Code_Aster ®
Version
8.2
Titrate:
DEMO006 Optimization of the radius of curvature of a bent piping
Date:
05/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER
Key: V3.03.131-A
Page:
1/6
Organization (S): EDF-R & D/AMA, DeltaCAD
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
V3.03.131 document
DEMO006 Optimization of the radius of curvature
of a bent piping
Summary:
This test of demonstration illustrates the use of the language python in Code_Aster.
The objective of this case-test is to optimize the value of the radius of curvature of a piping via a loop python.
The radius of curvature is modified repeatedly. The optimal value is obtained when the maximum constraint
of Von Mises is lower than a threshold.
The language python, in this case-test allows repeatedly:
·
to modify the file describing the geometry of the elbow,
·
of launching GMSH in order to net the elbow,
·
to recover the maximum constraint of Von Mises,
·
to evaluate a criterion of stop of the iterations,
·
of launching GMSH to carry out an interactive postprocessing.
This case-test takes again the problem of the case-test forma01f: bent piping, made up of an elastic material
linear, subjected to a force applied at its end, modelled by elements of hulls DKT.
Note:
To have the interactive functions of visualization, to put interactive = 1 at the beginning of the file of
order.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
8.2
Titrate:
DEMO006 Optimization of the radius of curvature of a bent piping
Date:
05/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER
Key: V3.03.131-A
Page:
2/6
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,
·
initial the Rc radius of the elbow is 0.3 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
Isotropic linear elastic material. The properties of material are those of A42 steel:
·
the Young modulus:
E = 1.8 1011 Pa,
·
the Poisson's ratio:
= 0.3,
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
8.2
Titrate:
DEMO006 Optimization of the radius of curvature of a bent piping
Date:
05/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER
Key: V3.03.131-A
Page:
3/6
1.3
Boundary conditions and loadings
· Boundary conditions: embedding on the level of section A,
· Loading: force constant FY directed according to the axis Y and applied to the section B.
The value of FY is calculated to leave:
of the average radius: RMOY = 0.19,
of the total force applied:
2
FTOT = 500000 NR/m,
Its expression is as follows:
FY = FTOT (2 RMOY) (418828.8)
· The limiting constraint of Von Mises is 2.0E+09 NR/m ²
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is obtained numerically. It is thus only about one test of not
regression.
2.2
Results of modeling
The optimal value of the radius of curvature, respecting the criterion put < 2.109 N.m-2 is of 1.1m,
obtained after 5 iterations. With each iteration the radius of curvature is increased by 0.2m.
Radii of
Constraint max of
Iterations
curvature
Von Mises
1
0.3 m
3.3315 E+09 NR/m ²
2
0.5 m
2.7647 E+09 NR/m ²
3
0.7 m
2.4256 E+09 NR/m ²
4
0.9 m
2.1727 E+09 NR/m ²
5
1.1 m
1.9670 E+09 NR/m ²
2.3
Uncertainty on the solution
Solution of nonregression.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
8.2
Titrate:
DEMO006 Optimization of the radius of curvature of a bent piping
Date:
05/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER
Key: V3.03.131-A
Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
Modeling in elements hulls (DKT).
Appear 3.1-a: geometry and grid of the half rolls (initial RC)
3.2
Characteristics of the grid
The grid is regenerated with each iteration because of the modification of the radius of curvature of
geometry. However the topological characteristics of the grid are unchanged:
·
1013 meshs (900 TRIA3, 110 SEG2, 3POI3)
·
507 nodes.
The groups of meshs correspond to:
·
GM30 <=> surface of the TUYAU
·
GM28 <=> section B (effort)
·
GM31 <=> not A1 (- R, 0, 0)
·
GM27 <=> section A (embedding)
·
GM29 <=> SYMETRIE
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
8.2
Titrate:
DEMO006 Optimization of the radius of curvature of a bent piping
Date:
05/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER
Key: V3.03.131-A
Page:
5/6
3.3 Commands
Aster
This paragraph describes the algorithm used in the command file and presents the commands
Code_Aster used.
·
Initialization of certain variables:
Radius of curvature: Rc = 0.3
Critère of convergence: crit = 2.0E+09 (forced of Von Mises targets)
·
One enters the loop python whose criterion of stop relates to the constraint max of Von
Settings. As long as the criterion is not respected, the following instructions are carried out:
Reconstruction of the grid:
one
redefines
Rc in the geometrical file .geo of GMSH
one launches gmsh via python to generate the file of grid .msh
Lecture of grid (PRE_GMSH) and generation of grid (LIRE_MAILLAGE). One uses
DEFI_GROUP to re-elect the groups of meshs according to the correspondence:
# GM30 <=> TUYAU
# GM28 <=> EFOND
# GM31 <=> A1
# GM27 <=> ENCAST
#
GM29
<=>
SYMETRIE
Définition of the finite elements used (AFFE_MODELE). The right pipes and the elbow are
modelled by elements of hull (DKT).
Réorientations of the normals to the elements: one uses MODI_MAILLAGE to direct all
elements in the same way, with a normal turned towards the interior.
Définition and assignment of material (DEFI_MATERIAU and AFFE_MATERIAU).
mechanical characteristics are identical on all the structure.
Affectation of the characteristics of the elements hulls (AFFE_CARA_ELEM): thickness,
vector V defining the reference mark of examination (key word ANGL_REP)
Définition of the boundary conditions and loading (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 an effort distributed FY directed according to the axis Y and applied to the section B, (the effort
distributed is such as the resultant 2Pi * RMOY. FY = FTOT, FTOT being the total force
that one wishes to apply). To apply the effort to the section B, one will use
FORCE_ARETE.
Résolution of the linear elastic problem (MECA_STATIQUE).
Calcul 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 to define the level of calculation in the thickness.
Calcul of the stress field equivalent by elements to the nodes calculated from
stress field (option “EQUI_ELNO_SIGM”).
Calcul of the preceding fields to the nodes (options “SIGM_NOEU_DEPL”,
Loop python of optimization of the radius of curvature
“EQUI_NOEU_SIGM”)
Impression of results (IMPR_RESU).
Détermination of a table containing calculations of averages of the stress field
equivalent to the nodes.(“POST_RELEVE_T')
Extraction of component VMIS of the preceding table via python.
Test of stop:
If VMIS is higher than CRIT, then one reiterates with Rc=Rc+0.2
If not one leaves the loop python.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Code_Aster ®
Version
8.2
Titrate:
DEMO006 Optimization of the radius of curvature of a bent piping
Date:
05/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER
Key: V3.03.131-A
Page:
6/6
4
Results of modeling A
4.1 Values
tested
Radii of
Constraint max of Von
Iterations
curvature
Settings
1
0.3 m
3.3315E+09 NR/m ²
2
0.5 m
2.7647E+09 NR/m ²
3
0.7 m
2.4256E+09 NR/m ²
4
0.9 m
2.1727E+09 NR/m ²
5
1.1 m
1.9670E+09 NR/m ²
5
Summary of the results
The optimal radius of curvature respecting the criterion: constraint max of Von Mises < to 2.0E+09 is of
1.1m. It was obtained after 5 iterations, and the maximum constraint of Von Mises found is of
1.9670E+09 NR/m ².
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/05/005/A
Outline document