SSNV146 - Analyze regularized limit. Spherotoric bottom tank

Code_Aster

Version

5.0

Titrate:

SSNV146 - Analyze regularized limit. Spherotoric bottom tank

Date:

06/11/01

Author (S):

F. VOLDOIRE

Key

V6.04.146-A

Page:

1/6

Manual of Validation

V6.04 booklet: Non-linear statics of the voluminal structures

HT-62/01/012/A

Organization (S):

EDF/RNE/AMV

Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.146

SSNV146 - Analyze regularized limit.
Spherotoric bottom tank

Summary

This test makes it possible to qualify the operators used analyzes regularized limit of it. One calculates the load limits by
a kinematic approach regularized by the method of Norton-Hoff-Friaâ.

One considers an axisymmetric spherotoric bottom tank (modeling A). The constitutive material checks it
criterion of von Mises and the structure is subjected to an internal pressure. Calculation makes it possible to obtain the load
limit in the direction of the loading.

The structure is modelized by incompressible elements and the loading is standardized.

The resolution by the regularized method of Norton-Hoff-Friaâ is carried out in the control

STAT_NON_LINE

. A postprocessing in the control

POST_ELEM

allows to obtain the value of a terminal

higher of the limiting load, as well as an estimate of the lower limit.

The reference solution results from a European benchmark, carried out within the framework of a project Brite EuRam
BE97-4547 “LISA”, in 1998, and the results are in perfect agreement with the values of reference.

Code_Aster

Version

5.0

Titrate:

SSNV146 - Analyze regularized limit. Spherotoric bottom tank

Date:

06/11/01

Author (S):

F. VOLDOIRE

Key

V6.04.146-A

Page:

2/6

Manual of Validation

V6.04 booklet: Non-linear statics of the voluminal structures

HT-62/01/012/A

Problem of reference

1.1 Geometry

The internal radius of the cylindrical part is: 49mm, while the thickness is: 2mm. the radius of
spherical part with the apex is 98mm, while the radius of the core of connection is of 20mm.

1.2

Material properties

The material is homogeneous:
Young modulus:

MPa

200 000

Poisson's ratio:

= 0.5

Elastic limit:

MPa

= 100

Coefficient of the law of Norton-Hoff:

101

1.3

Boundary conditions and loadings

The boundary conditions are: axial displacement no one on the end of the cylindrical part
(conditions of symmetry).

Conditions limit in AXIS:

on BORD_INF: DY = 0.

The loading parameterized by

is:

in AXIS:

Close = 1. on internal wall B_D.

Code_Aster

Version

5.0

Titrate:

SSNV146 - Analyze regularized limit. Spherotoric bottom tank

Date:

06/11/01

Author (S):

F. VOLDOIRE

Key

V6.04.146-A

Page:

3/6

Manual of Validation

V6.04 booklet: Non-linear statics of the voluminal structures

HT-62/01/012/A

Reference solution

2.1

Method of calculation used for the reference solution

This test of benchmark is referred: case-test LA6 and was carried out within the framework of a European project
Brite EuRam BE97-4547 “LISA”, in 1998, partly financed by the EC. This test was carried out with
even mesh by the three participating organizations. By considering a pipe of same dimensions,
the limiting load is: 4,0005MPa, and for the sphere of same dimensions: 4,04MPa.

2.2

Results of reference

One gives hereafter the results provided by EDF at the time of the benchmark, for three values of the parameter of
regularization

, as those provided by organizations LTAS in Liege (which uses another

regularized kinematic method, in the university software dedicated “ELSA”) and ForschungZentrum
of Jülich (which use a static method approximate by finite elements in displacements, and one
reduced representation of the fields of auto-contraintes, using the Permas code, supplemented of one
algorithm of optimization).

