Code_Aster
®
Version
7.4
Titrate:
SDNV104 - Dynamic response of a rigid shoe rubbing
Date:
15/09/05
Author (S):
S. LAMARCHE
Key
:
V5.03.104-A
Page:
1/12
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HT-66/05/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
V5.03.104 document
SDNV104 - Dynamic response of a rubbing shoe
rigid subjected to a pressure and a force of recall
Summary
One considers a mass in contact rubbing with a rigid plan. It is retained by a spring and one imposes to him
a side pressure. Friction is modelized by the law of Coulomb. Calculation is a dynamic calculation
direct.
The reference solution is analytical.
Modelings suggested use DYNA_NON_LINE with an elastic law of behavior in 2D, for
two solveurs. The contact is managed by various methods available in AFFE_CHAR_MECA.
Code_Aster
®
Version
7.4
Titrate:
SDNV104 - Dynamic response of a rigid shoe rubbing
Date:
15/09/05
Author (S):
S. LAMARCHE
Key
:
V5.03.104-A
Page:
2/12
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
The system considered consists of a shoe: square of 1m on 1m, posed on a support. It is subjected
with its weight, with the force of recall of a spring of stiffness K and with a side pressure. The contact is one
rubbing contact.
K
m
PTAN
1.2
Properties of the model
Mass:
7 10
3
kg
Stiffness of the spring:
24.10
3
NR/m
Coefficient of Coulomb:
0,3
Gravity:
70.000 AP
Side pressure:
200.000 AP
Young modulus of the shoe:
2,1. 10
11
AP
Young modulus of the solid mass:
1,0. 10
11
AP
Poisson's ratio:
0
1.3
Boundary conditions, conditions initial and loadings
The mass rests on the rigid level with the dimension X = 0.
The loadings of weight and side pressure are applied with a slope which reaches sound
maximum in 0,07 second.
The support is embedded in X and Y.
X
y
Code_Aster
®
Version
7.4
Titrate:
SDNV104 - Dynamic response of a rigid shoe rubbing
Date:
15/09/05
Author (S):
S. LAMARCHE
Key
:
V5.03.104-A
Page:
3/12
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HT-66/05/005/A
2
Reference solution
The reference solution is analytical.
If one regards the shoe as sufficiently stiff not vibrating (rigid movement of body),
there is an analytical solution with the problem.
One can then write the equation of the movement as follows:
N
T
F
F
F
F
X
K
X
m
µ
=
±
=
+
&&
One notes:
m
K
=
Stage 1:
F
F
kx
X
m
-
=
+
&&
with a X-coordinate and a null speed. One has then:
))
.
cos (
1
(
)
(
T
K
F
F
T
X
-
-
=
this result is valid as long as
0
x&
, i.e. until
=
T.
.
The first extremum of the curve
()
T
X
is
K
F
F
X
-
=.
2
1
.
Stage 2:
F
F
kx
X
m
+
=
+
&&
the initial X-coordinate is worth
1
X
, and speed is null. One has then, by posing the new X-coordinate of times
with
/
:
)
.
cos (
3
)
(
T
K
F
F
K
F
F
T
X
-
+
+
=
, until
=
T.
.
The second extremum of the curve
()
T
X
is
K
F
X
4
2
=
.
Stage N:
One separates the movement according to the sign speed.
One obtains in a general way:
(
)
(
)
(
)
,
2
.
2
1
2
2
2
1
2
2
1
2
K
PF
Pt
T
X
K
F
p
F
T
p
T
X
p
T
p
=
=
-
-
=
-
=
-
with
2
=
T
and
m
K
=
.
The stop of the movement occurs when
N
X
is included/understood enters
K
F
F
T
-
and
K
F
F
T
+
.
Code_Aster
®
Version
7.4
Titrate:
SDNV104 - Dynamic response of a rigid shoe rubbing
Date:
15/09/05
Author (S):
S. LAMARCHE
Key
:
V5.03.104-A
Page:
4/12
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HT-66/05/005/A
2.1
Results of reference
Modeling proposed Ci below correspond to the analytical solution until the stop of the shoe.
By preoccupations with a saving in calculating time, one tests only the two first extremum.
Time (S)
Displacement in X (m)
1,697 14,917
3,393 3,500
2.2
Uncertainty on the solution
The analytical solution gives an exact result for the assumption where the bodies are infinitely rigid.
3 Modeling
With
3.1
Characteristics of modeling
The problem is D_PLAN. The shoe and the support are modelized by surfaces with a grid in QUAD4.
An element 2d_DIS_T represents the spring, its component nonnull is in direction X.
