Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
1/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document:V6.04.127
SSNV127 - Roll in a boring with contact
and friction
Summary:
This problem corresponds to a quasi-static analysis of a problem of mechanics with contact and friction.
A cylinder is compressed in a cylindrical boring of slightly higher diameter by a force
concentrated applied to its axis.
This test, named “problem of Klang”, is rather largely used in the literature to validate
modelings of contact with friction and was in particular used by P. Alart and A. Curnier [bib1] to validate
their finite elements of contact and friction.
Five modelings 2D are proposed (A, B, C and D with linear elements and E with elements
quadratic):
Modeling A tests the “LAGRANGIAN” algorithm of the method with master-slave pairing.
Modeling B tests the “LAGRANGIAN” algorithm of the method with nodal pairing.
Modeling C tests the algorithm of the method “PENALIZATION” with master-slave pairing,
penalization relates only to friction.
Modeling D tests the algorithm of the method “PENALIZATION” with master-slave pairing,
penalization relates to the contact and friction.
Modeling E tests the “LAGRANGIAN” algorithm of the method with master-slave pairing.
Modelings F and H test the algorithm of the “CONTINUOUS” method with quadratic elements
(SEG3) and linear (SEG2) of contact, respectively.
The results are compared with an analytical solution given by Klang [bib2].
Instead of reproducing this relatively intricate analytical solution we will use the values of
pressures obtained from the aforementioned [bib1].
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
2/18
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V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
1
Problem of reference
1.1 Geometry
Plane stresses
= contact angle
= angle for the slip
X
y
Q
Radius of the cylinder: R = 5.999 cm.
Radius of boring: R = 6. cm.
Position of the points of reference on the surface of contact: a point all three degrees of angle with
to leave bottom, until 60°.
1.2
Material properties
Roll and boring:
Young modulus:
E = 2.1 10
11
NR/m
2
Poisson's ratio:
= 0.3
Coefficient of friction:
µ = 0.4
1.3
Boundary conditions and loadings
The solid mass containing boring is supposed infinite being, its displacements will be locked (according to X and y)
on a concentric circle with boring.
The cylinder is subjected to a force distributed Q according to thickness (Z) being worth: Q = 1875 10
3
NR/Mr.
This force is applied in an increment.
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
3/18
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V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is analytical [bib2].
2.2
Results of reference
Prediction on the area of contact: 60 degrees.
Prediction on the beginning of the area of slip: 26,2 degrees.
Efforts of pressure on the points of the surface of contact:
Identification
Reference
SIXX for an angle of 0°
1.7813E+07
SIXX 3°
1.7813E+07
SIXX 6°
1.7750E+07
SIXX 9°
1.7688E+07
SIXX 12°
1.7594E+07
SIXX 15°
1.7470E+07
SIXX 18°
1.7312E+07
SIXX 21°
1.7125E+07
SIXX 24°
1.6906E+07
SIXX 27°
1.6656E+07
SIXX 30°
1.6343E+07
SIXX 33°
1.5937E+07
SIXX 36°
1.5406E+07
SIXX 39°
1.4781E+07
SIXX 42°
1.4031E+07
SIXX 45°
1.3094E+07
SIXX 48°
1.1169E+07
SIXX 51°
1.0593E+07
2.3 References
bibliographical
[1]
P. Alart, A. Curnier “A mixed formulation for frictional contact problems” Methods Computer in
Applied Mechanics and Engineering (1991) p. 353-375
[2]
Mr. Klang “One interior contact under friction between cylindrical elastic bodies in contact”
Thesis, Linköping University, Linköping, 1979.
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
4/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
3 Modeling
With
3.1
Characteristics of modeling
The symmetry of the problem makes it possible to modelize of it only half (X 0).
60 finite elements SEG2 are laid out regularly on the initial surface of contact (3 degrees of angle
for each one).
The cylinder and circular volume surrounding boring are with a grid with elements QUA4 and TRIA3.
