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Titrate:
SDNL111 - Impact of two beams


Date:
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Author (S):
S. LAMARCHE, G. JACQUART Key
:
V5.02.111-B Page:
1/10

Organization (S): EDF-R & D/AMA

Handbook 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_CHAR_MECA/CONTACT with the methods
CONTRAINTE, LAGRANGE and CONTINUE.

Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-66/04/005/A

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Titrate:
SDNL111 - Impact of two beams


Date:
01/01/04
Author (S):
S. LAMARCHE, G. JACQUART Key
:
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2/10

1
Problem of reference

1.1 Geometry

X
has
B
B (A)
Z
- V
L
has
O
y
With
OJ
C
L
D
Z
y
Length of the beams

L = 1. m
Side of the section of the beams
= 2. cm have


1.2
Material properties

:
Beam
modulate

:
Young
E = 2.1011Pa
coeffician
:
Poisson

of
T
= 0.pour modlisati



for

0.3

and

1D,

one
modlisati



3D

one

3
voluminal

mass
= 7800kg/m

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 axis X:


an initial speed: v0 = - 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 OJ very weak: OJ = 105 Mr.
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-66/04/005/A

Code_Aster
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Titrate:
SDNL111 - Impact of two beams


Date:
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Author (S):
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:
V5.02.111-B Page:
3/10

2
Reference solution

2.1
Method of calculation used for the reference solution

Drawn from [bib1].

F (T)
ESVo
F (T): force contact in A;
2c p

V (X, T): speed;
T

U (X, T): displacement;
O
O + 2
= OJ;
V (X, T)
O
Vo
Vo

2 L
=
V
Duration of shock = 2;
O/2
C

p
T
O +
O
O + 2
- V
C
;
O/2
p
=
E (1 -)
(1+) (1 - 2)
- Vo
S = a2 section.
U (X, T)
for point A
OJ
T
O
O +
O + 2
- Vo/2


2.2 References
bibliographical

[1]
Algorithms of fast dynamics theoretical Description and examples of applications. Report/ratio
EDF/DER HP-61/93.115
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-66/04/005/A

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Titrate:
SDNL111 - Impact of two beams


Date:
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:
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3 Modeling
With

3.1
Characteristics of modeling

Discretization of the two beams by meshs SEG2 (50 each one) and 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 by specifying TYPE_VECT: “VITE”.

The vector generalized thus calculated can be introduced into command DYNA_TRAN_MODAL behind
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: 5.109 NR/m

Damping of shock: AMOR_NOR: 2.104 NS/m

The values of DIST_1 and DIST_2 which are fictitious here and only to model the contact are
chosen equal to DIST_1=DIST_2= OJ/2 so that there is contact at the beginning of calculation.

Temporal integration is carried out with the algorithm of Euler and a step of time of 106 S.

3.2
Characteristics of the grid

A number of nodes: 102

A number of meshs and types: 100 SEG2

Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-66/04/005/A

Code_Aster
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Titrate:
SDNL111 - Impact of two beams


Date:
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:
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3.3 Functionalities
tested

Commands
STANDARD DEFI_OBSTACLE
“BI_PLAN_Z”
“BI_PLAN_Y”
“BI_CERCLE”
DYNA_TRAN_MODAL SHOCK
NOEU_2
DIST_1
DIST_2
INTITULE
VITE_INIT_GENE

METHODE
“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 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 beams POUTRE1 and POUTRE2.

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: 5.109 NR/m

Damping of shock: AMOR_NOR: 2.104 NS/m

Temporal integration is carried out with the algorithm of Euler and a step of time of 106 S.

4.2
Characteristics of the grid

A number of nodes: 102

A number of meshs and types: 100 SEG2
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-66/04/005/A

Code_Aster
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Titrate:
SDNL111 - Impact of two beams


Date:
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4.3 Functionalities
tested

Commands
STANDARD DEFI_OBSTACLE
“BI_CERC_INT”
DYNA_TRAN_MODAL SHOCK
NOEU_2

DIST_1

DIST_2

INTITULE
VITE_INIT_GENE

METHODE
“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 modelled with meshs QUAD4 (50 by 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 modelled by loads of contact. One uses AFFE_CHAR_MECA with the key word
CONTACT.
Pairing is of master-slave type. The method used is CONTRAINTE.

Temporal integration is carried out with method HHT (= - 0.1) and a step of time of 106 S.
The subdivision of step of time is authorized. For the solvor, one uses method MULT_FRONT.

5.2
Characteristics of the grid

A number of nodes: 408

A number of meshs and types: 50 QUAD4
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-66/04/005/A

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Titrate:
SDNL111 - Impact of two beams


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5.3 Functionalities
tested

Commands


AFFE_CHAR_MECA CONTACT
CONTRAINTE

CREA_CHAMP OPERATION “AFFE”
TYPE_CHAM
“NOEU_DEPL_R”

AFFE
GROUP_NO
“POU1”
“POU2”
NOM_CMP
“DZ”
DYNA_NON_LINE METHOD
HHT


ETAT_INIT
VITE

5.4 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 320 mem_job 800Mo ncpus1

6 Modeling
D

6.1
Characteristics of modeling

The two beams are modelled with meshs QUAD4 (50 by 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 modelled 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 method HHT (= - 0.1) and a step of time of 106 S.
The subdivision of step of time is authorized. For the solvor, one uses method MULT_FRONT.

6.2
Characteristics of the grid

A number of nodes: 408

A number of meshs and types: 50 QUAD4
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-66/04/005/A

Code_Aster
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Titrate:
SDNL111 - Impact of two beams


Date:
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6.3 Functionalities
tested

Commands


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
VITE

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 modelled with meshs QUAD4 (50 by 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 modelled by loads of contact. One uses AFFE_CHAR_MECA with the key word
CONTACT.
Pairing is of master-slave type. The method used is CONTINUE, without friction.

Temporal integration is carried out with method HHT (= - 0.1) and a step of time of 106 S.
The subdivision of step of time is authorized. For the solvor, one uses method MULT_FRONT.

7.2
Characteristics of the grid

A number of nodes: 408

A number of meshs and types: 50 QUAD4
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-66/04/005/A

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Titrate:
SDNL111 - Impact of two beams


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7.3 Functionalities
tested

Commands


AFFE_CHAR_MECA CONTACT
CONTINUE

INTEGRATION
NOEUD

CREA_CHAMP OPERATION “AFFE”

TYPE_CHAM
“NOEU_DEPL_R”

AFFE
GROUP_NO
“POU1”
“POU2”
NOM_CMP
“DZ”
DYNA_NON_LINE METHOD
HHT


ETAT_INIT
VITE

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

Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-66/04/005/A

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Titrate:
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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 model 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 method CONTINUE.

Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear structures
HT-66/04/005/A

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