Impact simulation of a torque box beam column

Impact simulation of a torque box beam column

Citation for published version (APA):

Bruijs, W. E. M. (1987). Impact simulation of a torque box beam column. (DCT rapporten; Vol. 1987.039). Technische Universiteit Eindhoven.

Document status and date: Published: 01/01/1987 Document Version:

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BEAM COLUMN

Wim Bruijs June 1987

The aim of this report is to establish the feasibility o f the PISCES-3DELK program for the crash simulation of vehicles. Therefore a simulation of the

impact of a rigid mass to a torque box beam-column has been carried out. The

results o f this simulation are in good agreement with the results of

experiments described in literature. It i s concluded that the method the

program uses t o solve the basic continuum equations is very well suited t o

Introduction

The PISCES-3DELK program Problem description The calculatjm The results Conclusions References

1

2 3 6 7 2 4 25

1 INTRODUCTION

This report deals with the simulation o f the crash o f a torque box beam-

column. This beam is a component o f the front car structure.

The aim o f this simulation is to test whether the PISCES-3DELK program (a

three-dimensional Euler-Lagrange coupled finite-difference/finite-element

program) can be applied to crash simulation o f vehicles.

It has been chosen to simulate the crash of a torque box beam-column,

because results of calculations (Argyris, Balmer, Doltsinis & K u n , 1986)

and experiments (Ni, 1973) are reported in literature. It is remarked that

the boundary conditions and the results o f the simulations and experiments,

are not given completely in literature.

In chapter 2 , a description of the PISCES-3DELK program is given. The

model is described in chapter 3, and in chapter 4 the calculation will be

discussed. The results of the calculation will be presented in chapter 5,

2 THE PISCES-3DELK PROGRAM

The PISCES-3DELK program is a general purpose computer program, that has

been designed to analyze continuum mechanics problems in three dimensions. The partial differential equations describing conservation of mass, momentum and energy are solved using finite element and finite difference methods. The program contains an Euler processor and a thin shell processor, that can be coupled in one single computational task.

For the crash simulation only the thin shell processor has been used. The thin shell processor employs an explicit finite element scheme.

Quadrilateral regions are modeled by a pair of triangular elements. The

shell elements are formulated in corotational coordinate systems. Each triangular element has three nodes (in the angular points of the triangle). Each node has six degrees of freedom, three rotations and three

translations. The element is of the constant strain type for the membrane strains and of the linear type for the bending strains. The displacements

perpendicular to the plane o f the element are interpolated between the nodes

using cubic polynomials. The displacements in the plane are interpolated using linear functions.

The integration points are situated at the midpoints of the sides. The

number o f Gaussian integration points over the thickness can be chosen by

the user.

The thin shell elements can interact with each other by means o f a three-

dimensional impact logic. Using the impact logic, it is possible to define a

surface by a number of nodes that have to be part of that surface. An impact

can be modeled by defining another set o f nodes, that are not allowed to

penetrate the surface.

The program version used for the calculation is version 2, level 26.

Unaccurate results lead to the addition of second order terms to the matrix that is used to calcu1afz.e the new nodal coordinate systems out of the nodal coordinate systems st the beginning of the time step. The nodal base vectors are scaled to unity length after calculation in order to avoid the

3 PROBLEM DESCRIPTION

The geometry of the torque box beam-column, which is a representative

component of the front car structure, is given in fig. i .

Impact mass: 1932 kg

Impact velocity: 4 . 7 1 m/s

a

Fly. i : The geometry of the torque box beam-column

The torque box beams are fully clamped at the lower ends. At the upper end,

the torque box beams are struck by a mass of 1932 kg with a speed of 4 . 7 4

m/s. The upper ends are allowed t o move vertically, but rotations of the

upper ends are suppressed.

The torque box beam-columns are made of aluminum 6016-T6. The strain-rate effects of the material are ignored. The density of the material is 2760

kg/m

.

The other material properties are given in fig. 2. The isotropic work

hardening theory has been used.

