2373 structural optimization of the automobile frontal

Structural optimization of the automobilefrontal structure for pedestrian protectionand the low-speed impact testM-K Shin1, S-I Yi2, O-T Kwon2, and G-J Park3*1BK21 Division, Hanyang University, Ansan City, Republic of Korea2Department of Mechanical Engineering, Hanyang University, Ansan City, Republic of Korea3Division of Mechanical and Information Management Engineering, Hanyang University, Ansan City, Republic of Korea

The manuscript was received on 15 December 2007 and was accepted after revision for publication on 29 August 2008.

DOI: 10.1243/09544070JAUTO788

Abstract: A variety of regulations are involved in the design of an automobile frontalstructure. The regulations are pedestrian protection, the Federal Motor Vehicle Safety Standard(FMVSS) part 581 bumper test, and the Research Council for Automobile Repairs (RCAR) test.The frontal structure consists of the bumper system and a crash box that connects the bumpersystem and the main body. The detailed design of the bumper system is performed to meet twoconditions: first, regulation for pedestrian protection (lower-legform impact test); second,FMVSS part 581. In the two regulations, the stiffness requirements of the bumper systemconflict with each other. In order to meet lower leg protection, a relatively soft bumper systemis required, while a relatively stiff system is typically needed to manage the pendulum impact. Anew bumper system is proposed by adding new components and is analysed by using the non-linear finite element method. An optimization problem is formulated to incorporate theanalysis results. Each regulation is considered as a constraint from a loading condition, and twoloading conditions are used. Response surface approximation optimization is utilized to solvethe formulated problem. RCAR requires reduction in the repair cost when an accident happens.The repair cost in a low-speed crash could be reduced by using an energy-absorbing structuresuch as the crash box. The crash box is analysed by using the non-linear finite element method.An optimization problem for the crash box is formulated to incorporate the analysis results.Discrete design using orthogonal arrays is utilized to solve the formulated problem in a discretespace.

Keywords: structural optimization, automobile frontal structure, pedestrian protection, low-speed impact test

1 INTRODUCTION

Many automobile companies and governments have

made much effort to enhance the safety of the dri-

vers and passengers. As a result, the number of casu-

alties and occupants’ injuries during an automobile

accident has decreased [1–4]. However, research

in certain areas is still lacking. Few studies have

examined vehicle–pedestrian accidents. It is essen-

tial to explore the design of the automobile frontal

structure to protect a pedestrian in a vehicle–pedes-

trian accident. Recently, many issues have been dis-

cussed in an effort to protect pedestrians in a vehicle–

pedestrian accident [5, 6], and the United Nations

Economic Commission for Europe/Working Party 29

(UNECE/WP29) has established pedestrian regula-

tions, which are global technical regulations (GTRs)

[7].

Various regulations are related to the automobile

frontal structure. They are pedestrian protection, the

East European Constitutional Review (ECER) 42 [8],

the Federal Motor Vehicle Safety Standard (FMVSS)

*Corresponding author: Department of Mechanical Engineering,

Hanyang University, 1271, Sa 1-Dong, Ansan City, Kyeonggi Do,

426-791, Republic of Korea. email: [email protected]

2373

JAUTO788 F IMechE 2008 Proc. IMechE Vol. 222 Part D: J. Automobile Engineering

at PENNSYLVANIA STATE UNIV on September 13, 2016pid.sagepub.comDownloaded from

http://pid.sagepub.com/

part 581 bumper test [9], and the Research Council

for Automobile Repairs (RCAR) test [10]. ECER 42,

FMVSS part 581, and the RCAR test are carried out at

a low speed. These regulations require a stiff bumper

for protecting the occupants and reducing the repair

cost; however, the bumper should be soft to reduce

pedestrian injuries.

According to the establishment of the GTR, many

researchers have examined vehicle design for pedes-

trian protection. Many studies proposed designing

methods for the frontal structures to meet pedes-

trian protection [3, 11, 12]. McMahon et al. [13]

performed structural design of the bumper energy

absorber to satisfy pedestrian protection. However,

since the stiffness of the bumper decreases, it is

difficult to satisfy other bumper regulations. Glasson

et al. [14] reported that it is difficult to meet various

regulations simultaneously through the structural

design of the front end module of the car. Therefore,

a new design method is needed to achieve this.

A design process is proposed for structural optim-

ization of the frontal structure of the vehicle. The

proposed design process has two steps. As men-

tioned earlier, the frontal structure is composed of a

bumper system and a crash box. Each compon-

ent is designed to satisfy different regulations.

First, a new bumper system is proposed in order

to satisfy the pedestrian protection test as well as the

FMVSS part 581 bumper test. The proposed bumper

system is designed by adding a thin plate and three

springs to meet the two regulations simultaneously.

