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Version
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Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
1/20
Organization (S): EDF/IMA/MN
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.015
SSNP15 - Plaque in traction-shearing -
Von Mises (isotropic work hardening)
Summary:
This test quasi-static 2D forced plane, from guide VPCS, enters within the framework of the validation of
relations of elastoplastic behavior. A plate, made up of a plastic material with work hardening
isotropic linear, is subjected to a one and tractive effort of shearing.
The principal interest of this test lies in the nonradial character of the loading.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
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Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
2/20
1
Problem of reference
1.1 Geometry
y
1
2
1 mm
3
4
X
1 mm
1.2
Material properties
Elastoplastic law of behavior to linear kinematic work hardening.
AND
Y
E = 195.000 MPa
= 0.3
E
Y = 181 MPa
AND = 1930 MPA
1.3
Boundary conditions and loadings
The plate is blocked according to OX along the side [2,4] while being subjected to a traction D and one
shearing force D.
D
D
D
D
D
The way of loading is as follows:
D
D
D
With
(MPa) (MPa)
To 151.2
93.1
B
B 257.2
33.1
D
0
Handbook of Validation
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Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
3/20
2
Reference solution
2.1
Method of calculation used for the reference solution
In the plan (,
3), the standard of von Mises results in the traditional distance, so that one
can immediately predict the phases of load and discharge at the time of the way of loading,
since they are respectively the phases where the standard grows or decrease:
Way of loading
Numerical values (; )
Phases of loading
3
With
A0 (123,8; 76,23)
O-A0 charges elastic
B0
To (151,2; 93,1)
A0-A charges plastic
A0
B0 (158,23; 89,12)
A-B0 discharges
B (257,2; 33,1)
B0-B charges plastic
B
2.1.1 Step of resolution
Mechanically, it is about a test 0D controlled in constraint, the material being elastoplastic with criterion
of von Mises and linear isotropic work hardening. For a loading controlled in constraint, one determines
easily cumulated plastic deformation:
y
-
F (, p)
y
eq
= - - R p 0
p =
eq
in load
éq 2.1.1-1
R
The integration of the plastic deformation is of course more delicate. The equation of flow is written:
~
p
3
3
=
eq
p
p
~
=
2
2 R
in load
éq 2.1.1-2
eq
eq
Lastly, one will deduce the deformation via the relation from state:
p
p
= p + -
E 1:
xx = xx +
and
xy = xy +
éq 2.1.1-3
E
2 µ
Handbook of Validation
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Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
4/20
2.1.2 Processing of the phase of radial loading
Let us notice that in phase of radial loading, the law of flow [éq 2.1.2-1] is integrated directly:
~
p
= 3 p
2
éq 2.1.2-1
eq
The cumulated plastic deformation is then given by [éq 2.1.1-1], the plastic deformation by
[éq 2.1.2-1] and total deflection by [éq 2.1.1-3]. With:
E
= 195.000 MPa
2µ
= 150.000 MPa
R'
= 1.949, 29 Mpa
One obtains:
p (A)
= 2, 0547 102
pxx (A)
= 1, 4054 102
xx (A)
= 1, 4830 102
pxy (A)
= 1, 2981 102
xy (A)
= 1, 3601 102
2.1.3 Processing of the phase of nonradial loading
In the phase of loading nonradial B0 - B, one can parameterize the way of constraint by:
0
0
(Q) = B + Q (B - B)
with
0 Q 1
éq 2.1.3-1
fixed direction
As the way of loading remains confined in the traction-shearing plan (,), there will be interest with
to represent the state of stress by a complex number:
= +
0
0
I
= and (Q) = B + Q B
3
0
eq
(-) éq 2.1.3-2
fixed direction
The integration of the law of flow [éq 2.1.1-2], followed by an integration by part, makes it possible to express
plastic deformation:
1
1
2 R [
p] 1
1
eq
1
~
~
~
2
=
dq = ln ()
eq
-
ln
dq
3
0
[
]
eq
0
2
()
eq
0 0
0
~ B
- ~B
The adoption of the complex plan allows an easy calculation of the last integral:
1
1
1
1
1
1
(
ln () -
ln 2
=
=
+
=
eq) dq
(
ln
) dq (
ln
) dq (
ln
) dq 2Re (
ln
) dq = 2Re
B
B0
0
0
0
0
0
-
0
Finally, the increment of plastic deformation on the B0 way - B is worth:
[
B
ln () -
p] B
3
B
3
~ B
~ B0
=
ln () ~
-
Re
-
éq 2.1.3-4
0
eq
B
[
]
2 R
B0
2 R
B
B0
()
-
B0
Handbook of Validation
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Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
5/20
2.2
Results of reference
By calculating the plastic deformation cumulated by [éq 2.1.1-1], the plastic deformation by [éq 2.1.3-4]
and the total deflection by [éq 2.1.1-3], one obtains:
p (B)
= 4, 2329 102
pxx (B)
= 3, 3946 102
xx (B)
= 3, 5265 102
One obtains:
pxy (B)
= 2, 0250 102
xy (B)
= 2, 0471 102
One will be interested in the values of the constraints, the deformations and the cumulated plastic deformation
at points A and B of the way of loading.
