Code_Aster
®
Version
4.0
Titrate:
SSNL110 Arises nonlinear including friction of Coulomb
Date:
01/12/98
Author (S)
:
J.M. PROIX, B. QUINNEZ
Key:
V6.02.110-A
Page:
1/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/98/040 - Ind A
Organization (S)
: EDF/IMA/MN
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.110
SSNL110 - Nonlinear spring including of
friction of Coulomb
Summary:
This two-dimensional problem makes it possible to test the law of behavior used to modelize the connection roasts
mix fuel pins of the fuel assemblies.
A reduction according to the time of the rigidity of the connection is taken into account in this test.
This test of nonlinear statics has only one modeling.
Code_Aster
®
Version
4.0
Titrate:
SSNL110 Arises nonlinear including friction of Coulomb
Date:
01/12/98
Author (S)
:
J.M. PROIX, B. QUINNEZ
Key:
V6.02.110-A
Page:
2/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
Imposed displacement
G T X
O
()
y
X
N2
()
H T y
O
Imposed displacement
N1
1.2
Material properties
Linear elastic rigidity of the connection (for the three directions of translation and rotation):
K
NR m
E
=
10
3
/
Initial voltage of the spring in translation according to the direction
X
:
R
NR
NR 0
2
10
= -
Coefficient of Coulomb:
µ =
0 4
.
Function of evolution of rigidity in translation according to
X
:
()
F T
T
=
-
1 10
1.3
Boundary conditions and loadings
N1 node:
embedding:
U
v
W
X
y
Z
= = =
=
=
=
0
0
Node N2:
()
()
U
G T X
v
H T y
X
y
O
O
O
O
=
=
=
=
with
0 1
0 01
.
.
Two cases are considered:
Case 1:
Case 2:
()
()
H T
G T
T
=
1
10
()
()
H T
T
G T
T
=
=
10
10
1.4 Conditions
initial
For the node N2 there are following imposed displacements:
U
v
=
=
0
0
.
.
Code_Aster
®
Version
4.0
Titrate:
SSNL110 Arises nonlinear including friction of Coulomb
Date:
01/12/98
Author (S)
:
J.M. PROIX, B. QUINNEZ
Key:
V6.02.110-A
Page:
3/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/98/040 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
R
NR
R
T
U
T
U
NR
NR
T
T
NR
effort in the direction
effort in the direction
displacement in the direction
displacement in the direction
2
T
1
NR
One a:
()
()
()
()
(
)
R
T
F T
R
K U
U
NR
NO
E
NR
T
NR
T
=
+
-
min
,
2
1
0
At every moment
T
, one calculates:
()
(
)
(
)
()
(
)
(
)
()
()
(
)
R
R
K
U
U
U
T
U
T
T
U
T
U
T
T
If
R
R T
R
R
R
R T
R
R
Te
T
E
T
T
T
T
T
T
Te
N
T
Te
T
N
Te
Te
=
+
=
-
-
-
-
-
< -
=
= -
-
+
+
with
then
If not
there is slip
2
2
1
1
µ
µ
2.1.1 Case
1
In case 1, as long as there is not slip, one a:
()
()
()
[
]
R
K y
R T
F T R
K G T X
T
T
T
T
Te
E O
N
NR
E
O
=
=
=
+
= -
-
+
×
×
= -
+
-
10
1 10
100 1000
10
0 1
100
20
0
2
.
There will be slip when:
()
R
R T
Te
N
= -
µ
I.e.:
(
)
10
0 4
100
20
2
= -
-
+
-
.
T
T
T
=
5
is root of this equation.
One thus has in short:
()
()
()
()
(
)
T
T
R
T
K y
R
T
T
T
R
T
T
T
R
T
T
T
T
E O
NR
NR
T
<
=
=
= -
+
-
= -
+
-
=
×
-
+
5
5
10
10
100
20
100
20
0 4
100
20
2
2
2
.
.
.
.
No slip
There is slip
Code_Aster
®
Version
4.0
Titrate:
SSNL110 Arises nonlinear including friction of Coulomb
Date:
01/12/98
Author (S)
:
J.M. PROIX, B. QUINNEZ
Key:
V6.02.110-A
Page:
4/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/98/040 - Ind A
2.1.2 Case
2
In case 2, as long as there is not slip, one a:
()
()
()
()
()
[
]
R
T
K
H T y
T
R T
F T R
K G T X
T
T
Te
E
O
N
NR
E
O
=
=
=
+
= -
+
-
0
2
100
20
There will be slip when:
()
()
R
T
R T
Te
N
= -
µ
I.e.:
(
)
T
T
T
= -
× -
+
-
0 4
100
20
2
.
T
=
6 096
.
is root of this equation.
