work of the basic training to the use of Code_Aster. It is about one
bent piping, made up of a linear elastic material, subjected to various loadings: force applied
with the end, internal pressure, thermal transient.

Modelings used are as follows:

· modeling a: beams (POU_D_T), which corresponds to the TP1,
· modeling b: hulls DKT, grid GIBI,
· modeling F: hulls DKT, grid GMSH, identical (with the grid near) to modeling B,
· modeling C: solid elements 3D, grid GIBI,
· modeling D: beams (POU_D_T), dynamic calculation,
· modeling E: elements TUYAU.
· Modeling G: solid elements 3D, (linear grid GMSH),
· Modeling H: solid elements 3D, (quadratic grid GMSH).

The chapter 1 “Problčme of reference” presents the problem to be treated and the data common to
all modelings; the statements of Travaux Pratiques of the formation are included in it
document:

· TP1: “beams” to see modeling A,
· TP2: “hulls” to see modeling F,
· TP3: “elastic thermo 3D” to see modeling H,
· TP4: “dynamic” to see modeling D.
Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
HT-66/03/008/A

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Version
6.4

Titrate:
FORMA01 - TP of the basic training to the use of Code_Aster
Date:
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Author (S):
J.M. PROIX, I. BAKER, E. BOYERE
Key: V7.15.100-B
Page:
2/28

1
Problem of reference

1.1 Geometry

The study relates to a piping including/understanding two right pipes and an elbow [Figure 1.1-a].

The geometrical data of the problem are as follows:

· length LG of the two right pipes is 3 m,
· the Rc radius of the elbow is 0.6 m,
· the angle of the elbow is 90 degrees,
· the thickness of the right pipes and the elbow is 0.02 m,
· and the radius external Re of the right pipes and the elbow is of 0.2 Mr.

LG

D
B
section D
section B
RC
C
O
section C
Z
Y
E
L
Z
G
X
Re
X
With
section A

Appear 1.1-a
Note:

The geometry of the problem has a symmetry compared to the plan (A, X, Y).

1.2
Material properties

For all modelings:
Isotropic linear elastic material. the properties of material are those of A42 steel:
· the Young modulus E = 204.000. 10+6 NR/m2,
· the Poisson's ratio = 0.3,

· For elastic thermo calculation (modelings C, G H)
-
the thermal dilation coefficient =10.92 10­6/°C,
-
thermal conduction = 54.6 W/m °C,
-
voluminal heat CP = 3.71 106 J/m3 °C,
Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
HT-66/03/008/A

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Version
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Titrate:
FORMA01 - TP of the basic training to the use of Code_Aster
Date:
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Author (S):
J.M. PROIX, I. BAKER, E. BOYERE
Key: V7.15.100-B
Page:
3/28

· For dynamic calculation (modeling D)
-
The Young modulus is worth 210.000. 10+6 NR/m2
-
density = 7800 kg/m3,
- the damping of the clean modes will be taken to 2% for the first 2 modes, 3% for
3rd, 4% for the fourth and 5% for the fifth.

1.3
Boundary conditions and loadings

The boundary conditions for all modelings are as follows:

· for the mechanical loadings, there is an embedding on the level of section A,
· for the thermomechanical loading, there is embedding on the level of section A and of
section B.

With regard to static calculations (modeling A, B, C, E, F, G, H), the loadings applied
are of three types:

· force constant FY = 100.000. NR directed according to the axis Y and applied to the section B,
· pressure interns P = 15. E+6 NR/m2, (modelings B, C, E, F, G, H)
· thermomechanical loading with a transient of temperature imposed on the face
intern of piping (gone up 20°C with 70°C in 10 seconds) and a condition of exchange
no one on the external face of piping (heat insulator) (modeling C only).

With regard to dynamic calculation (modeling D), the loading applied is a force
transient (in Newton):

FY (T) = 1 00.000. * cos (2 ** Freq1 * T)

directed according to the axis Y and applied to the section B,

Freq1 such as = 2** Freq1 = 121 rad/S.

Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
HT-66/03/008/A

Code_Aster ®
Version
6.4

Titrate:
FORMA01 - TP of the basic training to the use of Code_Aster
Date:
16/05/03
Author (S):
J.M. PROIX, I. BAKER, E. BOYERE
Key: V7.15.100-B
Page:
4/28

2
Reference solution

2.1
Method of calculation used for the reference solution

The reference solution is obtained numerically, it thus acts only of the tests of not
regression. However below the results of various modelings are compared.

2.2
Results of various modelings:

2.2.1 Static calculation, Force FY

For the loading of force constant FY applied to the section B, one compares displacement with
not B for various modelings (or at the point of co-ordinates (Lg+Rc, Lg+Rc, Re) for
modelings hull and 3D):

Loading forces constant FY
Modeling DX
DY
DRZ
A1: beam flexibility = 1
­ 2.657E02 6.702E
2.097E02
02
A2: beam flexibility RCCM
­ 2.983E02 1.156E
3.530E02
01
B: Coque (grid GIBI, 1260 QUAD4) ­ 2.90E02
1.06E01
3.27E02
F: Hull (grid GMSH, 2240 TRIA3, 700 QUAD4)
­ 2.89E02
1.053E
3.24E02
01
C: 3D (grid GIBI, 800 HEXA20)
­ 2.914E02 1.065E
-
01
G: 3D (grid GMSH, 7260 TETRA4, 1240 PENTA6)
­ 2.65E02
0.731E
-
01
H: 3D (grid GMSH, 7260 TETRA10, 1240 PENTA15) ­ 2.94E02
1.056E
-
01
E: pipe
­ 2.935E02 1.083E
3.326E02
01
Maximum relative variation (without taking account of A1 nor G)
3%
9%
8%

