wp5 - computational mechanics acceleration … project department of aerospace engineering* -...

ROBUST PROJECT Department of Aerospace engineering* - Politecnico di Milano WP5 - Computational Mechanics Acceleration transducers on Finite Element vehicle models for crash simulations with Ls-Dyna MAIN REPORT Volume 1 of 1

(*)via La Masa, 34 Milan-ITALY tel: +39 02 23998316 - fax: +39 02 23998334 Jan 2005 Doc. No.: ROBUST-05-007 - Rev. 0

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Department of Aerospace engineering Politecnico di Milano Doc. No.: ROBUST-05-007 - Rev. 0 WP5 - Computational Mechanics Acceleration transducers on Finite Element vehicle models for crash simulations with Ls-Dyna

MAIN REPORT

MAIN REPORT

Report title: WP5 - Computational Mechanics Acceleration transducers on Finite Element vehicle models for crash simulations with Ls-Dyna Doc. No.: ROBUST-05-007 - Rev. 0 Reporter(s):

Mario Mongiardini Abstract: The Robust Project aims to improve scientific and technical knowledge on the main issues still open in the new European standards on road restraint system EN 1317 [1-2]. The knowledge acquired will form the basis of updated standards for EN1317 and lead to more advanced road restraint systems and improve road-users safety. This report is part of the deliverables from Work Package 5 (WP5) - Computational Mechanics. KEYWORDS: Road restraint system, crash testing, Finite Element simulation

Rev. Date Prepared by Checked by Approved by Others

0 17/01/2005

Marco Anghileri Elisa Oldani

Mario Mongiardini

ROBUST project Pageii


MAIN REPORT

CONTENTS

ROBUST PROJECT.......................................................0

1 INTRODUCTION ..........................................................1

2 SUMMARY ...................................................................2

3 OUTPUT FREQUENCY................................................3

4 LOCATION OF THE ACCELERATION SENSOR. ....17

5 CONCLUSIONS .........................................................28

REFERENCES.................................................................30

ROBUST project Page1/30


MAIN REPORT

1 INTRODUCTION The Robust Project aims to improve scientific and technical knowledge on the main issues still open in the new European standards on road restraint system EN 1317 [1-2]. The knowledge acquired will form the basis of updated standards for EN1317 and lead to more advanced road restraint systems and improve road-users safety. This report is part of the deliverables from Work Package 5 - Computational Mechanics. The objective of WP5 is:

• Evaluation and enhancement of the use of computational mechanics to complement experimental activity

• Criteria and procedures for the validation of computational mechanics results through comparison with test results

• Reconstruction of real life accidents • Identification of the activity needed for further enhancement of the use of

computational mechanics. This report documents the influence of the sampling rate over the acquisition of acceleration data using Finite Element vehicle models for crash simulations. The influence of the location of the accelerometers has been investigated, as well. The code used to perform the simulations is Ls-dyna [3-4].



MAIN REPORT

2 SUMMARY The crash test scenario of a 900 kg small passenger car (Geo-Metro [5]) striking a rigid concrete Round Robin barrier at a speed of 100 km/hr and with an angle of 20 deg. was considered. The impact conditions comply with the European Committee for Standardization (CEN) specifications for the homologation of a roadside safety barrier [1-2]. The impact scenario is shown in Figure 1.

x

y

Figure 1: Impact scenario, top and front view.

In order to collect the acceleration and velocity-time histories of the vehicle and to consequently assess the occupant risk factors during the impact simulation, an accelerometer sensor was included in the vehicle model. For this purpose, a standard element is available in LS-DYNA [3-4], defined by the card *ELEMENT_SEATBELT_ACCELEROMETER. This element is represented by a rigid brick that must be properly connected to the vehicle (at the centrum of gravity of the vehicle), usually by means of a rigid link to a massive part in the model in order to attenuate the high elemental frequencies. With these built-in features, the user can collect the acceleration-time histories in a local coordinate system moving with the sensor, defined by three nodes of the element-accelerometer. This device proves to be very useful when comparing the simulation results with data measured in a full-scale crash test, where accelerometers are mounted similarly on the test vehicle. The output nodes are set in the card *DATABASE_HISTORY_NODE, while the output frequency is specified with the card *DATABASE_NODOUT. Nodal accelerations, velocities and displacements are written in the NODOUT ASCII file as they are computed by the solver without any data filtering or processing. According to these considerations, it is responsibility of the user to choose a reasonable output frequency to avoid aliasing phenomena. A practical rule to determine a suitable output frequency is to refer to the maximum frequencies in the model and, therefore, to the integration timestep, related for stability reasons to the upper bound of the frequencies of the model. If no other methods can guarantee the absence of aliasing phenomena at a chosen output frequency, it is advisable to set a sampling period of the same order of magnitude of the timestep.