One thus has in short:
()
()
()
()
(
)
T
T
R
T
T
R
T
T
T
R
T
T
T
R
T
T
T
T
NR
NR
T
<
=
= -
+
-
= -
+
-
=
×
-
+
6 096
6 096
10
100
20
100
20
0 4
100
20
2
2
2
.
.
.
.
No slip
There is slip
2.2
Results of reference
For various moments, there are the following results:
Case 1
Moment
R
T
R
NR
Slip
0.5
10.
90.25
Not
4.5
10.
25.
Not
5.5
8.1
20.25
Yes
9.5
0.1
0.25
Yes
Case 2
Moment
R
T
R
NR
Slip
0.5
0.5
90.25
Not
6.
6.
16.
Not
6.5
4.9
12.25
Yes
9.5
0.1
0.25
Yes
2.3
Uncertainty on the solution
Analytical solution.
Code_Aster
®
Version
4.0
Titrate:
SSNL110 Arises nonlinear including friction of Coulomb
Date:
01/12/98
Author (S)
:
J.M. PROIX, B. QUINNEZ
Key:
V6.02.110-A
Page:
5/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/98/040 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
N2
N1
Discrete element of rigidity
DIS_T
Characteristics of the elements
DISCRETE
:
Stamp rigidity
K_T_D_L
in total reference mark
Characteristics agent the bonding (N1 N2)
Coefficient of Coulomb:
COULOMB
= 0.4
Initial voltage of compression:
EFFO_N_INIT
: 100.
Function of evolution of rigidity:
RIGI_N_FO
:
()
F T
Boundary conditions
Embedding N1 node:
NODE: N1
DX:0.
DY:0.
DZ:0.
Case 1:
Displacement imposed node N2
DX
DY
:
.
: .
T
10
0 1
0 01
×
Case 2:
Displacement imposed node N2
DX
DY
:
.
:
.
T
T
10
0 1
10
0 01
×
×
3.2
Characteristics of the mesh
A number of nodes: 2
A number of meshs and types: 1 SEG2
3.3 Functionalities
tested
Controls
Keys
AFFE_MODELE
“MECHANICAL”
“DIS_T'
[U4.22.01]
AFFE_CARA_ELEM
DISCRETE
GROUP_MA
“K_T_D_L'
[U4.24.01]
DEFI_MATERIAU
DIS_CONTACT
[U4.23.01]
AFFE_CHAR_MECA
DDL_IMPO
[U4.25.01]
STAT_NON_LINE
EXCIT
CHARGE
FONC_MULT
[U4.32.01]
COMP_INCR
“DIS_CONTACT”
Code_Aster
®
Version
4.0
Titrate:
SSNL110 Arises nonlinear including friction of Coulomb
Date:
01/12/98
Author (S)
:
J.M. PROIX, B. QUINNEZ
Key:
V6.02.110-A
Page:
6/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/98/040 - Ind A
4
Results of modeling A
4.1 Values
tested
One tests the components NR and VY of the field
SIEF_ELGA
and the variable interns (field
VARI_ELGA
)
who is worth 1 when there is slip (if not it is worth 0.).
Case 1:
Identification
Reference
Aster
% difference
Tolerance
Sequence number
Moment
Variable
1
0.05
VY
10.
10.
0.
10
4
VARI
0.
0.
0.
10
4
(absolute)
9
4.5
VY
10.
10.
0.
10
4
VARI
0.
0.
0.
10
4
(absolute)
11
5.5
VY
8.1
8.1
0.
10
4
VARI
1.
1.
0.
10
4
19
9.5
VY
0.1
0.1
0.
10
4
VARI
1.
1.
0.
10
4
Case 2:
Identification
Reference
Aster
% difference
Tolerance
Sequence number
Moment
Variable
1.
0.05
VY
0.5
0.5
0.
10
4
NR
90.25
90.25
0.
10
4
VARI
0.
0.
0.
10
4
(absolute)
12.
6.
VY
6.
6.
0.
10
4
NR
16.
16.
0.
10
4
VARI
0.
0.
0.
10
4
(absolute)
13.
6.5
VY
4.9
4.9
0.
10
4
NR
12.25
12.25
0.
10
4
VARI
1.
1.
0.
10
4
19.
9.5
VY
0.1
0.1
0.
10
4
NR
0.25
0.25
0.
10
4
VARI
1.
1.
0.
10
4
4.2 Parameters
of execution
Version: 4.2.24
Machine: CRAY C90
System: UNICOS 8.0
Overall dimension memory: 8 megawords
Time CPU To use: 33 seconds
5
Summary of the results
The results coincide perfectly with the reference solution. This test thus validates the element of
arises nonlinear allowing to modelize a contact with friction of Coulomb.