Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
1/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
Organization (S)
: EDF-R & D/AMA
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
V6.02.106 document
SSNL106 - Elastoplastic beam in traction
and pure bending
Summary:
This test validates elastoplasticity in a right beam in traction and bending, for a behavior
elastoplastic perfect or with linear work hardening.
·
Analyze static
·
Elastoplastic behavior of beam:
VMIS_POUTRE
or of
PIPE
·
3 sections: rectangular, circular full, hollow circular
·
3 types of work hardening: no one, linear (
ECRO_LINE
), nonlinear (
ECRO_FLEJOU
)
8 modelings make it possible to test the elements
POU_D_TG
,
POU_D_E
,
POU_D_T
,
PIPE
(3 and 4 nodes)
COQUE_3D, POU_D_EM and POU_D_T_GM.
The test makes it possible to validate the operation of the integration of these laws of behavior and of the algorithm of
resolution until complete plasticization of the beam.
One also tests plasticization in alternating bending. Moreover, the two methods of resolution are tested
for modelings of beams with total plasticity (POU_D_TG, POU_D_E, POU_D_T): implicit integration or
by Runge-Kutta of command 4.
The ninth modeling makes it possible to test the operation of DYNA_NON_LINE on a calculation
quasi-static of traction of a beam modelized in POU_D_TG.
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
2/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
Right beam length L = 1, direction X.
O
B
L
L = 1
y
X
Z O
One calculates simultaneously 2 types of section:
1 circular section
2 v = 0.2
Z
y
B = 0.1
1 rectangular section
R
R = 0.1
R = 0.1
E = 0.001
E
For modeling D, one calculates 1 section of thin tube:
1.2
Material properties
E = 2. 10
11
AP
= 0.3
ECRO_LINE
:
ECRO_FLEJOU:
SY =
y
= 150 10
6
AP
EP = 2.E10
H =
D_SIGM_EPSI
= 2 10
9
AP or 0
SY = 150.E6
KNOWN = 160.E6
THEN = 1
VMIS_POUTRE
: rectangular section:
normal effort limits NP
= 3. 10
6
NR
elastic moment MEZ
= 10
5
Nm
limiting moment MPZ
= 1.5 10
5
Nm
coefficient AZ
= 0.84
coefficient
BZ =
0.0013
MEY, MPY, MT, AY, BY
= without object
VMIS_POUTRE
: circular section:
normal effort limits NP
= 4.712389 10
6
NR
MEZ = MEY
= 117809.72 Nm
MPZ = MPY
= 200.000 Nm
MT =
without
object
AY = AZ
= 0.84
BY = BZ
= 0.0012
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
3/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
1.3
Boundary conditions and loadings
Embedding out of O
Displacement imposed out of B
DX
L
E
DX
DX
DX
E
y
E
E
=
=
.
0.75 10
m
vary
with
3
3
Rotation imposed out of B
DRZ
DRZ
DRZ
DRZ
DRZ
E
E
E
E
=
×
- ×
0.75 10
m
vary
with
then decrease until
2
20
2
Note:
In pure bending,
MZ
DRZ
and
do not depend on
X
. Curvature
(
)
=
=
D DRZ
dx
DRZ
L
like
L
= 1
()
= DRZ B
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
4/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
2.1.1 Pure bending - linear Work hardening
Analytical solution:
X
v
v
0
xx
=
. y
:
curvature
xx
X
v
v
0
y
xx
U
U
Calculation of the moment by:
()
()
M U
y y ds
E
y
U
H
E
U
y
v
xx
S
xx
xx
xx
y
xx
y
=
=
=
+
-
<
.
for 0
for
One obtains:
for the rectangular section:
M
M
H
E
H
E
M
I.E.(internal excitation)
M
I
v
E
E
E
E
E
E
Z
y
=
-
-
+
=
=
1
3
2
1
2
2
with
.
for the circular section:
()
(
)
(
)
(
)
(
)
M
R
E
H
E H
E H Arc
U
R
ER
y
y
E
µ
µ
µ
µ
µ µ
µ
µ
µ
=
+
-
-
+
-
-
-
-
=
=
=
3
2 3 2
2
2
4
4
3
1
2
1 2
1
/
sin
with
In discharge, after having reached the limiting load charges some, one obtains a limiting load of sign
opposite.
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
5/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
for the tubular section:
(assumption of beam of Navier-Bernoulli)
The limiting load (H = 0) is worth:
M
M
E
= 4
The complete solution for a thin tube is [bib1]:
()
(
)
(
)
M
M
E
E
H
E H
E
T
µ
µ
µ
µ µ
µ
=
+
-
+
-
=
=
+
2 1
1
2
arcsin
with
2.1.2 Traction - linear Work hardening
Analytical solution: one has immediately
NR S
H
E
HS
L DX
y
=
-
+
1
.
