Code_Aster ®
Version
6.3
Titrate:
SSNL108 - Liaison tube-grid with friction of Coulomb
Date:
23/10/02
Author (S):
J.M. PROIX, B. QUINNEZ
Key: V6.02.108-B Page: 1/6
Organization (S): EDF-R & D/AMA
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.108
SSNL108 - Liaison tube-grid with 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. This test of nonlinear statics has only one
only modeling.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.3
Titrate:
SSNL108 - Liaison tube-grid with friction of Coulomb
Date:
23/10/02
Author (S):
J.M. PROIX, B. QUINNEZ
Key: V6.02.108-B Page: 2/6
1
Problem of reference
1.1 Geometry
Imposed displacement
N4
y
N2
X
N1
N3
1.2
Material properties
Linear elastic rigidity of the connection (for the three directions of translation and rotation):
K
NR m
E = 103
/
Initial tension of the spring following direction X: R
NR
No = - 102
Young modulus of the beam: E = 105
Poisson's ratio of the beam: = 0 3
.
Function of evolution of rigidity: F (T) 1
Coefficient of Coulomb: µ = 0 4
.
Modulate work hardening: KTT=0, then KTT=100N/m
1.3
Boundary conditions and loadings
Embedded N1 node: U = v = W = 0
X = y = Z = 0
Nodes N2, N3, N4 movement according to y
U = W = 0
X = y = Z = 0
Nodes N2, N3, N4 movement imposed according to y
v = 0 0
. 1 G (T)
G (T)
with
10.
0.
10.
20.
T
Two calculations are carried out: one without work hardening, with all the way above, the other with
work hardening, for the first part of the way (0<t<10).
1.4 Conditions
initial
With T = 0, the spring of connection are compressed and the beam is in initial position.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.3
Titrate:
SSNL108 - Liaison tube-grid with friction of Coulomb
Date:
23/10/02
Author (S):
J.M. PROIX, B. QUINNEZ
Key: V6.02.108-B Page: 3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is obtained analytically. Three nodes of the beam having the same one
imposed displacement, the beam is thus indeformable.
The node N2 not having displacement according to X one a:
R = R
T
N
No
In addition one a: U = U = 0 0
. 1 G (T
T
Y
)
1ère phase: R
= K U < µ R = µ R
, U
T
E
T
N
No
T increases.
In this phase, RT is strictly lower than µ RN and one thus does not have friction.
Limit T1 of this phase is defined by
: R = K U = µ R
T
E
T
No i.e. for
0 0
. 1 K G (T1) = µ R
E
No.
One finds T1 = 4.
Without work hardening:
2nd phase: R
= µ R = µ R
, U
T
N
No
T increases.
The tangential force reached the value of the threshold µ Rno and one thus has slip. This phase is
delimited by the moments T = 4. and T
1
2 = 10. (moment when U T starts to decrease).
3rd phase: R
= K U < µ R = µ R
, U
T
E
T
N
No
T decreases.
In this phase, RT is lower than the value of the threshold µ RN and one is thus in a phase
rubber band R = - K U + µ R
T
E
T
No.
The limits of this phase are T = 10. and T
2
3 defined by:
- 0 0
. 1k G (T) + µ R = - R
T
E
No
No
> 10
3
3
.
One finds T3 = 18.
4th phase: R
= µ R
, U
T
No
T decreases.
In this phase, one reached the threshold of slip again. One a: R = µ R
T
No Cette phase is
delimited by the moments T3 = 18. and t4 = 20.
With work hardening:
K
2nd phase:
Tt
R = µ R 1
+ K U
.
.
T
N
Tt
T
K
Te
The tangential force reached the value of the threshold µ Rno and one thus has slip. This phase is
delimited by the moments T = 4. and T
1
2 = 10. There is an effect of work hardening.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.3
Titrate:
SSNL108 - Liaison tube-grid with friction of Coulomb
Date:
23/10/02
Author (S):
J.M. PROIX, B. QUINNEZ
Key: V6.02.108-B Page: 4/6
2.2
Results of reference
For the various remarkable moments, the value of RT is equal to:
Without work hardening:
T =.
4
RT =.
40
T =.
10
RT =.
40
T =.
18
RT = -.
40
T =
.
20
RT = -.
40
With work hardening:
T =.
4
T
R =
.
40
T =.
10
T
R =
.
46
2.3
Uncertainty on the solution
Analytical solution.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.3
Titrate:
SSNL108 - Liaison tube-grid with friction of Coulomb
Date:
23/10/02
Author (S):
J.M. PROIX, B. QUINNEZ
Key: V6.02.108-B Page: 5/6
3 Modeling
With
3.1
Characteristics of modeling
N4
N1
N2
N3
Characteristics of the elements
POUTRE:
POU_D_E for the meshs (N3 N2) and (N2 N4)
E = 105 Naked Pa = 0 3
.
DISCRET:
K_TR_D_L for the mesh (N1 N2)
K = K = K = 103 NR/m
X
y
Z
K = K = K = 103 NR/m
X-ray
ry
rz
Characteristics agent the bonding (mesh (N1 N2)) :
Coefficient of Coulomb: COULOMB = 0.4
Initial tension of compression: EFFO_N_INIT: 100. NR
Function of evolution of rigidity: RIGI_N_FO: F (T) 1
Boundary conditions
DDL_IMPO: (NOEUD: N1
DX
:0.
DY
:0.
DZ
:0.
DRX:0.
DRY:0.
DRZ:0.
)
DDL_IMPO: (NOEUD: (N2, N3, N4)
DX
:0.
DY
:0.01
DZ
:0.
DRX:0.
DRY:0.
DRZ:0.
)
3.2
Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 3 SEG2
3.3 Functionalities
tested
Commands
AFFE_MODELE
MODELISATION
MECANIQUE
POU_D_E
MODELISATION
MECANIQUE
DIS_TR
AFFE_CARA_ELEM
POUTRE
GROUP_MA
“RECTANGLE”
DISCRET
GROUP_MA
“K_TR_D_L'
DEFI_MATERIAU
DIS_CONTACT
ELAS
AFFE_CHAR_MECA
DDL_IMPO
NOEUD
DEFI_FONCTION
NOM_PARA
“INST”
STAT_NON_LINE
EXCIT
FONC_MULT
COMP_ELAS
GROUP_MA
“ELAS”
COMP_INCR
GROUP_MA
“DIS_CONTACT”
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.3
Titrate:
SSNL108 - Liaison tube-grid with friction of Coulomb
Date:
23/10/02
Author (S):
J.M. PROIX, B. QUINNEZ
Key: V6.02.108-B Page: 6/6
4
Results of modeling A
4.1 Values
tested
One tests component VY of field “SIEF_ELGA” at various moments:
With work hardening:
Identification Reference
Aster %
Tolérance difference
Sequence number
Moment
VY (NR)
1 4.
40.
39.9999
0.
0.01
2 10.
40.
40. 0.
0.01
3 18.
40.
39.9999
0.
0.01
4 20.
40.
39.9999
0.
0.01
Without work hardening:
Identification Reference
Aster %
Tolérance difference
Sequence number
Moment
VY (NR)
1 4.
40.
39.9999
0.
0.01
2 10.
46.
46. 0.
0.01
5
Summary of the results
The results are identical to the reference solution. This test validates the slip with friction of
Coulomb introduced via a discrete element. This development allows in particular
to model the connection between the grids and the fuel pins.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
Outline document