3

Fig. 2: The material properties o f aluminum 606l-T6

Because of symmetry considerations, only a half part of one torque box beam-

column is modeled. The column is divided in 182 zones (fig. 3). Each zone i5

again divided in two triangular shell elements (except for the four

triangular zones). The mesh has been refined at the places where the largest

deformations are expected.

For the boundary conditions it is referred to fig. 4.

impact end

clamped end

Because it is not possible to define rigid bodies, the impact mass has been

modeled using shell elements too. In each node, the displacements in the x

and y direction and the rotations in the

x i

y and

z

directions are

prescribed to be equal to zero. This implies that the behaviour of the mass

will be close to the behaviour o f a rigid body.

The impact is modeled by defining a plane through the nodes of the impact

mass. The nodes o f the impact end (see fig. 3 ) are not allowed to penetrate

this plane.

2

t,

X:

x

J -

0 : zy-symmetry displacements equal to zero: x-direction rotations equal to zero: y-direction z-direction clamped end displacements equal to zero: x-direction y-direction z-direction rotations equal to zero: x-direction y-direction z-direction impact end displacements equal to zero: x-direction y-direction rotations equal to zero: x-direction y-direction z-direction

4 THE CALCULATION

The program calculates the maximum stable time increment using: d

A t =

-

_C

where d is the height of the smallest triangular element and c is the wave

velocity :

In this equation E is the Youngs modulusr p the density and v is the Poisson

ratio.

Five integration points were used in the thickness direction.

For the crash simulation, the time increment was equal to 2.13 H S . The

program uses a safety factor o f 0.8, so the time increment used for the

calculations was 1.70 ms.

The calculation involved 6000 time increments and consumed 45.5 hours CPU

time on a VAX 11-780 computer. The impact time was 10.19 ms. The calculation

is stopped, because no interesting data were expected from a continuation o f

5 THE RESULTS

Deformations

The deformations are presented in fig. 5 . A frontal view of the deformations

i s given in fig. 6 . It is remarked that the displacements in fig. 5 are

multiplied by a factor 2, in order to get a better impression of the

deformed shape of the torque box beam-column. The displacements in fig. 6

are the real values

time = 3.4 ms time = 6 . 8 ms time = 10.2 ms

cycle 2000 time = 3.4: ms displacement upper end = 16 mm cycle 4000 time = 6.8 ns displacement upper end = 33 mm cycle 6000 time = 1 8 . 2 ms displacement upper end = 50 mm

Fig. 6 Frontal view of the stages of deformation

The deformations of the section marked in fig. 7 are given in fig. 8. The sections are viewed in the negative z-direction.

I

time = 5.1 ms

Forces

In fig. 8a, the nodal components of the reactioon force on the wall are

plotted as a function of the time (ZR, see fig. I ) . In fig. 8a and 9, the

total reaction force on the wall is given as a function of the time and the

displacements of the impact end respectively (2R, see fig. 1 ) . In fig. I O ,

the force applied by the torque box beam-column on the rigid mass, the so-

called barrier force is plotted against the time. It is remarked that less points were used €or this plot. In fig. 1 1 , the reaction force is plotted against the time using different filter frequencies as recommended by SAE J211b. In all these plots, the forces of two full torque box beam-columns are given. These results can be compared with the results of the experiments

of Ni (1973). Ni found a maximum in the barrier force of about: 89 kN at a

displacement of the impact end of about 12 mm (fig. 12). From fig. 10 it

appears that the maximum barrier force is about 90 kN at a time of about 2

ms or a displacement of the impact end of about 10 min. Because the reaction

force differs from the barrier force approximately only by a shift along the

time axis, the mnximum can also be read from the figs. 8 and 9 . This also

results in a maximum value of the force of a h u t 90 kR. At the end of the

calculations, the barrier force is about 60 kN and the displacement of the

impact end is about 50 mm. Ni (1973) found from his experiments a force of

about 60 kN at a displacement of 50 mm.