.
2.1.3 Traction - nonlinear Work hardening
The analytical solution is obtained here for a particular case: the model of work hardening
(
ECRO_FLEJOU
) is written into uniaxial:
=
+
+
=
-
=
-
y
p
p
p
U
U
U
y
p
p
E
E
E
E H
E H
.
.
1
1
with
and
If
= 1
, one finds
according to
while solving:
(
)
-
+
=
y
p
U
p
p
E
1
.
What leads to the equation of the 2nd degree in
:
(
)
(
)
(
)
(
)
(
)
(
)
(
)
2
2
2
0
4
1
2
-
+
+
+
+
=
=
+
-
+
=
+
+
±
E
E
E
E E
E
U
U
y U
U
U
U
p
U
U
U
Then:
and
.
.
The solution corresponding to the beginning of plasticization (
growing from
y
) is that
corresponding to the sign -.
Thus the normal effort in the beam is:
()
()
NR
S.E.U BL
E U B
L
E E
U
U
U
U
p U
=
+
+
-
+
-
+
2
4
2
2
2.2 References
bibliographical
[1]
J.H. LAU and T.T. LAU: Newspaper off Presses Vessel Technology vol. 106 p188-195 - May 1984.
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
6/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
3 Modeling
With
3.1
Characteristics of modeling
2 elements
POU_D_TG
by type of section. There are thus 2 groups of elements comprising each one 2
elements.
Group GR1:
rectangular section
GC1:
circular section
Simple traction:
on GR1 (
ECRO_FLEJOU
) and GC1 (
ECRO_LINE
)
Pure bending:
on GR1 and GC1 without work hardening
3.2
Characteristics of the mesh
2 X 2 elements
POU_D_TG
3.3 Functionalities
tested
Controls
STAT_NON_LINE COMP_INCR RELATION
:
“VMIS_POUTRE”
DEFI_MATERIAU VMIS_POUTRE
ECRO_LINE
ECRO_FLEJOU
STAT_NON_LINE CONVERGENCE
RESO_INTE
:
“RUNGE_KUTTA_4”
4
Results of modeling A
4.1 Values
tested
Traction
()
DX B
DX
E
N°ordre
GROUP_MA
Identification Reference Aster Difference
(%)
2 11
GR1 NR
3.123 10
6
3.123
10
6
0
3 21
GR1 NR
3.1529 10
6
3.1532
10
6
0.01
2 21
GC1 NR
4.75951 10
6
4.75951
10
6
0
3 31
GC1 NR
4.80664 10
6
4.80664
10
6
0
Bending
()
DRZ B
DRZ
E
N°ordre
GROUP_MA
Identification Reference Aster Difference
(%)
1 1
GR1
MFZ
(Nm)
10
5
10
5
0
5 21
MFZ 1.48 10
5
1.477
10
5
0.23
10 31
MFZ 1.495 10
5
1.489
10
5
0.39
20 41
MFZ 1.499 10
5
1.495
10
5
0.26
1 1
GC1 MFZ 1.1781 10
5
1.1781 10
5
0
5 21
MFZ 1.9602 10
5
1.955 10
5
0.27
10 31
MFZ 1.99 10
5
1.98
10
5
0.53
20 41
MFZ 1.998 10
5
1.99
10
5
0.36
2 71 GR1 MFZ 1.5 10
5
1.499
10
5
0.08
2 71 GC1 MFZ 2. 10
5
1.994
10
5
0.32
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
7/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
5 Modeling
B
5.1
Characteristics of modeling
2 elements
POU_D_T
by type of section. There are thus 2 groups of elements comprising each one 2
elements.