MAIN REPORT

In this document the results of the impact simulation are reported, evaluating the influence of the output frequency on the computation of the acceleration-time histories and occupant risk factors. The same impact scenario and finite element model were used to evaluate the effect of the location of the accelerometer sensor. In particular, other nodes in the model were included in the nodal history output, either belonging to the body to which the accelerometer is connected, or external. The location of the accelerometer in the model is shown in 2.

Figure 2: Location of the element-accelerometer.

3 OUTPUT FREQUENCY Three output frequencies were considered:

• 854 kHz (sampling time equal to the integration timestep) • 100 kHz • 10 kHz.

The data output in the NODOUT ASCII file were used to compute the occupant risk factors, as prescribed in the CEN specifications, by means of the Test Risk Assessment Program (TRAP), a piece of software developed by Texas Trasportation Institute for this purpose [6]. The output data were initially filtered with a standard 180kHz SAE filter and then processed by the software. The occupant risk factors are summarized in Table 1. The acceleration-time histories obtained with the three different output frequencies are compared in Figure 3 through Figure 5.



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Table 1: Occupant Risk Factors according to CEN standards.

2.1.1.1.1 Occupant Risk Factors • Impact Velocity (m/s): the occupant is idealized as a lumped mass located within a

compartment. The occupant after vehicular impact can move freely within the compartment until contact with the front and side of it occurs. The impact velocity is computed when the hypothetical head of the occupant hits the front or side of the compartment, located at a distance of 0.6 m and 0.3 m respectively.

o Vx o Vy

• Theoretical Head Impact Velocity (THIV): Resultant of the x and y components of the impact velocity at the instant when contact of the occupant’s head with the front or side of the compartment occurs.

o THIV (km/hr) o THIV (m/s)

• Acceleration Severity Index (ASI): The acceleration severity index ASI is a function of time, computed with the following equation (1) :

( ) ( ) ( ) ( )[ ]ASI t = ax / ax + ay / ay + az / az2 2 1/2$ $ $ 2

where :

âx, ây and âz are limit values for the components of the acceleration along the body axes x,y and z ; ax, ay and az are the components of the acceleration of a selected point P of the vehicle, averaged over a moving time interval δ = 50 ms, so that :

ax tt

ay tt

a tt

= 1 ax dt ; = 1 ay dt ; z = 1 az dt ;δ

δ

δ

δ

δ

δ+ + +∫ ∫ ∫ (2)

The index ASI is intended to give a measure of the severity of the vehicle motion for a person seated in the proximity of point P during an impact.

• Ridedown Accelerations (g’s): 10 ms moving average ridedown accelerations of the occupant’s head subsequent to contact with the compartment.

o Ax o Ay o Az

• Maximum vehicular rotation angles (deg.): o Roll o Pitch o Yaw



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0 0.025 0.05 0.075 0.1 0.125 0.15-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5x 106

Time [s]

Acc

eler

atio

n [m

m/s

2 ]Ax 854kHz Ax 100kHzAx 10kHz

Figure 3: Longitudinal Acceleration-time history at three different sampling

frequencies.

0 0.025 0.05 0.075 0.1 0.125 0.15-2

-1.5

-1

-0.5

0

0.5

1

1.5

2x 106

Time [s]

Acc

eler

atio

n [m

m/s

2 ]

Ay 854kHzAy 100kHzAy 10kHz

Figure 4: Lateral Acceleration-time history at three different sampling frequencies.