X
bd4
Q/2
bd3
ad2
NO
2
ad1
ad3
ad4
cc4
cc3
bcc1
bcc2
CONTACT
METHOD = “LAGRANGIAN”
COULOMB = 0.4
APPARIEMENT=' MAIT_ESCL'
Master: bcc1
Slave: bcc2
Boundary condition:
·
on the GROUP_MA
CC4:
DX = 0, DY = 0.
·
on the GROUP_MA
AD1, AD2, AD3, AD4, BD3, and BD4:
DX = 0.
Loadings:
The symmetry of the problem compared to the plan
X
= 0 make it possible to modelize the force concentrated by one
nodal force Fy = 937.5 10
3
NR, equivalent to Q/2 for a cylinder length unit, applied to
group nodes O
2
, center of the cylinder.
This force is applied into 1 increment.
3.2
Characteristics of the mesh
A number of nodes:
1281
A number of meshs and types:
128 SEG2
156 TRIA3
1108 QUAD4
3.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = “C_PLAN”
DEFI_MATERIAU ELAS
AFFE_CHAR_MECA
CONTACT
METHOD = “LAGRANGIAN”
FRICTION = “COULOMB”
COULOMB = 0.4
STAT_NON_LINE
COMP_ELAS
RELATION = “ELAS”
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
5/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
4
Results of modeling A
4.1
Values tested: SIEF_ELNO_ELGA
One tests the efforts of normal pressure generated by contact-friction. These efforts defined in
polar co-ordinates are expressed in MPa.
Identification Reference
Aster %
difference
SIXX for an angle of
0°
1.7813E+07
1.79080E+07
0.534
SIXX 3°
1.7813E+07
1.88485E+07
5.814
SIXX 6°
1.7750E+07
1.89858E+07
6.962
SIXX 9°
1.7688E+07
1.88134E+07
6.363
SIXX 12°
1.7594E+07
1.85821E+07
5.616
SIXX 15°
1.7470E+07
1.83315E+07
4.931
SIXX 18°
1.7312E+07
1.78831E+07
3.299
SIXX 21°
1.7125E+07
1.74723E+07
2.028
SIXX 24°
1.6906E+07
1.67279E+07
1.053
SIXX 27°
1.6656E+07
1.60957E+07
3.364
SIXX 30°
1.6343E+07
1.56801E+07
4.056
SIXX 33°
1.5937E+07
1.57565E+07
1.132
SIXX 36°
1.5406E+07
1.55705E+07
1.068
SIXX 39°
1.4781E+07
1.51262E+07
2.336
SIXX 42°
1.4031E+07
1.43093E+07
1.984
SIXX 45°
1.3094E+07
1.33902E+07
2.262
SIXX 48°
1.1169E+07
1.24478E+07
11.450
SIXX 51°
1.0593E+07
1.11500E+07
5.259
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
6/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
5 Modeling
B
5.1
Characteristics of modeling
This modeling is identical to modeling A (and in particular mesh). Only differs
method of pairing which here is “NODAL”.
X
bd4
Q/2
bd3
ad2
NO
2
ad1
ad3
ad4
cc4
cc3
bcc1
bcc2
CONTACT
METHOD = “LAGRANGIAN”
COULOMB = 0.4
APPARIEMENT=' NODAL'
5.2 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = “C_PLAN”
AFFE_CHAR_MECA
CONTACT
PAIRING = “NODAL”
METHOD = “LAGRANGIAN”
FRICTION = “COULOMB”
COULOMB = 0.4
STAT_NON_LINE
COMP_ELAS
RELATION = “ELAS”
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
7/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
6
Results of modeling B
6.1
Values tested: SIEF_ELNO_ELGA
One tests the efforts of normal pressure generated by contact-friction. These efforts defined in
polar co-ordinates are expressed in MPa.
