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Titrate:
SSNP15 Plates 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
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.015
SSNP15 - Plate 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 tensile load of shearing.
The main interest of this test lies in the nonradial character of the loading.
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Titrate:
SSNP15 Plates in traction-shearing - Von Mises
Date:
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Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C
Page:
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V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
y
X
1
2
3
4
1 mm
1 mm
1.2
Material properties
Elastoplastic law of behavior to linear kinematic work hardening.
Y
E
E
T
E
= 195.000 MPa
= 0.3
Y
= 181 MPa
E
T
= 1930 MPA
1.3
Boundary conditions and loadings
The plate is locked 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:
0
With
B
D
D
D
To 151.2
93.1
B 257.2
33.1
D
(MPa)
(MPa)
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Titrate:
SSNP15 Plates 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
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
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 conventional 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:
With
0
WITH B
0
B
3
Way of loading
With
0
(123,8; 76,23)
To (151,2; 93,1)
B
0
(158,23; 89,12)
B (257,2; 33,1)
Numerical values
(
)
;
O-A
0
charge elastic
With
0
- A charges plastic
A-B
0
discharge
B
0
- B charges plastic
Phases of loading
2.1.1 Step of resolution
Mechanically, it is about a test 0D controlled in stress, the material being elastoplastic with criterion
of von Mises and linear isotropic work hardening. For a loading controlled in stress, one determines
easily cumulated plastic deformation:
()
F
p
R p
p
R
eq
y
eq
y
,
=
-
-
=
-
0
in load
éq 2.1.1-1
The integration of the plastic deformation is of course more delicate. The equation of flow is written:
~
~
p
p
=
=
3
2
3
2
p
R
eq
eq
eq

in load
éq 2.1.1-2
Lastly, one will deduce the deformation via the relation from state:
=
+
=
+
=
+
-
p
E
1
2
:
µ
xx
xx
p
xy
xy
p
E
and
éq 2.1.1-3
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Titrate:
SSNP15 Plates in traction-shearing - Von Mises
Date:
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Key:
V6.03.015-C
Page:
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V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
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
2 p
eq
~
éq 2.1.2-1
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
2
µ
= 150.000 MPa
R'
= 1.949, 29 Mpa
One obtains:
p (A)
= 2, 0547 10
­ 2
pxx
(A)
= 1, 4054 10
­ 2
xx
(A)
= 1, 4830 10
­ 2
pxy
(A)
= 1, 2981 10
­ 2
xy
(A)
= 1, 3601 10
­ 2
2.1.3 Processing of the phase of nonradial loading
In the phase of loading nonradial B0 - B, one can parameterize the way of stress by:
(
)
()
Q
Q
Q
=
+
-
B
B
B
0
0
fixed direction
with
0
1
éq 2.1.3-1
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:
(
)
= +
=
=
+
-
I
Q
Q
eq
B
B
3
0
0
0
and
fixed direction
()
éq 2.1.3-2
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:
[]
[
]
()
2
3
1
2
0
1
0
1
0
1
2
0
=
=
-
-
R
dq
dq
eq
eq
eq
eq
B
B
0
1
p
~
ln (
) ~
~
ln
~
~

The adoption of the complex plan allows an easy calculation of the last integral:
()
()
()
()
()
ln
ln
ln
ln
Re
ln
Re
ln ()
eq
B
B
dq
dq
dq
dq
dq
2
0
1
2
2
0
0
1
0
1
0
1
0
1
0
1
=
=
+
=




=
-
-




Finally, the increment of plastic deformation on the B0 way - B is worth:
[]
[
]
(
)
p
B
B
eq
B
B
B
B
B
B
B
B
R
R
0
0
0
0
0
3
2
3
2
=
-
-
-




-
ln (
) ~
Re
ln ()
~
~
éq 2.1.3-4
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Titrate:
SSNP15 Plates 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
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V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
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 10
­ 2
pxx
(B)
= 3, 3946 10
­ 2
xx
(B)
= 3, 5265 10
­ 2
One obtains:
pxy
(B)
= 2, 0250 10
­ 2
xy
(B)
= 2, 0471 10
­ 2
One will be interested in the values of the stresses, 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 the Mechanics. Guide validation of the software packages of structural analysis
(VPCS). Technical AFNOR, 1990.
