Code_Aster
®
Version
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Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
02/11/05
Author (S):
J. ANGLES
Key
:
V3.04.135-B
Page:
1/14
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
V3.04.135 document
SSLV135 Endommagement by fatigue under
alternate biaxial loading
Summary:
One presents a test here having an analytical reference [bib1]. The geometry treated here is a cube without defect
with which one carries out a linear elastic mechanical calculation followed calculation of the plan of shearing criticizes in
each point of Gauss and in each node.
Each of four modelings tests a criterion:
·
modeling a: criterion MATAKE;
·
modeling b: criterion DANG_VAN_MODI_AC;
·
modeling C: criterion DOMM_MAXI;
·
modeling D: criterion DANG_VAN_MODI_AV,
·
modeling E: criterion FATEMI_SOCIE.
The first two criteria are said “to plan of critical shearing”, they are adapted to the loadings
periodicals. The last two criteria can be qualified criteria “in plan of critical damage”, they
can be used when the loading is not periodical.
Code_Aster
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Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
02/11/05
Author (S):
J. ANGLES
Key
:
V3.04.135-B
Page:
2/14
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
The cube has 10 mm on side.
1.2
Material properties
Young modulus: E = 200000 MPa
Poisson's ratio:
= 0.3
Ultimate stress:
0
.
850
=
U
MPa
Curve of Wöhler (alternate traction and compression controlled in stress):
Half amplitude of stress
(MPa)
138.0 152.0 165.0 180.0 200.0 250.0 295.0
A number of cycles
1.0E+6 0.5E+
6
0.2E+
6
0.1E+
6
0.05E+
6
0.02E+
6
12.0E+
4
Half amplitude of stress
(MPa)
305.0 340.0 430.0 540.0 690.0 930.0 1210.0
A number of cycles
10.0E+
4
5.0E+
3
2.0E+
3
1.0E+
3
5.0E+2 2.0E+2 1.0E+2
Half amplitude of stress
(MPa)
1590.0 2210.0 2900.0
A number of cycles
50.0
20.0
10.0
Table 1.2-1: Curve of Wöhler
P1
P2
P4
P3
P8
P6
P5
P7
Face 1
(above)
Face 4
(on the right-hand side)
Face 2
(below)
Face 3
(on the left-hand side)
Face 6
(in front of)
Face 5
(behind)
X
Y
Z
has
= 10 mm have
P1
P2
P4
P3
P8
P6
P5
P7
P1
P2
P4
P3
P8
P6
P5
P7
Face 1
(above)
Face 4
(on the right-hand side)
Face 2
(below)
Face 3
(on the left-hand side)
Face 6
(in front of)
Face 5
(behind)
X
Y
Z
X
Y
Z
has
= 10 mm have
Code_Aster
®
Version
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Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
02/11/05
Author (S):
J. ANGLES
Key
:
V3.04.135-B
Page:
3/14
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V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
1.3
Boundary conditions and loadings
·
Displacements according to axis X of face 3 are locked (DX=0.0).
·
Displacements according to the axis Y of face 2 are locked (DY=0.0).
·
Displacements of the P3 point are locked according to axis Z (DZ=0.0).
·
We apply an alternate biaxial loading (traction and compression) according to axes X and Y.
Fx (T) represents the alternate efforts applied to face 4 according to axis X and Fy (T) represents them
alternate efforts applied to face 1 according to axis Y.
Loading for modelings A and b:
Loading for modelings C and D:
1.4 Conditions
initial
Without object for a static analysis.
Fx (T)
T
Fy (T)
100N
200N
0
- 100N
- 200N
1s
2s
Fx (T)
T
Fy (T)
100N
200N
0
- 100N
- 200N
Fx (T)
T
Fy (T)
100N
200N
0
- 100N
- 200N
1s
2s
Code_Aster
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Version
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Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
02/11/05
Author (S):
J. ANGLES
Key
:
V3.04.135-B
Page:
4/14
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
In the case of an alternate biaxial loading where the pressures applied are such as:
y
X
=
,
with
1
>
and
0
<
, it is shown [bib1] that it half amplitude of maximum shearing
(
)
4
2
y
X
+
=
, where
2
X
and
2
y
represent the half amplitudes of stresses
applied according to axes'
X
and
y
. Moreover, there are two critical plans in which shearing
is maximum:
2.2
Results of reference for modelings A and B
See the references [bib2] and [R7.04.01].