For the loading of pressure, one compares displacement with the point B for the different ones
modelings:
Loading
pressure
Modeling DX
DY
DRZ
B: Coque (grid GIBI, 1260 QUAD4) ­ 2.903E01 4.687E01
1.305E01
F: Hull (grid GMSH, 2240 TRIA3, 700 QUAD4)
­ 2.890E01 4.654E01 1.296E01
C: 3D (grid GIBI, 800 HEXA20)
­ 2.766E01 4.473E01
-
G: 3D (grid GMSH, 7260 TETRA4, 1240 PENTA6)
­ 2.622E01 3.967E01
-
H: 3D (grid GMSH, 7260 TETRA10, 1240 PENTA15)
­ 2.734E01
4.41E01
-
E: pipe
­ 2.763E01 4.505E01 1.257E01
Maximum relative variation
9%
17%
4%

Note:

So that the results of modeling beam are comparable with the different one
modelings, it is necessary to take into account the coefficients of flexibility of the elbows
(AFFE_CARA_ELEM):
65
.
1
er
C
with
courb
=
(value recommended by the RCCM, current regulation).
flex =

2
Rmoy
Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
HT-66/03/008/A

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Version
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Titrate:
FORMA01 - TP of the basic training to the use of Code_Aster
Date:
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Author (S):
J.M. PROIX, I. BAKER, E. BOYERE
Key: V7.15.100-B
Page:
5/28

With regard to dynamics, one tests the constraints obtained after restitution in base
physique of transitory calculation by modal recombination (on the basis of clean mode the first 5)
piping subjected to force FY (T), the moment 0.2s, point b:

Component SIXX
SIYY
Constraints at the point B, urgent 0.2s
­ 5.29775E+05
9.40503E+05

2.3
Uncertainty on the solution

The difference between the various solutions lies between 3% and 17%. This is due on the one hand to
modelings themselves (corrective terms for flexibility in the beams, and coefficient on
pressure in the hulls), and in addition with the grids used, which are not very fine (so that it
time of resolution is not an embarrassment for the TP of the formation.

Note:

The results 3D are much more precise with a quadratic grid.
For modeling hull, the pressure is applied to the average surface of Rmoy radius.
One thus took into account a corrective factor on the value of the pressure to be applied:
P * =P. Rint/Rmoy

Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
HT-66/03/008/A

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Titrate:
FORMA01 - TP of the basic training to the use of Code_Aster
Date:
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Key: V7.15.100-B
Page:
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3 Modeling
With

3.1
Characteristics of modeling

3.1.1 Grid
GMSH

The telegraphic grid could be built inter-actively using GMSH (or GIBI). It is enough to define
the points A, B, C D, then the two lines AC and dB, item 0 and rings it BC. Size of the elements
could be defined like parameter. In GMSH, one will be able to declare “physical” the points A and B,
then lines AC and data base, then circle BC. Once grid carried out, to save it (format msh).

The elbow will be modelled initially by at least four elements of right beams
(to provide for GMSH a density lower than 0.25).

With regard to the right pipes, the discretization does not have an influence on the result, because them
elements of right beam of Timoshenko (POU_D_T) of Code_Aster provide results
correct with the nodes of the grid, even for a discretization with very little element, in
STATIQUE LINEAIRE only [R3.08.01].

3.2
To drive Aster commands

· Reading of grid (PRE_GMSH) and generation of grid (LIRE_MAILLAGE).

· Definition of the finite elements used (AFFE_MODELE). One will affect initially to
group meshs composing the elbow, as on the right parts, modeling
POU_D_T.

· Definition and assignment of material (DEFI_MATERIAU and AFFE_MATERIAU).
The mechanical characteristics are identical on all the structure.

· Assignment of the characteristics of the elements beams (AFFE_CARA_ELEM).
The section of all the pipes is circular.

· Definition of the boundary conditions and loading (AFFE_CHAR_MECA).
Piping is embedded in its base, on the level of point A.

The loading is a specific force FY applied to the point B.

· Resolution of the elastic problem (MECA_STATIQUE).
Calculation of the field of efforts generalized by element with the nodes, the field of
calculated displacement (option “EFGE_ELNO_DEPL”).

· Impression of results (IMPR_RESU).
One will print in form listing displacement at the point B and the maximum values of
efforts.

One will also print the field of displacement to format GMSH, for one
visualization of the results with GMSH. (to use DEFUFI to define the output file).

Optional calculation: curved beams and coefficient of flexibility

One will be able to check the impact of a coefficient of flexibility of the elbow on displacements with
not B. This coefficient of flexibility is defined in the level of command AFFE_CARA_ELEM
(key word DEFI_ARC).