Modeling case

lim

sup

lim

inf

estimated

EDF

=21

2D axis

3,9514 MPa

3,6049 MPa

EDF

=31

2D axis

3,9456 MPa

3,7090 MPa

EDF

=71 2D

axis

3,9404 MPa

3,8372 MPa

Univ. of Liege/LTAS

2D axis

3,931 MPa

nothing

Research center FZJ

2D axis

nothing 3,997

MPa

The methods regularized kinematics of EDF and the LTAS give very nearby results. One
note a fault however: the lower limit of the FZJ is higher on the higher terminal of ULg
and EDF, which is impossible.

The convergence of the method suggested by Code_Aster is visualized on the diagram
below.

Pressure tank

0,5

1,5

2,5

3,5

4,5

Command N (Norton-Hoff)

Charge limit

F_sup (MPa)
F_inf (MPa)

2.3 References

bibliographical

[1]

Voldoire F.: Calculation of load limits with Code_Aster and benchmark of Brite EuRam
“LISA”. Note HI-74/98/026/A.

[2] Heitzer

Mr. “

Traglast- und Einspielanalyse zur Bewertung der Sicherheit to passivate

Komponenten. “Thesis., RWTH Aachen (1999).

[3]

Yan A. direct M. “Contributions to the limit state analysis off plastified and cracked
structures “. Thesis, Univ. Liege, (1999).

Code_Aster

Version

5.0

Titrate:

SSNV146 - Analyze regularized limit. Spherotoric bottom tank

Date:

06/11/01

Author (S):

F. VOLDOIRE

Key

V6.04.146-A

Page:

4/6

Manual of Validation

V6.04 booklet: Non-linear statics of the voluminal structures

HT-62/01/012/A

3 Modeling

With

3.1

Characteristics of modeling

One considers a cylinder modelized by axisymmetric elements QUAD8 of the incompressible type:

miaxqu8

, according to a regulated mesh. The required precision is of

on balance.

3.2

Characteristics of the mesh

The mesh contains two Q8 elements in the thickness, and in all there are 34 elements, and 141 nodes.
Here a sight of the mesh and deformation for

=31.

3.3 Functionalities

tested

Controls

Key word factor

Single-ended spanner word

Argument

DEFI_MATERIAU NORTON-HOFF

MACRO_CHAR_F_U CHARGES

STAT_NON_LINE

COMP_INCR RELATION

“NORTON_HOFF”

RECH_LINEAIRE

ETAT_INIT

EVOL_NOLI

SOLVEUR

METHOD

“LDLT”

POST_ELEM CHAR_LIMITE

ALL

“YES”

TEST_TABLE

COUNT

“CHAR_LIMI_SUP”
“CHAR_LIMI_ESTIM”

Code_Aster

Version

5.0

Titrate:

SSNV146 - Analyze regularized limit. Spherotoric bottom tank

Date:

06/11/01

Author (S):

F. VOLDOIRE

Key

V6.04.146-A

Page:

5/6

Manual of Validation

V6.04 booklet: Non-linear statics of the voluminal structures

HT-62/01/012/A

Results of modeling A

4.1 Values

tested

Identification Reference

Aster %

difference

Tolerance

N = 21

Charge higher limit

3,9514 3,9514 0.05% 0.1%

Charge estimated limit

3,6049 3,6049 0.05% 0.1%

N = 31

Charge higher limit

3,9456 3,9456 0.05% 0.1%

Charge estimated limit

3,7090 3,7090 0.05% 0.1%

N = 51

Charge higher limit

3,9417 3,9417 0.05% 0.1%

Charge estimated limit

3,7978 3,7978 0.05% 0.1%

N = 71

Charge higher limit

3,9404 3,9404 0.05% 0.1%

Charge estimated limit

3,8372 3,8372 0.05% 0.1%

N = 101

Charge higher limit

3,931 3,9396 0.2% 0.3%

Charge estimated limit

3,90

3,8673

0.8%

0.9%

4.2 Parameters

of execution

Version: STA 5.06

Machine: Claster

System:

IRIX 64

Overall dimension memory: 64 MO

Time CPU To use:

12.15 seconds