Identification Reference
Aster %
difference
SIXX for an angle of 0°
1.7813E+07
1.86019E+07
4.429
SIXX 3°
1.7813E+07
1.93157E+07
8.436
SIXX 6°
1.7750E+07
1.93512E+07
9.021
SIXX 9°
1.7688E+07
1.91026E+07
7.998
SIXX 12°
1.7594E+07
1.88145E+07
6.937
SIXX 15°
1.7470E+07
1.85112E+07
5.960
SIXX 18°
1.7312E+07
1.80078E+07
4.019
SIXX 21°
1.7125E+07
1.75572E+07
2.524
SIXX 24°
1.6906E+07
1.67641E+07
0.839
SIXX 27°
1.6656E+07
1.63429E+07
1.879
SIXX 30°
1.6343E+07
1.63762E+07
0.203
SIXX 33°
1.5937E+07
1.63898E+07
2.842
SIXX 36°
1.5406E+07
1.59991E+07
3.850
SIXX 39°
1.4781E+07
1.53865E+07
4.097
SIXX 42°
1.4031E+07
1.44452E+07
2.952
SIXX 45°
1.3094E+07
1.34146E+07
2.449
SIXX 48°
1.1169E+07
1.23898E+07
10.931
SIXX 51°
1.0593E+07
1.08630E+07
2.549
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
8/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
7 Modeling
C
7.1
Characteristics of modeling
This modeling is identical to modeling A (and in particular mesh). Only differs
method of resolution which is here “PENALIZATION” with penalization only on friction.
X
bd4
Q/2
bd3
ad2
NO
2
ad1
ad3
ad4
cc4
cc3
bcc1
bcc2
CONTACT
METHOD = `PENALIZATION
COULOMB = 0.4
APPARIEMENT=' MAIT_ESCL'
Master: bcc1
Slave: bcc2
7.2 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = “C_PLAN”
AFFE_CHAR_MECA
CONTACT
METHOD = “LAGRANGIAN”
FRICTION = “COULOMB”
COULOMB = 0.4
E_T =6.E9
COEF_MATR_FROT =0.3
STAT_NON_LINE
COMP_ELAS
RELATION = “ELAS”
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
9/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
8
Results of modeling C
8.1
Values tested: SIEF_ELNO_ELGA
One tests the efforts of normal pressure generated by contact-friction. These efforts defined in
polar co-ordinates are expressed in MPa.
Identification Reference
Aster %
difference
SIXX for an angle of 0°
1.7813E+07
1.86714E+07
4.819
SIXX 3°
1.7813E+07
1.97269E+07
10.745
SIXX 6°
1.7750E+07
1.99928E+07
12.636
SIXX 9°
1.7688E+07
1.98849E+07
12.421
SIXX 12°
1.7594E+07
1.97193E+07
12.080
SIXX 15°
1.7470E+07
1.95408E+07
11.854
SIXX 18°
1.7312E+07
1.91611E+07
10.681
SIXX 21°
1.7125E+07
1.88051E+07
9.811
SIXX 24°
1.6906E+07
1.82459E+07
7.926
SIXX 27°
1.6656E+07
1.78217E+07
6.999
SIXX 30°
1.6343E+07
1.71305E+07
4.819
SIXX 33°
1.5937E+07
1.64093E+07
2.964
SIXX 36°
1.5406E+07
1.55834E+07
1.152
SIXX 39°
1.4781E+07
1.46776E+07
0.699
SIXX 42°
1.4031E+07
1.36676E+07
2.589
SIXX 45°
1.3094E+07
1.27603E+07
2.548
SIXX 48°
1.1169E+07
1.24156E+07
11.161
SIXX 51°
1.0593E+07
1.08692E+07
2.608
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
10/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
9 Modeling
D
9.1
Characteristics of modeling
This modeling is identical to modeling A (and in particular mesh). Only differs
method of resolution which is here “PENALIZATION” with penalization on the contact and friction.
X
bd4
Q/2
bd3
ad2
NO
2
ad1
ad3
ad4
cc4
cc3
bcc1
bcc2
CONTACT
METHOD = `PENALIZATION
COULOMB = 0.4
APPARIEMENT=' MAIT_ESCL'
Master: bcc1
Slave: bcc2
9.2 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = “C_PLAN”
AFFE_CHAR_MECA
CONTACT
METHOD = “LAGRANGIAN”
FRICTION = “COULOMB”
COULOMB = 0.4
E_N =1.E18
E_T =6.E9
COEF_MATR_FROT =0.3
STAT_NON_LINE
COMP_ELAS
RELATION = “ELAS”
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
11/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
10 Results of modeling D
10.1 Values tested: SIEF_ELNO_ELGA
One tests the efforts of normal pressure generated by contact-friction. These efforts defined in
polar co-ordinates are expressed in MPa.