2.3 References
bibliographical
[1]
French company of Mécaniciens. Guide validation of the software packages of structural analysis
(VPCS). Technical AFNOR, 1990.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
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Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
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3 Modeling
With
3.1
Characteristics of modeling
HEXA8
Z
N07
N05
N08
N06
y
N03
N01
N04
N02
X
The loading and the boundary conditions are modelled by:
DDL_IMPO: (NOEUD: N04, DX: 0., DY:0.)
DDL_IMPO: (NOEUD: N08, DX: 0., DY:0., DZ:0.)
DDL_IMPO: (NOEUD: N02, DX: 0.)
DDL_IMPO: (NOEUD: N06, DX: 0.)
surface forces imposed (key word FORCE_FACE) on the faces (meshs of skin) (1, 5, 6,
2), (1, 5, 7, 3), (3, 4, 8, 7) and (4, 8, 6, 2).
3.2
Characteristics of the grid
A number of nodes: 8
A number of meshs and types: 1 HEXA8, 4 QUAD4
3.3 Functionalities
tested
Commands
Keys
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
[U4.23.01]
SY
STAT_NON_LINE
COMP_INCR
RELATION
VMIS_ISOT_LINE
[U4.32.01]
CALC_ELEM
OPTION
EPSI_ELNO_DEPL
[U4.61.02]
RECU_CHAMP
NOM_CHAM
VARI_ELNO_ELGA
[U4.62.01]
CALC_ELEM
OPTION
RADI_ELNO_SIGM
[U4.61.02]
DCHA_ELNO_SIGM
Handbook of Validation
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Code_Aster ®
Version
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Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
7/20
4
Results of modeling A
4.1 Values
tested
Identification
Moments
Reference
Aster
% difference
xx
With
151.2
151.2
0
xy
With
93.1
93.1
0
xx
With
1.4830 102
1.4830 102
0.002
xy
With
1.3601 102
1.3601102
0.003
p
With
2.055 102
2.055 102
0.001
pxx
With
1.4054 102
1.4054 102
0.002
p
With
1.2981 102
1.2981 102
0.002
xy
xx
B
3.5265 102
3.5325 102
0.170
xy
B
2.0471 102
2.0351 102
0.584
p
B
4.2329 102
4.2329 102
0.001
pxx
B
3.3946 102
3.4006 102
0.176
p
B
2.0250 102
2.0131 102
0.589
xy
as well as the indicators of load-discharge:
Identification
Moments
Reference
Aster
% difference
IND_ENER
With
0.
0
0
IND_SEUIL
With
0.
0
0
IND_ENER
B
3.26 102
3.33 102
2.5
IND_SEUIL
B
9.71 102
9.64 102
0.7
4.2 Notice
The phases A and B are tested. 41 increments of loading are used:
· 1 for phase A,
· 40 for the phase B.
4.3 Parameters
of execution
Version: 5.00.09
Machine:
Obstruction memory:
8 MW
Time CPU To use:
84 seconds
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
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Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
8/20
5 Modeling
B
5.1
Characteristics of modeling
Modeling in plane constraints: C_PLAN
y
N01
N02
N03
N04
X
The loading and the boundary conditions are modelled by:
DDL_IMPO: (NOEUD: N04, DX: 0., DY:0.)
(NOEUD: N02, DX: 0.
)
surface forces imposed (key word FORCE_CONTOUR) on the faces (meshs of skin SEG2)
(1, 2), (2, 4), (4, 3) and (3, 1).
