Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
1/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.503
SSNV503 - Shoe slipping on a rigid level
Summary:
This test represents a calculation of contact of a shoe slipping on a rigid level. The objective of this test is of
to allow to validate in an unquestionable way calculation of the criterion of Coulomb and the good transmission of
pressure.
Various modelings of the area of contact tested are as follows:
·
Modeling A (2D): contact node-mesh, Lagrangian method for the contact and friction, play
geometrical.
·
Modeling B (2D): contact node-mesh with Lagrangian method and play defined by a function.
·
Modeling C (2D): contact node-mesh, method Lagrangian for the contact and penalized for
friction, geometrical play.
·
Modeling D (2D): contact node-mesh, method penalized for the contact and friction, play
geometrical.
·
Modeling E (3D): contact node-mesh, method Lagrangian for the contact and penalized for
friction, geometrical play.
·
Modeling F (3D): contact node-mesh, method Lagrangian for the contact and penalized for
friction, play defined by a function.
·
Modeling G (3D): contact node-mesh, method penalized for the contact and friction, play
geometrical.
·
Modeling H (2D): contact node-mesh, method continues for the contact and friction, play
geometrical.
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
2/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Shoe
P
N
P
T
20.
40.
Shoe: thickness = 20.mm
width = 20.mm
Rigid plan: thickness = 5.mm
width = 60.mm
Play: 2.mm
Y
X
2.
Dimensions in mm
5.
10.
10.
Rigid plan
The shoe is located in the middle of
rigid plan
1.2
Properties of material
Shoe:
E
=
2.1 10
6
NR/mm ²
Young modulus
=
0
Poisson's ratio
Rigid plan by conditions kinematics.
Area of contact:
µ
=
0.3
Coefficient of friction
1.3
Boundary conditions and loadings
Boundary conditions:
·
All the nodes of the rigid plan are embedded.
3 cases of loading:
·
Normal pressure P
N
= 300N/mm ²
·
Normal pressure P
N
= 300N/mm ² and tangential pressure P
T
= 178.2 NR/mm ²
·
Normal pressure P
N
= 300N/mm ² and tangential pressure P
T
= 181.8 NR/mm ²
1.4 Conditions
initial
None.
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
3/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Shoe
P
N
P
T
Y
X
K
WITH B
D
C
F
N
F
T
F
T
=
µ
F
T
Design assumption: The deformation of the shoe is neglected.
·
Loading 1 (normal Pressure P
N:
300N/mm ²): one checks:
- good transmission of the normal efforts on the level of the area of contact: pressure
normal on the level of the area of contact is equal to the pressure applied
(
)
contact
N
N
P
P
=
-
that the vertical displacement of the shoe on the level of the area of contact AB is equal to the play.
·
Loading 2 (P
N:
300N/mm ² and P
T
= 178.2N/mm ²): it is checked that the nodes of the shoe located
in the area of slip (AB) do not move tangentially:
99
.
0
AD
CD
N
T
S
S
P
P
µ
=
·
Loading 3 (P
N:
300N/mm ² and P
T
= 181.8N/mm ²): it is checked that the nodes of the shoe located
in the area of slip (AB) 9mm move according to X.
01
.
1
AD
CD
N
T
S
S
P
P
µ
=
Determination of the stiffness K of the spring: one wants to determine the stiffness of the spring according to
desired displacement. At the time of the slip, the force in the spring is of:
F
R
= F
T
µ
F
N
= 0,01
µ
F
N
with (F
T
= 181.8x20, F
N
= 300x40)
F
R
= K U
T
: force in the spring
F
T
= P
T
xS
AD
:
force
tangential
F
N
= P
N
xS
CD
: force
normal
U
T
:
displacement
tangential
S
AD
:
surface
S
Cd.
:
surface
For a displacement of 9. mm rigidity K within the competence must-to be of 0.01
µ
F
N
/9 = 4N/mm
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
4/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
2.2
Results of reference
·
Loading 1 (normal Pressure P
N
):
²
/
300
mm
NR
P
contact
N
=
·
Loading 2 (P
N:
300N/mm ² and P
T
= 178.2N/mm ²): it is checked that there is at least a node of
the surface of contact which does not slip. One test that at least one of the nodes located on the face
opposed to the application of the side loading does not slip.