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Titrate:
SSNP15 Plates in traction-shearing - Von Mises
Date:
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Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C
Page:
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V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
HEXA8
Z
X
y
N07
N05
N06
N08
N03
N01
N02
N04
The loading and the boundary conditions are modelized by:
DDL_IMPO: (NODE: N04, DX: 0., DY:0.)
DDL_IMPO: (NODE: N08, DX: 0., DY:0., DZ:0.)
DDL_IMPO: (NODE: N02, DX: 0.)
DDL_IMPO: (NODE: N06, DX: 0.)
imposed surface forces (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 mesh
A number of nodes: 8
A number of meshs and types: 1 HEXA8, 4 QUAD4
3.3 Functionalities
tested
Controls
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
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Titrate:
SSNP15 Plates 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
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
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 10
­ 2
1.4830 10
­ 2
­ 0.002
xy
With
1.3601 10
­ 2
1.360110
­ 2
0.003
p
With
2.055 10
­ 2
2.055 10
­ 2
0.001
p
xx
With
1.4054 10
­ 2
1.4054 10
­ 2
0.002
xy
p
With
1.2981 10
­ 2
1.2981 10
­ 2
­ 0.002
xx
B
3.5265 10
­ 2
3.5325 10
­ 2
0.170
xy
B
2.0471 10
­ 2
2.0351 10
­ 2
­ 0.584
p
B
4.2329 10
­ 2
4.2329 10
­ 2
0.001
p
xx
B
3.3946 10
­ 2
3.4006 10
­ 2
0.176
xy
p
B
2.0250 10
­ 2
2.0131 10
­ 2
­ 0.589
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 10
­ 2
3.33 10
­ 2
2.5
IND_SEUIL
B
9.71 10
­ 2
9.64 10
­ 2
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:
Overall dimension memory:
8 MW
Time CPU To use:
84 seconds
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SSNP15 Plates in traction-shearing - Von Mises
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E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C
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V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
Modeling in plane stresses:
C_PLAN
y
X
N01
N02
N03
N04
The loading and the boundary conditions are modelized by:
DDL_IMPO: (NODE: N04, DX: 0., DY:0.)
(NODE: N02, DX: 0.
)
imposed surface forces (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 mesh
A number of nodes: 4
A number of meshs and types: 1 QUAD4, 4 SEG2
5.3 Functionalities
tested
Controls
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
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SSNP15 Plates in traction-shearing - Von Mises
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V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
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 10
­ 2
1.4830 10
­ 2
­ 0.002
xy
With
1.3601 10
­ 2
1.360110
­ 2
0.003
p
With
2.055 10
­ 2
2.055 10
­ 2
0.001
p
xx
With
1.4054 10
­ 2
1.4054 10
­ 2
0.002
xy
p
With
1.2981 10
­ 2
1.2981 10
­ 2
­ 0.002
xx
B
3.5265 10
­ 2
3.5325 10
­ 2
0.170
xy
B
2.0471 10
­ 2
2.0351 10
­ 2
­ 0.584
p
B
4.2329 10
­ 2
4.2329 10
­ 2
0.001
p
xx
B
3.3946 10
­ 2
3.4006 10
­ 2
0.176
xy
p
B
2.0250 10
­ 2
2.0131 10
­ 2
­ 0.589
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 10
­ 2
3.33 10
­ 2
2.5
IND_SEUIL
B
9.71 10
­ 2
9.64 10
­ 2
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:
Overall dimension memory:
8 MW
Time CPU To use:
84 seconds
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SSNP15 Plates in traction-shearing - Von Mises
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V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
7 Modeling
C
7.1
Characteristics of modeling
Modeling hull DKT-DKQ
7.2 Geometry
0,8 mm
0,6 mm
y
X
1
2
3
4
Z
N01
N02
N03
N04
MA2
MA1
N05
N06
MA3
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: (NODE: N04, DY: 0., DZ:0.)