It will then be necessary to assign to the group of meshs composing the elbow modeling POU_C_T.
Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
HT-66/03/008/A

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Titrate:
FORMA01 - TP of the basic training to the use of Code_Aster
Date:
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Author (S):
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Key: V7.15.100-B
Page:
7/28

4
Results of modeling A

4.1 Values
tested

The results obtained with 2 elements in each right part and 4 elements in the elbow are:

Without coefficient of flexibility:

Loading Value
tested
Reference
Aster %
difference
Force concentrated Fy out of B Déplacement out of B Dx
­ 2.657E02 ­ 2.657E02
0

Displacement out of B Dy
6.702E02 6.702E02
0

Rotation out of B DRZ
2.097E02 2.097E02
0

With coefficient of flexibility:

Loading Value
tested
Reference
Aster %
difference
Force concentrated Fy out of B Déplacement out of B Dx
­ 2.983E02 ­ 2.983E02
0

Displacement out of B Dy
1.156E01 1.156E01
0

Rotation out of B DRZ
3.530E02 3.530E02
0

Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
HT-66/03/008/A

Code_Aster ®
Version
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Titrate:
FORMA01 - TP of the basic training to the use of Code_Aster
Date:
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Author (S):
J.M. PROIX, I. BAKER, E. BOYERE
Key: V7.15.100-B
Page:
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5 Modeling
B

5.1
Characteristics of modeling

In the case of modeling in elements hulls, the grid consists of the discretization of
surface average piping. Geometry being symmetrical compared to the plan (A, X, Y), one
net that a half-surface.


5.2
Characteristics of the grid

The grid is created using GIBI. It comprises 1260 meshs QUAD4, and 1356 nodes

5.3 Commands
Aster

The principal stages of calculation with Aster will be:

· Reading of grid (PRE_GIBI) and generation of grid (LIRE_MAILLAGE).

· Definition of the finite elements used (AFFE_MODELE). The right pipes and the elbow will be
modelled by elements of hull (DKT).

· Reorientations of the normals to the elements: one will use MODI_MAILLAGE to direct all
elements in the same way, with a normal turned towards the interior of the pipe (being
data the convention of sign on the pressure) in order to give a positive value to
pressure.

Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
HT-66/03/008/A

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FORMA01 - TP of the basic training to the use of Code_Aster
Date:
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Key: V7.15.100-B
Page:
9/28

· Definition and assignment of material (DEFI_MATERIAU and AFFE_MATERIAU).
mechanical characteristics are identical on all the structure.

· Assignment of the characteristics of the elements hulls (AFFE_CARA_ELEM): thickness

· Definition of the boundary conditions and loadings (AFFE_CHAR_MECA).

· Piping is embedded in its base, on all the nodes located in the Y=0 plan.
piping presents a symmetry plane Z=0.

· One calculates two loading cases:

- an effort distributed F * directed according to the axis Y and applied to the section B, (the effort distributed is such
that the resultant 2Pi * Rmoy F * = FY, FY being the total force which one wishes to apply).
To apply the effort to the section B, FORCE_ARETE will be used,
-
a pressure interns P.

Note:

The value of the pressure P is positive according to the contrary direction of the normal with
the element. To direct this normal MODI_MAILLAGE should be used/
ORIEN_NORM_COQUE: to define in A1 a vector giving the direction of the normal
(opposed to the pressure).

· Resolution of the elastic problem for each loading case (2 calls to MECA_STATIQUE).

· Impression of results (IMPR_RESU).

· One will print in form listing displacement for each result on the section B. One
will also print with format GMSH, displacements.

One will be able in the second Aster calculation to evaluate the constraints with the nodes:

· One adds in the characteristics hulls (AFFE_CARA_ELEM) the vector V defining it
locate examination (key word ANGL_REP). One can take for example V=Oz.

· Calculation of the stress field by elements to the nodes for each loading case (option
“SIGM_ELNO_DEPL”). The constraints are calculated in the definite local reference mark for each
element using the vector V (preceding key word ANG_REP). To use NIVE_COUCHE for
to define the level of calculation in the thickness.

6
Results of modeling B

6.1 Values
tested

Loading Value
tested
Reference
Aster %
difference
Force concentrated Fy out of B Déplacement out of B Dx
­ 2.901E02 ­ 2.901E02
0

Displacement out of B Dy
1.060E01 1.060E01
0

Rotation out of B DRZ
3.274E02 3.274E02
0





Internal pressure
Displacement out of B Dx
­ 2.903E01 ­ 2.903E01
0

Displacement out of B Dy
4.687E-01 4.687E-01
0

Rotation out of B DRZ
1.305E-01 1.305E-01
0
Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
HT-66/03/008/A

Code_Aster ®
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Titrate:
FORMA01 - TP of the basic training to the use of Code_Aster
Date:
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Key: V7.15.100-B
Page:
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7 Modeling
C

7.1
Characteristics of modeling

The right pipes and the elbow are modelled by isoparametric solid elements
quadratic. Piping presents a symmetry plane Z=0. Only one half volume is netted.

Y
X
With
d2 A
With D A
e2
i2
i1
1
e1
d2
L
With
2
With
i1
P
L
With
i2
P
L
i1
2
With
i1
1
e2
e1
P
L
e1
1
D
P
1
e1
Z

Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
HT-66/03/008/A

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Titrate:
FORMA01 - TP of the basic training to the use of Code_Aster
Date:
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Key: V7.15.100-B
Page:
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7.2
Characteristics of the grid

4240 meshs HEXA20, 5913 nodes

7.3 Commands
Aster

In the case of load thermal, the study requires the first transitory thermal calculation followed of one
mechanical calculation.