·
Loading 3 (P
N:
300N/mm ² and P
T
= 181.8/mm ²): it is checked that all the nodes of the surface of
contact slip. One tests that all the nodes located on the face opposed to the application of
side loading slip.
2.3
Uncertainties on the solution
< 0,1%
2.4 References
bibliographical
Without Object
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
5/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
A modeling “
D_PLAN
” with elements QUAD4 testing the functionalities of contact node
net with friction treated with the Lagrangian method was implemented.
The play between the shoe and the jig is defined by the geometrical co-ordinates of the mesh.
To avoid the movements of rigid body, the shoe is maintained by springs of low rigidity:
RES_LAT
: K
= 2 NR/mm
RES_HAUT
: K
= 0,005 NR/mm
Boundary conditions:
Loose lead of the springs:
DX
=
DY
=0.
Jig:
DX
=
DY
=0.
3.2
Characteristics of the mesh
A number of nodes: 53
Numbers and types of meshs: 33 QUAD4, 32 SEG2
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
6/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
3.3 Functionalities
tested
Controls Key word
factor
Key word
MODI_MAILLAGE
ORIE_PEAU_2D
AFFE_MODELE
AFFE
MODELING: “D_PLAN”
DEFI_MATERIAU
ELAS
AFFE_CHAR_MECA
CONTACT
PAIRING: “MAIT_ESCL”
SEEK: “NOEUD_BOUCLE”
METHOD: “LAGRANGIAN”
FRICTION: “COULOMB”
COULOMB: 0.3
STAT_NON_LINE
COMP_ELAS
RELATION: “ELAS”
4
Results of modeling A
4.1 Values
tested
Identification Reference Aster
% difference
Loading 1
Force normal contact
1.200000 E+04 NR
1.199998 E+04 NR
1.69E04
Tangential force of contact
0. NR
1.999547 E05 NR
2.00E05
DX (not A)
1.000 mm
1.000000 E+00 mm
1.01E07
DY (not A)
1.732 mm
1.732051 E+00 mm
0.003
DX (not B)
1.000 mm
1.000000 E+00 mm
1.42E08
DY (not B)
1.732 mm
1.732055 E+00 mm
0.003
Loading 2
Force normal contact
1.200000 E+04 NR
1.199998 E+04 NR
1.68E04
Tangential force of contact
3.564000 E+04 NR
3.563962 E+03 NR
- 0.001
DX (not A)
1.000 mm
1.021344 E+00 mm
2.134
DY (not A)
1.732 mm
1.719728 E+00 mm
0.709
DX (not B)
1.000 mm
1.000000 E+00 mm
4.48E11
DY (not B)
1.732 mm
1.732051 E+00 mm
0.003
Loading 3
Force normal contact
1.200000 E+04 NR
1.199998 E+04 NR
1.70E04
Tangential force of contact
3.624000 E+04 NR
3.599992 E+03 NR
- 0.662
DX (not A)
8.787 mm
8.809533 E+00 mm
0.177
DY (not A)
2.768 mm
2.776785 E+00 mm
0.317
DX (not B)
8.787 mm
8.786943 E+00 mm
0.080
DY (not B)
2.768 mm
2.763743 E+00 mm
0.154
4.2 Remarks
·
The play is defined in this case in a geometrical way. One with the possibility of defining it via the words
keys “
DIST_1
” and “
DIST_2
”. This is done in the following model.
·
The pressures normal and tangential on the level of the area of contact are checked while testing
total force of contact in the normal and tangential direction:
(
)
(
)
3
Loading
2
Loading
NR
S
p
F
NR
S
p
F
NR
S
p
F
AD
T
CTAC
T
AD
T
CTAC
T
Cd.
N
CTAC
N
36240
1
*
20
*
8
.
181
35640
1
*
20
*
2
.
178
12000
1
*
40
*
300
=
=
=
=
=
=
=
=
=
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
7/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
A modeling “
D_PLAN
” with elements QUAD4 testing the functionalities of contact node
net with friction treated with the Lagrangian method was implemented.
The play between the shoe and the jig is defined by a function using the key word “
DIST_2
”.
To avoid the movements of rigid body, the shoe is maintained by springs of low rigidity:
RES_LAT
: K
= 2 NR/mm
RES_HAUT
: K
= 0,005 NR/mm
Boundary conditions:
Loose lead of the springs:
DX
=
DY
=0.