(ALL: YES DX: 0.)
LIAISON_DDL:
(NODE:(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.
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SSNP15 Plates in traction-shearing - Von Mises
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HI-75/98/040 - Ind A
7.3
Characteristics of the mesh
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 the control
ANGL_REP
. The values are thus those given by the problem of reference.
7.5 Functionalities
tested
Controls
Keys
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
[U4.23.01]
SY
AFFE_CARA_ELEM
HULL
THICK
[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
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Titrate:
SSNP15 Plates in traction-shearing - Von Mises
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E. LORENTZ, P. MIALON, P. MASSIN
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V6.03.015-C
Page:
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Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
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 10
­ 2
1.86722 10
­ 2
0
DZ N01
­ 3.25413 10
­ 2
­ 3.25413 10
­ 2
0
DY N06
1.224 10
­ 2
1.224 10
­ 2
0
DZ N06
­ 1.88485 10
­ 2
­ 1.84485 10
­ 2
0
DY N02
5.8O782 10
­ 3
5.80782 10
­ 3
0
DZ N02
­ 4.35586 10
­ 3
­ 4.35586 10
­ 3
0
Stresses (
SIGM_ELNO_VARI
).
Identification
Reference
Aster
% difference
SIXX MA2 N01
1.512 10
2
1.51199 10
2
­ 2.27 10
­ 6
SIXY MA2 N01
93.1
93.1002
2.82 10
­ 6
SIXX MA1 N03
1.512 10
2
1.51199 10
2
­ 2.27 10
­ 6
SIXY MA1 N03
93.1
93.1002
2.82 10
­ 6
SIXX MA2 N03
1.512 10
2
1.51199 10
2
­ 2.27 10
­ 6
SIXY MA2 N03
93.1
93.1002
2.82 10
­ 6
SIXX MA3 N02
1.512 10
2
1.51199 10
2
­ 2.27 10
­ 6
SIXY MA3 N02
93.1
93.1002
2.82 10
­ 6
Efforts generalized by elements with the nodes (
SIEF_ELNO_ELGA
).
Identification
Reference
Aster
% difference
NXX MA2 N01
3.024 10
2
3.02399 10
2
­ 2.27 10
­ 6
NXY MA2 N01
1.862 10
2
1.862005 10
2
2.82 10
­ 6
NXX MA1 N03
3.024 10
2
3.02399 10
2
­ 2.27 10
­ 6
NXY MA1 N03
1.862 10
2
1.862005 10
2
2.82 10
­ 6
NXX MA2 N03
3.024 10
2
3.02399 10
2
­ 2.27 10
­ 6
NXY MA2 N03
1.862 10
2
1.862005 10
2
2.82 10
­ 6
NXX MA3 N02
3.024 10
2
3.02399 10
2
­ 2.27 10
­ 6
NXY MA3 N02
1.862 10
2
1.862005 10
2
2.82 10
­ 6
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Titrate:
SSNP15 Plates in traction-shearing - Von Mises
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Author (S):
E. LORENTZ, P. MIALON, P. MASSIN
Key:
V6.03.015-C
Page:
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Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Deformations by element with the nodes starting from displacements (
EPSI_ELNO_DEPL
).
