Code_Aster
®
Version
8.3
Titrate:
SDNL111 - Impact of two beams
Date:
04/05/06
Author (S):
NR. GREFFET, S. LAMARCHE
,
G. JACQUART
Key
:
V5.02.111-C
Page:
1/10
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-62/06/005/A
Organization (S):
EDF-R & D/AMA, EDF-Pole Industry/CNPE of Tricastin
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
V5.02.111 document
SDNL111 - Impact of two beams
Summary:
This problem is a problem of impact of two beams in traction and compression. A first free beam is
animated an initial speed parallel with the axis of the two beams and comes to run up against one embedded second against its
base. Non-linearity comes from the conditions of contact between the two structures. This test comprises a solution
analytical of reference.
Initially, one uses a transitory analysis by modal recombination of a non-linear system
constituted of structures of beams (modelings has and b).
The beams are discretized by finite elements of type
POU_D_T
. Operators
DEFI_OBSTACLE
[U4.44.21] and
DYNA_TRAN_MODAL
[U4.53.21] are tested. The variations with the values of reference do not exceed
not 4.5%.
In the second time, one makes a direct calculation on physical basis, with elements 3D (modelings C, D
and E). The operators tested are:
DYNA_NON_LINE
,
AFFE
_
TANK
_
MECA
/
CONTACT
with the methods
STRESS, LAGRANGE and CONTINUOUS.
Code_Aster
®
Version
8.3
Titrate:
SDNL111 - Impact of two beams
Date:
04/05/06
Author (S):
NR. GREFFET, S. LAMARCHE
,
G. JACQUART
Key
:
V5.02.111-C
Page:
2/10
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-62/06/005/A
1
Problem of reference
1.1 Geometry
B
With
L
B (A)
has
has
L
C
D
- V
O
J
O
Z
y
y
Z
X
Length of the beams
L = 1. m
Side of the section of the beams
= 2. cm have
1.2
Material properties
3
kg/m
voluminal
mass
3D
one
modélisati
for
0.3
and
1D,
one
modélisati
for
:
Poisson
of
T
coeffician
AP
:
Young
of
modulate
.
=
7800
0
10
.
2
11
=
=
E
:
Beam
1.3
Boundary conditions and loadings
The problem is one-way according to
X
.
The beam CD is embedded in D, beam AB is completely free in translation according to
X
.
1.4 Conditions
initial
All the nodes of beam AB are imposed according to the axis
X
:
·
an initial speed:
v
0
1
= -
m/s
The nodes of the beam CD have a speed and an initial displacement no one.
The points A and C are separated from an initial play
J
O
very weak:
J
O
= 10
5
Mr.
Code_Aster
®
Version
8.3
Titrate:
SDNL111 - Impact of two beams
Date:
04/05/06
Author (S):
NR. GREFFET, S. LAMARCHE
,
G. JACQUART
Key
:
V5.02.111-C
Page:
3/10
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-62/06/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Fired from [bib1].
F T
()
ESV
O
2c
p
O
T
V X, T
(
)
V
O
V
O/2
- V
O/2
- V
O
O
T
O
+
O
+ 2
T
O
O
+
O
+ 2
J
O
- V
O
/2
U X, T
()
F (T)
: force contact in A;
V (X, T)
: speed;
U (X, T)
: displacement;
O
+ 2
O
= J
O
V
O
;
= 2 L
C
p
Duration of shock
= 2
;
C
p
=
E (1
-
)
(1
+
) (1
- 2
);
S
= has
2
section.
for point A
2.2 References
bibliographical
[1]
Algorithms of fast dynamics theoretical Description and examples of applications. Report/ratio
EDF/DER HP-61/93.115
Code_Aster
®
Version
8.3
Titrate:
SDNL111 - Impact of two beams
Date:
04/05/06
Author (S):
NR. GREFFET, S. LAMARCHE
,
G. JACQUART
Key
:
V5.02.111-C
Page:
4/10
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-62/06/005/A
3 Modeling
With
3.1
Characteristics of modeling
Discretization of the two beams by meshs
SEG2
(50 each one) and of the finite elements of type
POU_D_T
.
A modal base of 40 clean modes (20 by beams) is used for the modal superposition.
A contractual reduced modal damping by 0.1% is applied to each clean mode.
The conditions initial speeds are imposed by building a field on the nodes of
displacement via groups of nodes:
GROUP_NO: BARRE1
(initial speed
DX = - 1.