Jig:
DX
=
DY
=0.
5.2
Characteristics of the mesh
A number of nodes: 53
Numbers and types of meshs: 33 QUAD4, 32 SEG2
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
8/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
5.3 Functionalities
tested
Controls Key word
factor
Key word
MODI_MAILLAGE
ORIE_PEAU_2D
AFFE_MODELE
AFFE
MODELING: “D_PLAN”
DEFI_MATERIAU
ELAS
AFFE_CHAR_MECA
CONTACT
PAIRING: “MAIT_ESCL”
SEEK: “NOEUD_BOUCLE”
METHOD: “LAGRANGIAN”
FRICTION: “COULOMB”
COULOMB: 0.3
DIST_2: - 2.
STAT_NON_LINE
COMP_ELAS
RELATION: “ELAS”
6
Results of modeling B
6.1 Values
tested
Identification Reference Aster
% difference
Loading 1
Force normal contact
1.200000 E+04 NR
1.199998 E+04 NR
1.71E04
Tangential force of
contact
0. NR
7.724662 E05 NR
7.72E05
DX (not A)
1.000 mm
9.999999 E01 mm
3.83E09
DY (not A)
1.732 mm
1.732055 E+00 mm
0.003
DX (not B)
1.000 mm
1.000000 E+00 mm
3.32E08
DY (not B)
1.732 mm
1.732055 E+00 mm
0.003
Loading 2
Force normal contact
1.200000 E+04 NR
1.199998 E+04 NR
1.70E04
Tangential force of
contact
3.564000 E+04 NR
3.563962 E+03 NR
0.001
DX (not A)
1.000 mm
1.021344 E+00 mm
2.134
DY (not A)
1.732 mm
1.719727 E+00 mm
0.709
DX (not B)
1.000 mm
1.000000 E+00 mm
1.81E08
DY (not B)
1.732 mm
1.732051 E+00 mm
0.003
Loading 3
Force normal contact
1.200000 E+04 NR
1.199998 E+04 NR
1.70E04
Tangential force of
contact
3.624000 E+04 NR
3.599992 E+03 NR
0.662
DX (not A)
8.787 mm
8.809533 E+00 mm
0.177
DY (not A)
2.768 mm
2.776785 E+00 mm
0.317
DX (not B)
8.787 mm
8.786943 E+00 mm
0.080
DY (not B)
2.768 mm
2.763743 E+00 mm
0.154
6.2 Notice
The play is defined in this case by a function. There is no difference with the preceding model where
the play is defined in a geometrical way.
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
9/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
7 Modeling
C
7.1
Characteristics of modeling
A modeling “
D_PLAN
” with elements QUAD4 testing the functionalities of contact node
net with friction treated with the method Lagrangian for the contact and penalized for
friction was implemented.
The play between the shoe and the jig is defined by the geometrical co-ordinates of the mesh.
To avoid the movements of rigid body, the shoe is maintained by springs of low rigidity:
RES_LAT
: K
= 2 NR/mm
RES_HAUT
: K
= 0,005 NR/mm
Boundary conditions:
Loose lead of the springs:
DX
=
DY
=0.
Jig:
DX
=
DY
=0.