Identification
Reference
Aster
% difference
EPXX MA2 N01
1.48297 10
­ 2
1.48296 10
­ 2
­ 3.65 10
­ 6
EPYY MA2 N01
­ 7.25977 10
­ 3
­ 7.25972 10
­ 3
­ 7.14 10
­ 6
EPXY MA2 N01
1.36014 10
­ 2
1.36014 10
­ 2
2.48 10
­ 6
EPXX MA1 N03
1.48297 10
­ 2
1.48296 10
­ 2
­ 3.65 10
­ 6
EPYY MA1 N03
­ 7.25977 10
­ 3
­ 7.25972 10
­ 3
­ 7.14 10
­ 6
EPXY MA1 N03
1.36014 10
­ 2
1.36014 10
­ 2
2.48 10
­ 6
EPXX MA2 N03
1.48297 10
­ 2
1.48296 10
­ 2
­ 3.65 10
­ 6
EPYY MA2 N03
­ 7.25977 10
­ 3
­ 7.25972 10
­ 3
­ 7.14 10
­ 6
EPXY MA2 N03
1.36014 10
­ 2
1.36014 10
­ 2
2.48 10
­ 6
EPXX MA3 N02
1.48297 10
­ 2
1.48296 10
­ 2
­ 3.65 10
­ 6
EPYY MA3 N02
­ 7.25977 10
­ 3
­ 7.25972 10
­ 3
­ 7.14 10
­ 6
EPXY MA3 N02
1.36014 10
­ 2
1.36014 10
­ 2
2.48 10
­ 6
EPXX MA3 N04
1.48297 10
­ 2
1.48296 10
­ 2
­ 3.65 10
­ 6
EPYY MA3 N04
­ 7.25977 10
­ 3
­ 7.25972 10
­ 3
­ 7.14 10
­ 6
EPXY MA3 N04
1.36014 10
­ 2
1.36014 10
­ 2
2.48 10
­ 6
Elastic stresses by element with the nodes starting from displacements (use in elasticity)
(
SIGM_ELNO_DEPL
)
Identification
Reference
Aster
% difference
SIXX MA2 N01
2.71109 10
3
2.71108 10
3
­ 3.05 10
­ 6
SIYY MA2 N01
­ 6.02328 10
2
­ 6.02320 10
2
­ 10
­ 3
SIXY MA2 N01
2.04021 10
3
2.04021 10
3
2.48 10
­ 6
SIXX MA1 N03
2.71109 10
3
2.71108 10
3
­ 3.05 10
­ 6
SIYY MA1 N03
­ 6.02328 10
2
­ 6.02320 10
2
­ 10
­ 3
SIXY MA1 N03
2.04021 10
3
2.04021 10
3
2.48 10
­ 6
SIXX MA2 N03
2.71109 10
3
2.71108 10
3
­ 3.05 10
­ 6
SIYY MA2 N03
­ 6.02328 10
2
­ 6.02320 10
2
­ 10
­ 3
SIXY MA2 N03
2.04021 10
3
2.04021 10
3
2.48 10
­ 6
SIXX MA3 N02
2.71109 10
3
2.71108 10
3
­ 3.05 10
­ 6
SIYY MA3 N02
­ 6.02328 10
2
­ 6.02320 10
2
­ 10
­ 3
SIXY MA3 N02
2.04021 10
3
2.04021 10
3
2.48 10
­ 6
8.2 Parameters
of execution
Version: 4.02.31
Machine: CRAY C90
Overall dimension memory:
15.32 MW
Time CPU To use:
26.93 seconds
background image
Code_Aster
®
Version
4.0
Titrate:
SSNP15 Plates 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
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
9 Modeling
D
9.1
Characteristics of modeling
Modeling hull COQUE_3D
9.2 Geometry
0,8 mm
0,6 mm
y
X
1
2
3
4
Z
N01
N02
N03
N04
MA2
MA1
N05
N06
MA3
N07
N08
N09
N017
N016
N015
N011
N012
N014
N013
N010
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
background image
Code_Aster
®
Version
4.0
Titrate:
SSNP15 Plates 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
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Boundary conditions:
DDL_IMPO: (NODE: N04, DY: 0., DZ:0.)
(ALL: YES DX: 0.)
LIAISON_DDL: (NODE:(N02 N02) DDL:(“DY” “DZ”)
COEF_MULT: (0.75 1.) COEF_IMP: 0. )
LIAISON_DDL: (NODE:(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 mesh
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 the control
ANGL_REP
. The values are thus those given by the problem of reference.
