Code_Aster
®
Version
6.0
Titrate:
SSNL117 - Bend in elastoplastic bending
Date:
24/10/02
Author (S):
J.M. PROIX, P. MASSIN
Key
:
V6.02.117-B
Page:
1/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.117
SSNL117 - Bend in bending in elastoplasticity
Summary:
This test validates the modeling of the phenomena of ovalization in pipings in the field
elastoplastic with the elements PIPE: an elbow, prolonged by right pipes is subjected to a bending
in its plan. Piping is thick (of size similar to the elbows of the primary education circuits).
reference solution is numerical: it is obtained with Code_Aster using a mesh 3D of the elbow.
Two modelings make it possible to validate the elements PIPE (with right and bent elements with 3
nodes for modeling A and of the right and bent elements with 4 nodes for modeling B) in
elastoplasticity.
In modeling B, a term of “total” rotation, developed by EDF, ECA and FRAMATOME [bib2],
for pipings under seism, is introduced via a Python macro-control.
Code_Aster
®
Version
6.0
Titrate:
SSNL117 - Bend in elastoplastic bending
Date:
24/10/02
Author (S):
J.M. PROIX, P. MASSIN
Key
:
V6.02.117-B
Page:
2/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Piping bent in plan XY. The right parts have as a length L = 1 Mr.
The elbow has as a radius of curvature: Rc = 1.25m
L
With
B
Mz
C
D
Rc
L
X
Y
The tubular section has for average radius R = 395.5mm and a thickness E = 77mm.
1.2
Properties of materials
The material is elastoplastic with isotropic linear work hardening.
E = 2.E11 AP
= 0.3
Elastic limit SIGY = 200.10
6
AP
Modulate work hardening
D_SIGM_EPSI
= 2.10
10
AP
1.3
Boundary conditions and loadings
Embedding of A (locked DDL of beam, but free DDL of ovalization).
Moment MZ imposed in D increasing:
Increment 1
Mz = 3086702.1520853 Nm
10 equal increments until:
Increment 11
Mz = 7091146.5935484 Nm
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
6.0
Titrate:
SSNL117 - Bend in elastoplastic bending
Date:
24/10/02
Author (S):
J.M. PROIX, P. MASSIN
Key
:
V6.02.117-B
Page:
3/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Comparison with other numerical results obtained with Code_Aster (version 4.3 [bib1]) with one
mesh 3D of the elbow and the right parts, connected at the ends with right beams. This mesh
3D comprises 1024 meshs HEXA20. A modeling of the elbow in elements COQUE_3D gave
results comparable with calculation 3D (see [§2.2]).
2.2
Results of reference
For one moment applied Mz in D, displacement DY of the same point D is worth [bib1]:
Moment
Dy not D (m) (3D)
Dy not D (m) (COQUE_3D)
0. 0.
0.
3.08670D+06 1.09349D02
1.08875D02
3.48715D+06 1.23536D02
3.88759D+06 1.37891D02
1.37381D02
4.28804D+06 1.52727D02
4.68848D+06 1.68128D02
5.08892D+06 1.84085D02
5.48937D+06 2.01272D02
5.88981D+06 2.20836D02
6.29026D+06 2.43502D02
6.69070D+06 2.70438D02
7.09115D+06 3.04756D02
2.3
Precision on the results of reference
Owing to the fact that the reference solution is numerical, one can evaluate the precision according to [§2.2] to 2% by
comparison of the 3D solutions and COQUE_3D.
2.4 References
bibliographical
[1]
J.M. PROIX, A. BEN HAJ YEDDER: “Project CACIP: study of a piping bent in
bending “. Note EDF/DER HI-75/98/001/0
[2]
C. CHURN (SEPTEN), MN. BERTON, NR. BLAY (ECA), F. THE BRETON ONE
(FRAMATOME-ANP): “Project of new coding of the criteria of dimensioning
seismic of pipings “. Note EDF/SEPTEN E-N-ES-MS/01-01004-A.
Code_Aster
®
Version
6.0
Titrate:
SSNL117 - Bend in elastoplastic bending
Date:
24/10/02
Author (S):
J.M. PROIX, P. MASSIN
Key
:
V6.02.117-B
Page:
4/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
The structure is with a grid in elements pipes (meshs SEG3, modeling PIPE).
3.2
Characteristics of the mesh
20 meshs SEG3 (the mesh is regular: 10 elements in the elbow, 5 in each right pipe)
3.3 Functionalities
tested
Controls
AFFE_MODELE
MODELING
PIPE
STAT_NON_LINE
TUYAU_NCOU
AFFE_CARA_ELEM
ORIENTATION
CARA
GENE_TUYAU
STAT_NON_LINE
TUYAU_NSEC
4
Results of modeling A
4.1 Values
tested
Increment of load
DY of the point D
Reference
Aster %
diff
1: Mz =3.08670D+06Nm
DY (m)
1.09349D02
1.118834D02
2.3
8: Mz =5.88981D+06Nm
DY (m)
2.20836D02
2.269183D02
2.75
Code_Aster
®
Version
6.0
Titrate:
SSNL117 - Bend in elastoplastic bending
Date:
24/10/02
Author (S):
J.M. PROIX, P. MASSIN
Key
:
V6.02.117-B
Page:
5/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
The structure is with a grid in elements pipes with 4 nodes (meshs SEG4, modeling PIPE).