7.2
Characteristics of the mesh
A number of nodes: 53
Numbers and types of meshs: 33 QUAD4, 32 SEG2
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
10/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
7.3 Functionalities
tested
Controls Key word
factor
Key word
MODI_MAILLAGE
ORIE_PEAU_2D
AFFE_MODELE
AFFE
MODELING: “D_PLAN”
DEFI_MATERIAU
ELAS
AFFE_CHAR_MECA
CONTACT
PAIRING: “MAIT_ESCL”
SEEK: “NOEUD_BOUCLE”
METHOD: “PENALIZATION”
E_T: 1.E+05
FRICTION: “COULOMB”
COULOMB: 0.3
COEF_MATR_FROT: 0.9
STAT_NON_LINE
COMP_ELAS
RELATION: “ELAS”
8
Results of modeling C
8.1 Values
tested
Identification Reference Aster
% difference
Loading 1
Force normal contact
1.200000 E+04 NR
1.199998 E+04 NR
1.69E04
Tangential force of
contact
0. NR
7.731180 E06 NR
7.73E06
DX (not A)
1.000 mm
9.999999 E01 mm
6.84E08
DY (not A)
1.732 mm
1.732055 E+00 mm
0.003
DX (not B)
1.000 mm
1.000000 E+00 mm
1.07E04
DY (not B)
1.732 mm
1.732055 E+00 mm
0.003
Loading 2
Force normal contact
1.200000 E+04 NR
1.199998 E+04 NR
1.69E04
Tangential force of
contact
3.564000 E+04 NR
3.563959 E+03 NR
0.001
DX (not A)
1.000 mm
1.026850 E+00 mm
2.185
DY (not A)
1.732 mm
1.719435 E+00 mm
0.725
DX (not B)
1.000 mm
1.000506 E+00 mm
0.051
DY (not B)
1.732 mm
1.731759 E+00 mm
0.014
Loading 3
Force normal contact
1.200000 E+04 NR
1.199998 E+04 NR
1.69E04
Tangential force of
contact
3.624000 E+04 NR
3.599992 E+03 NR
0.662
DX (not A)
8.787 mm
8.809533 E+00 mm
0.177
DY (not A)
2.768 mm
2.776785 E+00 mm
0.317
DX (not B)
8.787 mm
8.786944 E+00 mm
0.080
DY (not B)
2.768 mm
2.763743 E+00 mm
0.154
8.2 Notice
The play is defined in this case in a geometrical way. One with the possibility of defining it via the key words
“
DIST_1
” and “
DIST_2
”. After checking, this second case does not change anything with the result.
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
11/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
9 Modeling
D
9.1
Characteristics of modeling
A modeling “
D_PLAN
” with elements QUAD4 testing the functionalities of contact node
net with friction treated with the method penalized for the contact and friction was put in
work.
The play between the shoe and the jig is defined by the geometrical co-ordinates of the mesh.
To avoid the movements of rigid body, the shoe is maintained by springs of low rigidity:
RES_LAT
: K
= 2 NR/mm
RES_HAUT
: K
= 0,005 NR/mm
Boundary conditions:
Loose lead of the springs:
DX
=
DY
=0.
Jig:
DX
=
DY
=0.
9.2
Characteristics of the mesh
A number of nodes: 53
Numbers and types of meshs: 33 QUAD4, 32 SEG2
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
12/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
9.3 Functionalities
tested
Controls Key word
factor
Key word
MODI_MAILLAGE
ORIE_PEAU_2D
AFFE_MODELE
AFFE
MODELING: “D_PLAN”
DEFI_MATERIAU
ELAS
AFFE_CHAR_MECA
CONTACT
PAIRING: “MAIT_ESCL”
SEEK: “NOEUD_BOUCLE”
METHOD: “PENALIZATION”
E_T: 1.E+05
E_N: 1.E+05
FRICTION: “COULOMB”
COULOMB: 0.3
COEF_MATR_FROT: 0.9
STAT_NON_LINE
COMP_ELAS
RELATION: “ELAS”
10 Results of modeling D
10.1 Values
tested
Identification Reference Aster
% difference
Loading 1
Force normal contact
1.200000 E+04 NR
1.199998 E+04 NR
1.70E-04
Tangential force of
contact
0. NR
7.484511 E-06 NR
7.48E-06
DX (not A)
1.000 mm
1.004111 E+00 mm
0.411
DY (not A)
1.732 mm
1.741004 E+00 mm
0.520
DX (not B)
1.000 mm
1.005698 E+00 mm
0.570
DY (not B)
1.732 mm
1.740088 E+00 mm
0.467
Loading 2
Force normal contact
1.200000 E+04 NR
1.199979 E+04 NR
1.70E-04
Tangential force of
contact
3.564000 E+04 NR
3.563930 E+03 NR
0.002
DX (not A)
1.000 mm
1.025709 E+00 mm
2.571
DY (not A)
1.732 mm
1.723129 E+00 mm
0.512
DX (not B)
1.000 mm
1.013353 E+00 mm
1.335
DY (not B)
1.732 mm
1.742276 E+00 mm
0.593
Loading 3
Force normal contact
1.200000 E+04 NR
1.199998 E+04 NR
1.70E-04
Tangential force of
contact
3.624000 E+04 NR
3.599992 E+03 NR
0.662
DX (not A)
8.787 mm
8.807222 E+00 mm
0.150
DY (not A)
2.768 mm
2.769538 E+00 mm
0.056
DX (not B)
8.787 mm
8.793625 E+00 mm
0.004
DY (not B)
2.768 mm
2.749434 E+00 mm
0.671
10.2 Notice
The play is defined in this case in a geometrical way. One with the possibility of defining it via the key words
“
DIST_1
” and “
DIST_2
”. After checking, this second case does not change anything with the result.