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0 0.025 0.05 0.075 0.1 0.125 0.15-4

-3

-2

-1

0

1

2

3x 106

Time [s]

Acc

eler

atio

n [m

m/s

2 ]

Az 854kHzAz 100kHzAz 10kHz

Figure 5: Vertical Acceleration-time history at three different sampling frequencies.

Excellent agreement is found in histories output at 854 kHz and 100 kHz, while histories output at 10 kHz prove strongly discordant. The results shown in Figure 3 through Figure 5 were all filtered with the same 180Hz-sae filter. In Figure 6 through Figure 11velocities and displacements obtained as output in the NODOUT file are compared to the corresponding histories obtained by integrating the acceleration-time histories sampled at the three different output frequencies. Integration was performed using a simple trapezoidal rule, applied once to obtain the velocities and twice for displacements. All time-histories shown in Figure 3 through 11 are diagrammed in the global reference system shown in Figure 1. The corresponding velocity and displacement-time histories sampled at different frequencies are in good agreement. On the other hand, the integrated histories show some significant differences. Histories resulted from integration of data collected at 854 kHz and 100 kHz show only negligible differences from the corresponding sampled histories, due to numerical error in the integration procedure. Considering instead histories sampled at 10 kHz, all the integrated velocities and displacements diverge significantly from the simulation output. This behaviour is a clear sign of aliasing present in the 10kHz-sampled acceleration-time histories.



MAIN REPORT

0 0.025 0.05 0.075 0.1 0.125 0.152.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8x 104

Time [s]

Vel

ocity

[mm

/s]

Vx 854kHz SampledVx 854kHz Integrated

Figure 6: Longitudinal velocity-time history sampled at 854-kHz and corresponding

integrated history.

0 0.025 0.05 0.075 0.1 0.125 0.152.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8x 104

Vel

ocity

[mm

/s]



integrated history.



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0 0.025 0.05 0.075 0.1 0.125 0.152

2.5

3

3.5

4

4.5x 104

Time [s]

Vel

ocity

[mm

/s]



integrated history.

0 0.025 0.05 0.075 0.1 0.125 0.15-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

Time [s]

Vel

ocity

[mm

/s]

Vy 854kHz SampledVy 854kHz Integrated

Figure 9: Lateral velocity-time history sampled at 854-kHz and corresponding

integrated history.



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0 0.025 0.05 0.075 0.1 0.125 0.15-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000V

eloc

ity [m

m/s

]Vy 100kHz SampledVy 100kHz Integrated


integrated history.

0 0.025 0.05 0.075 0.1 0.125 0.15-14000

-12000

-10000

-8000

-6000

-4000

-2000

0

2000

Time [s]

Vel

ocity

[mm

/s]

Vy 10kHz SampledVy 10kHz Integrated


integrated history.



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0 0.025 0.05 0.075 0.1 0.125 0.15-1000

-500

0

500

1000

1500

2000

2500

3000

3500

4000

Time [s]

Vel

ocity

[mm

/s]

Vz 854kHz SampledVz 854kHz Integrated

Figure 12: Vertical velocity-time history sampled at 854-kHz and corresponding

integrated history.

0 0.025 0.05 0.075 0.1 0.125 0.15-1000

-500

0

500

1000

1500

2000

2500

3000

3500

4000

Time [s]

Vel

ocity

[mm

/s]



integrated history.



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0 0.025 0.05 0.075 0.1 0.125 0.15-2000

0

2000

4000

6000

8000

10000

Time [s]

Vel

ocity

[mm

/s]



integrated history.

0 0.025 0.05 0.075 0.1 0.125 0.150

500

1000

1500

2000

2500

3000

3500

Time [s]

Dis

plac

emen

t [m

m]

Dx 854kHz SampledDx 854kHz Integrated

Figure 15: Longitudinal displacement-time history sampled at 854-kHz and

corresponding integrated history.



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0 0.025 0.05 0.075 0.1 0.125 0.150

500

1000

1500

2000

2500

3000

3500

Time [s]

Dis

plac

emen

t [m

m]




0 0.025 0.05 0.075 0.1 0.125 0.150

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Time [s]

Dis

plac

emen

t [m

m]






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0 0.025 0.05 0.075 0.1 0.125 0.15-900

-800

-700

-600

-500

-400

-300

-200

-100

0

100

Time [s]

Dis

plac

emen

t [m

m]

Dy 854kHz SampledDy 854kHz Integrated

Figure 18: Lateral displacement-time history sampled at 854-kHz and corresponding

integrated history.