In order to use the possibilities of recovery of a calculation, one will make two successive and coupled executions
with Aster. In the first execution, one will make the resolution of the various loading cases, in
second of postprocessings on the thermomechanical loading case.

The principal stages of the first execution with Aster will be:

Reading of grid (PRE_GIBI) and generation of grid (LIRE_MAILLAGE) in elements
quadratic.

· Definition of the finite elements used (AFFE_MODELE). One will define a model for calculation
thermics and a mechanical model.

· Definition and assignment of material (DEFI_MATERIAU and AFFE_MATERIAU).
thermal characteristics and mechanics are identical on all the structure.

· Definition of the boundary conditions thermal (DEFI_FONCTION and AFFE_CHAR_THER_F):
There is a transient of temperature imposed on the interior surface of piping (assembled
of 20°C with 70°C in 10s). It is considered that piping is insulated and thus one applies
a condition of null exchange on external surface.
· Resolution of the thermal problem (THER_LINEAIRE). The calculation of the field of temperature
be carried out for the two moments of the transient (5. and 10. S).

· Definition of the three mechanical loading cases: boundary conditions and loading
mechanics or thermics (AFFE_CHAR_MECA):

- an effort FY directed according to the axis Y and applied to the section B, (to use FORCE_FACE.
value of the surface effort of Fy resultant can be calculated in Aster using
DEFI_VALEUR),
-
an internal pressure,
-
the thermal transient previously calculated,
- piping is embedded in its base (Ae1, Ai1, Ae2, Ai2), on all the nodes located
in the plan of Y=0 equation. In the case of load thermal, the section B of
piping is also embedded.

· Resolution for the various loading cases from the mechanical problem and calculation of the field of
constraints with the nodes by element (3 calls to MECA_STATIQUE)

· Using CALC_ELEM, calculation of the constraints by elements extrapolated with the nodes
(SIEF_ELNO_ELGA) and of the equivalent constraints of Von Mises (EQUI_ELNO_SIGM).

· Impression of results (IMPR_RESU).

- One will print in form listing on the one hand displacement on the section B, and of other
leaves the maximum values the tensor of constraints, in the case of load
mechanics.
- One will print for thermomechanical calculation, displacements, and the component
VMIS on field EQUI_ELNO_SIGM with format CASTEM.
Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
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FORMA01 - TP of the basic training to the use of Code_Aster
Date:
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Key: V7.15.100-B
Page:
12/28

The principal stages of the second execution with Aster will be:

· Creation of a table per extraction of values on a path (INTE_MAIL_3D and
POST_RELEVE_T).

· One will extract from the values of temperature and displacement for an azimuth on the level from
the input of elbow in the case of load thermomechanical. The azimuth is defined by the path
ends (0. 3. 0.1) and (0. 3. 0.2).

· Impression of curves (IMPR_COURBE).

· One will print with format AGRAF the change of the temperature and the component following Y
field of displacement, along the preceding azimuth. One will be able to then visualize these
curves by means of AGRAF.

8
Results of modeling C

8.1 Values
tested

Loading Value
tested
Reference
Aster %
difference
Force concentrated Fy out of B
Displacement out of B Dx
­ 2.907E02 ­ 2.907E02 0

Displacement out of B Dy
1.065E01 1.065E01 0





Internal pressure
Displacement out of B Dx
­ 2.763E01 ­ 2.763E01 0

Displacement out of B Dy
4.472E01 4.472E01 0





Temperature at the moment 10s Température in AI1
70 70 0

Constraint of Von
1.2383 108 1.2383
108 0
Settings maximum
Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
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FORMA01 - TP of the basic training to the use of Code_Aster
Date:
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Key: V7.15.100-B
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9 Modeling
D

9.1
Characteristics of modeling

The geometry is identical to that of modeling A. the grid must be enough fine to obtain
a correct solution in dynamics, in particular to describe the clean modes correctly:
bend and the right pipes will be modelled chacuns by at least 5 elements of right beams of
Timoshenko POU_D_T.

One first of all wishes to know the first clean modes.

Then one will make a transitory analysis of the response of the pipe to the sinusoidal force between 0.0 and 2.0 S.
The structure is initially at rest. One will be able initially to make the analysis on basis
modal. One will be able to compare the results of the analysis on modal basis with a direct analysis on
base physical.

9.2
Characteristics of the grid

9.2.1 Grid
GMSH

The grid will be obtained with GMSH, as for modeling A. Attention not being forgotten in
the command file ASTER to create the groups of “physical” meshs and, then, in
command file ASTER to create the groups of nodes corresponding to the groups of meshs
thanks to command DEFI_GROUP.

9.2.2 Alternative grid: with GIBI

For those which prefer GIBI, one will be able to create the grid using this maillor, in the following way:
one will create with the editor a data file which will include/understand the list of the instructions that one will subject
with GIBI. The various stages of modeling with GIBI will be:

· Definition of the options of grid by procedure OPTION.
The co-ordinates of the points will be introduced in dimension 3.
The elements will be of type SEG2.

· Definition of the points A, B, C, D, O.
The points will be named Pa, PB, PC, PD, PO.

· Grid of piping
For the grid of piping, one will use operators DROITE, CERCLE and AND.
Cutting will be of only one element for the right pipes and the elbow.

· Visualization of the final grid.
Visualization is done by the procedure TRACER, for which one must specify a point, which
indicate the position of the eye which looks at the object.

