Code_Aster ®
Version
6.1
Titrate:
SSNV129 - Contact of 2 simple bearing plates


Date:
19/08/02
Author (S):
P. Key MASSIN, R. FERNANDES
:
V6.04.129-A Page:
1/10

Organization (S): EDF/AMA, CS IF
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
V6.04.129 document

SSNV129 - Contact of 2 simple bearing plates
of which is subjected to pressure

Summary:

A rectangular plate is subjected to a uniform compressive force and is compressed on a plate
identical where it undergoes forces of contact.

This test comprises two modelings (linear elements QUAD4 with modeling DKT - elements
quadratic QUAD9 with modeling COQUE_3D). Calculations of reference were carried out without contact.
The results of Code_Aster with contact are obtained in nonregression and are analyzed compared to the results
obtained without contact.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.1
Titrate:
SSNV129 - Contact of 2 simple bearing plates


Date:
19/08/02
Author (S):
P. Key MASSIN, R. FERNANDES
:
V6.04.129-A Page:
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1
Problem of reference

1.1 Geometry

Pressure
L
D
C
L
Z
With
B
E
y
X

Thickness of the plate: E = 0,5 cm.
Width of the plate: L = 5 cm.
Length of the plate: L = 10 cm.

Co-ordinates of the points of reference (cm)

X y Z
With 0 ­ 2.5
0
B 10 ­ 2.5 0
C 10.2.5 0
D 0.2.5 0

1.2
Material properties

Plates:

Poisson's ratio: 0.3
15
Young modulus: 2. 10 NR/m2

1.3
Boundary conditions and loadings

The plate is blocked:

· on AB and CD for displacements according to X and Z,
· on BC and DA for displacements according to y and Z,
· on AB and CD for rotations according to y,
· on AB and CD for rotations according to X.


One also blocks the central node of each plate to leave him the only possibility of
to move along axis Z.

The plate is subjected to a vertical pressure distributed on the higher plate:

·
12
Pressure: p = 2.5 10 NR/m2,
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
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Titrate:
SSNV129 - Contact of 2 simple bearing plates


Date:
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2
Reference solution

2.1 Reference
Bibliographical

The reference solution comes from the results obtained in “Formulas for Stress and Strain” from
ROARK' S (6th edition - McGraw-Hill International Editions)

2.2
Analytical results of reference without contact

The results obtained were calculated on a simple bearing plate subjected to a pressure
vertical (not of contact).

· Calculation of the arrow in the center of the plate:
- pb4
max
y
=

Et3

· Calculation of the constraint in the center of the plate according to the width of the plate:
2

- Pb
=

B
T 2

· p indicates the pressure applied to the plate,
· E the Young modulus,
· with the length,
· B the width,
· T the thickness,
·
, being two coefficients obtained starting from the report/ratio/B has.


= 0.1110


= 0.6102

That is to say:

y =

cm
0.69375


= 1.5255 1010

NR/cm2


Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.1
Titrate:
SSNV129 - Contact of 2 simple bearing plates


Date:
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2.3
Results obtained without contact with Code_Aster

2.3.1 Modeling
DKT

Modeling: DKT to test the contact between two plates.

256 finite elements QUAD4 are laid out on the initial surface of contact. The grid has only one
elements in the thickness of the plate sleep.

2.3.2 Characteristics of the grid

A number of nodes: 289 nodes
A number of meshs and type: 256 QUAD4

2.3.3 Values of reference Aster
Identification Reference
Aster (DKT) Error
DZ in the center of the plate
0.69375
0.69138
0.35%
in the center of the plate
1.5255 E+10
1.5298 E+10
0.28%

2.3.4 Modeling
COQUE_3D

Modeling: COQUE_3D to test the contact between two plates.

256 finite elements QUAD9 are laid out on the initial surface of contact. The grid has only one
elements in the thickness of the plate sleep.

2.3.5 Characteristics of the grid

A number of nodes: 578 nodes
A number of meshs and type: 256 QUAD9

2.3.6 Values of reference Aster
Identification Reference
Aster (COQUE_3D) Error
DZ in the center of the plate
0.69375
0.65927
4.97%
in the center of the plate
1.5255 E+10
1.41316 E+10
7.36%

2.4 Comments

It is noted that the results obtained without contact are very satisfactory for a modeling of
type DKT. The error obtained for a modeling of the COQUE_3D type can be explained by the catch in
count effects of transverse shearing which should not be negligible for this plate
relatively thick since the ratio L/E is worth 1/10.
Moreover, the effect of the size of the grid would be also to analyze by taking grids 100x100 with
place of grid 16x16.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
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Titrate:
SSNV129 - Contact of 2 simple bearing plates


Date:
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3 Modeling
With

3.1
Characteristics of modeling

Modeling: DKT to test the contact between two plates.

256 finite elements QUA4 are laid out on the initial surface of contact. The grid has only one
elements in the thickness of the plate sleep.

C

D
*
B
With


where * indicates the node medium of the plate.
With = DR1 or DR21,
B = DR2 or DR22,
C = DR3 or DR23,
D = DR4 or DR24.

The nodes to which one applies the boundary conditions are the nodes N177 and N466 located
in the center of each plate.

3.2
Characteristics of the grid

A number of nodes: 289 nodes
A number of meshs and type: 256 QUA4
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
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Titrate:
SSNV129 - Contact of 2 simple bearing plates


Date:
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3.3 Functionalities
tested

3.3.1 Calculation
1

Commands



AFFE_MODELE
MODELISATION
“DKT”

CONTACT
METHODE
“CONTRAINTE”

CONTACT
REAC_GEOM_INTE

STAT_NON_LINE
COMP_INCR
RELATION
“ELAS”


Calculation by the method of the active constraints is carried out without geometrical reactualization and on
only one step of time.