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
13/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
11 Modeling
E
11.1 Characteristics of modeling
A modeling 3D with elements CUB8 testing the functionalities of contact node-mesh
with friction treated with the method Lagrangian for the contact and penalized for friction has
summer implemented.
The play between the shoe and the jig is defined by the geometrical co-ordinates of the mesh.
To avoid the movements of rigid body, the shoe is maintained by springs of low rigidity:
RES_LAT
: K
= 1 NR/mm
RES_FOND
: K = 1 NR/mm
RES_HAUT
: K
= 20 NR/mm
Boundary conditions:
Loose lead of the springs:
DX
=
DY
=
DZ
=0.
Jig:
DX
=
DY
=
DZ
=0.
11.2 Characteristics of the mesh
A number of nodes: 269
Numbers and type of meshs: 129 CUB8, 103 QUAD4
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
14/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
11.3 Functionalities
tested
Controls Key word
factor
Key word
MODI_MAILLAGE
ORIE_PEAU_3D
AFFE_MODELE
AFFE
MODELING: “3D”
DEFI_MATERIAU
ELAS
AFFE_CHAR_MECA
CONTACT
PAIRING: “MAIT_ESCL”
SEEK: “NOEUD_BOUCLE”
METHOD: “PENALIZATION”
E_T: 1.E+06
FRICTION: “COULOMB”
COULOMB: 0.3
COEF_MATR_FROT: 0.9
STAT_NON_LINE
COMP_ELAS
RELATION: “ELAS”
12 Results of modeling E
12.1 Values
tested
Identification Reference Aster %
difference
Loading 1
Force normal contact
2.0784 E+05 NR
2.078391 E+05 NR
4.05E04
Tangential force of
contact
1.2000 E+05 NR
1.199959 E+05 NR
0.003E06
DX (not A)
1.000 mm
9.999999 E01 mm
3.33E06
DY (not A)
1.732 mm
1.731051 E+00 mm
0.003
DX (not B)
1.000 mm
1.000001 E+00 mm
3.32E06
DY (not B)
1.732 mm
1. 731051 E+00 mm
0.003
DX (point C)
1.000 mm
1.000001 E+00 mm
3.32E06
DY (point C)
1.732 mm
1. 731051 E+00 mm
0.003
DX (not D)
1.000 mm
9.999999 E01 mm
3.33E06
DY (not D)
1.732 mm
1.731051 E+00 mm
0.003
Loading 2
Force normal contact
1.7220 E+05 NR
1.721992 E+05 NR
4.12E04
Tangential force of
contact
1.8173 E+05 NR
1.817260 E+05 NR
0.002
DX (not A)
1.000 mm
1.004172 E+00 mm
0.417
DY (not A)
1.732 mm
1.729642 E+00 mm
0.136
DX (not B)
1.000 mm
1.002000 E+00 mm
0.200
DY (not B)
1.732 mm
1.730896 E+00 mm
0.064
DX (point C)
1.000 mm
1.002000 E+00 mm
0.200
DY (point C)
1.732 mm
1.730896 E+00 mm
0.064
DX (not D)
1.000 mm
1.004172 E+00 mm
0.417
DY (not D)
1.732 mm
1.729642 E+00 mm
0.136
Loading 3
Force normal contact
1.714896 E+05 NR
1.718404 E+04 NR
0.207
Tangential force of
contact
1.829770 E+05 NR
1.823477 E+05 NR
0.344
DX (not A)
8.79 mm
8.821717 E+00 mm
0.315
DY (not A)
2.77 mm
2.783820 E+00 mm
0.572
DX (not B)
8.79 mm
8.819386 E+00 mm
0.289
DY (not B)
2.77 mm
2.782474 E+00 mm
0.523
DX (point C)
8.79 mm
8.819386 E+00 mm
0.289
DY (point C)
2.77 mm
2.782474 E+00 mm
0.523
DX (not D)
8.79 mm
8.821717 E+00 mm
0.315
DY (not D)
2.77 mm
2.783820 E+00 mm
0.572
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
15/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
12.2 Remarks
·
The play is defined in this case in a geometrical way, the results are identical to those found
in preceding modeling.