0 0.025 0.05 0.075 0.1 0.125 0.15-900

-800

-700

-600

-500

-400

-300

-200

-100

0

100

Dis

plac

emen

t [m

m]

Dy 100kHz SampledDy 100kHz Integrated


integrated history.



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0 0.025 0.05 0.075 0.1 0.125 0.15-900

-800

-700

-600

-500

-400

-300

-200

-100

0

100D

ispl

acem

ent [

mm

]Dy 10kHz SampledDy 10kHz Integrated


integrated history.

0 0.025 0.05 0.075 0.1 0.125 0.15-10

0

10

20

30

40

50

60

70

80

90

Time [s]

Dis

plac

emen

t [m

m]

Dz 854kHz SampledDz 854kHz Integrated

Figure 21: Vertical displacement-time history sampled at 854-kHz and corresponding

integrated history.



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0 0.025 0.05 0.075 0.1 0.125 0.15-20

0

20

40

60

80

100

Time [s]

Dis

plac

emen

t [m

m]



integrated history.

0 0.025 0.05 0.075 0.1 0.125 0.15-50

0

50

100

150

200

250

300

350

400

450

Dis

plac

emen

t [m

m]



integrated history.



MAIN REPORT

To complete the overview of results, occupant risk factors are compared in Table 2.

Table 2: Comparison between acceleration data collected at different sampling

frequencies.

Occupant Risk Factors fc 854 kHz fc 100 kHz fc 10 kHz

Impact Velocity, Vx [m/s] 5.3 5.6 10.1

Impact Velocity, Vy [m/s] -7.2 -7.6 -14.2THIV [m/s] 8.7 9 16.5

Ridedown Acc., Ax [g] 3.6 -2.9 -85.3

Ridedown Acc, Ay [g] 6.5 4.5 -85.6PHD 11.1 15.3 158.4

ASI 1.85 1.95 4.39

Ax(50msec avg) [g] -10.4 -11.1 -33.7

Ay(50msec avg) [g] 15.7 16.4 30.3Az(50msec avg) [g] -7.3 -7.5 31.5Max. Roll [deg] 10 9.6 9.6

Max. Pitch [deg] 2.6 2.7 2.7

Max. Yaw [deg] 19.8 20.3 20.1

Again, data output at 854 kHz and 100 kHz show practically equivalent results. On the other hand, parameters computed from histories output at 10 kHz disagree completely with the others, except for the maximum rotation angles of the vehicle. It can be noticed that error is maximum for parameters computed in an instant in time (ridedown accelerations), and minimum for those that result averaged over time (impact velocities, rotation angles). The best choice of output frequency appears, therefore, to be 100 kHz, since it avoids aliasing phenomena and reduces the number of points to be collected with respect to the timestep sampling period. A practical criterion for the determination of a suitable output frequency can be identified: the sampling time should be the same order of magnitude of the integration timestep, because of its relation with the maximum frequencies in the model. To minimize the amount of information to be collected, it would be necessary to run several simulations, decreasing the output frequency until no aliasing phenomena occur. This method, however, does not provide a general indication, since the optimum output frequency depends on the features of the model, its mesh and material properties. Several analyses would, therefore, be necessary for any change in the model.



MAIN REPORT

4 LOCATION OF THE ACCELERATION SENSOR. The accelerometer block is connected to the vehicle by means of a rigid link in order to create a rigid body with a certain number of nodes belonging to other parts of the vehicle. The nodes that define this rigid body are highlighted in Figure 24.

Figure 24: Nodes belonging to the accelerometer block (rigid body)

In order to assess the influence of the accelerometer location, a few nodes around the accelerometer were considered, either belonging to the rigid body to which the element-accelerometer is connected, or belonging to other (deformable) parts of the vehicle. Regarding these last nodes, two locations were monitored: a location forward and a location on the left side of the accelerometer block. The examined locations are shown in Figure 25.

Figure 25: Locations of the nodes used as acceleration sensors.