9.5 Functionalities
tested
Controls
Keys
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
[U4.23.01]
SY
AFFE_CARA_ELEM
HULL
THICK
[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]
background image
Code_Aster
®
Version
4.0
Titrate:
SSNP15 Plates 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
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
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 10
­ 2
1.86722 10
­ 2
0
DZ N01
­ 3.25413 10
­ 2
­ 3.25413 10
­ 2
0
DY N08
1.224 10
­ 2
1.224 10
­ 2
0
DZ N08
­ 1.84485 10
­ 2
­ 1.84485 10
­ 2
0
DY N02
5.80782 10
­ 3
5.80782 10
­ 3
0
DZ N02
­ 4.35586 10
­ 3
­ 4.35586 10
­ 3
0
Efforts generalized by elements with the nodes (
SIEF_ELNO_ELGA
).
Identification
Reference
Aster
% difference
NXX MA1 N01
3.024 10
2
3.02399 10
2
­ 2.2 10
­ 6
NXY MA1 N01
1.862 10
2
1.862005 10
2
2.9 10
­ 6
NXX MA1 N03
3.024 10
2
3.02399 10
2
­ 2.2 10
­ 6
NXY MA1 N03
1.862 10
2
1.862005 10
2
2.9 10
­ 6
NXX MA2 N03
3.024 10
2
3.02399 10
2
­ 2.2 10
­ 6
NXY MA2 N03
1.862 10
2
1.862005 10
2
2.9 10
­ 6
NXX MA3 N02
3.024 10
2
3.02399 10
2
­ 2.2 10
­ 6
NXY MA3 N02
1.862 10
2
1.862005 10
2
2.9 10
­ 6
Deformations by element with the nodes starting from displacements (
EPSI_ELNO_DEPL
).
Identification
Reference
Aster
% difference
EPXX MA1 N01
1.48297 10
­ 2
1.48296 10
­ 2
­ 3.24 10
­ 6
EPYY MA1 N01
­ 7.25977 10
­ 3
­ 7.25973 10
­ 3
­ 6.69 10
­ 6
EPXY MA1 N01
1.36014 10
­ 2
1.36014 10
­ 2
2.91 10
­ 6
EPXX MA1 N03
1.48297 10
­ 2
1.48296 10
­ 2
­ 3.24 10
­ 6
EPYY MA1 N03
­ 7.25977 10
­ 3
­ 7.25973 10
­ 3
­ 6.69 10
­ 6
EPXY MA1 N03
1.36014 10
­ 2
1.36014 10
­ 2
2.91 10
­ 6
EPXX MA2 N03
1.48297 10
­ 2
1.48296 10
­ 2
­ 3.24 10
­ 6
EPYY MA2 N03
­ 7.25977 10
­ 3
­ 7.25973 10
­ 3
­ 6.69 10
­ 6
EPXY MA2 N03
1.36014 10
­ 2
1.36014 10
­ 2
2.91 10
­ 6
EPXX MA3 N02
1.48297 10
­ 2
1.48296 10
­ 2
­ 3.24 10
­ 6
EPYY MA3 N02
­ 7.25977 10
­ 3
­ 7.25973 10
­ 3
­ 6.69 10
­ 6
EPXY MA3 N02
1.36014 10
­ 2
1.36014 10
­ 2
2.91 10
­ 6
EPXX MA3 N04
1.48297 10
­ 2
1.48296 10
­ 2
­ 3.24 10
­ 6
EPYY MA3 N04
­ 7.25977 10
­ 3
­ 7.25973 10
­ 3
­ 6.69 10
­ 6
EPXY MA3 N04
1.36014 10
­ 2
1.36014 10
­ 2
2.91 10
­ 6
background image
Code_Aster
®
Version
4.0
Titrate:
SSNP15 Plates 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
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Elastic stresses by element with the nodes starting from displacements (use in elasticity)
(
SIGM_ELNO_DEPL
)
Identification
Reference
Aster
% difference
SIXX MA1 N01
2.71109 10
3
2.71108 10
3
­ 2.64 10
­ 6
SIYY MA1 N01
­ 6.02328 10
2
­ 6.02321 10
2
­ 10
­ 3
SIXY MA1 N01
2.04021 10
3
2.04021 10
3