One uses operator DYNA_NON_LINE to carry out dynamic calculation. The efforts of contact are
taken into account by AFFE_CHAR_MECA/CONTACT, with the method LAGRANGIAN.
3.2
Characteristics of the mesh
A number of nodes:
42
a number of meshs and types:
26 QUAD4
26 SEG2
3.3 Functionalities
tested
Controls
AFFE_CHAR_MECA CONTACT
FRICTION
“COULOMB”
AFFE_CHAR_MECA CONTACT
METHOD “LAGRANGIAN”
AFFE_CHAR_MECA CONTACT
PAIRING
“MAIT_ESCL”
AFFE_CHAR_MECA CONTACT
SEEK
“NOEUD_BOUCLE”
AFFE_CHAR_MECA CONTACT
REAC_GEOM
“Control”
DYNA_NON_LINE SOLVEUR “MULT_FRONT”
DYNA_NON_LINE NEWTON
STAMP
“TANGENT”
Code_Aster
®
Version
7.4
Titrate:
SDNV104 - Dynamic response of a rigid shoe rubbing
Date:
15/09/05
Author (S):
S. LAMARCHE
Key
:
V5.03.104-A
Page:
5/12
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HT-66/05/005/A
Controls
AFFE_CHAR_MECA CONTACT
FRICTION
“COULOMB”
AFFE_CHAR_MECA CONTACT
METHOD “LAGRANGIAN”
AFFE_CHAR_MECA CONTACT
PAIRING
“MAIT_ESCL”
AFFE_CHAR_MECA CONTACT
SEEK
“NOEUD_BOUCLE”
AFFE_CHAR_MECA CONTACT
REAC_GEOM
“Control”
DYNA_NON_LINE SOLVEUR “LDLT”
DYNA_NON_LINE NEWTON
STAMP
“TANGENT”
4
Results of modeling A
4.1
Values tested for the method LAGRANGIAN, MULT_FRONT
T Reference
Aster %
difference
1,697 14,91 14,84
- 0,5%
3,393 3,50 3,62
3,6%
4.2
Values tested for the method LAGRANGIAN, LDLT
T Reference
Aster %
difference
1,697 14,91 14,83
- 0.5%
3,393 3,50 3,62
3,6%
tps_job 200 mem_job 64MB ncpus1
Code_Aster
®
Version
7.4
Titrate:
SDNV104 - Dynamic response of a rigid shoe rubbing
Date:
15/09/05
Author (S):
S. LAMARCHE
Key
:
V5.03.104-A
Page:
6/12
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HT-66/05/005/A
5 Modeling
B
5.1
Characteristics of modeling
The problem is D_PLAN. The shoe and the support are modelized by surfaces with a grid in QUAD4.
An element 2d_DIS_T represents the spring, its component nonnull is in direction X.
One uses operator DYNA_NON_LINE to carry out dynamic calculation. The efforts of contact are
taken into account by AFFE_CHAR_MECA/CONTACT, with the method PENALIZATION.
5.2
Characteristics of the mesh
A number of nodes:
42
a number of meshs and types:
26 QUAD4
26 SEG2
5.3 Functionalities
tested
Controls
AFFE_CHAR_MECA CONTACT FRICTION
“COULOMB”
AFFE_CHAR_MECA CONTACT METHOD
“PENALIZATION”
AFFE_CHAR_MECA CONTACT PAIRING
“MAIT_ESCL”
AFFE_CHAR_MECA CONTACT SEEKS “NOEUD_BOUCLE”
AFFE_CHAR_MECA CONTACT REAC_GEOM “CONTROLS”
DYNA_NON_LINE SOLVEUR “MULT_FRONT”
DYNA_NON_LINE NEWTON STAMPS “TANGENT”
Controls
AFFE_CHAR_MECA CONTACT FRICTION
“COULOMB”
AFFE_CHAR_MECA CONTACT METHOD
“PENALIZATION”
AFFE_CHAR_MECA CONTACT PAIRING
“MAIT_ESCL”
AFFE_CHAR_MECA CONTACT SEEKS “NOEUD_BOUCLE”
AFFE_CHAR_MECA CONTACT REAC_GEOM “CONTROLS”
DYNA_NON_LINE SOLVEUR “LDLT”
DYNA_NON_LINE NEWTON STAMPS “TANGENT”
Code_Aster
®
Version
7.4
Titrate:
SDNV104 - Dynamic response of a rigid shoe rubbing
Date:
15/09/05
Author (S):
S. LAMARCHE
Key
:
V5.03.104-A
Page:
7/12
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HT-66/05/005/A
6
Results of modeling B
6.1
Values tested for the method PENALIZATION, MULT_FRONT
T Reference
Aster %
difference
1,697 14,91 14,84 - 0.5%
3,393 3,50 3,62 3,6%
6.2
Values tested for the method PENALIZATION, LDLT
T Reference
Aster %
difference
1,697 14,91 14,83 - 0,5%
3,393 3,50 3,62 3,6%
tps_job 1000 mem_job 100MB ncpus1
7 Modeling
C
7.1
Characteristics of modeling
The problem is D_PLAN. The shoe and the support are modelized by surfaces with a grid in QUAD4.
