Code_Aster ®
Version
4.0
Titrate:
Nonlinear SSNL110 Ressort including of the friction of Coulomb
Date: 01/12/98
Author (S)
:
J.M. PROIX, B. QUINNEZ
Key:
V6.02.110-A Page:
1/6
Organization (S): EDF/IMA/MN
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.110
SSNL110 - Nonlinear Ressort including of
friction of Coulomb
Summary:
This two-dimensional problem makes it possible to test the law of behavior used to model 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.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Nonlinear SSNL110 Ressort including of the friction of Coulomb
Date: 01/12/98
Author (S)
:
J.M. PROIX, B. QUINNEZ
Key:
V6.02.110-A Page:
2/6
1
Problem of reference
1.1 Geometry
(
H T) yo imposed Déplacement
y
Imposed displacement
G (T) X
O
N2
X
N1
1.2
Material properties
Linear elastic rigidity of the connection (for the three directions of translation and rotation):
K = 103 NR/m
E
2
Initial tension of the spring in translation according to direction X: R
= - 10 NR
NR 0
Coefficient of Coulomb: µ = 0 4
.
T
Function of evolution of rigidity in translation according to X: F (T) = 1 -
10
1.3
Boundary conditions and loadings
N1 node:
embedding: U = v = W = 0
= = =
X
y
Z
0
Node N2:
U = G (T) X
v = H (T) y
with
X =
O
O
O
0 1
.
y =
O
0 0
. 1
Two cases are considered:
Case 1:
Case 2:
(
H T) 1
(
T
H T) =
T
10
G (T) = 10
T
G (T) = 10
1.4 Conditions
initial
For the node N2 there are following imposed displacements:
U = 0.
v = 0.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Nonlinear SSNL110 Ressort including of the friction of Coulomb
Date: 01/12/98
Author (S)
:
J.M. PROIX, B. QUINNEZ
Key:
V6.02.110-A Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
T
R
effort in the directio NR
NR
N
NR
R
effort in the directio T
T
N
1
2
U
displacement in the directio T
T
N
U
displacement in the directio NR
NR
N
One a:
T
T
R (T) = min F (T)
()
()
R
+ K
,
2
1
0
(U - U
NR
NO
E
NR
NR)
At every moment T, one calculates:
-
R
= R + K U
with
U
=
2
-
2
-
Te
T
E
T
T
(UT (T) UT (T T))
- (U 1 - 1 -
T (T)
U T (T
T))
If
R
< - µ R
Te
N (T)
then
+
R
= R
T
Te
If not
R
+
R
= - µ R
Te
T
N (T)
(there is slip)
RTe
2.1.1 Case
1
In case 1, as long as there is not slip, one a:
R
= K y =
Te
E O
10
T
T
R (T)
= F (T)
0 +
= 1
N
[R
K G (T) X
NR
E
O]
100 1000
0 1
.
10 -
+
×
×
10
= - 100 + T
20 - T 2
There will be slip when: R
= - µ R (T)
Te
N
I.e.: 10
0 4
. (100 20
2
= -
-
+ T - T)
T = 5 is root of this equation.
One thus has in short:
T < 5.
5. T 10.
R (T) = K y = 10
R (T) = - 100 + 20t - T 2
T
E O
NR
R (T) = - 100 + 20 T - T 2
R (T) = 0 4
. × 100 - 20 + 2
NR
T
(
T
T)
No slip
There is slip
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Nonlinear SSNL110 Ressort including of the friction of Coulomb
Date: 01/12/98
Author (S)
:
J.M. PROIX, B. QUINNEZ
Key:
V6.02.110-A Page:
4/6
2.1.2 Case
2
In the case 2, as long as there is not slip, one a:
R (T) = K
H (T) y = T
Te
E
O
R (T) = F (T)
2
0 +
= - 100 + 20 -
N
[R
K G (T) X
NR
E
O]
T
T
There will be slip when: R
(T) = - µ R (T)
Te
N
2
I.e.: T = - 0 4
. × (- 100 + 20 T - T)
T = 6 096
.
is root of this equation.
One thus has in short:
T < 6 096
.
6 096
.
T 10.
R
=
= - 100 + 20 - 2
T (T)
T
RN (T)
T
T
R
= - 100 + 20 - 2
= 0 4
. × 100 - 20 + 2
NR (T)
T
T
RT (T)
(
T
T)
No slip
There is slip
2.2
Results of reference
For various moments, there are the following results:
Case 1
Moment
R
Slip
T
RN
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
Slip
T
RN
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.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Nonlinear SSNL110 Ressort including of the friction of Coulomb
Date: 01/12/98
Author (S)
:
J.M. PROIX, B. QUINNEZ
Key:
V6.02.110-A Page:
5/6
3 Modeling
With
3.1
Characteristics of modeling
N1
N2
Discrete element of rigidity DIS_T
Characteristics of the elements
DISCRET:
Stamp rigidity K_T_D_L in total reference mark
Characteristics agent the bonding (N1 N2)
Coefficient of Coulomb: COULOMB = 0.4
Initial tension of compression: EFFO_N_INIT: 100.
Function of evolution of rigidity: RIGI_N_FO: F (T)
Boundary conditions
Embedding N1 node:
NOEUD: N1
DX:0.
DY:0.
DZ:0.
Case 1:
Displacement imposed node N2
T
DX:
×.
0 1
DY: .
0 01
10
Case 2:
Displacement imposed node N2
T
T
DX:
×.
0 1
DY:
×.
0 01
10
10
3.2
Characteristics of the grid
A number of nodes: 2
A number of meshs and types: 1 SEG2
3.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
“MECANIQUE”
“DIS_T'
[U4.22.01]
AFFE_CARA_ELEM
DISCRET
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”
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Nonlinear SSNL110 Ressort including of the friction of Coulomb
Date: 01/12/98
Author (S)
:
J.M. PROIX, B. QUINNEZ
Key:
V6.02.110-A Page:
6/6
4
Results of modeling A
4.1 Values
tested
One tests the components NR and VY of 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.
104
VARI
0.
0.
0.
104 (absolute)
9
4.5
VY
10.
10.
0.
104
VARI
0.
0.
0.
104 (absolute)
11
5.5
VY
8.1
8.1
0.
104
VARI
1.
1.
0.
104
19
9.5
VY
0.1
0.1
0.
104
VARI
1.
1.
0.
104
Case 2:
Identification
Reference
Aster
% difference
Tolerance
Sequence number
Moment
Variable
1.
0.05
VY
0.5
0.5
0.
104
NR
90.25
90.25
0.
104
VARI
0.
0.
0.
104 (absolute)
12.
6.
VY
6.
6.
0.
104
NR
16.
16.
0.
104
VARI
0.
0.
0.
104 (absolute)
13.
6.5
VY
4.9
4.9
0.
104
NR
12.25
12.25
0.
104
VARI
1.
1.
0.
104
19.
9.5
VY
0.1
0.1
0.
104
NR
0.25
0.25
0.
104
VARI
1.
1.
0.
104
4.2 Parameters
of execution
Version: 4.2.24
Machine: CRAY C90
System: UNICOS 8.0
Obstruction 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 model a contact with friction of Coulomb.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/98/040 - Ind A