Group GR1:
rectangular section
GC1:
circular section
Simple traction:
on GR1 (
ECRO_FLEJOU
) and GC1 (
ECRO_LINE
)
Pure bending:
on GR1 and GC1 without work hardening
5.2
Characteristics of the mesh
2 X 2 elements
POU_D_T
5.3 Functionalities
tested
Controls
STAT_NON_LINE COMP_INCR
RELATION
:
“VMIS_POUTRE”
DEFI_MATERIAU VMIS_POUTRE
ECRO_LINE
ECRO_FLEJOU
STAT_NON_LINE CONVERGENCE
RESO_INTE
:
“IMPLICIT”
6
Results of modeling B
6.1 Values
tested
Traction
()
DX B
DX
E
N°ordre
GROUP_MA
Identification Reference Aster Difference
(%)
2 11
GR1 NR
3.123 10
6
3.125
10
6
0.08
3 21
GR1 NR
3.1529 10
6
3.15
10
6
0.09
2 21
GC1 NR
4.75951 10
6
4.7596
10
6
0.004
3 31
GC1 NR
4.80664 10
6
4.8068
10
6
0.004
Bending
()
DRZ B
DRZ
E
N°ordre
GROUP_MA
Identification Reference Aster Difference
(%)
1 1
GR1
MFZ
(Nm)
10
5
10
5
0
5 21
MFZ
1.48 10
5
1.477
10
5
0.20
10 31
MFZ
1.495 10
5
1.489
10
5
0.37
20 41
MFZ
1.499 10
5
1.495
10
5
0.24
2 71 GR1 MFZ
1.5 10
5
1.496
10
5
0.23
2 71 GC1 MFZ
2 10
5
1.993
10
5
0.33
1 1
GC1 MFZ
1.1781 10
5
1.1781
10
5
0
5 21
MFZ
1.9602 10
5
1.955
10
5
0.24
10 31
MFZ
1.99 10
5
1.98
10
5
0.50
20 41
MFZ
1.998 10
5
1.99
10
5
0.33
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
8/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
7 Modeling
C
7.1
Characteristics of modeling
2 elements
POU_D_E
by type of section. There are thus 2 groups of elements comprising each one 2
elements.
Group GR1:
rectangular section
GC1:
circular section
Simple traction:
on GR1 (
ECRO_FLEJOU
) and GC1 (
ECRO_LINE
)
Pure bending:
on GR1 and GC1 without work hardening
7.2
Characteristics of the mesh
2 X 2 elements
POU_D_E
7.3 Functionalities
tested
Controls
STAT_NON_LINE COMP_INCR RELATION
:
“VMIS_POUTRE”
DEFI_MATERIAU VMIS_POUTRE
ECRO_LINE
ECRO_FLEJOU
STAT_NON_LINE CONVERGENCE
RESO_INTE
“IMPLICIT”
“RUNGE_KUTTA_4”
8
Results of modeling C
8.1 Values
tested
Traction
()
DX B
DX
E
N°ordre
GROUP_MA
Identification Reference Aster Difference
(%)
2 11
GR1 NR
3.123 10
6
3.123
10
6
0
3 21
GR1 NR
3.1529 10
6
3.1532
10
6
0.01
2 21
GC1 NR
4.75951 10
6
4.75951
10
6
0
3 31
GC1 NR
4.80664 10
6
4.80664
10
6
0
Bending
()
DRZ B
DRZ
E
N°ordre
GROUP_MA
Identification Reference Aster Difference
(%)
1 1
GR1
MFZ
(Nm)
10
5
10
5
0
5 21
MFZ
1.48 10
5
1.477
10
5
0.23
10 31
MFZ
1.495 10
5
1.489
10
5
0.39
20 41
MFZ
1.499 10
5
1.495
10
5
0.26
2 71 GR1 MFZ
1.5 10
5
1.499
10
5
0.08
2 71 GC1 MFZ
2 10
5
1.994
10
5
0.32
1 1
GC1 MFZ
1.1781 10
5
1.1781
10
5
0
5 21
MFZ
1.9602 10
5
1.955
10
5
0.27
10 31
MFZ
1.99 10
5
1.98
10
5
0.53
20 41
MFZ
1.998 10
5
1.99
10
5
0.36
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
9/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
9 Modeling
D
9.1
Characteristics of modeling
2 elements
PIPE
for the tubular section.
Simple traction:
(
ECRO_LINE
)
Pure bending:
without work hardening
Moreover, one locks the DDL which correspond to the mode 3d' ovalization: U03 V03 W03
9.2
Characteristics of the mesh
2 elements
PIPE
(METUSEG3)
9.3 Functionalities
tested
Controls
STAT_NON_LINE COMP_INCR
RELATION
: “VMIS_ISOT_LINE”
TUYAU_NCOU
:
3
TUYAU_NSEC
:
16
AFFE_MODELE
MODELING
:
PIPE
AFFE_CHAR_MECA
DDL_IMPO
U03: 0.
V03: 0.
W03: 0.
10 Results of modeling D
10.1 Values
tested
Traction
()
DX B
DX
E
N°ordre Identification Reference Aster Difference
(%)
2 11
NR
9.47 10
4
9.47
10
4
0
3 21
NR
9.565 10
4
9.565 0
Bending
()
DRZ B
DRZ
E
N°ordre Identification Reference Aster Difference
(%)
1 1
MFZ
4.642 10
3
4.642
10
3
0
5 21
MFZ
5.9106 10
3
5.9365
10
3
0.4
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
10/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
11 Modeling
E
11.1 Characteristics of modeling
2 elements
PIPE
with 4 nodes for the tubular section.
