Code_Aster
®
Version
6.0
Titrate:
SSNA105 - Hollow roll subjected to a pressure, linear viscoelasticity
Date:
19/08/02
Author (S):
PH. BONNIERES, D. NUNEZ
Key
:
V6.01.105-A
Page:
1/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
Organization (S):
EDF/AMA, CS IF
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
V6.01.105 document
SSNA105 - Hollow roll subjected to a pressure,
linear viscoelasticity, contact
Summary:
This case-test makes it possible to in the case of validate the law of LEMAITRE established in Code_Aster behavior
viscoelastic linear. The found results are compared with an analytical solution.
This test takes again same modeling as the case-test SSNA104A to which one adds a cylinder (pellet) and one
draft the contact.
Code_Aster
®
Version
6.0
Titrate:
SSNA105 - Hollow roll subjected to a pressure, linear viscoelasticity
Date:
19/08/02
Author (S):
PH. BONNIERES, D. NUNEZ
Key
:
V6.01.105-A
Page:
2/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
The diagram is not on the scale, the difference between the two cylinders was amplified for the best
visibility.
R
1
0.82
R
2
0.92
R
3
1.
R
4
2.
1.2
Properties of materials
The pellet is made up of an elastic material, the sheath consists of a viscoelastic material.
The elastic data coincide for two materials.
Young modulus: E= 1 MPa
Poisson's ratio:
=0.3
Law of LEMAITRE:
N
m
K
T
G
=
1
1
)
,
,
(
with
1
,
0
1
,
1
1
=
=
=
N
m
K
Code_Aster
®
Version
6.0
Titrate:
SSNA105 - Hollow roll subjected to a pressure, linear viscoelasticity
Date:
19/08/02
Author (S):
PH. BONNIERES, D. NUNEZ
Key
:
V6.01.105-A
Page:
3/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
1.3
Boundary conditions and loading
Boundary conditions:
The cylinder is locked out of DY on the sides [AP, LP], [AG, BG] and [CP, PD] [CG, PG].
Loading:
The cylinder is subjected to an internal pressure on [DP, AP], this pressure is calculated of such kind
that at the moment t=0, the sheath has the same behavior as the cylinder modelized in the test ssna104a.
(
)
(
)
(
)
(
)
[
]
<
+
+
+
+
-
-
-
-
-
=
-
5
0
0
1
1
2
1
)
(
2
3
2
1
2
1
2
2
2
3
1
T
if
K
HT
Ge
D
C
R
R
B
With
T
if
R
R
R
E
R
R
T
p
Ekt
with
(
)
-
-
=
1
2
2
1
2
1
2
2
R
R
R
With
,
)
1
(
2
+
=
R
E
B
,
2
3
2
4
3
3
0
R
R
R
P
C
-
=
with P
0
=1.E-3 MPa, pressure of the test ssna104a.
(
)
(
)
-
+
+
=
2
1
2
3
1
1
2
3
2
4
R
R
E
D
,
(
)
E
G
2
2
1
2
-
-
=
,
2
3
2
4
2
3
R
R
K
H
=
,
+
-
-
=
2
2
2
1
2
1
2
2
2
2
0
2
1
R
R
R
R
R
P
K
One treats the contact between the two cylinders.
Code_Aster
®
Version
6.0
Titrate:
SSNA105 - Hollow roll subjected to a pressure, linear viscoelasticity
Date:
19/08/02
Author (S):
PH. BONNIERES, D. NUNEZ
Key
:
V6.01.105-A
Page:
4/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
2
Reference solutions
2.1
Method of calculation used for the reference solutions
The whole of this demonstration can be read with more details in the document [bib1].
Phase without contact
One wants to find the value of
)
(
1
T
p
to apply to the internal wall of the pellet for which the contact
place has.
For the pellet, one finds:
+
-
=
2
0
0
0
1
0
0
0
1
2
2
2
2
2
2
R
R
R
R
where
2
1
2
2
2
1
1
)
(
R
R
R
T
p
-
=
(
)
R
W
R
R
E
=
+
-
+
=
2
2
2
2
1
1
.