A thin-plate structure is added between a bumper

energy absorber and a bumper rail and is connected

to the bumper rail by three springs. The thicknesses

of the plate and spring coefficients are determined

through size optimization. Each regulation is con-

sidered as a constraint in the optimization process.

Size optimization is performed by using response

surface approximate optimization (RSAO) [15, 16].

In general, since a crash problem has high non-

linearity and oscillation, sensitivity information is

difficult to calculate. Therefore, approximated meth-

ods, such as response surface methods (RSMs), are

widely used to solve the optimization problem [15].

RSAO is a type of RSM.

Second, a new type of crash box is proposed

to meet the RCAR test which evaluates the repair

cost of the frontal structure. If the crash box absorbs

more impact energy, the repair cost is expected to

be reduced. The shape of the proposed crash box

is determined in a discrete space. Thus, a detailed

shape of the crash box is determined to maximize

energy absorption by using discrete design using

orthogonal arrays (DOA) [17, 18]. LS-DYNA3D is

used for non-linear finite element analysis [19], and

VisualDOC is used for structural optimization using

RSAO [20].

2 REGULATIONS RELATED TO THE FRONTALSTRUCTURE

2.1 The frontal structure of a vehicle

In the case of a collision at a low speed, the frontal

structure of a vehicle should efficiently absorb the

impact energy to prevent occupants from injury and

to reduce damage to the car. Figure 1 presents a

schematic view of the frontal structure of a vehicle.

The structure consists of a bumper cover, a bumper

energy absorber, a bumper rail, a crash box, etc. [21].

In this research, the bumper system is defined as the

frontal structure in front of the crash box. Thus, the

frontal structure consists of the bumper system and

the crash box.

Figure 2 presents the frontal structure of an exist-

ing vehicle model. This is for a compact car which

is currently on the market. According to the pilot

study, the existing model does not satisfy pedes-

trian protection while satisfying FMVSS part 581,

which is for the stiffness of the bumper. The pedes-

trian protection regulation requires a soft bumper.

However, if the stiffness of the frontal structure

is low, it would be difficult to meet the other reg-

ulations. Therefore, a new frontal structure of the

vehicle is needed to satisfy the conflicting regula-

tions simultaneously. An improved design is pur-

sued on the basis of the existing frontal structure

model.

Fig. 1 A schematic diagram of the frontal structure ofa vehicle

2374 M-K Shin, S-I Yi, O-T Kwon, and G-J Park

Proc. IMechE Vol. 222 Part D: J. Automobile Engineering JAUTO788 F IMechE 2008



2.2 Regulations for pedestrian protection

Since 1987, pedestrian regulations such as GTRs

have been developed [5–7, 22]. In pedestrian reg-

ulations, pedestrian protection tests are classified

into a headform impact test, an upper-legform im-

pact test, and a lower-legform impact test. Of the

three tests, the lower-legform impact test is the most

important in designing the frontal structure of the

vehicle. Figure 3 shows the lower-legform impact

test with a lower-legform impactor. The lower-

legform impactor has two rigid parts: a femur sec-

tion and a tibia section covered with foams. The

legform impactor has a mass of 13.4 kg. The femur

section and the tibia section are connected by a knee

joint. During the lower-legform impact test, the

impactor hits the frontal bumper of the vehicle. The

number of target points should be more than three

including the centre and the side of the bumper. The

impact speed is 40 km/h. According to the GTR, the

requirements are as follows: first, the dynamic knee

bending angle should be less than 19u; second,

the knee shearing displacement should be less

than 6 mm; third, the acceleration at the upper

tibia should be less than 170g [7]. These conditions

should be considered to reduce the leg injury and

they are used as constraints in the optimization

process of a bumper system.

2.3 Low-speed vehicle test: FMVSS part 581

The National Highway Traffic Safety Administration

(NHTSA) has proposed the strength requirement of

the frontal structure in FMVSS part 581. In general,

the regulation has two kinds of test: the barrier test

and the pendulum impact test. Figure 4 illustrates

the FMVSS part 581 bumper test. The target points of

the test are the centre of the bumper, 300 mm offset

from the centre of the bumper, and 30u corner side.

In Fig. 4(b), h is the height of the centre of the pen-

dulum from the ground. In the case of the pendulum

impact test, the height h of the pendulum should

be located between 0.4 m and 0.5 m (between 16 in

and 20 in). The speed of the impact test is 8 km/h

(5 mile/h). Both the frontal and the rear bumper im-

pact tests are performed [9].