MAIN REPORT

The accelerometer data can be output in a local coordinate system moving with the vehicle, distinct from the fixed global reference frame. In order to output all the nodal histories in the same coordinate frame, a new frame coincident with the accelerometer one was defined by means of the option *DEFINE_COORDINATE_NODES. Time-histories for nodes 41381, 41379 and 40345 were output in this local coordinate frame by setting the card *DATABASE_HISTORY_NODE_SET_LOCAL. It is important to notice that occupant risk parameters are computed on the basis of acceleration-time histories referred to a local reference frame moving with the vehicle with its origin in the vehicle centrum of gravity. The local system definition, according to the general convention for the computation of occupant risk factors, is shown in Figure 26.

Figure 26: Local reference system convention.

Node 41381 belongs to the rigid body that includes the element-accelerometer, while nodes 41379 and 40345 belong to the floor of the vehicle, a deformable part of the vehicle model. In this phase of the analysis the output frequency of 100 kHz was used for the file NODOUT. The time histories collected at node 41381 show very good agreement with the corresponding histories at node 700002 (reference node of the element-accelerometer). The summary of the computed occupant risk factors is shown in Table 3.



MAIN REPORT

Table 3: Comparison of occupant risk factors at nodes 700002 and 41381.

Occupant Risk Factors Node 700002 Node 41381

Impact Velocity, Vx [m/s] 5.6 5.7

Impact Velocity, Vy [m/s] -7.6 -7.8THIV [m/s] 9 9.2

Ridedown Acc., Ax [g] -2.9 -3.1

Ridedown Acc, Ay [g] 4.5 4.3PHD 15.3 15

ASI 1.95 1.99

Ax(50msec avg) [g] -11.1 -11

Ay(50msec avg) [g] 16.4 16.9Az(50msec avg) [g] -7.5 -8.3Max. Roll [deg] 9.6 9.6

Max. Pitch [deg] 2.7 2.7

Max. Yaw [deg] 20.3 20.3 Acceleration, velocity, rotational velocity, angle and displacement-time histories of the vehicle computed at nodes 41379 and 40345 are compared with the corresponding time histories at node 700002 in Figure 27 through Figure 41. Acceleration, velocity and displacement-time histories are referred to the global reference frame, while roll, pitch and yaw angular velocities and rotation angles refer to the local reference frame.



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0 0.025 0.05 0.075 0.1 0.125 0.15-8

-6

-4

-2

0

2

4

6x 105

Time [s]

Acc

eler

atio

n [m

m/s

2 ]

Ax 100kHz @ CGAx 100kHz @ 41379Ax 100kHz @ 40345

Figure 27: Longitudinal acceleration-time history

0 0.025 0.05 0.075 0.1 0.125 0.15-10

-8

-6

-4

-2

0

2

4

6

8x 105

Time [s]

Acc

eler

atio

n [m

m/s

2 ]

Ay 100kHz @ CGAy 100kHz @ 41379Ay 100kHz @ 40345

Figure 28: Lateral acceleration-time history.



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0 0.025 0.05 0.075 0.1 0.125 0.15-3

-2

-1

0

1

2

3x 106

Time [s]

Acc

eler

atio

n [m

m/s

2 ]

Az 100kHz @ CGAz 100kHz @ 41379Az 100kHz @ 40345

Figure 29: Vertical acceleration-time history.

0 0.025 0.05 0.075 0.1 0.125 0.152.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8x 104

Time [s]

Vel

ocity

[mm

/s]

Vx 100kHz @ CGVx 100kHz @ 41379Vx 100kHz @ 40345

Figure 30: Longitudinal velocity-time history.



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0 0.025 0.05 0.075 0.1 0.125 0.15-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

Time [s]

Vel

ocity

[mm

/s]

Vy 100kHz @ CGVy 100kHz @ 41379Vy 100kHz @ 40345

Figure 31: Lateral velocity-time history.