Simple traction:
(
ECRO_LINE
)
Pure bending:
without work hardening
Moreover, one locks the DDL which correspond to the mode 3d' ovalization: U03 V03 W03
11.2 Characteristics of the mesh
2 elements
PIPE
(meshs SEG4)
11.3 Functionalities
tested
Controls
STAT_NON_LINE COMP_INCR
RELATION
: “VMIS_ISOT_LINE”
TUYAU_NCOU
:
3
TUYAU_NSEC
:
16
AFFE_MODELE
MODELING
:
PIPE
AFFE_CHAR_MECA
DDL_IMPO
U03: 0.
V03: 0.
W03: 0.
MODI_MAILLAGE
OPTION
SEG3_4
12 Results of modeling E
12.1 Values
tested
Traction
()
DX B
DX
E
N°ordre Identification Reference
Aster Difference
(%)
2 11
NR
9.47 10
4
9.47
10
4
0
3 21
NR
9.565 10
4
9.565 0
Bending
()
DRZ B
DRZ
E
N°ordre Identification Reference
Aster Difference
(%)
1 1 MFZ 4.642 10
3
4.642
10
3
0
5 21 MFZ 5.9106 10
3
5.9365
10
3
0.4
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
11/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
13 Modeling
F
13.1 Characteristics of modeling
112 elements
COQUE_3D
for the tubular section, and 2 elements pipe to apply the conditions
with the limits. The length of the mesh hulls is of 0.98m. the length of each element pipe is
of 0.01m.
A connection COQUE_TUYAU is applied at each end of the mesh hulls, with an element
pipe. Moreover, one locks the DDL of the pipes which correspond to the mode 3d' ovalization: U03 V03
W03
Simple traction:
(
ECRO_LINE
)
Pure bending:
without work hardening
13.2 Characteristics of the mesh
112 meshs QUAD9 and 2 meshs SEG3.
13.3 Functionalities
tested
Controls
STAT_NON_LINE COMP_INCR RELATION
: “VMIS_ISOT_LINE”
COQUE_NCOU
:
1
AFFE_MODELE
MODELING:
COQUE_3D, TUYAU_3M
AFFE_CHAR_MECA
DDL_IMPO
Ui3: 0.
Vi3: 0.
Wi3: 0.
Uo3: 0.
Vo3: 0.
Wo3: 0.
AFFE_CHAR_MECA LIAISON_ELEM
OPTION
“COQ_TUYAU”
14 Results of modeling F
14.1 Values
tested
Traction
()
DX B
DX
E
N°ordre Identification Reference
Aster Difference
(%)
2 11
NR
9.47 10
4
9.473
10
4
0.02
3 21
NR
9.565 10
4
9.569 E+04
0.04
Bending
()
DRZ B
DRZ
E
N°ordre Identification Reference
Aster Difference
(%)
1 1 MFZ 4.642 10
3
4.6415
10
3
0.01
2.8 19
MFZ 5.7824 10
3
5.7836
10
3
0.02
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
12/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
15 Modeling
G
15.1 Characteristics of modeling
2 elements
POU_D_EM
for the tubular section.
The section is with a grid in QUAD4: it is discretized by a mesh in the thickness, and 90 meshs
on the circumference.
Simple traction:
(
ECRO_LINE
)
Pure bending:
without work hardening
15.2 Characteristics of the mesh
2 meshs SEG2 for the beam. 90 meshs QUAD4 for the section.
15.3 Functionalities
tested
Controls
STAT_NON_LINE COMP_INCR
RELATION
: “VMIS_ISOT_LINE”
AFFE_CARA_ELEM BEAM SECTION
GENERAL
AFFE_SECT
MESH
AFFE_MODELE
MODELING
:
POU_D_EM
16 Results of modeling G
16.1 Values
tested
Traction
()
DX B
DX
E
N°ordre Identification Reference
Aster Difference
(%)
2 11
NR
9.47 10
4
9.471
10
4
0.01
3 21
NR
9.565 10
4
9.5647 0.01
Bending
()
DRZ B
DRZ
E
N°ordre Identification Reference
Aster Difference
(%)
1 1 MFZ 4.642 10
3
4.641
10
3
0.01
5 21 MFZ 5.9106 10
3
5.90
10
3
0.02
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
13/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
17 Modeling
H
17.1 Characteristics of modeling
2 elements
POU_D_TGM
for the tubular section.