As illustrated in Fig. 5, an intrusion and a deflec-

tion are defined for judging damage to the vehicle

during the impact test. The intrusion is the relative

displacement of the front centre of the bumper rail

Fig. 3 Lower-legform impact test

Fig. 2 Frontal structure of an existing vehicle model

Fig. 4 Side view of the FMVSS 581 bumper test

The automobile frontal structure for pedestrian protection 2375




with respect to the rear end of the crash box during

the impact test. The intrusion is used for judging

damage to the outer part of the vehicle, such as

the leading edge of the hood. The deflection is the

relative displacement of the rear centre of the

bumper rail with respect to the rear end of the crash

box during the impact test. The deflection is used for

judging damage to the inner part of the vehicle, such

as the radiator. The distance is measured from the

front bumper cover to the leading edge of the hood.

If the intrusion is shorter than the distance, the

leading edge of the hood would not be damaged by

the impact. Another distance is measured from the

rear centre of the bumper rail to the radiator. If the

deflection is shorter than the distance, the radiator

would not be damaged by the impact [23]. The

intrusion and the deflection are used as constraints

in the optimization process of the bumper system.

2.4 Research Council for Automobile Repairs test

The RCAR is an international organization working

towards reducing insurance costs by improving

automotive damageability, repairability, safety, and

security [10]. The objectives of RCAR are to evaluate

the cost of the motor insurance for insurers and

to make motor vehicles safer, less damageable, and

more cost effective to repair after an accident occurs

[24].

Among a series of the RCAR tests, there is a test for

designing the frontal structure of a vehicle. It is

considered when designing the frontal structure of

a vehicle. The crash box and the side rail should

efficiently absorb the impact energy in a low-speed

impact to protect the interior components of the

vehicle and to reduce the repair cost. A computer

simulation is performed for describing the impact

test as illustrated in Fig. 6. The frontal structure

without the bumper cover and foam hits a flat rigid

barrier, and the impact speed is 15 km/h. In this

paper, the design process of the crash box is per-

formed to maximize the absorbed impact energy.

The absorbed impact energy is measured by the

strain energy of the frontal structure. If the strain

energy is maximized, the impact energy transmitted

to the other parts of the vehicle would decrease [25,

26]. This leads to lower repair costs. In achieving this

goal, a new crash box is proposed and a detailed

design process is carried out by DOA.

3 BACKGROUND THEORIES FOROPTIMIZATION

3.1 Response surface approximationoptimization

An optimization formulation of a design problem

with constraints is expressed as follows. Find

b [Rn ð1aÞ

to minimize

f bð Þ ð1bÞ

Fig. 6 A view of the RCAR test

Fig. 5 The intrusion and deflection distances





subject to

hi bð Þ~0 i~1, 2, � � � , lð Þ ð1cÞ

gj bð Þ¡0 j~1, 2, � � � , mð Þ ð1dÞ

bL¡b¡bU ð1eÞ

where b [Rn is the design variable vector, f(b) is the

objective function, hi(b) is the ith equality con-

straint, gj is the jth inequality constraint, n is the

number of design variables, l is the number of

equality constraints, m is the number of inequality

constraints, and bL and bU are the vectors for the

lower bound and upper bound respectively.

In general, the sensitivity information is difficult to

calculate in the optimization process of equations

(1). Therefore, approximation methods, such as the

RSM, are frequently used to solve the optimization

problem. In the RSM, the functions in equations (1b)

to (1d) are approximated to explicit functions [18,

27]. First, candidate design points are selected, and

the functions in equations (1b)–(1d) are calculated at

the candidate points. The explicit functions are gen-

erated from the function values through a curve-

fitting technique. The least-squares fitting method

is generally used for curve fitting. The optimization

process is performed by using approximated func-

tions.

RSAO is one of the engineering algorithms for

optimization [15, 16, 20]. It is a modified method

of the general RSM. The RSAO generates response

surfaces with a few selected candidate design points.

An optimum from the approximated surfaces is ob-

tained and added to the set of candidate points. New

response surfaces are made again and the process

continues in an iterative manner until the new

candidate point does not change. As the iteration

proceeds, constant, linear, and quadratic terms are

sequentially produced for the approximated func-

tions. Since RSAO is a kind of RSM, it has the advan-

tage of reducing the number of function calls.

Because RSAO utilizes an approximated function

instead of a real function, it may not find a

mathematical optimum satisfying the Kuhn–Tucker

necessary condition. However, since a useful solu-

tion can be found with a small number of analyses,

this method can be exploited in a crash problem,

which has high non-linearity and difficulty in calcul-

ating sensitivity. Structural optimization of the frontal

structure of the vehicle is carried out by RSAO.