An element 2d_DIS_T represents the spring, its component nonnull is in direction X.
One uses operator DYNA_NON_LINE to carry out dynamic calculation. The efforts of contact are
taken into account by AFFE_CHAR_MECA/CONTACT, with the method CONTINUES.
7.2
Characteristics of the mesh
A number of nodes:
42
a number of meshs and types:
26 QUAD4
26 SEG2
7.3 Functionalities
tested
Controls
AFFE_CHAR_MECA CONTACT FRICTION
“COULOMB”
AFFE_CHAR_MECA CONTACT METHOD
“CONTINUES”
AFFE_CHAR_MECA CONTACT PAIRING
“MAIT_ESCL”
AFFE_CHAR_MECA CONTACT SEEKS “NOEUD_BOUCLE”
AFFE_CHAR_MECA CONTACT REAC_GEOM “CONTROLS”
DYNA_NON_LINE SOLVEUR
“MULT_FRONT”
DYNA_NON_LINE NEWTON STAMPS “TANGENT”
Code_Aster
®
Version
7.4
Titrate:
SDNV104 - Dynamic response of a rigid shoe rubbing
Date:
15/09/05
Author (S):
S. LAMARCHE
Key
:
V5.03.104-A
Page:
8/12
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HT-66/05/005/A
Controls
AFFE_CHAR_MECA CONTACT FRICTION
“COULOMB”
AFFE_CHAR_MECA CONTACT METHOD
“CONTINUES”
AFFE_CHAR_MECA CONTACT PAIRING
“MAIT_ESCL”
AFFE_CHAR_MECA CONTACT SEEKS “NOEUD_BOUCLE”
AFFE_CHAR_MECA CONTACT REAC_GEOM “CONTROLS”
DYNA_NON_LINE SOLVEUR
“LDLT”
DYNA_NON_LINE NEWTON STAMPS “TANGENT”
8
Results of modeling C
8.1
Values tested for the method CONTINUES, MULT_FRONT
T Reference
Aster %
difference
1,697 14,91 14,84 - 0,5%
3,393 3,50 3,62 3,6%
8.2
Values tests for the method CONTINUES, LDLT
T Reference
Aster %
difference
1,697 14,91 14,83 - 0,5%
3,393 3,50 3,62 3,6%
tps_job 400 mem_job 64MB ncpus1
Code_Aster
®
Version
7.4
Titrate:
SDNV104 - Dynamic response of a rigid shoe rubbing
Date:
15/09/05
Author (S):
S. LAMARCHE
Key
:
V5.03.104-A
Page:
9/12
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HT-66/05/005/A
9 Modeling
D
9.1
Characteristics of modeling
The problem is D_PLAN. The shoe and the support are modelized by surfaces with a grid in QUAD8.
An element 2d_DIS_T represents the spring, its component nonnull is in direction X.
One uses operator DYNA_NON_LINE to carry out dynamic calculation. The efforts of contact are
taken into account by AFFE_CHAR_MECA/CONTACT, with the method LAGRANGIAN.