The section is with a grid in QUAD4: it is discretized by a mesh in the thickness, and 90 meshs
on the circumference.
Simple traction:
(
ECRO_LINE
)
Pure bending:
without work hardening
17.2 Characteristics of the mesh
2 meshs SEG2 for the beam. 90 meshs QUAD4 for the section.
17.3 Functionalities
tested
Controls
STAT_NON_LINE COMP_INCR
RELATION
: “VMIS_ISOT_LINE”
AFFE_CARA_ELEM BEAM SECTION
GENERAL
AFFE_SECT
MESH
AFFE_MODELE
MODELING
:
POU_D_TGM
18 Results of modeling H
18.1 Values
tested
Traction
()
DX B
DX
E
N°ordre Identification Reference
Aster Difference
(%)
2 11
NR
9.47 10
4
9.471
10
4
0.01
3 21
NR
9.565 10
4
9.5647 0.01
Bending
()
DRZ B
DRZ
E
N°ordre Identification Reference
Aster Difference
(%)
1 1 MFZ 4.642 10
3
4.641
10
3
0.01
5 21 MFZ 5.9106 10
3
5.90
10
3
0.02
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
14/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
19 Modeling
I
19.1 Characteristics of modeling
2 elements
POU_D_TG
by type of section. There are thus 2 groups of elements comprising each one 2
elements.
Group GR1:
rectangular section
GC1:
circular section
Simple traction:
on GR1 (
ECRO_FLEJOU
) and GC1 (
ECRO_LINE
)
Pure bending:
on GR1 and GC1 without work hardening
19.2 Characteristics of the mesh
2 X 2 elements
POU_D_TG
19.3 Functionalities
tested
The characteristic of modeling I is to test the operation of DYNA_NON_LINE in calculation
of quasi-static traction of a beam modelized in POU_D_TG. This type of modeling has for
characteristic to reveal null pivots on the lines of the matrix of mass corresponding
with the degrees of freedom of roll. In this case, the initialization of the diagram of NEWMARK
fact more by inversion of the matrix of mass, which is singular, but by resetting of acceleration
initial.
Controls
DYNA_NON_LINE COMP_INCR
RELATION
:
“VMIS_POUTRE”
DEFI_MATERIAU VMIS_POUTRE
ECRO_LINE
ECRO_FLEJOU
STAT_NON_LINE CONVERGENCE RESO_INTE
:
“RUNGE_KUTTA_4”
20 Results of modeling I
20.1 Values
tested
Traction
()
DX B
DX
E
N°ordre
GROUP_MA
Identification
Reference
Aster Difference
(%)
2 11 GR1 NR
3.123 10
6
3.123
10
6
0.009
3 21 GR1 NR
3.1529 10
6
3.153
10
6
0.012
2 21 GC1 NR
4.75951 10
6
4.760
10
6
0.0003
3 31 GC1 NR
4.80664 10
6
4.807
10
6
0.0003
20.2 Observations
It is noticed that the results in traction resulting from DYNA_NON_LINE are identical to those given
by STAT_NON_LINE.
An alarm informs the user who the matrix of mass is singular, which should attract sound
caution.
Indeed for the majority of the finite elements the matrix of mass is definite positive. A message invites it
thus to check the assignments of its model. In the framework of this modeling, the presence of
degrees of freedom of roll naturally involves the singularity of the matrix of mass.
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
15/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
21 Summary of the results
The results obtained for a traction correspond exactly to the analytical solution. On the other hand
in bending, the difference reaches 0.5%. This is due to the criterion of plasticity chosen, whose form does not allow
not to find the analytical solution exactly. It is necessary to adjust as well as possible parameters AY, BY, AZ,
BZ.
With regard to modelings pipe and hull, the conclusions are the same ones, but this time
the difference with the analytical solution comes from this solution which is valid for a beam of
very mean tubular section, without effect of ovalization. This ovalization is locked at the ends, it
who allows to obtain a solution with less than 0.4% of the analytical solution.
Two modelings in multifibre beams provide a solution to less than 0.02% of
analytical solution, for a very weak time calculation, compared to modeling pipe and hull,
but without it being necessary to adjust parameters as for modelings of beam with
total plasticity. The only approximation comes from the mesh of the section.
Code_Aster
®
Version
7.3
Titrate:
SSNL106 - Elastoplastic beam in traction and pure bending
Date:
25/10/04
Author (S)
:
J.M. PROIX, J.L. FLEJOU
Key:
V6.02.106-C
Page:
16/16
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/04/005/A
Intentionally white left page.