· Back up grid for its use in Aster.
To be able to read again the grid by Aster it should be backed up in a formatted file, this
back up is done by procedure SAUVER with key word FORMAT. The file which will be creates
the same name will have as the data file GIBI, but will have as an extension “.mgib”.

· Stop of the execution of GIBI.
To leave GIBI it should be indicated by directive FIN.

Note:

Any instruction GIBI ends in the symbol “;”.
Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
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Key: V7.15.100-B
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9.3 Commands
Aster

The principal stages of calculation with Aster will be:

9.3.1 Preparation of the data and analyzes modal

· Grid (not to forget the PRE_GMSH or the PRE_GIBI).

· Definition of the finite elements used (AFFE_MODELE).

· One will use the groups of meshs envisaged in GMSH (or GIBI).

· Definition and assignment of material (DEFI_MATERIAU and AFFE_MATERIAU).

· The mechanical characteristics are identical on all the structure.

· Assignment of the characteristics of the elements beams (AFFE_CARA_ELEM).

· The section of all the pipes is circular, of radius 0.2 m and thickness
0.02 Mr.

· The elbow constitutes of an arc of circle of center the point O and radius 0.6 Mr. Pour to define
the curved element, one will use key word DEFI_ARC.

· Definition of the boundary conditions and loading (AFFE_CHAR_MECA). Point A is
embedded.

· Definition of the matrices of the elastic problem (MACRO_MATR_ASSE).

· Calculation of the first 5 clean modes (MODE_ITER_SIMULT).

· Impression of the clean modes (IMPR_RESU): one will print the grid and the modes with the format
GMSH for a visualization in GMSH (or with format CASTEM, for a visualization of
results with GIBI). In the case of GMSH, not to forget to open the logical unit of the file of
postprocessing by a DEFUFI!

9.3.2 Analyze
transient

Construction of the specific force

· Definition of the load forces at the point B (AFFE_CHAR_MECA FORCE_NODALE).
· Calculation of the elementary vectors forces (CALC_VECT_ELEM).
· Assembly of the vector forces (ASSE_VECTEUR).
· Definition of the function evolution of time (FORMULE).

Transient on modal basis
· Projection of the problem assembled on the basis of clean mode (MACRO_PROJ_BASE).
· Transitory calculation by modal recombination (DYNA_TRAN_MODAL).
· Recovery of displacements, speed in there of B, C, D (RECU_FONCTION).
· Impression of these functions to the format listing and AGRAF (IMPR_COURBE).
· One will be able to possibly determine constraints MIN and MAX due to the efforts
generalized during the transient while passing by a restitution on the physical basis
(REST_BASE_PHYS), a calculation of constraints (CALC_ELEM), a skilful postprocessing for
to calculate the maximum in the course of time (CREA_CHAMP) and a writing in the file result
(IMPR_RESU).
Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
HT-66/03/008/A

Code_Aster ®
Version
6.4

Titrate:
FORMA01 - TP of the basic training to the use of Code_Aster
Date:
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Author (S):
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Key: V7.15.100-B
Page:
15/28

Direct calculation on physical basis: transient on physical basis
· Direct transitory calculation by Newmark (DYNA_LINE_TRAN).
· Recovery of displacements, speed in there of B, C, D (RECU_FONCTION).
· Impression of these functions to the format listing and AGRAF (IMPR_COURBE).
· Calculation of the MAX (space and temporal) of the constraints due to the generalized efforts.

9.3.3 Postprocessings

One will visualize with GMSH or GIBI the grid and the first five clean modes of the structure.
One will also trace using AGRAF the evolution of displacements according to time at the points
B, C and D.
Lastly, one will be able to determine the maximum (and minimum) space and temporal of the constraints due to
generalized efforts, in order to consider the stresses maximum which the pipe during this test undergoes.

9.3.3.1 Help for postprocessing with GMSH

Postprocessing in GMSH is rather intuitive. However some points are to be known:

· One must put GMSH in Post-Processing mode.
· In Tools/Options, the Aspect miter makes it possible to specify Displacement like Vector display,
i.e to observe the modes like a structural deformation. One will be able to also specify
the amplitude of the deformation thanks to the box Vector size.
· The Step button of the General miter makes it possible, as for him, to make ravel the various modes
(which is seen in GMSH like “steps of time”).

9.3.3.2 Help for postprocessing with GIBI (possibly)

One will provide a command file GIBI allowing to carry out graphic postprocessings.
Principal commands GIBI used are:

* Second reading of the file result to format “CASTEM” coming from Aster:
OPTI REST FORMAT “nom_de_fichier.cast”;
REST FORMAT;
* Recovery of the number of moments calculated in the object “resu” resulting
of Aster
ninst = DIME resu;
* One can display it:
LIST ninst;
i=0;
* Loop over every filed moment:
to repeat ninst boucl1:
I = i+1;

Ti = resu. I. inst;
* Recovery of the fields of displacements in the result:
C = resu. I. depl;
* visualization of the deformation
defo1 = defo red mall C 100.;
defo0 = defo mall green C 0.;
titrate “urgent Tuyauterie deformed” Ti;
trac oe (defo1 and defo0);
end boucl1;
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9.3.3.3 Help for postprocessing with AGRAF

Visualization of curves of results printed with format AGRAF. In the continuation, one will replace
<résultat> by the name of the file result of the type AGRAF produced by command IMPR_COURBE in
the command file.