)
GROUP_NO: BARRE2
(initial speed
DX = 0.
)
and by projecting this field with the nodes on the modal basis while specifying
TYPE_VECT: “QUICKLY”
.
The vector generalized thus calculated can be introduced into the control
DYNA_TRAN_MODAL
behind
the key word
VITE_INIT
.
The parameters of modeling of the law of shock used are:
The first modeling (possible):
·
the normal in the plan of the shock is selected according to Z:
NORM_OBST: (0. 0. 1. )
·
an obstacle of the type
BI_PLAN_Z
is selected
The second modeling:
·
the normal in the plan of the shock is selected according to Y:
NORM_OBST: (0. 1. 0. )
·
an obstacle of the type
BI_PLAN_Y
is selected
The third modeling:
·
the normal in the plan of the shock is selected according to Y:
NORM_OBST: (0. 1. 0. )
·
an obstacle of the type
BI_CERCLE
is selected
·
Stiffness of shock:
RIGI_NOR
: 5.10
9
NR/m
·
Damping of shock:
AMOR_NOR
: 2.10
4
NS/m
Values of
DIST_1
and
DIST_2
who are fictitious here and only to modelize the contact are
chosen equal to
DIST_1=DIST_2
= J
O
/2 so that there is contact at the beginning of calculation.
Temporal integration is carried out with the algorithm of Euler and a pitch of time of 10
6
S.
3.2
Characteristics of the mesh
A number of nodes: 102
A number of meshs and types: 100
SEG2
Code_Aster
®
Version
8.3
Titrate:
SDNL111 - Impact of two beams
Date:
04/05/06
Author (S):
NR. GREFFET, S. LAMARCHE
,
G. JACQUART
Key
:
V5.02.111-C
Page:
5/10
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-62/06/005/A
3.3 Functionalities
tested
Controls
STANDARD DEFI_OBSTACLE
“BI_PLAN_Z”
“BI_PLAN_Y”
“BI_CERCLE”
DYNA_TRAN_MODAL SHOCK
NOEU_2
DIST_1
DIST_2
ENTITLE
VITE_INIT_GENE
METHOD
“EULER”
3.4 Values
tested
Identification Reference
Aster %
difference
DX at point A t=2.0e-4 S
1.E-4
1.008E-4
0.78
DX at point A t=4.0e-4 S
2.E-4
1.939E-4
3.071
DX at point A t=6.0e-4 S
1.E-4
9.558E-5
4.417
DX at point A t=8.0e-4 S
0. 8.036E-6
ABS:
8.04E-6
DX at point A t=1.0e-3 S
2.E-4
2.063E-4
3.138
4 Modeling
B
4.1
Characteristics of modeling
Discretization of the two beams by meshs
SEG2
(50 each one) and of the finite elements of type
POU_D_T
.
A modal base of 40 clean modes (20 by beams) is used for the modal superposition.
A contractual reduced modal damping by 0.1% is applied to each clean mode.
The conditions initial speeds are imposed by building an initial field speed applied
with the beams
BEAM
1
and
BEAM
2
.
The parameters of modeling of the law of shock used are:
·
the normal in the plan of the shock is selected according to Z:
NORM_OBST: (0. 1. 0. )
·
an obstacle of the type
BI_CERC_INT
is selected
·
Stiffness of shock:
RIGI_NOR
: 5.10
9
NR/m
·
Damping of shock:
AMOR_NOR
: 2.10
4
NS/m
Temporal integration is carried out with the algorithm of Euler and a pitch of time of 10
6
S.
4.2
Characteristics of the mesh
A number of nodes: 102
A number of meshs and types: 100
SEG2
Code_Aster
®
Version
8.3
Titrate:
SDNL111 - Impact of two beams
Date:
04/05/06
Author (S):
NR. GREFFET, S. LAMARCHE
,
G. JACQUART
Key
:
V5.02.111-C
Page:
6/10
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-62/06/005/A
4.3 Functionalities
tested
Controls
STANDARD DEFI_OBSTACLE
“BI_CERC_INT”
DYNA_TRAN_MODAL SHOCK
NOEU_2
DIST_1
DIST_2
ENTITLE
VITE_INIT_GENE
METHOD
“EULER”
4.4 Values
tested
Identification Reference
Aster %
difference
DX at point A t=2.0e-4 S
1.E-4
1.008E-4
0.8
DX at point A t=4.0e-4 S
2.E-4
1.937E-4
- 3.15
DX at point A t=6.0e-4 S
1.E-4
9.558E-5
- 4.42
DX at point A t=8.0e-4 S
0. 6.565E-6
ABS:
6.56E-6
DX at point A t=1.0e-3 S
1.E-4
1.069E-4
6.9
DX at point A t=1.2e-3 S
2.E-4
1.914E-4
- 4.3
DX at point A t=1.4e-3 S
1.E-4
9.335E-5
- 6.65
DX at point A t=1.6e-3 S
0.