·
The pressures normal and tangential on the level of the area of contact are checked while testing
total force of contact in the normal and tangential direction:
000N
4
2
x40x20
300
=
=
=
Cd.
N
CTAC
N
S
p
F
NR
x20x20
71280
2
.
178
=
=
=
AD
T
CTAC
T
S
p
F
(Loading 2)
NR
72720
x20x20
8
.
181
=
=
=
AD
T
CTAC
T
S
p
F
(Loading 3)
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
16/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
13 Modeling
F
13.1 Characteristics of modeling
A modeling 3D with elements CUB8 testing the functionalities of contact node-mesh
with friction treated with the method Lagrangian for the contact and penalized for friction has
summer implemented.
The play between the shoe and the jig is defined by the function using the key word “
DIST_2
”.
To avoid the movements of rigid body, the shoe is maintained by springs of low rigidity:
RES_LAT
: K
= 1 NR/mm
RES_FOND
: K = 1 NR/mm
RES_HAUT
: K
= 20 NR/mm
Boundary conditions:
Loose lead of the springs:
DX
=
DY
=
DZ
=0.
Jig:
DX
=
DY
=
DZ
=0.
13.2 Characteristics of the mesh
A number of nodes: 269
Numbers and types of meshs: 129 CUB8, 103 QUAD4
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
17/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
13.3 Functionalities
tested
Controls Key word
factor
Key word
MODI_MAILLAGE
ORIE_PEAU_3D
AFFE_MODELE
AFFE
MODELING: “3D”
DEFI_MATERIAU
ELAS
AFFE_CHAR_MECA
CONTACT
PAIRING: “MAIT_ESCL”
SEEK: “NOEUD_BOUCLE”
METHOD: “PENALIZATION”
E_T: 1.E+06
FRICTION: “COULOMB”
COULOMB: 0.3
COEF_MATR_FROT: 0.9
DIST_2: “- 2.”
STAT_NON_LINE
COMP_ELAS
RELATION: “ELAS”
14 Results of modeling F
14.1 Values
tested
Identification Reference Aster
% difference
Loading 1
Force normal contact
2.0784 E+05 NR
2.078391 E+05 NR
4.05E04
Tangential force of
contact
1.2000 E+05 NR
1.199959 E+05 NR
0.003E06
DX (not A)
1.000 mm
9.999999 E-01 mm
3.33E06
DY (not A)
1.732 mm
1.731051 E+00 mm
0.003
DX (not B)
1.000 mm
1.000001 E+00 mm
3.32E06
DY (not B)
1.732 mm
1.731051 E+00 mm
0.003
DX (point C)
1.000 mm
1.000001 E+00 mm
3.32E06
DY (point C)
1.732 mm
1.731051 E+00 mm
0.003
DX (not D)
1.000 mm
9.999999 E-01 mm
3.33E06
DY (not D)
1.732 mm
1.731051 E+00 mm
0.003
Loading 2
Force normal contact
1.7220 E+05 NR
1.721992 E+05 NR
4.12E04
Tangential force of
contact
1.8173 E+05 NR
1.817260 E+05 NR
0.002
DX (not A)
1.000 mm
1.004172 E+00 mm
0.417
DY (not A)
1.732 mm
1.729642 E+00 mm
0.136
DX (not B)
1.000 mm
1.002000 E+00 mm
0.200
DY (not B)
1.732 mm
1.730896 E+00 mm
0.064
DX (point C)
1.000 mm
1.002000 E+00 mm
0.200
DY (point C)
1.732 mm
1.730896 E+00 mm
0.064
DX (not D)
1.000 mm
1.004172 E+00 mm
0.417
DY (not D)
1.732 mm
1.729642 E+00 mm
0.136
Loading 3
Force normal contact
1.714896 E+05 NR
1.718404 E+04 NR
0.207
Tangential force of
contact
1.829770 E+05 NR
1.823477 E+05 NR
0.344
DX (not A)
8.79 mm
8.821717 E+00 mm
0.315
DY (not A)
2.77 mm
2.783820 E+00 mm
0.572
DX (not B)
8.79 mm
8.819386 E+00 mm
0.289
DY (not B)
2.77 mm
2.782474 E+00 mm
0.523
DX (point C)
8.79 mm
8.819386 E+00 mm
0.289
DY (point C)
2.77 mm
2.782474 E+00 mm
0.523
DX (not D)
8.79 mm
8.821717 E+00 mm
0.315
DY (not D)
2.77 mm
2.783820 E+00 mm
0.572
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
18/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
14.2 Notice
In this modeling, the play is defined using a function, the results are identical to those
found in preceding modeling.