Half amplitude of maximum shearing:
2
X
(MPa)
2
y
(MPa)
2
(MPa)
100.200.150
Note:
The half amplitude of maximum shearing is identical for the two critical plans.
Normal vectors in the two critical plans:
1
N
2
N
Component
X
2
1
-
2
1
Component
y
2
1
2
1
Component
Z
0
0
Normal maximum stresses in the fields of the normals
1
N
and
2
N
:
MPa
NR
50
)
(
1
max
=
N
and
MPa
NR
50
)
(
2
max
=
N
.
X
Y
Z
Two plans of maximum shearing
N
1
N
2
X
Y
Z
X
Y
Z
Two plans of maximum shearing
N
1
N
1
N
2
N
2
N
2
N
1
Code_Aster
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Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
02/11/05
Author (S):
J. ANGLES
Key
:
V3.04.135-B
Page:
5/14
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
Hydrostatic pressure maximum, independent with respect to the plans of normals
1
N
and
2
N
:
MPa
P
33333
,
33
=
.
Normal mean stresses in the fields of the normals
1
N
and
2
N
:
MPa
NR
m
0
)
(
1
=
N
and
MPa
NR
m
0
)
(
2
=
N
.
Normal maximum deformations in the fields of the normals
1
N
and
2
N
:
4
1
max
10
75
,
1
)
(
-
=
N
and
4
2
max
10
75
,
1
)
(
-
=
N
Normal average deformations in the fields of the normals
1
N
and
2
N
:
0
)
(
1
=
N
m
and
0
)
(
2
=
N
m
.
Criterion of MATAKE
2
,
1
,
)
(
2
)
(
max
=
+
I
B
NR
has
I
I
N
N
where
1
=
has
and
2
=
B
.
Equivalent stresses within the meaning of MATAKE in the fields of the normals
1
N
and
2
N
:
2
,
1
,
)
(
2
)
(
)
(
max
=
+
=
I
T
F
NR
has
I
I
I
eq
N
N
N
where
F
and
T
represent, respectively, the limit of endurance in alternating bending and the limit
of endurance in alternate torsion. Here
T
F
is equal to
5
,
1
. Consequently we have:
MPa
eq
300
)
(
1
=
N
and
MPa
eq
300
)
(
2
=
N
.
Numbers of cycles to the rupture in the fields of the normals
1
N
and
2
N
:
From the curve of Wöhler, cf [Table 1.2-1], and equivalent stresses within the meaning of
MATAKE, we obtain:
10946
)
(
)
(
2
1
=
=
N
N
Cr
Cr
Nb
Nb
cycles.
Damage in the fields of the normals
1
N
and
2
N
:
5
2
1
10
13565
9
)
(
)
(
-
,
ENDO
ENDO
=
=
N
N
.
Criterion of Dang Van adapted to the periodic loadings:
DANG_VAN_MODI_AC
2
,
1
,
2
)
(
=
+
I
B
P
has
I
N
where
1
=
has
and
2
=
B
.
Code_Aster
®
Version
8.2
Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
02/11/05
Author (S):
J. ANGLES
Key
:
V3.04.135-B
Page:
6/14
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
Equivalent stresses within the meaning of DANG VAN in the fields of the normals
1
N
and
2
N
:
2
,
1
,
2
)
(
)
(
=
+
=
I
T
C
P
has
I
I
eq
N
N
where
C
and
T
represent, respectively, the limit of endurance in alternate shearing and the limit
of endurance in alternate traction and compression. Here
T
C
is equal to
5
,
1
. Consequently we have:
MPa
eq
275
)
(
1
=
N
and
MPa
eq
275
)
(
2
=
N
.
Numbers of cycles to the rupture in the fields of the normals
1
N
and
2
N
From the curve of Wöhler, cf [Table 1.2-1], and equivalent stresses within the meaning of DANG
VAN, we obtain:
14903
)
(
)
(
2
1
=
=
N
N
Cr
Cr
Nb
Nb
cycles.