CRASH

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- - _ _ _ _ _ _ _ _ _

1

R O A D - V E H I C L E S RESEARCH I N S T I T U T E 8 7 0 6 1 1 l ! h h I m p a c t r e s p o n s e o f c u r v e d b o x b e a m F i i t e r f r e q u e n c y i n f l u e n c e

I

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ - - - Y 1 e Y2 -d- Y3

+

Y4

*

95.83 ( x = Z . 1 4 ) 86.98 (x=2.351 7 8 . 4 i ( ~ ~ 6 . 0 7 ) -0.000 ( x = O . 119) m a x . 9 8 . 1 1 ( x = 2 . 1 1 ) m i n . m e a n I e v e I c u m 3 m s c o n 3 m s i n t s c -0.000 (x=O. 1 1 9) - 0 . 0 0 0 ( * = O . 1 1 9) - 0 . 0 0 0 ( x = O . 1 1 9) H I C I : Y 1 C k N 3 ¶ 80 i 60 140 ? 20

-

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U o L LL 80 60 4 0 20 O l _i I I I I I _{I !} 0.00 I I I L I I I _I I I I I I I 1 I I I I I -90 60 I t 1 , I u 3 o O O I c C C U c I L L

:

i 1 c < ti 3 0 1 . S O 3.00 4.50 6 - 0 0 7 . 5 0 T i m e ( m s e c ) 9.00 10.50 12.00

Fig. 11: The reaction force as a function of the time using different filter

Displacement and velocity history

In fig. 13, the displacements of the impact end of the torque box beam-

column i.s given as a function of the time. Fig. I 4 shows the velocity

history of the impact mass.

If the surface under the curve of fig. 8b is calculated and divided by the mass of the rigid body, the result is an approximation of the decrease of the velocity of the impact mass. The resulting velocity decrease will be a too small approximation, because of the shift along the time axis of the reaction force, when compared to the barrier force. The decrease of the

velocity according to this method is 0 . 3 8 m/s (fig. 1 5 ) . The velocity

decrease resulting from the crash simulation is 0.39 m/s (fig. 1 4 )

Energy

In fig. 16 and 17, the kinetic energy of the impact mass and the total

energy are plotted as a function of the time. It is remarked that the energy

plotted is the energy of the modeled part of the construction only. Stresses

In fig. 18 the stresses are given at a time of 10.2 ms related to the

undeformed configuration. it is remarked that the stress plotted is the average mi.dplane stress of the element. This explains why the stresses are still in the elastic range.

CRASH

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+

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I I I i I I I I I I i I I I I O

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CRASH

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_ _ _ _ _ _ _ _ _ _ _ _

ROAD-VEHICLES

RESEARCH

INSTITUTE

870611

I m p a c t r e s p o n s e o f c u r v e d b o x b e a m _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ - - _ - - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ - - - Y + Yi

+

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-

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+

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0

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.-

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I I I I I I I I I I I I I I I

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UN U T

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T

:-

6 CONCLUSIONS

The aim o f this simulation was to test the feasibility of the PISCES-3DELK

program for the crash simulation o f vehicles. The following remarks are

made.

The results o f this simulation fit well with the experimental findings

reported by N i ( 1 9 7 3 ) .

The CPU time of 45.5 hours is too long for a practical application o f crash

simulation.

The CPU time necessary for the impact logic is not known. This can become an

important factor of the total CPU time of the simulation o f a complete car

crash.

In closing it ia remarked that, for this simulation a construction part of the vehicle, that can be modeled by triangular elements completely, is

chosen. For .the simulation of the impact of a complete vehicle structure,

it is desired to extend the code with other elements like beam and rigid

elements. I t can be concluded that the method the grogram uses to solve the

basic continuum equations, is very well suited to be applied t o crash

simulation. However, until the extensions mentioned earlier are made, it is

Argyris, J., Balmer, H.A., Doltsinis, J.St. & Kurz, A. ( 1 9 8 6 ) . Computer Simulation of Crash Phenomena. International Journal for Numerical Methods in Ensineerinq, 22, 497-519.

Ni, C. (1973). Impact response of curved box beam-columns with large global and local deformations. ASME/AIAA/SAE, 14th Strutures. Structural Dynamics and Materials Conf., Williamsburg, VA, U . S . A .