9.2
Characteristics of the mesh
A number of nodes:
110
a number of meshs and types:
26 QUAD 8
24 SEG3
2 SEG 2
9.3 Functionalities
tested
Controls
AFFE_CHAR_MECA CONTACT FRICTION
“COULOMB”
AFFE_CHAR_MECA CONTACT METHOD
“LAGRANGIAN”
AFFE_CHAR_MECA CONTACT PAIRING
“MAIT_ESCL”
AFFE_CHAR_MECA CONTACT SEEKS “NOEUD_BOUCLE”
AFFE_CHAR_MECA CONTACT REAC_GEOM “CONTROLS”
DYNA_NON_LINE SOLVEUR “MULT_FRONT”
DYNA_NON_LINE NEWTON STAMPS “TANGENT”
Controls
AFFE_CHAR_MECA CONTACT FRICTION
“COULOMB”
AFFE_CHAR_MECA CONTACT METHOD
“LAGRANGIAN”
AFFE_CHAR_MECA CONTACT PAIRING
“MAIT_ESCL”
AFFE_CHAR_MECA CONTACT SEEKS “NOEUD_BOUCLE”
AFFE_CHAR_MECA CONTACT REAC_GEOM “CONTROLS”
DYNA_NON_LINE SOLVEUR “LDLT”
DYNA_NON_LINE NEWTON STAMPS “TANGENT”
Code_Aster
®
Version
7.4
Titrate:
SDNV104 - Dynamic response of a rigid shoe rubbing
Date:
15/09/05
Author (S):
S. LAMARCHE
Key
:
V5.03.104-A
Page:
10/12
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HT-66/05/005/A
10 Results of modeling D
10.1 Values tested for the method LAGRANGIAN, MULT_FRONT
T Reference
Aster %
difference
1,697 14,91
14,83 - 0., 5%
3,393 3,50 3,62 3,6%
10.2 Values tested for the method LAGRANGIAN, LDLT
T Reference
Aster %
difference
1,697 14,91
14,83 - 0., 5%
3,393 3,50
3,62 3,6%
tps_job 400 mem_job 64MB ncpus1
11 Modeling
E
11.1 Characteristics of modeling
The problem is D_PLAN. The shoe and the support are modelized by surfaces with a grid in QUAD8.
An element 2d_DIS_T represents the spring, its component nonnull is in direction X.
One uses operator DYNA_NON_LINE to carry out dynamic calculation. The efforts of contact are
taken into account by AFFE_CHAR_MECA/CONTACT, with the method PENALIZATION.
11.2 Characteristics of the mesh
A number of nodes:
110
a number of meshs and types:
26 QUAD 8
24 SEG3
2 SEG 2
Code_Aster
®
Version
7.4
Titrate:
SDNV104 - Dynamic response of a rigid shoe rubbing
Date:
15/09/05
Author (S):
S. LAMARCHE
Key
:
V5.03.104-A
Page:
11/12
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HT-66/05/005/A
11.3 Functionalities
tested
Controls
AFFE_CHAR_MECA CONTACT FRICTION
“COULOMB”
AFFE_CHAR_MECA CONTACT METHOD
“PENALIZATION”
AFFE_CHAR_MECA CONTACT PAIRING
“MAIT_ESCL”
AFFE_CHAR_MECA CONTACT SEEKS “NOEUD_BOUCLE”
AFFE_CHAR_MECA CONTACT REAC_GEOM “CONTROLS”
DYNA_NON_LINE SOLVEUR
“MULT_FRONT”
DYNA_NON_LINE NEWTON STAMPS “TANGENT”
Controls
AFFE_CHAR_MECA CONTACT FRICTION
“COULOMB”
AFFE_CHAR_MECA CONTACT METHOD
“PENALIZATION”
AFFE_CHAR_MECA CONTACT PAIRING
“MAIT_ESCL”
AFFE_CHAR_MECA CONTACT SEEKS “NOEUD_BOUCLE”
AFFE_CHAR_MECA CONTACT REAC_GEOM “CONTROLS”
DYNA_NON_LINE SOLVEUR
“LDLT”
DYNA_NON_LINE NEWTON STAMPS “TANGENT”
12 Results of modeling E
12.1 Values tested for the method PENALIZATION, MULT_FRONT
T Reference
Aster %
difference
1,697 14,91 14,83 - 0., 5%
3,393 3,50 3,62 3,6%
12.2 Values tested for the method PENALIZATION, LDLT
T Reference
Aster %
difference
1,697 14,91 14,83 - 0., 5%
3,393 3,50 3,62 3,6%
tps_job 1000 mem_job 100MB ncpus1
Code_Aster
®
Version
7.4
Titrate:
SDNV104 - Dynamic response of a rigid shoe rubbing
Date:
15/09/05
Author (S):
S. LAMARCHE
Key
:
V5.03.104-A
Page:
12/12
Manual of Validation
V5.03 booklet: Nonlinear dynamics of the voluminal structures
HT-66/05/005/A
13 Summary of the results
The results obtained on the whole of this case test are satisfactory, as well into linear in
quadratic. The values obtained are with less than 1% from/to each other; and less than 4% of
reference solution.
It is noted that the value of reference of the second point is lower than the two others, which
increase the percentage of error artificially.
The choice of the coefficients of the penalized method is delicate. But it is noted that once them
coefficients chosen, the result is stable with respect to the choice of the finite elements and the solvor.