Code_Aster
®
Version
4.0
Titrate:
SSNA01 Rolls infinite under pressure: viscoelasticity of Lemaître
Date:
30/01/98
Author (S):
PH. BONNIERES
Key:
V6.01.001-A
Page:
1/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/96/042 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
Document: V6.01.001
SSNA01 - Infinite cylinder under pressure:
viscoelasticity of Lemaître
Summary:
This test of nonlinear quasi-static mechanics consists in modelizing 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 mesh. This test is drawn from guide VPCS of the SFM.
The cylinder is modelized by axisymmetric elements 2D (QUAD8).
Results obtained by
Code_Aster
are very close to the reference solution.
Code_Aster
®
Version
4.0
Titrate:
SSNA01 Rolls infinite under pressure: viscoelasticity of Lemaître
Date:
30/01/98
Author (S):
PH. BONNIERES
Key:
V6.01.001-A
Page:
2/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/96/042 - Ind A
1
Problem of reference
1.1 Geometry
Z
.E
p
With
B
C
1
R
D
20
20
1.2
Material properties
E = 210.000 MPa
= 0.3
Viscoelastic relation of behavior of Lemaître
(
)
(
)
NR
K
K
m
m
=
=
=
=
=
-
11
1
3 28410
3045
1
0 17857
5 6
4
.
.
.
1.3
Boundary conditions and loadings
On AB: U
Z
= 0
On CD = U
Z
uniform
Loading below: uniform pressure p following along AD.
T
p
100 MPa
60 S
100 H
Code_Aster
®
Version
4.0
Titrate:
SSNA01 Rolls infinite under pressure: viscoelasticity of Lemaître
Date:
30/01/98
Author (S):
PH. BONNIERES
Key:
V6.01.001-A
Page:
3/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/96/042 - Ind A
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
v
rr
and
v
zz
at moment 60 S at the point E located at a distance
D
= -
3
3
6
interior surface of
roll.
2.3
Uncertainty on the solution
Uncertainty lower than 0.01%.
2.4 References
bibliographical
[1]
Card-index SSNA01/89 of Commission VPCS.
Code_Aster
®
Version
4.0
Titrate:
SSNA01 Rolls infinite under pressure: viscoelasticity of Lemaître
Date:
30/01/98
Author (S):
PH. BONNIERES
Key:
V6.01.001-A
Page:
4/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/96/042 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
C
D
N1
E
F
H
G
E
Z
has
B
GROUP_MA: AH
GROUP_NO: NOEHGFE
47 elements
R
The loading and the boundary conditions are modelized by:
DDL_IMPO: (GROUP_NO: NOEHGFE, DY: 0.)
LIAISON_DDL:(NODE:(N1 NXXX), DDL:(“DY”, “DY”), COEF_MULT:(1, - 1),
COEF_IMPO:0.)
for all the nodes belonging to edge AD (U
Z
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 mesh
A number of nodes:
381
A number of meshs and types:
94 elements
QUAD8
3.3 Functionalities
tested
Controls
Key
AFFE_MODELE
AFFE
MODELING
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]
Code_Aster
®
Version
4.0
Titrate:
SSNA01 Rolls infinite under pressure: viscoelasticity of Lemaître
Date:
30/01/98
Author (S):
PH. BONNIERES
Key:
V6.01.001-A
Page:
5/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/96/042 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
v
rr
at the point E with T = 60 S
1.08 10
4
1.077 10
4
0.262%
v
zz
at the point E with T = 60 S
1.84 10
5
1.843 10
5
0.314%
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
Overall dimension memory: 8
MW
Time CPU To use: 116.57
seconds
Code_Aster
®
Version
4.0
Titrate:
SSNA01 Rolls infinite under pressure: viscoelasticity of Lemaître
Date:
30/01/98
Author (S):
PH. BONNIERES
Key:
V6.01.001-A
Page:
6/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HI-75/96/042 - Ind A
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.