0 0.025 0.05 0.075 0.1 0.125 0.15-3000

-2000

-1000

0

1000

2000

3000

4000

5000

Time [s]

Vel

ocity

[mm

/s]

Vz 100kHz @ CGVz 100kHz @ 41379Vz 100kHz @ 40345

Figure 32: Vertical velocity-time history



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0 0.025 0.05 0.075 0.1 0.125 0.150

500

1000

1500

2000

2500

3000

3500

4000

Time [s]

Dis

plac

emen

t [m

m/s

]Dx 100kHz @ CGDx 100kHz @ 41379Dx 100kHz @ 40345

Figure 33: Displacement-time history in the longitudinal direction.

0 0.025 0.05 0.075 0.1 0.125 0.15-1000

-800

-600

-400

-200

0

200

Time [s]

Dis

plac

emen

t [m

m/s

]

Dy 100kHz @ CGDy 100kHz @ 41379Dy 100kHz @ 40345

Figure 34: Displacement-time history in the lateral direction.



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0 0.025 0.05 0.075 0.1 0.125 0.15-20

0

20

40

60

80

100

Time [s]

Dis

plac

emen

t [m

m/s

]

Dz 100kHz @ CGDy 100kHz @ 41379Dz 100kHz @ 40345

Figure 35: Displacement-time history in the vertical direction.

0 0.025 0.05 0.075 0.1 0.125 0.15-3000

-2000

-1000

0

1000

2000

3000

Time [s]

Rol

l Rat

e [d

eg/s

]

roll rate @ CGroll rate @ 41379roll rate @ 40345

Figure 36: Roll rate time history.



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0 0.025 0.05 0.075 0.1 0.125 0.15-4000

-3000

-2000

-1000

0

1000

2000

3000

Time [s]

Pitc

h R

ate

[deg

/s]

pitch rate @ CGpitch rate @ 41379pitch rate @ 40345

Figure 37: Pitch rate time history.

0 0.025 0.05 0.075 0.1 0.125 0.15-6000

-4000

-2000

0

2000

4000

6000

Time [s]

Yaw

Rat

e [d

eg/s

]

yaw rate @ CGyaw rate @ 41379yaw rate @ 40345

Figure 38: Yaw rate time history.



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0 0.025 0.05 0.075 0.1 0.125 0.15-2

0

2

4

6

8

10

Time [s]

Rol

l Ang

le [d

eg]

roll @ CGroll @ 41379roll @ 40345

Figure 39: Roll angle time history.

0 0.025 0.05 0.075 0.1 0.125 0.15-2

0

2

4

6

8

10

Time [s]

Pitc

h A

ngle

[deg

]

pitch @ CGpitch @ 41379pitch @ 40345

Figure 40: Pitch angle time history.



MAIN REPORT

0 0.025 0.05 0.075 0.1 0.125 0.15-20

-10

0

10

20

30

40

Time [s]

Yaw

Ang

le [d

eg]

yaw @ CGyaw @ 41379yaw @ 40345

Figure 41: Yaw angle time history.

The summary of the occupant risk factors computed at the three different sensor locations is shown in Table 4.

Table 4: Comparison between occupant risk factors computed at different location of the acceleration sensor.

Occupant Risk Factors Node 700002 Node 41379 error % 41379 Node 40345 error % 40345

Impact Velocity, Vx [m/s] 5.3 5.3 0.00 3.4 35.85

Impact Velocity, Vy [m/s] -7.2 -8.6 19.44 -8.9 23.61THIV [m/s] 8.7 37.2 327.59 7.6 12.64

Ridedown Acc., Ax [g] 3.6 -11.8 427.78 -20.1 658.33

Ridedown Acc, Ay [g] 6.5 12.5 92.31 14.5 123.08PHD 11.1 32.5 192.79 44.1 297.30

ASI 1.85 2.08 12.43 2.05 10.81

Ax(50msec avg) [g] -10.4 -11.5 10.58 -8.1 22.12

Ay(50msec avg) [g] 15.7 17.5 11.46 18.3 16.56Az(50msec avg) [g] -7.3 -10 36.99 -7.8 6.85Max. Roll [deg] 10 7.3 27.00 5.7 43.00