2.91 10
­ 6
SIXX MA1 N03
2.71109 10
3
2.71108 10
3
­ 2.64 10
­ 6
SIYY MA1 N03
­ 6.02328 10
2
­ 6.02321 10
2
­ 10
­ 3
SIXY MA1 N03
2.04021 10
3
2.04021 10
3
2.91 10
­ 6
SIXX MA2 N03
2.71109 10
3
2.71108 10
3
­ 2.64 10
­ 6
SIYY MA2 N03
­ 6.02328 10
2
­ 6.02321 10
2
­ 10
­ 3
SIXY MA2 N03
2.04021 10
3
2.04021 10
3
2.91 10
­ 6
SIXX MA3 N02
2.71109 10
3
2.71108 10
3
­ 2.64 10
­ 6
SIYY MA3 N02
­ 6.02328 10
2
­ 6.02321 10
2
­ 10
­ 3
SIXY MA3 N02
2.04021 10
3
2.04021 10
3
2.91 10
­ 6
10.2 Parameters
of execution
Version: 4.02.31
Machine: CRAY C90
Overall dimension memory:
15.32 MW
Time CPU To use:
10.11 seconds
background image
Code_Aster
®
Version
4.0
Titrate:
SSNP15 Plates 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
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
11 Modeling
E
11.1 Characteristics of modeling
Modeling hull 3D (MEC3TR7H)
y
X
N01
N02
N03
N04
N08
N07
N06
N05
N09
N010
Boundary conditions:
DDL_IMPO:
(NODE: N04, DX: 0., DY:0.)
(NODE: N02, DX: 0.
)
(NODE: NO7, DX:0.)
(NODE: (N01, N02, N03) DZ:0.)
Loading
FORCE_NODALE:
(NODE: N01, FX: - 9.683333, FY:- 15.516666)
(NODE: N02, FX: 15.516666, FY: 15.516666)
(NODE: N03, FX:- 40.716666, FY:- 15.516666)
(NODE: N04, FX:- 15.516666, FY: 15.516666)
(NODE: N05, FX:- 100.8, FY:- 62.066666)
(NODE: N06, FX:- 62.066666)
(NODE: N07, FX: 62.066666)
(NODE: N08, FX: 62.066666)
11.2 Characteristics of the mesh
A number of nodes: 11
A number of meshs and types: 2 TRIA7
11.3 Functionalities
tested
Controls
Keys
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
[U4.23.01]
SY
AFFE_CARA_ELEM
HULL
THICK
[U4.24.01]
STAT_NON_LINE
COMP_INCR
VMIS_ISOT_LINE
[U4.32.01]
background image
Code_Aster
®
Version
4.0
Titrate:
SSNP15 Plates 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
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
12
Results of modeling E
12.1 Values
tested
The displacement of the N01 node results easily from the reference solution since the deformation
is homogeneous. It is tested not of A but also in a point
(
)
=
=
O
D
D
123 8
76 2
.
.
way
OA. The cumulated plastic deformation is also tested.
Identification
Moments
Reference
Aster
% difference
DX N01
O
­ 6.349 10
­ 4
­ 6.349 10
­ 4
0
DY N01
O
­ 1.207 10
­ 3
­ 1.207 10
­ 3
0
DY N01
With
­ 3.431 10
­ 2
­ 3.446 10
­ 2
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
Overall dimension memory:
8 MW
Time CPU To use:
8.5 seconds
background image
Code_Aster
®
Version
4.0
Titrate:
SSNP15 Plates 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
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
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%.