Identification Reference
Aster %
difference
SIXX for an angle of 0°
1.7813E+07
1.867141E+07
4.819
SIXX 3°
1.7813E+07
1.972695E+07
10.745
SIXX 6°
1.7750E+07
1.999288E+07
12.636
SIXX 9°
1.7688E+07
1.988495E+07
12.421
SIXX 12°
1.7594E+07
1.971935E+07
12.080
SIXX 15°
1.7470E+07
1.954087E+07
11.854
SIXX 18°
1.7312E+07
1.916115E+07
10.681
SIXX 21°
1.7125E+07
1.880513E+07
9.811
SIXX 24°
1.6906E+07
1.824592E+07
7.926
SIXX 27°
1.6656E+07
1.782171E+07
6.999
SIXX 30°
1.6343E+07
1.713057E+07
4.819
SIXX 33°
1.5937E+07
1.640937E+07
2.964
SIXX 36°
1.5406E+07
1.558344E+07
1.152
SIXX 39°
1.4781E+07
1.467761E+07
0.699
SIXX 42°
1.4031E+07
1.366763E+07
2.590
SIXX 45°
1.3094E+07
1.276022E+07
2.549
SIXX 48°
1.1169E+07
1.241550E+07
11.160
SIXX 51°
1.0593E+07
1.086923E+07
2.608
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
12/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
11 Modeling
E
11.1 Characteristics of modeling
The symmetry of the problem makes it possible to modelize of it only half (X 0).
30 finite elements SEG3 are laid out regularly on surface of contact. Because of curvature
of these elements, one uses the method of projection “QUADRATIC”.
The cylinder and circular volume surrounding boring are with a grid with elements QUA8 and TRIA6.
X
bd4
Q/2
bd3
ad2
NO
2
ad1
ad3
ad4
cc4
cc3
bcc1
bcc2
CONTACT
METHOD = “LAGRANGIAN”
COULOMB = 0.4
APPARIEMENT=' MAIT_ESCL'
Master: bcc1
Slave: bcc2
Boundary condition:
·
on the GROUP_MA
CC4:
DX = 0, DY = 0.
·
on the GROUP_MA
AD1, AD2, AD3, AD4, BD3, and BD4:
DX = 0.
Loadings:
The symmetry of the problem compared to the plan
X
= 0 make it possible to modelize the force concentrated by one
nodal force Fy = 937.5 10
3
NR, equivalent to Q/2 for a cylinder length unit, applied to
group nodes O
2
, center of the cylinder.
This force is applied into 1 increment.
11.2 Characteristics of the mesh
A number of nodes:
1603
A number of meshs and types:
88 SEG3
58 TRIA6
456 QUAD8
11.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = “C_PLAN”
DEFI_MATERIAU ELAS
AFFE_CHAR_MECA
CONTACT
METHOD = “LAGRANGIAN”
FRICTION = “COULOMB”
COULOMB = 0.4
PROJECTION =QUADRATIQUE
STAT_NON_LINE
COMP_ELAS
RELATION = “ELAS”
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
13/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
12 Results of modeling E
12.1 Values tested: SIEF_ELNO_ELGA
One tests the efforts of normal pressure generated by contact-friction. These efforts defined in
polar co-ordinates are expressed in MPa.