The various stages of the visualization of the results with AGRAF are:

· launching of AGRAF: to type “agraf” in a Unix window,
· opening of a Directives file: small Directives (cf Tableau 1),
· to select Ouvrir, give a name of directive by the BSF (for example <résultat>.digr),
to click in the BSF on Ouvrir Directives, and to confirm the creation of a new file of
directives,
· reading of the results resulting from Aster: small Données (cf Tableau 1),
· to select the file <résultat>.dogr thanks to the BSF,
· definition of the graph to be traced: small Graphiques,
· to select Spécifier/a window entitled Spécification of the curves of a graph opens,
· a Titer zone makes it possible to give a title to the graph, to replace graphic Nouveau by
titrate your graph (ex: Displacement of the pipe) - in lower parts, actionable with wish by
a toggle-short prop, appear of the lines of definition of the curves to trace,

· zone Abscisses one defines the n° table and the n° of the column constituting the data in
to put in X-coordinates of the curve (1 1 for the L era curves),
· zone Ordonnées one defines No of the table and No of the column constituting the data in
to put in ordinates of the curve (1 2 for the first curve),
· zone Marqueur one defines the shape of the marker, the periodicity of layout of this marker (all
N points of the curve), (10),
· Légende zone makes it possible to give a text of legend following the curve curve (DY-B),
· to click on Sauvegarder to record the definition of the graph,
· Back up and updating of the graph to be traced: small Graphiques,
-
Sauvegarder button,
-
Tracer button,
· Impression POSTSCRIPT of the graph: fenestrate Tracé,
· Imprimer button Tracé,
Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
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Key: V7.15.100-B
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10 Results of modeling D

10.1 Values
tested

This test is a test of nonregression. The values of reference are the results obtained with
version 6.4 of Code_Aster.

Loading
Value tested
Reference
Aster %
difference
Force concentrated
Constraint out of B due to the effort
­ 6.20356 104 ­ 6.20356
104
0
Fy out of B
normal SN

In addition to this result of nonregression, one can observe displacement according to Y of the point D:



One observes that the modes of the structure are excited during the first second transient, it
who explains the chahutée shape of the curve of displacement. Then movements of the modes
clean are deadened and there remains only the stationary movement regulated on the frequency of
sinusoidal force at the point B.
Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
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11 Modeling
E

11.1 Characteristics of modeling

Modeling PIPE. The elbow is modelled by 20 elements of the segment type to 3 nodes.
The right pipes are modelled by 20 elements of the segment type to 3 nodes.
The first two loadings (specific force FY and pressure intern) are treated.

11.2 Characteristics of the grid

60 meshs SEG3, 126 nodes

11.3 Functionalities
tested

Commands



AFFE_CHAR_MECA FORCE_TUYAU
PRES

MECA_STATIQUE


CALC_ELEM OPTION
SIGM_ELNO_DEPL

AFFE_CHAR_MECA FORCE_NODALE
FY


12 Results of modeling E
12.1 Values
tested

Loading Value
tested
Reference
Aster %
difference
Force concentrated Fy out of B Déplacement out of B Dx
­ 2.935E02 ­ 2.935E02 0

Displacement out of B Dy
1.083E01 1.083E01 0
(Reference pipe)
Rotation out of B DRZ
3.326E02 3.326E02 0





Internal pressure
Displacement out of B Dx
­ 2.7624E01 ­ 2.7624E
0
01

Displacement out of B Dy
4.505E01 4.505E01 0

Rotation out of B DRZ
1.257E01 1.257E01 0

Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
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13 Modeling
F

13.1 Characteristics of modeling

This modeling in elements hulls, is in all points identical to modeling B, except
grid, generated using GMSH.




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13.2 Characteristics of the grid

700 meshs QUAD4, 2240 meshs TRIA3, 1344 nodes

Grid GMSH built in quadrilaterals and triangles is available in the base of the tests:
geometrical data file names forma01f.datg. (to change the extension into “.geo”). It
the numbers of the entities “physical corresponds to the geometry above (to find” which
correspond to the groups of meshs, to use Tools/Visibility/Physical). The groups correspond
with:

GM30 <=> surface of the TUYAU
GM28 <=> section B (effort)
GM31 <=> not A1 (- R, 0, 0)
GM27 <=> section A (embedding)
GM29 <=> SYMETRIE

13.3 Commands
Aster

· Reading of grid (PRE_GMSH) and generation of grid (LIRE_MAILLAGE). One can
to use DEFI_GROUP to re-elect the groups of meshs according to the correspondence:

# GM30 <=> TUYAU
# GM28 <=> EFOND
# GM31 <=> A1
# GM27 <=> ENCAST
# GM29 <=> SYMETRIE

· Definition of the finite elements used (AFFE_MODELE). The right pipes and the elbow will be
modelled by elements of hull (DKT).

· Reorientations of the normals to the elements: one will use MODI_MAILLAGE to direct all
elements in the same way, with a normal turned towards the interior of the pipe (being
data the convention of sign on the pressure) in order to give a positive value to
pressure.

· Definition and assignment of material (DEFI_MATERIAU and AFFE_MATERIAU).
mechanical characteristics are identical on all the structure.

· Assignment of the characteristics of the elements hulls (AFFE_CARA_ELEM): thickness

· Definition of the boundary conditions and loadings (AFFE_CHAR_MECA).

· Piping is embedded in its base, on all the nodes located in the Y=0 plan.
piping presents a symmetry plane Z=0.

