Code_Aster ®
Version
6.0
Titrate:
SSNL117 - Coude in elastoplastic inflection


Date:
24/10/02
Author (S):
J.M. PROIX, Key P. MASSIN
:
V6.02.117-B Page:
1/6

Organization (S): EDF-R & D/AMA
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.117

SSNL117 - Coude in inflection in elastoplasticity

Summary:

This test validates the modeling of the phenomena of ovalization in pipings in the field
elastoplastic with elements TUYAU: an elbow, prolonged by right pipes is subjected to an inflection
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 grid 3D of the elbow.

Two modelings make it possible to validate elements TUYAU (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-command.


Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL117 - Coude in elastoplastic inflection


Date:
24/10/02
Author (S):
J.M. PROIX, Key P. MASSIN
:
V6.02.117-B Page:
2/6

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


With
L
B
Rc
L
Y
Mz
C
D
X


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 Pa
= 0.3
Elastic limit SIGY = 200.106 Pa
Modulate work hardening D_SIGM_EPSI = 2.1010 Pa

1.3
Boundary conditions and loadings

Embedding of A (blocked 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.

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL117 - Coude in elastoplastic inflection


Date:
24/10/02
Author (S):
J.M. PROIX, Key P. MASSIN
:
V6.02.117-B Page:
3/6

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
grid 3D of the elbow and the right parts, connected at the ends with right beams. This grid
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
inflection “. 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.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL117 - Coude in elastoplastic inflection


Date:
24/10/02
Author (S):
J.M. PROIX, Key P. MASSIN
:
V6.02.117-B Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

The structure is with a grid in elements pipes (meshs SEG3, modeling TUYAU).

3.2
Characteristics of the grid

20 meshs SEG3 (the grid is regular: 10 elements in the elbow, 5 in each right pipe)

3.3 Functionalities
tested

Commands


AFFE_MODELE
MODELISATION
TUYAU
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

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL117 - Coude in elastoplastic inflection


Date:
24/10/02
Author (S):
J.M. PROIX, Key P. MASSIN
:
V6.02.117-B Page:
5/6

5 Modeling
B

5.1
Characteristics of modeling

The structure is with a grid in elements pipes with 4 nodes (meshs SEG4, modeling TUYAU).

5.2
Characteristics of the grid

11 meshs SEG4 (5 elements in the elbow, 3 in each right pipe)

5.3
Calculation of the term of Rotation “Globale”

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
G
R =
R
X + R
y + R
Z

where
R
X = DRX sortiecoude - DRXentréecoude
R
y =
output
DRY
bend -
input
DRY
bend
R
Z = DRZsortiecoude - DRZentréecoude

This term is calculated by the macro-command Python MACR_ROTA_GLOBALE which is integrated in
body of the command file. The result of this macro-command is a Aster function of
total rotation according to the moment. A test of not-regression comes to validate this function.

5.4 Functionalities
tested

Commands


AFFE_MODELE
MODELISATION
TUYAU
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

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL117 - Coude in elastoplastic inflection


Date:
24/10/02
Author (S):
J.M. PROIX, Key P. MASSIN
:
V6.02.117-B Page:
6/6

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 Aster
of command
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
Aster
of command
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 TUYAU, it would be appropriate to model the right parts
over a bigger length, and to adopt a finer grid for each modeling. This
was not made within the framework of this test, to keep reasonable execution times.

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Outline document