Code_Aster ®
Version
4.0
Titrate:
SSNA01 infinite Cylindre under pressure: viscoelasticity of Lemaître
Date:
30/01/98
Author (S):
PH. BONNIERES
Key:
V6.01.001-A Page:
1/6
Organization (S): EDF/IMA/MN
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
Document: V6.01.001
SSNA01 - Infinite Cylindre under pressure:
viscoelasticity of Lemaître
Summary:
This test of nonlinear quasi-static mechanics consists in modelling an infinite cylinder subjected to a pressure
intern depend on time. One thus validates the relation of nonlinear behavior of viscoelasticity of
Lemaître into axisymmetric, and on a complete grid. This test is drawn from guide VPCS of the SFM.
The cylinder is modelled by axisymmetric elements 2D (QUAD8).
The results obtained by Code_Aster are very close to the reference solution.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/96/042 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNA01 infinite Cylindre under pressure: viscoelasticity of Lemaître
Date:
30/01/98
Author (S):
PH. BONNIERES
Key:
V6.01.001-A Page:
2/6
1
Problem of reference
1.1 Geometry
Z
C
D
p
.E
1
With
B
R
20
20
1.2
Material properties
E = 210.000 MPa
= 0.3
Viscoelastic relation of behavior of Lemaître
1
-
1
NR = 11
= 328410 4
.
(K =
)
3045
= 017857
.
(m = 5. )
6
K
m
1.3
Boundary conditions and loadings
On AB: uz = 0
On CD = uz uniform
Loading below: uniform pressure p following along AD.
p
100 MPa
T
60 S
100 H
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/96/042 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNA01 infinite Cylindre under pressure: viscoelasticity of Lemaître
Date:
30/01/98
Author (S):
PH. BONNIERES
Key:
V6.01.001-A Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
Calculation carried out with various codes of finite elements using various explicit algorithms,
semi-implicit or implicit.
2.2
Results of reference
3 -

3
v
and
at moment 60 S at the point E located at a distance D =
interior surface of
rr
vzz
6
roll.
2.3
Uncertainty on the solution
Uncertainty lower than 0.01%.
2.4 References
bibliographical
[1]
Card-index SSNA01/89 of Commission VPCS.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/96/042 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNA01 infinite Cylindre under pressure: viscoelasticity of Lemaître
Date:
30/01/98
Author (S):
PH. BONNIERES
Key:
V6.01.001-A Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
Z
C
D
has
B
N1
GROUP_MA: AH
E
H
G
F
E
R
47 elements
GROUP_NO: NOEHGFE
The loading and the boundary conditions are modelled by:
DDL_IMPO: (GROUP_NO: NOEHGFE, DY: 0.)
LIAISON_DDL:(NOEUD:(N1 NXXX), DDL:(“DY”, “DY”), COEF_MULT:(1, - 1),
COEF_IMPO:0.)
for all the nodes belonging to edge AD (uz uniform on AD)
PRES_REP: (GROUP_MA: AH, NEAR: p (T))
or p (T) is the higher definite positive function [§1.3].
3.2
Characteristics of the grid
A number of nodes:
381
A number of meshs and types:
94 elements QUAD8
3.3 Functionalities
tested
Commands
Key
AFFE_MODELE
AFFE
MODELISATION
AXIS
[U4.22.01]
DEFI_MATERIAU
LEMAITRE
NR
[U4.23.01]
N_SUR_K
UN_SUR_M
AFFE_CHAR_MECA
PRES_REP
GROUP_MA
[U4.25.01]
STAT_NON_LINE
COMP_INCR
RELATION
LEMAITRE
[U4.32.01]
CALC_ELEM
OPTION
EPSI_ELNO_DEPL
[U4.61.01]
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/96/042 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNA01 infinite Cylindre under pressure: viscoelasticity of Lemaître
Date:
30/01/98
Author (S):
PH. BONNIERES
Key:
V6.01.001-A Page:
5/6
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
v at the point E with T = 60 S
­ 1.08 10­4
­ 1.077 10­4
­ 0.262%
rr
v at the point E with T = 60 S
­ 1.84 10­5
­ 1.843 10­5
­ 0.314%
zz
4.2 Remarks
One stopped with T = 60 S not to have time too long calculation.
4.3 Parameters
of execution
Version: 3.04.02
Machine: CRAY C90
Obstruction memory: 8
MW
Time CPU To use: 116.57
seconds
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/96/042 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNA01 infinite Cylindre under pressure: viscoelasticity of Lemaître
Date:
30/01/98
Author (S):
PH. BONNIERES
Key:
V6.01.001-A Page:
6/6
5
Summary of the results
The precision necessary for this test was fixed at 0.5% instead of 0.1% not not to lengthen time too much
of calculation. However, one checks that by refining the discretization in time, the error made compared to
the reference solution tends towards zero.
Handbook of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/96/042 - Ind A