Damage in the fields of the normals
1
N
and
2
N
:
5
2
1
10
709959
,
6
)
(
)
(
-
ENDO
ENDO
=
=
N
N
.
2.3
Results of reference for modelings C and D
See the references [bib2] and [R7.04.01].
Half amplitude of stress:
2
X
(MPa)
2
y
(MPa)
100 200
Criterion of MATAKE adapted to the nonperiodic loadings: DOMM_MAXI
For this criterion there are no analytical results.
Criterion of Dang Van adapted to the nonperiodic loadings:
DANG_VAN_MODI_AV
For this criterion there are no analytical results.
Code_Aster
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Version
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Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
02/11/05
Author (S):
J. ANGLES
Key
:
V3.04.135-B
Page:
7/14
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling 3D: 125 quadratic elements of volume:HEXA8.
Mesh of the cube made with GIBI 2000
Appear of the mesh of the cube
Test criterion MATAKE.
3.2
Characteristics of the mesh
The mesh of the cube was obtained starting from the version 2000 of maillor GIBI.
A number of nodes: 216
A number of meshs: 465
Code_Aster
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Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
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Author (S):
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Key
:
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Page:
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V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
3.3 Functionalities
tested
Controls Options
LIRE_MAILLAGE
DEFI_GROUP CREA_GROUP_NO
CREA_GROUP_MA
DEFI_FONCTION NOM_PARA
Interpol
“SIGM”
“LOG”
DEFI_FONCTION NOM_PARA
“INST”
DEFI_MATERIAU ELAS
TIRE
CISA_PLAN_CRIT
DEFI_LIST_REEL
“MECHANICAL” AFFE_MODELE
“3D”
AFFE_MATERIAU ALL
AFFE_CHAR_MECA DDL_IMPO
FACE_IMPO
FORCE_FACE
GROUP_NO
GROUP_MA
GROUP_MA
STAT_NON_LINE
MECA_STATIQUE
CALC_FATIGUE TYPE_CALCUL
OPTION
TYPE_CHARGE
RESULT
CHAM_MATER
GROUP_MA
GROUP_NO
MESH
CRITERION
METHOD
“FATIGUE_MULTI”
“DOMA_ELGA”
“DOMA_NOEUD”
“PERIODIC”
GROUND
CHECHMATE
“FACE1”, “FACE2”, “FACE3”
“FACE4”, “FACE5”, “FACE6”
“FACE4”, “FACE5”, “FACE6”
CUBIC
“MATAKE”
“CERCLE_EXACT”
Code_Aster
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Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
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Author (S):
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Key
:
V3.04.135-B
Page:
9/14
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
4
Results of modeling A
4.1 Values
tested
Identification
Type of value
Reference
Aster Variation
(%)
Nodes:N1;N206;
Net: M60,
Not Gauss: 3
xx
(Moment: 3)
1.00000E+02
1.00000E+02
0.0
,
yy
(Moment: 3)
2.00000E+02
2.00000E+02
0.0
,
2
)
(
1
N
1.500000E+02
1.500000E+02
0.0
,
component
X
of
1
N
7.071068E01 7.071068E01
0.0
,
component
y
of
1
N
7.071068E01 7.071068E01
0.0
,
component
Z
of
1
N
0.0 6.123234E17
0.0
,
)
(
1
max
N
NR
5.000000E+01 5.000000E+01
0.0
,
)
(
1
N
m
NR
0.0 4.235754E14
0.0
,
)
(
1
max
N
1.750000E04 1.750000E04
0.0
,
)
(
1
N
m
0.0 1.564995E19
0.0
,
)
(
1
N
eq
3.000000E+02 3.000000E+02
0.0
,
)
(
1
N
Cr
Nb
1.094600E+04 1.094600E+04
0.0
,
)
(
1
N
ENDO
9.135647E05 9.135647E05
0.0
,
2
)
(
2
N
1.500000E+02 1.500000E+02 0.0
,
component
X
of
2
N
7.071068E01 7.071068E01
0.0
,
component
y
of
2
N
7.071068E01 7.071068E01
0.0
,
component
Z
of
2
N
0.0 6.123234E17
0.0
,
)
(
2
max
N
NR
5.000000E+01 5.000000E+01
0.0
,
)
(
2
N
m
NR
0.0 4.235754E14
0.0
,
)
(
2
max
N
1.750000E04 1.750000E04
0.0
,
)
(
2
N
m
0.0 1.564995E19
0.0
,
)
(
2
N
eq
3.000000E+02 3.000000E+02
0.0
Nodes:N1;N206;
Net: M60,
Not Gauss: 7
)
(
2
N
Cr
Nb
1.094600E+04 1.094600E+04
0.0
,
)
(
2
N
ENDO
9.135647E05 9.135647E05
0.0
The variations being lower than 1.0E-08 we put zero in the table above.