Identification Reference
Aster %
difference
SIXX for an angle of 0°
1.7813E+07
1.87916E+07
5.494
SIXX 3°
1.7813E+07
1.87072E+07
5.020
SIXX 6°
1.7750E+07
1.85202E+07
4.340
SIXX 9°
1.7688E+07
1.83433E+07
3.705
SIXX 12°
1.7594E+07
1.81013E+07
2.884
SIXX 15°
1.7470E+07
1.77266E+07
1.469
SIXX 18°
1.7312E+07
1.74321E+07
0.694
SIXX 21°
1.7125E+07
1.68102E+07
1.838
SIXX 24°
1.6906E+07
1.64256E+07
2.841
SIXX 27°
1.6656E+07
1.62913E+07
2.189
SIXX 30°
1.6343E+07
1.57932E+07
3.364
SIXX 33°
1.5937E+07
1.55232E+07
2.596
SIXX 36°
1.5406E+07
1.48572E+07
3.562
SIXX 39°
1.4781E+07
1.41428E+07
4.317
SIXX 42°
1.4031E+07
1.28218E+07
8.618
SIXX 45°
1.3094E+07
1.19407E+07
8.808
SIXX 48°
1.1169E+07
1.07287E+07
3.942
SIXX 51°
1.0593E+07
9.70591E+06
8.374
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
14/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
13 Modeling
F
13.1 Characteristics of modeling
The symmetry of the problem makes it possible to modelize of it only half (X 0).
60 finite elements SEG3 are laid out regularly on the initial surface of contact (3 degrees of angle
for each one).
The cylinder and circular volume surrounding boring are with a grid with elements QUA8 and TRIA6.
X
bd4
Q/2
bd3
ad2
NO
2
ad1
ad3
ad4
cc4
cc3
bcc1
bcc2
CONTACT
METHOD = “CONTINUES”
COULOMB = 0.4
APPARIEMENT=' MAIT_ESCL'
Master: bcc1
Slave: bcc2
Boundary condition:
·
on the GROUP_MA
CC4:
DX = 0, DY = 0.
·
on the GROUP_MA
AD1, AD2, AD3, AD4, BD3, and BD4:
DX = 0.
Loadings:
The symmetry of the problem compared to the plan
X
= 0 make it possible to modelize the force concentrated by one
nodal force Fy = 937.5 10
3
NR, equivalent to Q/2 for a cylinder length unit, applied to
group nodes O
2
, center of the cylinder.
This force is applied into 1 increment.
13.2 Characteristics of the mesh
A number of nodes:
1603
A number of meshs and types:
88 SEG3
58 TRIA6
456 QUAD8
13.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = “C_PLAN”
DEFI_MATERIAU ELAS
AFFE_CHAR_MECA
CONTACT
METHOD = “CONTINUES”
FRICTION = “COULOMB”
COULOMB = 0.4
PROJECTION =QUADRATIQUE
STAT_NON_LINE
COMP_ELAS
RELATION = “ELAS”
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
15/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
14 Results of modeling F
14.1 Values tested: SIEF_ELNO_ELGA
One tests the efforts of normal pressure generated by contact-friction. These efforts defined in
polar co-ordinates are expressed in MPa.
Identification Reference
Aster %
difference
SIXX for an angle of
0°
1.7813E+07
1.88235E+07
5.673
SIXX 3°
1.7813E+07
1.87386E+07
5.196
SIXX 6°
1.7750E+07
1.85220E+07
4.349
SIXX 9°
1.7688E+07
1.84104E+07
4.084
SIXX 12°
1.7594E+07
1.81071E+07
2.917
SIXX 15°
1.7470E+07
1.78019E+07
1.900
SIXX 18°
1.7312E+07
1.73913E+07
0.458
SIXX 21°
1.7125E+07
1.68233E+07
1.762
SIXX 24°
1.6906E+07
1.65322E+07
2.211
SIXX 27°
1.6656E+07
1.63678E+07
1.730
SIXX 30°
1.6343E+07
1.60549E+07
1.763
SIXX 33°
1.5937E+07
1.56070E+07
2.071
SIXX 36°
1.5406E+07
1.48829E+07
3.395
SIXX 39°
1.4781E+07
1.41776E+07
4.082
SIXX 42°
1.4031E+07
1.29292E+07
7.852
SIXX 45°
1.3094E+07
1.19737E+07
8.555
SIXX 48°
1.1169E+07
1.06929E+07
4.263
SIXX 51°
1.0593E+07
0.96396E+07
8.999
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
16/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
15 Modeling
H
15.1 Characteristics of modeling
The symmetry of the problem makes it possible to modelize of it only half (X 0).
60 finite elements SEG2 are laid out regularly on the initial surface of contact (3 degrees of angle
for each one).