3.3.2 Calculation
2

Commands



AFFE_MODELE
MODELISATION
“DKT”

CONTACT
METHODE
“LAGRANGIEN”

CONTACT
REAC_GEOM_INTE

STAT_NON_LINE
COMP_INCR
RELATION
“ELAS”


Calculation by the method of Lagrangian is carried out with two geometrical reactualizations for
each of the 5 steps of time.

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.1
Titrate:
SSNV129 - Contact of 2 simple bearing plates


Date:
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4
Results of modeling A

4.1
Values of reference Aster

4.1.1 Calculation
1

Identification of the central node
Aster without contact
Aster Error
(/2)
DZ
3.4569 E-01
3.42675 E-01
0.87%

7.6491 E+09
7.67191 E+09
0.30%

One also tests the following values in nonregression:

Identification
Aster
DZ with the N132 node
­ 2.86558 E01
DZ with the N204 node
­ 2.74507 E01
DZ with the N211 node
­ 2.45747 E01
with the N132 node
6.57215 E+09
with the N204 node
6.28349 E+09
with the N211 node
5.71108 E+09

4.1.2 Calculation
2

Identification of the central node
Aster without contact
Aster Error
(/2)
DZ
3.4569 E-01
3.47470 E-01
0.51%

7.6491 E+09
7.5768 E+09
0.94%

One also tests the following values in nonregression:

Identification
Aster
Error Calcul2/Calcul1
DZ with the N132 node
­ 2.90536 E01
1.4%
DZ with the N204 node
­ 2.81684 E01
2.6%
DZ with the N211 node
­ 2.48085 E01
1.0%
with the N132 node
6.67510 E+09
1.6%
with the N204 node
6.50562 E+09
3.5%
with the N211 node
5.76723 E+09
1.0%

4.2 Parameters
of execution

Version:
6.1.10
Machine:
SGI - Origin 2000
Time CPU To use:
214 seconds

4.3 Comments

The results obtained with contact are very satisfactory since one obtains, with less than 1%
of error, results obtained without contact except for a factor of 2. It is indeed the result
awaited since to add the contact between two plates identical to that of paragraph 2 returns to
to suppose a plate subjected to pressure with a rigidity twice higher.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.1
Titrate:
SSNV129 - Contact of 2 simple bearing plates


Date:
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5 Modeling
B

5.1
Characteristics of modeling

Modeling: COQUE_3D to test the contact between two plates.

256 finite elements QUA9 are laid out on the initial surface of contact. The grid has only one
elements in the thickness of the plate sleep.

C

D
*
B
With


where * indicates the node medium of the plate.
With = DR1 or DR21,
B = DR2 or DR22,
C = DR3 or DR23,
D = DR4 or DR24.

The nodes to which one applies the boundary conditions are the nodes N241 and N1074 located
in the center of each plate.

5.2
Characteristics of the grid

A number of nodes: 578 nodes
A number of meshs and type: 256 QUA9

5.3 Functionalities
tested

Commands



AFFE_MODELE
MODELISATION
“COQUE_3D”

CONTACT
METHODE
“CONTRAINTE”

CONTACT
REAC_GEOM_INTE

STAT_NON_LINE
COMP_INCR
RELATION
“ELAS”


Commands



AFFE_MODELE
MODELISATION
“COQUE_3D”

CONTACT
METHODE
“LAGRANGIEN”

CONTACT
REAC_GEOM_INTE

STAT_NON_LINE
COMP_INCR
RELATION
“ELAS”

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.1
Titrate:
SSNV129 - Contact of 2 simple bearing plates


Date:
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Author (S):
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:
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6
Results of modeling B

6.1
Values of reference Aster

Identification of the central node
Aster without contact
Aster Error
(/2)
DZ
3.29636 E-01
3.27176 E-01
0.75%

7.06580 E+09
7.03945 E+09
0.37%

One also tests the following values in nonregression:

Identification
Aster
DZ with the N192 node
­ 2.07642 E01
DZ with the N246 node
­ 2.05704 E01
DZ with the N314 node
­ 1.73742 E01
with the N192 node
4.71388 E+09
with the N246 node
4.57802 E+09
with the N314 node
4.07646 E+09

6.2 Parameters
of execution

Version:
6.1.10
Machine:
SGI Origin 2000
Time CPU To use:
280 seconds

6.3 Comments

The results obtained with contact are very satisfactory since one obtains, with less than 1% of error,
results obtained without contact except for a factor of 2. It is indeed the awaited result
since to add the contact between two plates identical to that of paragraph 2 amounts supposing one
plate subjected to pressure with a rigidity twice higher.

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.1
Titrate:
SSNV129 - Contact of 2 simple bearing plates


Date:
19/08/02
Author (S):
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:
V6.04.129-A Page:
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7
Summary of the results

One notes very good results in the presence of contact for two modelings.

Modeling A (DKT) has very satisfactory results compared to the analytical results
(­ 1% of error with or without contact). When one replaces a plate under pressure by two
plates from which one comes to be stuck to the other, the multiplication of rigidity by two results in one
division by two of the maximum arrow as well as constraint in the center of the plates.

Modeling B (COQUE_3D) gives a behavior are equivalent to that met for
modeling A in DKT when one replaces a plate under pressure by two plates in contact.
One observes a division by two of the maximum arrow as well as constraint in the center of
plates. Moreover, the value of the arrow obtained is rather satisfactory (~7% of error) compared to
analytical results. This difference can be explained by the taking into account of shearing
transverse for the COQUE_3D for a plate which is altogether relatively thick since
l/e = 1/10.

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

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