5.2
Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 1 QUAD4, 4 SEG2
5.3 Functionalities
tested
Commands
Keys
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
[U4.23.01]
SY
STAT_NON_LINE
COMP_INCR
RELATION
VMIS_ISOT_LINE
[U4.32.01]
CALC_ELEM
OPTION
EPSI_ELNO_DEPL
[U4.61.02]
RECU_CHAMP
NOM_CHAM
VARI_ELNO_ELGA
[U4.62.01]
CALC_ELEM
OPTION
RADI_ELNO_SIGM
[U4.61.02]
DCHA_ELNO_SIGM
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
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Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
9/20
6
Results of modeling B
6.1 Values
tested
Identification
Moments
Reference
Aster
% difference
xx
With
151.2
151.2
0
xy
With
93.1
93.1
0
xx
With
1.4830 102
1.4830 102
0.002
xy
With
1.3601 102
1.3601102
0.003
p
With
2.055 102
2.055 102
0.001
pxx
With
1.4054 102
1.4054 102
0.002
p
With
1.2981 102
1.2981 102
0.002
xy
xx
B
3.5265 102
3.5325 102
0.170
xy
B
2.0471 102
2.0351 102
0.584
p
B
4.2329 102
4.2329 102
0.001
pxx
B
3.3946 102
3.4006 102
0.176
p
B
2.0250 102
2.0131 102
0.589
xy
as well as the indicators of load-discharge:
Identification
Moments
Reference
Aster
% difference
IND_ENER
With
0.
0
0
IND_SEUIL
With
0.
0
0
IND_ENER
B
3.26 102
3.33 102
2.5
IND_SEUIL
B
9.71 102
9.64 102
0.7
6.2 Notice
The phases A and B are tested. 41 increments of loading are used:
· 1 for phase A,
· 40 for the phase B.
6.3 Parameters
of execution
Version: 5.00.09
Machine:
Obstruction memory:
8 MW
Time CPU To use:
84 seconds
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
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Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
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7 Modeling
C
7.1
Characteristics of modeling
Modeling hull DKT-DKQ
7.2 Geometry
2
N01
N06
N02
MA2
Z
1
4
MA3
0,8 mm
MA1
N03
N05
N04
y
3
0,6 mm
X
Dimensions of the structure do not change compared to the problem of reference, only differs
its orientation.
Co-ordinates of the nodes:
Nodes
X
y
Z
N01
0
0.8
0.6
N02
0
0.2
1.4
N03
0
0
0
N04
0
0.6
0.8
N05
0
0.3
0.4
N06
0
0.5
1
Boundary conditions:
DDL_IMPO: (NOEUD: N04, DY: 0., DZ:0.)
(TOUT: YES DX: 0.)
LIAISON_DDL:
(NOEUD:(N02 N02) DDL:(“DY” “DZ”)
COEF_MULT: (0.75 1.) COEF_IMP: 0. )
Loading:
One imposes surface forces (key word FORCE_ARETE) on the faces (meshs of skin SEG2)
(1,2), (2,4), (4,3) and (3,1).
Specificity DKT and DKQ:
Two layers in the thickness for plasticity.
Handbook of Validation
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Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
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Key:
V6.03.015-C Page:
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7.3
Characteristics of the grid
A number of nodes: 6
A number of meshs and types: 2 TRIA3 and 1 QUAD4
7.4 Values
tested
Displacements tested are those of the problem of reference by taking account of the rotation of
structure.
The generalized strains, stresses and efforts are tested in the reference mark definite user
by command ANGL_REP. The values are thus those given by the problem of reference.
7.5 Functionalities
tested
Commands
Keys
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
[U4.23.01]
SY
AFFE_CARA_ELEM
COQUE
EPAIS
[U4.24.01]
ANGL_REP
AFFE_CHAR_MECA
LIAISON_DDL
[U4.25.01]
FORCE_ARETE
STAT_NON_LINE
COMP_INCR
VMIS_ISOT_LINE
[U4.32.01]
COQUE_NCOU
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
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Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
12/20
8
Results of modeling C
8.1 Values
tested
The values are tested at point A of the way of loading OA. One tests as follows:
Displacements (DEPL). It result easily from the reference solution since the deformation
is homogeneous.