The condition of being written contact:
0
)
(
)
(
2
3
=
-
R
W
R
W
, one has
(
) ()
-
+
=
-
1
1
2
2
2
3
E
R
R
R
From where
(
)
2
2
3
1
2
1
-
-
=
E
R
R
(
)
(
)
2
2
1
2
1
2
2
2
3
1
1
2
1
lim
-
-
-
=
R
R
R
E
R
R
p
.
Phase with contact
It is wanted that as from the moment t=0, the sheath has same behavior as in the test ssna104a.
When there is contact, one a:
2
3
3
2
)
(
)
(
R
R
R
W
R
W
G
P
-
+
=
,
thus by recovering the value of displacements in the test ssna104, one must obtain:
(
)
(
)
(
)
+
-
-
-
+
+
-
+
-
=
-
T
R
R
K
E
R
R
E
R
R
R
p
R
R
R
W
Ekt
P
2
3
2
4
2
3
2
4
2
3
2
4
3
3
0
2
3
2
2
3
2
1
3
2
2
1
1
1
)
(
.
Code_Aster
®
Version
6.0
Titrate:
SSNA105 - Hollow roll subjected to a pressure, linear viscoelasticity
Date:
19/08/02
Author (S):
PH. BONNIERES, D. NUNEZ
Key
:
V6.01.105-A
Page:
5/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
The stress field of the pellet is given by
+
-
+
-
-
-
=
Z
R
R
R
R
R
R
R
R
0
0
0
1
1
0
0
0
1
1
2
2
2
0
2
2
2
1
2
2
2
0
2
2
2
1
with
2
1
2
2
2
1
1
1
R
R
R
p
-
=
and
2
1
2
2
2
1
0
0
R
R
R
p
-
=
.
Like
(
)
(
)
0
2
1
0
1
=
+
-
-
+
=
Z
Z
Z
E
E
, one finds:
(
)
0
1
2
-
=
Z
.
One thus has
(
)
(
) (
)
R
W
R
R
R
R
E
E
E
Z
R
=
-
+
-
-
+
=
+
+
-
+
=
2
2
1
0
2
2
2
1
0
1
2
1
1
1
(
)
+
-
-
-
+
=
2
2
2
1
0
1
2
2
2
1
1
2
1
)
(
R
R
R
E
R
W
P
, one finds
)
(
1
T
p
given by the formula a little more
high.
2.2
Results of reference
Displacement DX on the node B
2.3
Uncertainty on the solution
0%: analytical solution
2.4 References
bibliographical
[1]
PH. BONNIERES, two analytical solutions of axisymmetric problems in
linear viscoelasticity and with unilateral contact, Note HI-71/8301
Code_Aster
®
Version
6.0
Titrate:
SSNA105 - Hollow roll subjected to a pressure, linear viscoelasticity
Date:
19/08/02
Author (S):
PH. BONNIERES, D. NUNEZ
Key
:
V6.01.105-A
Page:
6/6
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
The problem is modelized in axisymetry
3.2
Characteristics of the mesh
750 meshs QUAD4
3.3
Functionalities tested
Controls
DEFI_MATERIAU
ELAS
LEMAITRE
AFFE_CHAR_MECA
CONTACT
STAT_NON_LINE
COMP_INCR
LEMAITRE
COMP_ELAS
ELAS
4
Results of modeling A
4.1 Values
tested
Identification Moments
Reference
Aster
Variation (%)
DX (B)
0.9
2.14 E3
2.14 E3
0.953
SIXX (B)
0.9
0.0
4.8168 E6
4.8168 E6
SIYY (B)
0.9
2.7912 E4
2.759 E4
1.5
SIZZ (B) 0.9 6.66
E4 6.635
E4
0.5
5
Summary of the results
The results calculated by Code_Aster are in agreement with the analytical solutions but depend
very strongly of the refinement of the mesh.