· One calculates two loading cases:

· An effort distributed F * directed according to the axis Y and applied to the section B, (the effort distributed is such as
the resultant 2Pi * Rmoy F * = FY, FY being the total force which one wishes to apply). For
to apply the effort to the section B, one will use FORCE_ARETE.

· A pressure interns P. Remarque: The value of the pressure p is positive according to the direction
opposite of the normal to the element. To direct this normal it is necessary to use
MODI_MAILLAGE/ORIEN_NORM_COQUE: to define in A1 a vector giving the direction of
normal (opposed to the pressure).
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· Resolution of the elastic problem for each loading case (2 calls to MECA_STATIQUE).

· Impression of results (IMPR_RESU).

· One will print in form listing displacement for each result on the section B. One
will also print with format GMSH, displacements.

One will be able in the second Aster calculation to evaluate the constraints with the nodes:

· One adds in the characteristics hulls (AFFE_CARA_ELEM) the vector V defining it
locate examination (key word ANGL_REP). One can take for example V=Oz.

· Calculation of the stress field by elements to the nodes for each loading case (option
“SIGM_ELNO_DEPL”). The constraints are calculated in the definite local reference mark for each
element using the vector V (preceding key word ANG_REP). To use NIVE_COUCHE for
to define the level of calculation in the thickness.

14 Results of modeling F
14.1 Values
tested

Loading Value
tested
Reference
Aster %
difference
Force concentrated Fy out of B Déplacement out of B Dx
­ 2.89E02 ­ 2.89E02
0

Displacement out of B Dy
1.053E01 1.053E01
0

Rotation out of B
3.24E02 3.24E02
0
DRZ





Internal pressure
Displacement out of B Dx
­ 2.890E01 ­ 2.890E01
0

Displacement out of B Dy
4.654E01 4.654E01
0

Rotation out of B
1.296E01 1.296E01
0
DRZ

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15 Modeling
G

15.1 Characteristics of modeling

Modeling in voluminal elements, grid being obtained using GMSH. Modeling is
in all points identical to modeling C. Les results obtained differ because the elements are
linear.


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15.2 Characteristics of the grid

A number of nodes:
6633
A number of meshs and types: 7260 TETRA4
1539 PENTA6
4319 QUAD4
7003 TRIA3

15.3 Commands
Aster

In the case of load thermal, the study requires the first transitory thermal calculation followed of one
mechanical calculation.

In order to use the possibilities of recovery of a calculation, one will make two successive and coupled executions
with Aster. In the first execution, one will make the resolution of the various loading cases, in
second of postprocessings on the thermomechanical loading case.

The principal stages of the first execution with Aster will be:

· Reading of grid (PRE_GMSH) and generation of grid (LIRE_MAILLAGE) in elements
linear. One can use DEFI_GROUP to re-elect the groups of meshs according to
correspondence:

TUYAU <=> GM10000
EFOND <=> GM10005
ENCAST <=> GM10001
SYMETRIE <=> GM10002
SURFINT <=> GM10004
SURFEXT <=> GM10003

· Definition of the finite elements used (AFFE_MODELE). One will define a model for calculation
thermics and a mechanical model.

· Definition and assignment of material (DEFI_MATERIAU and AFFE_MATERIAU).
thermal characteristics and mechanics are identical on all the structure.

· Definition of the boundary conditions thermal (DEFI_FONCTION and AFFE_CHAR_THER_F):
There is a transient of temperature imposed on the interior surface of piping (assembled
of 20°C with 70°C in 10s). It is considered that piping is insulated and thus one applies
a condition of null exchange on external surface.
· Resolution of the thermal problem (THER_LINEAIRE). The calculation of the field of temperature
be carried out for the two moments of the transient (5. and 10. S).

· Definition of the three mechanical loading cases: boundary conditions and loading
mechanics or thermics (AFFE_CHAR_MECA):

- an effort FY directed according to the axis Y and applied to the section B, (to use FORCE_FACE.
value of the surface effort of Fy resultant can be calculated in Aster using
DEFI_VALEUR),
-
an internal pressure,
-
the thermal transient previously calculated,
- piping is embedded in its base (Ae1, Ai1, Ae2, Ai2), on all the nodes located
in the plan of Y=0 equation. In the case of load thermal, the section B of
piping is also embedded.
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· Resolution for the various loading cases from the mechanical problem and calculation of the field of
constraints with the nodes by element (3 calls to MECA_STATIQUE)

· Using CALC_ELEM, calculation of the constraints by elements extrapolated with the nodes
(SIEF_ELNO_ELGA) and of the equivalent constraints of Von Mises (EQUI_ELNO_SIGM).

· Impression of results (IMPR_RESU).

- One will print in form listing on the one hand displacement on the section B, and of other
leaves the maximum values the tensor of constraints, in the case of load
mechanics.
- One will print for thermomechanical calculation, displacements, and the component
VMIS on field EQUI_ELNO_SIGM with format GMSH.

The principal stages of the second execution with Aster will be:

· Creation of a table per extraction of values on a path (INTE_MAIL_3D and
POST_RELEVE_T).

· One will extract from the values of temperature and displacement for an azimuth on the level from
the input of elbow in the case of load thermomechanical. The azimuth is defined by the path
ends (0. 3. 0.1) and (0. 3. 0.2).

· Impression of curves (IMPR_COURBE).