Identification
Reference
Aster
% difference
DY N01
1.86722 102
1.86722 102
0
DZ N01
3.25413 102
3.25413 102
0
DY N06
1.224 102
1.224 102
0
DZ N06
1.88485 102
1.84485 102
0
DY N02
5.8O782 103
5.80782 103
0
DZ N02
4.35586 103
4.35586 103
0
Constraints (SIGM_ELNO_VARI).
Identification
Reference
Aster
% difference
SIXX MA2 N01
1.512 102
1.51199 102
2.27 106
SIXY MA2 N01
93.1
93.1002
2.82 106
SIXX MA1 N03
1.512 102
1.51199 102
2.27 106
SIXY MA1 N03
93.1
93.1002
2.82 106
SIXX MA2 N03
1.512 102
1.51199 102
2.27 106
SIXY MA2 N03
93.1
93.1002
2.82 106
SIXX MA3 N02
1.512 102
1.51199 102
2.27 106
SIXY MA3 N02
93.1
93.1002
2.82 106
Efforts generalized by elements with nodes (SIEF_ELNO_ELGA).
Identification
Reference
Aster
% difference
NXX MA2 N01
3.024 102
3.02399 102
2.27 106
NXY MA2 N01
1.862 102
1.862005 102
2.82 106
NXX MA1 N03
3.024 102
3.02399 102
2.27 106
NXY MA1 N03
1.862 102
1.862005 102
2.82 106
NXX MA2 N03
3.024 102
3.02399 102
2.27 106
NXY MA2 N03
1.862 102
1.862005 102
2.82 106
NXX MA3 N02
3.024 102
3.02399 102
2.27 106
NXY MA3 N02
1.862 102
1.862005 102
2.82 106
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SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
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Key:
V6.03.015-C Page:
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Deformations by element with the nodes starting from displacements (EPSI_ELNO_DEPL).
Identification
Reference
Aster
% difference
EPXX MA2 N01
1.48297 102
1.48296 102
3.65 106
EPYY MA2 N01
7.25977 103
7.25972 103
7.14 106
EPXY MA2 N01
1.36014 102
1.36014 102
2.48 106
EPXX MA1 N03
1.48297 102
1.48296 102
3.65 106
EPYY MA1 N03
7.25977 103
7.25972 103
7.14 106
EPXY MA1 N03
1.36014 102
1.36014 102
2.48 106
EPXX MA2 N03
1.48297 102
1.48296 102
3.65 106
EPYY MA2 N03
7.25977 103
7.25972 103
7.14 106
EPXY MA2 N03
1.36014 102
1.36014 102
2.48 106
EPXX MA3 N02
1.48297 102
1.48296 102
3.65 106
EPYY MA3 N02
7.25977 103
7.25972 103
7.14 106
EPXY MA3 N02
1.36014 102
1.36014 102
2.48 106
EPXX MA3 N04
1.48297 102
1.48296 102
3.65 106
EPYY MA3 N04
7.25977 103
7.25972 103
7.14 106
EPXY MA3 N04
1.36014 102
1.36014 102
2.48 106
Elastic constraints by element with the nodes starting from displacements (use in elasticity)
(SIGM_ELNO_DEPL)
Identification
Reference
Aster
% difference
SIXX MA2 N01
2.71109 103
2.71108 103
3.05 106
SIYY MA2 N01
6.02328 102
6.02320 102
103
SIXY MA2 N01
2.04021 103
2.04021 103
2.48 106
SIXX MA1 N03
2.71109 103
2.71108 103
3.05 106
SIYY MA1 N03
6.02328 102
6.02320 102
103
SIXY MA1 N03
2.04021 103
2.04021 103
2.48 106
SIXX MA2 N03
2.71109 103
2.71108 103
3.05 106
SIYY MA2 N03
6.02328 102
6.02320 102
103
SIXY MA2 N03
2.04021 103
2.04021 103
2.48 106
SIXX MA3 N02
2.71109 103
2.71108 103
3.05 106
SIYY MA3 N02
6.02328 102
6.02320 102
103
SIXY MA3 N02
2.04021 103
2.04021 103
2.48 106
8.2 Parameters
of execution
Version: 4.02.31
Machine: CRAY C90
Obstruction memory:
15.32 MW
Time CPU To use:
26.93 seconds
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
14/20
9 Modeling
D
9.1
Characteristics of modeling
Modeling hull COQUE_3D
9.2 Geometry
N01
N012
N08
N016
N02
2
MA2
N014
MA3
Z
1
4
N010
N09
N017
N05
N07
0,8 mm
N013
y
3
MA1
0,6 mm
N03
N04
X
N011
N06
N015
Dimensions of the structure do not change compared to the problem of reference, only differs
its orientation.