Code_Aster
®
Version
8.2
Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
02/11/05
Author (S):
J. ANGLES
Key
:
V3.04.135-B
Page:
10/14
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
5 Modeling
B
5.1
Characteristics of modeling
Except the criterion of fatigue tested, modeling B is identical to modeling A.
Test criterion DANG_VAN_MODI_AC.
5.2
Characteristics of the mesh
Identical to modeling A.
5.3 Functionalities
tested
The functionalities tested are identical to modeling A. only the option CRITERION of
order CALC_FATIGUE is different:
Controls Options
CALC_FATIGUE CRITERION
“DANG_VAN_MODI_AC”
Code_Aster
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Version
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Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
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Author (S):
J. ANGLES
Key
:
V3.04.135-B
Page:
11/14
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
6
Results of modeling B
6.1 Values
tested
Identification
Type of value
Reference
Aster Variation
(%)
Nodes:N1;N206;
Net: M60,
Not Gauss: 3
xx
(Moment: 3)
1.00000E+02
1.00000E+02
0.0
,
yy
(Moment: 3)
2.00000E+02
2.00000E+02
0.0
,
)
(
1
N
1.500000E+02
1.500000E+02
0.0
,
component
X
of
1
N
7.071068E01 7.071068E01
0.0
,
component
y
of
1
N
7.071068E01 7.071068E01
0.0
,
component
Z
of
1
N
0.0 6.123234E17
0.0
,
)
(
1
max
N
NR
5.000000E+01 5.000000E+01
0.0
,
)
(
1
N
m
NR
0.0 4.235754E14
0.0
,
)
(
1
max
N
1.750000E04 1.750000E04
0.0
,
)
(
1
N
m
0.0 1.564995E19
0.0
,
)
(
1
N
eq
2.750000E+02 2.750000E+02
0.0
,
)
(
1
N
Cr
Nb
1.490300E+04 1.490300E+04
0.0
,
)
(
1
N
ENDO
6.709959E05 6.709959E05
0.0
,
)
(
2
N
1.500000E+02 1.500000E+02 0.0
,
component
X
of
2
N
7.071068E01 7.071068E01
0.0
,
component
y
of
2
N
7.071068E01 7.071068E01
0.0
,
component
Z
of
2
N
0.0 6.123234E17
0.0
,
)
(
2
max
N
NR
5.000000E+01 5.000000E+01
0.0
,
)
(
2
N
m
NR
0.0 4.235754E14
0.0
,
)
(
2
max
N
1.750000E04 1.750000E04
0.0
,
)
(
2
N
m
0.0 1.564995E19
0.0
,
)
(
2
N
eq
2.750000E+02 2.750000E+02
0.0
Nodes:N1;N206;
Net: M60,
Not Gauss: 7
)
(
2
N
Cr
Nb
1.490300E+04 1.490300E+04
0.0
,
)
(
2
N
ENDO
6.709959E05 6.709959E05
0.0
The variations being lower than 1.0E-08 we put zero in the table above.
Code_Aster
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Version
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Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
02/11/05
Author (S):
J. ANGLES
Key
:
V3.04.135-B
Page:
12/14
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
7 Modeling
C
7.1
Characteristics of modeling
Except the criterion of fatigue tested and the loading, cf [§ 1.3], modeling C is identical to
modeling A.
Test criterion DOMM_MAXI.
7.2
Characteristics of the mesh
Identical to modeling A.