· One will print with format AGRAF the change of the temperature and the component following Y
field of displacement, along the preceding azimuth. One will be able to then visualize these
curves by means of AGRAF.

16 Results of modeling G
16.1 Values
tested

Loading
Value tested
Reference
Aster %
difference
Force concentrated Fy out of B
Displacement out of B Dx
­ 2.65E02 ­ 2.65E02 0

Displacement out of B Dy
0.731E01 0.731E01
0
Internal pressure
Displacement out of B Dx
­ 2.622E01 ­ 2.622E01 0

Displacement out of B Dy
3.967E01 3.967E01
0
Temperature at the moment 10s Température in AI1
70 70 0
Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
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17 Modeling
H

17.1 Characteristics of modeling

Modeling in voluminal elements, grid being obtained using GMSH. Modeling is
in all points identical to modeling G. Les linear meshs generated by GMSH are
transforms in quadratic meshs by macro-command PRE_GMSH.



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17.2 Characteristics of the grid

A number of nodes:
5029
A number of meshs and types: 188 HEXA20
658 PENTA15
1136 QUAD8
28 TRIA6

17.3 Functionalities
tested

In the case of load thermal, the study requires the first transitory thermal calculation followed of one
mechanical calculation.

In order to use the possibilities of recovery of a calculation, one will make two successive and coupled executions
with Aster. In the first execution, one will make the resolution of the various loading cases, in
second of postprocessings on the thermomechanical loading case.

The principal stages of the first execution with Aster will be:

· Reading of grid (PRE_GMSH) and generation of the grid in quadratic elements (word
key MODI_QUAD). Call to LIRE_MAILLAGE to read this quadratic grid. One can use
DEFI_GROUP to re-elect the groups of meshs according to the correspondence:

TUYAU <=> GM10000
EFOND <=> GM10005
ENCAST <=> GM10001
SYMETRIE <=> GM10002
SURFINT <=> GM10004
SURFEXT <=> GM10003

· Definition of the finite elements used (AFFE_MODELE). One will define a model for calculation
thermics and a mechanical model.

· Definition and assignment of material (DEFI_MATERIAU and AFFE_MATERIAU).
thermal characteristics and mechanics are identical on all the structure.

· Definition of the boundary conditions thermal (DEFI_FONCTION and AFFE_CHAR_THER_F):
There is a transient of temperature imposed on the interior surface of piping (assembled
of 20°C with 70°C in 10s). It is considered that piping is insulated and thus one applies
a condition of null exchange on external surface.
· Resolution of the thermal problem (THER_LINEAIRE). The calculation of the field of temperature
be carried out for the two moments of the transient (5. and 10. S).

· Definition of the three mechanical loading cases: boundary conditions and loading
mechanics or thermics (AFFE_CHAR_MECA):

- an effort FY directed according to the axis Y and applied to the section B, (to use FORCE_FACE.
value of the surface effort of Fy resultant can be calculated in Aster using
DEFI_VALEUR),
-
an internal pressure,
-
the thermal transient previously calculated,
- Piping is embedded in its base (Ae1, Ai1, Ae2, Ai2), on all the nodes located
in the plan of Y=0 equation. In the case of load thermal, the section B of
piping is also embedded.
Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
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· Resolution for the various loading cases from the mechanical problem and calculation of the field of
constraints with the nodes by element (3 calls to MECA_STATIQUE)

· Using CALC_ELEM, calculation of the constraints by elements extrapolated with the nodes
(SIEF_ELNO_ELGA) and of the equivalent constraints of Von Mises (EQUI_ELNO_SIGM).

· Impression of results (IMPR_RESU).

- One will print in form listing on the one hand displacement on the section B, and of other
leaves the maximum values the tensor of constraints, in the case of load
mechanics.
- One will print for thermomechanical calculation, displacements, and the component
VMIS on field EQUI_ELNO_SIGM with format GMSH.

The principal stages of the second execution with Aster will be:

· Creation of a table per extraction of values on a path (INTE_MAIL_3D and
POST_RELEVE_T).

· One will extract from the values of temperature and displacement for an azimuth on the level from
the input of elbow in the case of load thermomechanical. The azimuth is defined by the path
ends (0. 3. 0.1) and (0. 3. 0.2).

· Impression of curves (IMPR_COURBE).

· One will print with format AGRAF the change of the temperature and the component following Y
field of displacement, along the preceding azimuth. One will be able to then visualize these
curves by means of AGRAF.

18 Results of modeling H
18.1 Values
tested

Loading
Value tested
Reference (3D
Aster %
MOD. C)
difference
Force concentrated Fy out of B
Displacement out of B Dx
­ 2.94E02 ­ 2.94E02 0

Displacement out of B Dy
1.056E01 1.056E01 0
Internal pressure
Displacement out of B Dx
­ 2.734E01 ­ 2.734E01 0

Displacement out of B Dy
4.41E01 4.410E01
0
Temperature at the moment 10s Température in AI1
70 70 0

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19 Summary of the results

The purpose of this test is not to validate functionalities, but is used for the formation. However, it
is interesting to compare certain modelings of the same problem. It is noted that the variations
remain relatively weak (5% of variation to the maximum between 3D (quadratic elements), hull and
pipe).

Handbook of Validation Fascicule V7.15: Thermomechanical linear statics of the voluminal systems (formation)
HT-66/03/008/A

Outline document