15 Modeling
G
15.1 Characteristics of modeling
A modeling 3D with elements CUB8 testing the functionalities of contact node-mesh
with friction treated with the method penalized for the contact and friction was implemented.
The play between the shoe and the jig is defined by the geometrical co-ordinates of the mesh.
To avoid the movements of rigid body, the shoe is maintained by springs of low rigidity:
RES_LAT
: K
= 1 NR/mm
RES_FOND
: K = 1 NR/mm
RES_HAUT
: K
= 20 NR/mm
Boundary conditions:
Loose lead of the springs:
DX
=
DY
=
DZ
=0.
Jig:
DX
=
DY
=
DZ
=0.
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
19/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
15.2 Characteristics of the mesh
A number of nodes: 269
Numbers and types of meshs: 129 CUB8, 103 QUAD4
15.3 Functionalities
tested
Controls Key word
factor
Key word
MODI_MAILLAGE
ORIE_PEAU_3D
AFFE_MODELE
AFFE
MODELING: “3D”
DEFI_MATERIAU
ELAS
AFFE_CHAR_MECA
CONTACT
PAIRING: “MAIT_ESCL”
SEEK: “NOEUD_BOUCLE”
METHOD: “PENALIZATION”
E_T: 1.E+06
E_N: 1.E+06
FRICTION: “COULOMB”
COULOMB: 0.3
COEF_MATR_FROT: 0.9
STAT_NON_LINE
COMP_ELAS
RELATION: “ELAS”
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
20/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
16 Results of modeling G
16.1 Values
tested
Identification Reference Aster
% difference
Loading 1
Force normal contact
2.0784 E+05 NR
2.078391 E+05 NR
4.12E04
Tangential force of
contact
1.2000 E+05 NR
1.199959 E+05 NR
0.003
DX (not A)
1.000 mm
1.001612 E+00 mm
0.161
DY (not A)
1.732 mm
1.735714 E+00 mm
0.214
DX (not B)
1.000 mm
1.002367 E+00 mm
0.237
DY (not B)
1.732 mm
1.735279 E+00 mm
0.189
DX (point C)
1.000 mm
1.002367 E+00 mm
0.237
DY (point C)
1.732 mm
1.735279 E+00 mm
0.189
DX (not D)
1.000 mm
1.001612 E+00 mm
0.161
DY (not D)
1.732 mm
1.735714 E+00 mm
0.214
Loading 2
Force normal contact
1.7220 E+05 NR
1.721992 E+05 NR
4.12E04
Tangential force of
contact
1.8173 E+05 NR
1.817260 E+05 NR
0.002
DX (not A)
1.000 mm
1.004302 E+00 mm
0.430
DY (not A)
1.732 mm
1.732257 E+00 mm
0.015
DX (not B)
1.000 mm
1.004636 E+00 mm
0.464
DY (not B)
1.732 mm
1.736183 E+00 mm
0.242
DX (point C)
1.000 mm
1.004636 E+00 mm
0.464
DY (point C)
1.732 mm
1.736183 E+00 mm
0.242
DX (not D)
1.000 mm
1.004302 E+00 mm
0.430
DY (not D)
1.732 mm
1.732257 E+00 mm
0.015
Loading 3
Force normal contact
1.714896 E+05 NR
1.718404 E+04 NR
0.207
Tangential force of
contact
1.829770 E+05 NR
1.823477 E+05 NR
0.344
DX (not A)
8.79 mm
8.821530 E+00 mm
0.313
DY (not A)
2.77 mm
2.781029 E+00 mm
0.471
DX (not B)
8.79 mm
8.821622 E+00 mm
0.314
DY (not B)
2.77 mm
2.776938 E+00 mm
0.323
DX (point C)
8.79 mm
8.821622 E+00 mm
0.314
DY (point C)
2.77 mm
2.776938 E+00 mm
0.323
DX (not D)
8.79 mm
8.821530 E+00 mm
0.313
DY (not D)
2.77 mm
2.781029 E+00 mm
0.471
16.2 Notice
The play is defined in this case in a geometrical way. The results are worse than those
obtained with the penalization only on friction. Moreover, this method is longer.