Co-ordinates of the nodes:
Nodes
X
y
Z
N01
0
0.8
0.6
N02
0
0.2
1.4
N03
0
0
0
N04
0
0.6
0.8
N05
0
0.4
0.3
N06
0
0.3
0.4
N07
0
0.2
1.1
N08
0
0.5
1
N09
0
0.1
0.7
N010
0
0.25
0.5
N011
0
0.15
0.2
N012
0
0.65
0.8
N013
0
0.06666
0.466666
N014
0
0.433333
0.533333
N015
0
0.45
0.6
N016
0
0.35
1.2
N017
0
0.05
0.9
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
15/20
Boundary conditions:
DDL_IMPO: (NOEUD: N04, DY: 0., DZ:0.)
(TOUT: YES DX: 0.)
LIAISON_DDL: (NOEUD:(N02 N02) DDL:(“DY” “DZ”)
COEF_MULT: (0.75 1.) COEF_IMP: 0. )
LIAISON_DDL: (NOEUD:(N07 N07) DDL:(“DY” “DZ”)
COEF_MULT: (0.75 1.) COEF_IMP: 0. )
Loading:
One imposes surface forces (key word FORCE_ARETE) on the faces (meshs of skin SEG3) (1,2),
(2,4), (4,3) and (3,1).
9.3
Characteristics of the grid
A number of nodes: 17
A number of meshs and types: 2 TRIA7 and 1 QUAD9
9.4 Values
tested
Displacements tested are those of the problem of reference by taking account of the rotation of
structure.
The generalized strains, stresses and efforts are tested in the reference mark definite user
by command ANGL_REP. The values are thus those given by the problem of reference.
9.5 Functionalities
tested
Commands
Keys
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
[U4.23.01]
SY
AFFE_CARA_ELEM
COQUE
EPAIS
[U4.24.01]
ANGL_REP
AFFE_CHAR_MECA
LIAISON_DDL
[U4.25.01]
FORCE_ARETE
STAT_NON_LINE
COMP_INCR
VMIS_ISOT_LINE
[U4.32.01]
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
16/20
10
Results of modeling D
10.1 Values
tested
The values are tested at point A of the way of loading OA. One tests as follows:
Displacements (DEPL). It result easily from the reference solution since the deformation
is homogeneous.
Identification
Reference
Aster
% difference
DY N01
1.86722 102
1.86722 102
0
DZ N01
3.25413 102
3.25413 102
0
DY N08
1.224 102
1.224 102
0
DZ N08
1.84485 102
1.84485 102
0
DY N02
5.80782 103
5.80782 103
0
DZ N02
4.35586 103
4.35586 103
0
Efforts generalized by elements with nodes (SIEF_ELNO_ELGA).
Identification
Reference
Aster
% difference
NXX MA1 N01
3.024 102
3.02399 102
2.2 106
NXY MA1 N01
1.862 102
1.862005 102
2.9 106
NXX MA1 N03
3.024 102
3.02399 102
2.2 106
NXY MA1 N03
1.862 102
1.862005 102
2.9 106
NXX MA2 N03
3.024 102
3.02399 102
2.2 106
NXY MA2 N03
1.862 102
1.862005 102
2.9 106
NXX MA3 N02
3.024 102
3.02399 102
2.2 106
NXY MA3 N02
1.862 102
1.862005 102
2.9 106
Deformations by element with the nodes starting from displacements (EPSI_ELNO_DEPL).