The cylinder and circular volume surrounding boring are with a grid with elements QUA4 and TRIA3.
X
bd4
Q/2
bd3
ad2
NO
2
ad1
ad3
ad4
cc4
cc3
bcc1
bcc2
CONTACT
METHOD = “CONTINUES”
COULOMB = 0.4
APPARIEMENT=' MAIT_ESCL'
Master: bcc1
Slave: bcc2
Boundary condition:
·
on the GROUP_MA
CC4:
DX = 0, DY = 0.
·
on the GROUP_MA
AD1, AD2, AD3, AD4, BD3, and BD4:
DX = 0.
Loadings:
The symmetry of the problem compared to the plan
X
= 0 make it possible to modelize the force concentrated by one
nodal force Fy = 937.5 10
3
NR, equivalent to Q/2 for a cylinder length unit, applied to
group nodes O
2
, center of the cylinder.
This force is applied into 1 increment.
15.2 Characteristics of the mesh
A number of nodes:
1282
A number of meshs and types:
128 SEG2
162 TRIA3
1106 QUAD4
15.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = “C_PLAN”
DEFI_MATERIAU ELAS
AFFE_CHAR_MECA
CONTACT
METHOD = “CONTINUES”
FRICTION = “COULOMB”
COULOMB = 0.4
STAT_NON_LINE
COMP_ELAS
RELATION = “ELAS”
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
17/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
16 Results of modeling H
16.1 Values tested: SIEF_ELNO_ELGA
One tests the efforts of normal pressure generated by contact-friction. These efforts defined in
polar co-ordinates are expressed in MPa.
Identification Reference
Aster %
difference
SIXX for an angle of
0°
1.7813E+07
1.79054E+07
0.519
SIXX 3°
1.7813E+07
1.88551E+07
5.850
SIXX 6°
1.7750E+07
1.89952E+07
7.015
SIXX 9°
1.7688E+07
1.88212E+07
6.407
SIXX 12°
1.7594E+07
1.85900E+07
5.661
SIXX 15°
1.7470E+07
1.83361E+07
4.958
SIXX 18°
1.7312E+07
1.78879E+07
3.327
SIXX 21°
1.7125E+07
1.74676E+07
2.001
SIXX 24°
1.6906E+07
1.67457E+07
0.948
SIXX 27°
1.6656E+07
1.60969E+07
3.357
SIXX 30°
1.6343E+07
1.56549E+07
4.211
SIXX 33°
1.5937E+07
1.57323E+07
1.284
SIXX 36°
1.5406E+07
1.55859E+07
1.168
SIXX 39°
1.4781E+07
1.51202E+07
2.295
SIXX 42°
1.4031E+07
1.42668E+07
1.680
SIXX 45°
1.3094E+07
1.33861E+07
2.230
SIXX 48°
1.1169E+07
1.24518E+07
11.485
SIXX 51°
1.0593E+07
1.11524E+07
5.280
Code_Aster
®
Version
8.3
Titrate:
SSNV127 - Roll in a boring with contact and friction
Date:
04/05/06
Author (S):
Mr. KHAM, S. LAMARCHE, P. MASSIN, Mr. TORKHANI
Key:
V6.04.127-C
Page:
18/18
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
17 Summary of the results
The results are of good quality if it is considered that they are compared with an analytical solution and
that the mesh used is not particularly fine.
The best solutions are given by modelings E and F (algorithms Lagrangien and continuous,
respectively) which uses quadratic elements with quadratic projection (without using
this projection, the results are false). Then modelings A and H come which, like
the preceding one, use the algorithms Lagrangien and continuous, respectively, with main pairing
slave. If one uses nodal pairing (modeling B), the solution is good but it is necessary to underline
that this technique of pairing is limited to the small slips. Finally modelings C come
and D which use the algorithm of penalization and which give acceptable results. Let us note that
convergence with these algorithms is much slower and difficult.
If one examines the extent of the surface of contact using the impression of the structure of data
VALE_CONT (see file of results), one notes that it is given very precisely (60°). In what
relate to adherent surface, the algorithms return an acceptable value about 30° to
place of 26.2° analytically.