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
21/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
17 Modeling
H
17.1 Characteristics of modeling
A modeling “
D_PLAN
” with elements QUAD4 testing the functionalities of contact node
net with friction treated with the method continues for the contact and friction was put in
work.
The play between the shoe and the jig is defined by the geometrical co-ordinates of the mesh.
To avoid the movements of rigid body, the shoe is maintained by springs of low rigidity:
RES_LAT
: K
= 2 NR/mm
RES_HAUT
: K
= 0,005 NR/mm
Boundary conditions:
Loose lead of the springs:
DX
=
DY
=0.
Jig:
DX
=
DY
=0.
17.2 Characteristics of the mesh
A number of nodes: 53
Numbers and types of meshs: 33 QUAD4, 32 SEG2
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
22/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
17.3 Functionalities
tested
Controls Key word
factor
Key word
MODI_MAILLAGE
ORIE_PEAU_2D
AFFE_MODELE
AFFE
MODELING: “D_PLAN”
DEFI_MATERIAU
ELAS
AFFE_CHAR_MECA
CONTACT
PAIRING: “MAIT_ESCL”
SEEK: “NOEUD_BOUCLE”
METHOD: “CONTINUES”
COEF_REGU_CONT: 1.E+02
COEF_REGU_FROT: 1.E+02
FRICTION: “COULOMB”
COULOMB: 0.3
COEF_MATR_FROT: 0.9
ITER_CONT_MAXI: 30
ITER_FROT_MAXI: 2
ITER_GEOM_MAXI:1
INTEGRATION: “NODE”
STAT_NON_LINE
COMP_ELAS
RELATION: “ELAS”
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
23/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
18 Results of modeling H
18.1 Values
tested
Identification Reference Aster
% difference
Loading 1
Force normal contact
1.200000 E+04 NR
1.199998 E+04 NR
1.70E04
Tangential force of
contact
0. NR
2.20752 E-06 NR
2.21E07
DX (not A)
1.000 mm
1.00000 E+00 mm
0.0
DY (not A)
1.732 mm
1.73205 E+00 mm
0.003
DX (not B)
1.000 mm
1.00000 E+00 mm
0.0
DY (not B)
1.732 mm
1.73205 E+00 mm
0.003
Loading 2
Force normal contact
1.200000 E+04 NR
1.199979 E+04 NR
1.70E04
Tangential force of
contact
3.564000 E+04 NR
3.563961 E+03 NR
0.001
DX (not A)
1.000 mm
1.021308 E+00 mm
2.131
DY (not A)
1.732 mm
1.719748 E+00 mm
0.707
DX (not B)
1.000 mm
1.000000 E+00 mm
0.0
DY (not B)
1.732 mm
1.7320508 E+00 mm
0.003
Loading 3
Force normal contact
1.200000 E+04 NR
1.199998 E+04 NR
1.70E04
Tangential force of
contact
3.624000 E+04 NR
3.599992 E+03 NR
0.662
DX (not A)
8.787 mm
8.809505 E+00 mm
0.256
DY (not A)
2.768 mm
2.7767695 E+00 mm
0.317
DX (not B)
8.787 mm
8.7869527 E+00 mm
0.180
DY (not B)
2.768 mm
2.7637484 E+00 mm
5.15 E04
Code_Aster
®
Version
6.4
Titrate:
SSNV503 - Shoe slipping on a rigid level
Date:
23/10/02
Author (S):
NR. TARDIEU, B. GREENHOUSE
Key
:
V6.04.503-A
Page:
24/24
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
19 Summary of the results
Whatever is modeling (2D or 3D) and the method of processing of contact-friction, them
results obtained are satisfactory. They are very close to the analytical results.