7.3 Functionalities
tested
The functionalities tested are identical to modeling A except the following options: CRITERION
is modified, METHOD is not used any more and PROJECTION is added:
Controls Options
CALC_FATIGUE CRITERION
POJECTION
“DOMM_MAXI”
“UN_AXE”
“DEUX_AXES”
8
Results of modeling C
8.1 Values
tested
Identification
Type of value
Reference
Aster Variation
(%)
Nodes:N1;N206;
Net: M60,
Not Gauss: 3
xx
(Moment: 3)
1.00000E+02
1.00000E+02
0.0
,
yy
(Moment: 3)
2.00000E+02
2.00000E+02
0.0
,
component
X
of
1
N
_ _ 3.746066E01
3.907311E01
_ _
,
component
y
of
1
N
_ _ 9.271839E01
9.205049E01
_ _
,
component
Z
of
1
N
_ _ 6.123234E17
_ _
,
)
(
1
N
ENDO
_ _ 7.049845E05
_ _
In the table above, the components
X
and
y
of
1
N
two values have because there are two
vectors which correspond to the same value of damage
)
(
1
N
ENDO
.
Code_Aster
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Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
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Author (S):
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Key
:
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Page:
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Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
9 Modeling
D
9.1
Characteristics of modeling
Except the criterion of fatigue tested and the loading, cf [§ 1.3], modeling D is identical to
modeling A.
Test criterion DANG_VAN_MODI_AV.
9.2
Characteristics of the mesh
Identical to modeling A.
9.3 Functionalities
tested
The functionalities tested are identical to modeling A except the following options: CRITERION
is modified, METHOD is not used any more and PROJECTION is added:
Controls Options
CALC_FATIGUE CRITERION
POJECTION
“DANG_VAN_MODI_AV”
“UN_AXE”
“DEUX_AXES”
10 Results of modeling D
10.1 Values
tested
Identification
Type of value
Reference
Aster Variation
(%)
Nodes:N1;N206;
Net: M60,
Not Gauss: 3
xx
(Moment: 3)
1.00000E+02
1.00000E+02
0.0
,
yy
(Moment: 3)
2.00000E+02
2.00000E+02
0.0
,
component
X
of
1
N
_ _ 7.071068E01
_ _
,
component
y
of
1
N
_ _ 7.071068E01
_ _
,
component
Z
of
1
N
_ _ 6.123234E17
_ _
,
)
(
1
N
ENDO
_ _ 1.341992E04
_ _
Code_Aster
®
Version
8.2
Titrate:
SSLV135 Endommagement by fatigue under alternate biaxial loading
Date:
02/11/05
Author (S):
J. ANGLES
Key
:
V3.04.135-B
Page:
14/14
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/05/005/A
11 Modeling
E
11.1 Characteristics of modeling
Except the criterion of fatigue tested and the loading, cf [§ 1.3], modeling E is identical to
modeling A.
Test criterion FATEMI_SOCIE.
11.2 Characteristics of the mesh
Identical to modeling A.
11.3 Functionalities
tested
The functionalities tested are identical to modeling A except the following options: CRITERION
is modified, METHOD and MECA_STATIQUE are not used any more and PROJECTION is added:
Controls Options
CALC_FATIGUE CRITERION
POJECTION
“FATEMI_SOCIE”
“UN_AXE”
“DEUX_AXES”
12 Results of modeling E
12.1 Values
tested
Identification
Type of value
Reference
Aster Variation
(%)
Nodes:N1;N206;
Net: M60,
Not Gauss: 3
xx
(Moment: 3)
1.00000E+02
1.00000E+02
0.0
,
yy
(Moment: 3)
2.00000E+02
2.00000E+02
0.0
,
xx
(Moment: 3)
- 8.00000E-04
- 8.00000E-04
0.0
,
yy
(Moment: 3)
1.15000E-03
1.15000E-03
0.0
,
zz
(Moment: 3)
- 1.50000E-04
- 1.50000E-04
0.0
,
component
X
of
1
N
_ _ ±4.383711E01
_ _
,
component
y
of
1
N
_ _ 8.987940E01
_ _
,
component
Z
of
1
N
_ _ 6.123234E17
_ _
,
)
(
1
N
ENDO
_ _ 1.682346E01
_ _
13 Summary of the results
The results obtained are in perfect agreement with the reference solution for modelings A
and B. modeling C, D and E do not have reference solutions associated with the criteria.