Max. Pitch [deg] 2.6 4.4 69.23 8.6 230.77

Max. Yaw [deg] 19.8 31.3 58.08 34.3 73.23



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Both acceleration-time histories computed outside the accelerometer block are characterized by numerical noise due to the high elemental frequencies. In fact, the accelerometer block is connected to a number of nodes by means of a rigid link and it refers, therefore, to a higher mass than nodes 41379 and 40345. Velocity and displacement time-histories at node 41379 and 40345 are in a fairly good agreement with the corresponding ones at node 700002 (accelerometer node, approximately centrum of gravity of the vehicle). Corresponding histories are qualitatively similar, but show offset values, as apparent in Figure 30 and in Figure 35. According to this considerations, occupant risk factors show good agreement on those parameters that result averaged over time (impact velocity, 50 msec average accelerations), while they are discordant on those others that are computed in an instant in time. High frequency components are particularly apparent in the diagrams of rotational velocity-time histories. (Figure 36 and Figure 37). The remarkable differences in the time histories of the changes in roll, pitch and yaw angle of the vehicle, measured at different locations may be determined by the local deformations of the vehicle floor pan around the nodes used as sensors. A deformation of the left side of the floor pan is apparent around node 40345, subsequently to the impact between the vehicle and the barrier; this event causes an increment in the local yaw and pitch angles with respect to the area where the element-accelerometer lies. It must be considered that the area surrounding the accelerometer is modelled as perfectly rigid. Figure 40 and 41 graphically describe this phenomenon. 5 CONCLUSIONS The analysis of the effects of the sampling frequency on the acquisition of acceleration data shows the need of choosing a sampling period with the same order of magnitude as the integration timestep. Otherwise, aliasing phenomena may occur. This fact leads to the necessity of acquiring a remarkable amount of data, considering the high frequencies in the model. In fact, the use of typical 5-mm element size for modelling metallic parts (aluminium, steel) with a density the order of 2700-7800 kg/m^3 and an elastic modulus of 70-210 GPa leads to an integration timestep for the explicit code of 1.0e-6 sec., in other words to an upper bound for the maximum frequency in the model of 2000 kHz. The maximum available sampling period remains the integration timestep (computed for the explicit code on the basis of stability considerations). According to the Shannon theorem, therefore, this sampling period allows the proper description of time histories with a maximum frequency component of 500 kHz, automatically filtering high frequency noise. Such a high frequency sampling is necessary to avoid aliasing phenomena, but it requires afterwards the filtering of the signals to identify the dynamics of the structure rather than the local vibrational frequencies of the elements. Usually filtering between 60 and 180 Hz is recommended. The identification of an optimum sampling frequency, in order to avoid aliasing phenomena thus minimizing at the same time the number of points to be collected, would require several subsequent finite element simulations, sampling the histories at decreasing frequencies, until aliasing occurs. This method would require, however,



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remarkable computational resources. In fact, the simulation of the impact scenario referenced in this work required about 20 CPU hours on a 1.7 GHz Personal Computer for 0.15 sec of effective simulated time. Besides, since the maximum frequencies depend on the features of the model, specifically of the mesh and of the material properties, these analyses should be repeated for any change in the model. The analysis of the effects of the location of the acceleration sensor showed the importance of a proper connection of the sensor to the rest of the model, in order to avoid the effects of local deformation in the measure area. In fact, the use of regular nodes proved unsuitable for determining the dynamics of the vehicle, because they are significantly affected by high frequency noise and the local deformations of the surrounding elements. The study should be completed by varying the position of the element-accelerometer, connecting the part to different node sets in the model.



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REFERENCES [1] CEN/EN 1317-1: Road restraint systems. Part 1: Terminology and general

criteria for test methods. European Committee for Standardization, 1998. [2] CEN/EN 1317-2: Road restraint systems. Part 2: Performance classes, impact

test acceptance criteria and test methods for safety barriers. European Committee for Standardization, 1998

[3] J. O. Hallquist, LS-DYNA Theory Manual, Livermore Software Technology Corp., Livermore, California, May 1998.

[4] J. O. Hallquist, LS-DYNA Keyword Manual Version 970, Livermore Software Technology Corp., Livermore, California, April 2003.

[5] TR-2004-0107: Evaluation of small car vehicle model GM_R2. Force Technology Norway AS, Rev. A, December 2004.

[6] B. Epperson, R. Bligh, and H. Ross, USER’S MANUAL – Test Risk Assessment Program (TRAP), Texas Transportation Institute, 1997.

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