Identification
Reference
Aster
% difference
EPXX MA1 N01
1.48297 102
1.48296 102
3.24 106
EPYY MA1 N01
7.25977 103
7.25973 103
6.69 106
EPXY MA1 N01
1.36014 102
1.36014 102
2.91 106
EPXX MA1 N03
1.48297 102
1.48296 102
3.24 106
EPYY MA1 N03
7.25977 103
7.25973 103
6.69 106
EPXY MA1 N03
1.36014 102
1.36014 102
2.91 106
EPXX MA2 N03
1.48297 102
1.48296 102
3.24 106
EPYY MA2 N03
7.25977 103
7.25973 103
6.69 106
EPXY MA2 N03
1.36014 102
1.36014 102
2.91 106
EPXX MA3 N02
1.48297 102
1.48296 102
3.24 106
EPYY MA3 N02
7.25977 103
7.25973 103
6.69 106
EPXY MA3 N02
1.36014 102
1.36014 102
2.91 106
EPXX MA3 N04
1.48297 102
1.48296 102
3.24 106
EPYY MA3 N04
7.25977 103
7.25973 103
6.69 106
EPXY MA3 N04
1.36014 102
1.36014 102
2.91 106
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
17/20
Elastic constraints by element with the nodes starting from displacements (use in elasticity)
(SIGM_ELNO_DEPL)
Identification
Reference
Aster
% difference
SIXX MA1 N01
2.71109 103
2.71108 103
2.64 106
SIYY MA1 N01
6.02328 102
6.02321 102
103
SIXY MA1 N01
2.04021 103
2.04021 103
2.91 106
SIXX MA1 N03
2.71109 103
2.71108 103
2.64 106
SIYY MA1 N03
6.02328 102
6.02321 102
103
SIXY MA1 N03
2.04021 103
2.04021 103
2.91 106
SIXX MA2 N03
2.71109 103
2.71108 103
2.64 106
SIYY MA2 N03
6.02328 102
6.02321 102
103
SIXY MA2 N03
2.04021 103
2.04021 103
2.91 106
SIXX MA3 N02
2.71109 103
2.71108 103
2.64 106
SIYY MA3 N02
6.02328 102
6.02321 102
103
SIXY MA3 N02
2.04021 103
2.04021 103
2.91 106
10.2 Parameters
of execution
Version: 4.02.31
Machine: CRAY C90
Obstruction memory:
15.32 MW
Time CPU To use:
10.11 seconds
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
18/20
11 Modeling
E
11.1 Characteristics of modeling
Modeling hull 3D (MEC3TR7H)
y
N08
N01
N02
N010
N05
N07
N09
N03
N06 N04
X
Boundary conditions:
DDL_IMPO:
(NOEUD: N04, DX: 0., DY:0.)
(NOEUD: N02, DX: 0.
)
(NOEUD: NO7, DX:0.)
(NOEUD: (N01, N02, N03) DZ:0.)
Loading
FORCE_NODALE:
(NOEUD: N01, FX: - 9.683333, FY:- 15.516666)
(NOEUD: N02, FX: 15.516666, FY: 15.516666)
(NOEUD: N03, FX:- 40.716666, FY:- 15.516666)
(NOEUD: N04, FX:- 15.516666, FY: 15.516666)
(NOEUD: N05, FX:- 100.8, FY:- 62.066666)
(NOEUD: N06, FX:- 62.066666)
(NOEUD: N07, FX: 62.066666)
(NOEUD: N08, FX: 62.066666)
11.2 Characteristics of the grid
A number of nodes: 11
A number of meshs and types: 2 TRIA7
11.3 Functionalities
tested
Commands
Keys
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
[U4.23.01]
SY
AFFE_CARA_ELEM
COQUE
EPAIS
[U4.24.01]
STAT_NON_LINE
COMP_INCR
VMIS_ISOT_LINE
[U4.32.01]
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
19/20
12
Results of modeling E
12.1 Values
tested
The displacement of the N01 node results easily from the reference solution since the deformation
D
D
is homogeneous. It is tested not of A but also in a point O
(=1238. = 762.) way
OA. The cumulated plastic deformation is also tested.
Identification
Moments
Reference
Aster
% difference
DX N01
O
6.349 104
6.349 104
0
DY N01
O
1.207 103
1.207 103
0
DY N01
With
3.431 102
3.446 102
0.4
p
With
2.055 10-2
2.055 10-2
0.
12.2 Notice
Only portion OA of the way of the loading is actually tested.
12.3 Parameters
of execution
Version: 4.01.05
Machine: CRAY C98
Obstruction memory:
8 MW
Time CPU To use:
8.5 seconds
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNP15 Plaque in traction-shearing - Von Mises
Date:
01/12/98
Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C Page:
20/20
13
Summary of the results
The results are identical whatever the selected modeling. The results are close to
reference solution since the variations are overall lower than 0.6%.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A