- 8.948E-6
ABS: 8.95E-6
5 Modeling
C
5.1
Characteristics of modeling
The two beams are modelized with meshs
QUAD4
(50 per beam) and of the finite elements 3D.
The behavior is elastic.
The conditions initial speeds are imposed by building a field initial speed
applied to the two beams:
DZ = - 1.0
for
POU1
and
DZ = 0.0
for
POU2
.
The shock is modelized by loads of contact. One uses
AFFE_CHAR_MECA
with the key word
CONTACT
.
Pairing is of master-slave type. The method used is
STRESS
.
Temporal integration is carried out with the method of modified average acceleration (key word
HHT
with
= - 0.1 and MODI_EQUI=' NON': default value) and a pitch of time of 10
6
S.
The subdivision of pitch of time is authorized. For the solvor, one uses the method
MULT_FRONT
.
One tests then another algorithm of temporal integration:
- method (key word
HHT
with
= - 0.3
and MODI_EQUI=' OUI') and a pitch of unchanged time of 10
6
S. The solvor is also unchanged.
5.2
Characteristics of the mesh
A number of nodes: 408
A number of meshs and types: 50
QUAD4
Code_Aster
®
Version
8.3
Titrate:
SDNL111 - Impact of two beams
Date:
04/05/06
Author (S):
NR. GREFFET, S. LAMARCHE
,
G. JACQUART
Key
:
V5.02.111-C
Page:
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Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-62/06/005/A
5.3 Functionalities
tested
Controls
AFFE_CHAR_MECA CONTACT
STRESS
CREA_CHAMP OPERATION “AFFE”
TYPE_CHAM
“NOEU_DEPL_R”
AFFE
GROUP_NO
“POU1”
“POU2”
NOM_CMP
“DZ”
DYNA_NON_LINE METHOD
HHT
ETAT_INIT
QUICKLY
5.4 Values
tested
Aster %
difference
Identification Reference
HHT
MODI_EQUI=
“NOT”
HHT
MODI_EQUI=
“YES”
HHT
MODI_EQUI=
“NOT”
HHT
MODI_EQUI=
“YES”
DZ at point A
t=2.0e-4 S
1.050E-4
1.050E-4
1.050E-4
0.00 0.00
DZ at point A
t=4.0e-4 S
1.550E-4
1.552E-4
1.554E-4
0.16 0.26
DZ at point A
t=6.0e-4 S
5.540E-5
5.541E-5
5.541E-5
0.01 0.01
DZ at point A
t=8.0e-4 S
9.920E-5
9.550E-5 9.707E-5
- 3.73 - 2.15
DZ at point A
t=1.0e-3 S
2.990E-4
2.955E-4 2.960E-4
- 1.15 - 1.00
tps_job 520 mem_job 512Mo ncpus1
6 Modeling
D
6.1
Characteristics of modeling
The two beams are modelized with meshs
QUAD4
(50 per beam) and of the finite elements 3D.
The behavior is elastic.
The conditions initial speeds are imposed by building a field initial speed
applied to the two beams:
DZ = - 1.0
for
POU1
and
DZ = 0.0
for
POU2
.
The shock is modelized by loads of contact. One uses
AFFE_CHAR_MECA
with the key word
CONTACT
.
Pairing is of master-slave type. The method used is
LAGRANGE
, without friction.
Temporal integration is carried out with the method
HHT
(
= - 0.1) and a pitch of time of 10
6
S.
The subdivision of pitch of time is authorized. For the solvor, one uses the method
MULT_FRONT
.
