Code_Aster
®
Version
6.3
Titrate:
SSNL108 - Connection 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
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
Organization (S)
: EDF-R & D/AMA
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.108
SSNL108 - Connection tube-grid with 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. This test of nonlinear statics has only one
only modeling.
Code_Aster
®
Version
6.3
Titrate:
SSNL108 - Connection 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
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
N3
y
X
N4
Imposed displacement
N2
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 following the direction
X
:
R
NR
No
= -
10
2
Young modulus of the beam:
E
=
10
5
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
X
y
Z
= = =
=
=
=
0
0
Nodes N2, N3, N4 movement according to
y U W
X
y
Z
= =
=
=
=
0
0
Nodes N2, N3, N4 movement imposed according to
()
y v
G T
=
0 01
.
G (T)
10.
0.
T
with
10.
20.
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 is compressed and the beam is in initial position.
Code_Aster
®
Version
6.3
Titrate:
SSNL108 - Connection 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
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
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 following displacement
X
one a:
R
R
T
N
No
=
In addition one a:
()
U
U
G T
T
Y
=
=
0 01
.
1
era
phase:
R
K U
R
R
U
T
E
T
N
No
T
=
<
=
µ
µ
,
increase.
In this phase,
R
T
is strictly lower than
µ
R
N
and there is not thus friction.
Limit
T
1
of this phase is defined by
:
R
K U
R
T
E
T
No
=
=
µ
i.e. for
()
0 01
1
.
K G T
R
E
No
=
µ
.
One finds
T
1
4
=
.
Without work hardening:
2
ème
phase:
R
R
R
U
T
N
No
T
=
=
µ
µ
,
increase.
The tangential force reached the value of the threshold
µ
R
No
and there is thus slip. This phase is
delimited by the moments
T
T
1
2
4
10
=
=
.
.
and
(moment when
U
T
start to decrease).
3
ème
phase:
R
K U
R
R
U
T
E
T
N
No
T
=
<
=
µ
µ
,
decrease.
In this phase,
R
T
is lower than the value of the threshold
µ
R
N
and one is thus in a phase
rubber band
R
K U
R
T
E
T
No
= -
+
µ
.
The limits of this phase are
T
T
2
3
10
=
.
and
defined by:
()
-
+
= -
>
0 01
10
3
3
.
.
K G T
R
R
T
E
No
No
µ
One finds
T
3
18
=
.
4
ème
phase:
R
R
U
T
No
T
=
µ
,
decrease.
In this phase, one reached the threshold of slip again. One a:
R
R
T
No
=
µ
. This phase is
delimited by the moments
T
3
18
=
.
and
T
4
20
=
.
With work hardening:
2
ème
phase:
T
Tt
Te
Tt
N
T
U
K
K
K
R
R
.
1
+
-
=
µ
.
The tangential force reached the value of the threshold
µ
R
No
and there is thus slip. This phase is
delimited by the moments
T
T
1
2
4
10
=
=
.
.
and
There is an effect of work hardening.
Code_Aster
®
Version
6.3
Titrate:
SSNL108 - Connection 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
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
2.2
Results of reference
For the various remarkable moments, the value of
R
T
is equal to:
Without work hardening:
.
40
.
20
.
40
.
18
.
40
.
10
.
40
.
4
-
=
=
-
=
=
=
=
=
=
T
T
T
T
R
T
R
T
R
T
R
T
With work hardening:
.
46
.
10
.
40
.
4
=
=
=
=
T
T
R
T
R
T
2.3
Uncertainty on the solution
Analytical solution.
Code_Aster
®
Version
6.3
Titrate:
SSNL108 - Connection 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
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
N3
N4
N2
N1
Characteristics of the elements
BEAM:
POU_D
_
E
for the meshs (N3 N2) and (N2 N4)
E
Naked AP
=
=
10
0 3
5
.
DISCRETE:
K_TR_D_L
for the mesh (N1 N2)
K
K
K
NR m
K
K
K
NR m
X
y
Z
X-ray
ry
rz
=
=
=
=
=
=
10
10
3
3
/
/
Characteristics agent the bonding (mesh (N1 N2)) :
Coefficient of Coulomb:
COULOMB
= 0.4
Initial voltage of compression:
EFFO_N_INIT
: 100. NR
Function of evolution of rigidity:
RIGI_N_FO
:
()
F T
1
Boundary conditions
DDL_IMPO: (NODE: N1
DX
:0.
DY
:0.
DZ
:0.
DRX:0.
DRY:0.
DRZ:0.
)
DDL_IMPO: (NODE: (N2, N3, N4)
DX
:0.
DY
:0.01
DZ
:0.
DRX:0.
DRY:0.
DRZ:0.
)
3.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 3 SEG2
3.3 Functionalities
tested
Controls
AFFE_MODELE
MODELING
MECHANICS
POU_D_E
MODELING
MECHANICS
DIS_TR
AFFE_CARA_ELEM
BEAM
GROUP_MA
“RIGHT-ANGLED”
DISCRETE
GROUP_MA
“K_TR_D_L'
DEFI_MATERIAU
DIS_CONTACT
ELAS
AFFE_CHAR_MECA
DDL_IMPO
NODE
DEFI_FONCTION
NOM_PARA
“INST”
STAT_NON_LINE
EXCIT
FONC_MULT
COMP_ELAS
GROUP_MA
“ELAS”
COMP_INCR
GROUP_MA
“DIS_CONTACT”
Code_Aster
®
Version
6.3
Titrate:
SSNL108 - Connection 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
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
One tests component VY of the field `
SIEF_ELGA
'at various moments:
With work hardening:
Identification Reference
Aster %
difference Tolerance
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 %
difference Tolerance
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 modelize the connection between the grids and the fuel pins.