5.2
Characteristics of the mesh
11 meshs SEG4 (5 elements in the elbow, 3 in each right pipe)
5.3
Calculation of the term of “Total” Rotation
This term of rotation “
total
” was developed within the framework of a tripartite action
EDF-CEA-FRAMATOME [bib2], for a future integration in the code of dimensioning
RCC-M.
It is expressed starting from rotations of two points representative of the elbow (entered and left), by:
2
2
2
Z
y
X
G
R
R
R
R
+
+
=
where
bend
input
bend
exit
Z
bend
input
bend
exit
y
bend
input
bend
exit
X
DRZ
DRZ
R
DRY
DRY
R
DRX
DRX
R
-
=
-
=
-
=
This term is calculated by the Python macro-control
MACR_ROTA_GLOBALE
who is integrated in
body of the command file. The result of this macro-control is an Aster function of
total rotation according to the moment. A test of not-regression comes to validate this function.
5.4 Functionalities
tested
Controls
AFFE_MODELE
MODELING
PIPE
STAT_NON_LINE
TUYAU_NCOU
AFFE_CARA_ELEM
ORIENTATION
CARA
GENE_TUYAU
STAT_NON_LINE
TUYAU_NSEC
CALC_ELEM
EQUI_ELGA_SIGM
EQUI_ELGA_EPSI
CALC_ELEM
VALE_NCOU_MAXI
EQUI_ELGA_SIGM
VMIS
MACR_ROTA_GLOBALE
Code_Aster
®
Version
6.0
Titrate:
SSNL117 - Bend in elastoplastic bending
Date:
24/10/02
Author (S):
J.M. PROIX, P. MASSIN
Key
:
V6.02.117-B
Page:
6/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
6
Results of modeling B
6.1 Values
tested
Increment of load
DY of the point D
Reference
Aster %
diff
1: Mz =3.08670D+06Nm
DY (m)
1.09349D02
1.097089D02
0.3
8: Mz =5.88981D+06Nm
DY (m)
2.20836D02
2.185D02
1.1
Test of not-regression for total rotation:
Moment
Aster
5.88981E+06 9.26451E03
Tests of nonregression for the options of
CALC_ELEM
:
Component option
Net
Not Under-point
Number
of command
Aster
EQUI_ELGA_SIGM
VMIS
M1 2
61
1 4.675554583E+07
EQUI_ELGA_SIGM
VMIS
M1 3
55
3 5.608141169E+07
EQUI_ELGA_EPSI
INVA_2
M1 1
77
4 2.590281477E-04
EQUI_ELGA_EPSI
INVA_2
M1 1
8
5 1.769279362E-04
Option Field
Component
Net
Not
Number
of command
Aster
VALE_NCOU_MAXI
EQUI_ELGA_SIGM
MAX
M1 1 1 8.84099E+07
VALE_NCOU_MAXI
EQUI_ELGA_SIGM
MIN
M1 1 5.88318E+06
VALE_NCOU_MAXI
EQUI_ELGA_SIGM
NCOUMAX
M2 2 1 1.00000E+00
VALE_NCOU_MAXI
EQUI_ELGA_SIGM
NCOUMIN
M3 3 1 1.00000E+00
VALE_NCOU_MAXI
EQUI_ELGA_SIGM
NSECMAX
M4 1 1 1.20000E+01
VALE_NCOU_MAXI
EQUI_ELGA_SIGM
NSECMIN
M5 2 1 1.60000E+01
VALE_NCOU_MAXI
EQUI_ELGA_SIGM
NPCOUMAX
M6 3 1 1.00000E+00
VALE_NCOU_MAXI
EQUI_ELGA_SIGM
NPCOUMIN
M7 1 1 2.00000E+00
VALE_NCOU_MAXI
EQUI_ELGA_SIGM
NPSECMAX
M8 2 1 3.00000E+00
VALE_NCOU_MAXI
EQUI_ELGA_SIGM
NPSECMIN
M9 3 1 3.00000E+00
VALE_NCOU_MAXI
EQUI_ELGA_SIGM
MAX
M1 2 4 1.27695E+08
VALE_NCOU_MAXI
EQUI_ELGA_SIGM
MIN
M5 3 5 2.20755E+07
7
Summary of the results
The reference solution not being analytical, but numerical (obtained by a modeling 3D),
the noted variations (from 1% to 3%) can be regarded as reasonable. To obtain one
better correspondence of the 3D solutions and PIPE, it would be appropriate to modelize the right parts
over a bigger length, and to adopt a finer mesh for each modeling. This
was not made within the framework of this test, to keep reasonable execution times.