6.2
Characteristics of the mesh
A number of nodes: 408
A number of meshs and types: 50
QUAD4
Code_Aster
®
Version
8.3
Titrate:
SDNL111 - Impact of two beams
Date:
04/05/06
Author (S):
NR. GREFFET, S. LAMARCHE
,
G. JACQUART
Key
:
V5.02.111-C
Page:
8/10
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-62/06/005/A
6.3 Functionalities
tested
Controls
AFFE_CHAR_MECA CONTACT
LAGRANGE
CREA_CHAMP OPERATION “AFFE”
TYPE_CHAM
“NOEU_DEPL_R”
AFFE
GROUP_NO
“POU1”
“POU2”
NOM_CMP
“DZ”
DYNA_NON_LINE METHOD
HHT
ETAT_INIT
QUICKLY
6.4 Values
tested
Identification Reference
Aster %
difference
DZ at point A t=2.0e-4 S
1.050E-4
1.050E-4
0.00
DZ at point A t=4.0e-4 S
1.550E-4
1.552E-4
0.16
DZ at point A t=6.0e-4 S
5.540E-5
5.541E-5
0.01
DZ at point A t=8.0e-4 S
9.920E-5
9.550E-5
- 3.73
DZ at point A t=1.0e-3 S
2.990E-4
2.955E-4
- 1.15
tps_job 720 mem_job 800Mo ncpus1
7 Modeling
E
7.1
Characteristics of modeling
The two beams are modelized with meshs
QUAD4
(50 per beam) and of the finite elements 3D.
The behavior is elastic.
The conditions initial speeds are imposed by building a field initial speed
applied to the two beams:
DZ = - 1.0
for
POU1
and
DZ = 0.0
for
POU2
.
The shock is modelized by loads of contact. One uses
AFFE_CHAR_MECA
with the key word
CONTACT
.
Pairing is of master-slave type. The method used is
CONTINUOUS
, without friction.
Temporal integration is carried out with the method
HHT
(
= - 0.1) and a pitch of time of 10
6
S.
The subdivision of pitch of time is authorized. For the solvor, one uses the method
MULT_FRONT
.
7.2
Characteristics of the mesh
A number of nodes: 408
A number of meshs and types: 50
QUAD4
Code_Aster
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Version
8.3
Titrate:
SDNL111 - Impact of two beams
Date:
04/05/06
Author (S):
NR. GREFFET, S. LAMARCHE
,
G. JACQUART
Key
:
V5.02.111-C
Page:
9/10
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-62/06/005/A
7.3 Functionalities
tested
Controls
AFFE_CHAR_MECA CONTACT
CONTINUOUS
INTEGRATION
NODE
CREA_CHAMP OPERATION “AFFE”
TYPE_CHAM
“NOEU_DEPL_R”
AFFE
GROUP_NO
“POU1”
“POU2”
NOM_CMP
“DZ”
DYNA_NON_LINE METHOD
HHT
ETAT_INIT
QUICKLY
7.4 Values
tested
Identification Reference
Aster %
difference
DZ at point A t=2.0e-4 S
1.050E-4
- 1.050E-4
0.00
DZ at point A t=4.0e-4 S
1.550E-4
- 1.522E-4
- 1.82
DZ at point A t=6.0e-4 S
5.540E-5
- 5.537E-5
- 0.05
DZ at point A t=8.0e-4 S
9.920E-5
9.550E-5
- 3.73
DZ at point A t=1.0e-3 S
2.990E-4
2.950E-4
- 1.33
tps_job 2100 mem_job 800Mo ncpus 1
Code_Aster
®
Version
8.3
Titrate:
SDNL111 - Impact of two beams
Date:
04/05/06
Author (S):
NR. GREFFET, S. LAMARCHE
,
G. JACQUART
Key
:
V5.02.111-C
Page:
10/10
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-62/06/005/A
8
Summary of the results
For modelings has and B (with
DYNA_TRAN_MODAL
):
The precision of calculation is relatively average what is due to the choice of the coefficients of
penalization used to modelize the contact. The increase in the stiffness of contact improves
considerably the field of displacement but generates the important oscillations of the field of
speed around the analytical solution.
For modelings C, D and E (with
DYNA_NON_LINE
):
The precision of calculation is very good (4% of maximum change). In this case, three methods used
results of comparable quality give. For this size of problem, the calculating time is more
length with the method CONTINUES.
Moreover, for modeling C, one also tested two types of diagrams of integration in time
implicit: modified average acceleration (key word HHT with option MODI_EQUI=' NON': option by
defect) and “complete” HHT (key word HHT with option MODI_EQUI=' OUI').
With “complete” diagram HHT, the maximum variation observed with the reference solution drops
slightly: 2,15% against 3,73% with the modified average acceleration. Other values tested
are impacted very little, with the choice of values of the parameter
diagrams employed in it
case-test (
=-0,1 for the modified average acceleration and =-0,3 for HHT).