The algorithm is installed in a commercial optim-

ization software system called VisualDOC, which is

used for structural optimization.

3.2 Discrete design using an orthogonal array

Generally, the formulation in equations (1) is for

problems where the design variables are defined in a

continuous space. However, in many practical prob-

lems, the design variables exist in a discrete space.

In other words, the design variables have certain

discrete values. A design problem of this research

is defined in a discrete space with the formulation

in equation (1).

Design of experiments (DOE) is employed to

determine the design variables in a discrete space.

The full factorial design in a discrete space can

find the best solution. However, it is an extrem-

ely expensive method because experiments should

be conducted for all combinations. The fractional

design is utilized to save cost since the factorial

design requires a large number of experiments. A

subset of the full factorial design is considered in

the fractional design. Among the fractional designs,

a method which directly uses orthogonal arrays is

selected. The method using an orthogonal array is

a type of DOE. This paper utilizes a method called

DOA to reduce the number of experiments. This

method can find a solution with a small number of

experiments (function calls) [28]. The method using

orthogonal arrays is defined for unconstrained prob-

lems. However, the general design problem formula-

ted in equations (1) has many constraints. There-

fore, a constrained problem must be transformed

into an unconstrained problem. For the transforma-

tion, an augment function Y(b) is introduced. An

augment function Y(b) is defined as [18]

Y bð Þ~f bð ÞzP bð Þ ð2Þ

P bð Þ~sXn

i~1

max 0, gj

� �, j~1, 2, � � � , m ð3Þ

where Y(b) is the characteristic function for con-

sidering the constraint violation, s is the scale fac-

tor, and P(b) is a penalty function to include the

maximum violation of constraints. The scale factor is

imposed in order to emphasize the constraint

violation. An excessive scale factor leads to neglect-

ing the effect of the objective function while the

penalty function with a small scale factor can cause

an infeasible design.





Using Y(b), equations (1) are changed to an un-

constrained problem as follows. Find

b [Rn ð4aÞ

to minimize

Y bð Þ ð4bÞ

subject to

bL¡b¡bU ð4cÞ

Therefore, the formulation in equations (4) is used

in the design of the crash box. In solving a discrete

design problem with constraints, the steps of DOA

are as follows [18].

Step 1. An appropriate orthogonal array is selected

according to the number of design variables and

the number of levels. In this paper, the L9(34)

orthogonal array is used and shown in Table 1. In

L9(34), the number of rows is 9, the number of

levels is 3, and the number of design variables is 4.

Step 2. The objective function Y(b) is calculated for

each row of the selected orthogonal array. This

process is called a matrix experiment.

Step 3. A one-way table is made for each design

variable. The one-way table is the process where

the levels of design variables with the smallest

objective function are found. Table 2 shows an

example of the one-way table of results from the

orthogonal array in Table 1.

Step 4. Using the one-way table, a new combination

of the design variables is chosen. In each row of the

one-way table, the smallest variable is selected.

Step 5. The solution of step 4 is verified by a confir-

mation experiment where the objective function

and constraints are evaluated. The confirmation

experiment is needed because the interaction

effect is ignored in the above matrix experiment.

The results of Table 1 and the confirmation ex-

periment are compared and the best result which

has the least object function without constraint

violation is finally selected.

4 STRUCTURAL OPTIMIZATION OF THEFRONTAL STRUCTURE OF THE VEHICLE

4.1 Overall design process of the frontal structureof the vehicle

As explained earlier, pedestrian protection and the

low-speed impact test are taken into account in

order to design the frontal structure of the vehicle.

Through many analyses, it has been found that the

existing bumper model does not fulfil all the reg-

ulations. Therefore, this research proposes a new

bumper system and a new type of crash box to

satisfy the regulations. Detailed designs of the new

bumper system and the new crash box are per-

formed using optimization. Based on the results of

several analyses, it has been found that the stiff-

ness of the crash box does not have much impact

on pedestrian protection and the bumper test. Con-

Table 1 L9(34) orthogonal array

Experiment

Column number assigned for the following design variables

Characteristic function YA B C D

1 1 1 1 1 Y1

2 1 2 2 2 Y2

3 1 3 3 3 Y3

4 2 1 2 3 Y4

5 2 2 3 1 Y5

6 2 3 1 2 Y6

7 3 1 3 2 Y7

8 3 2 1 3 Y8

9 3 3 2 1 Y9

Table 2 An example of the one-way table for an orthogonal array

Design variable

Value for the following levels

1 2 3

A mA1~ 1

3 Y1zY2zY3ð Þ mA2~ 1

3 Y4zY5zY6ð Þ mA3~ 1

3 Y7zY8zY9ð ÞB mB1

~ 13 Y1zY4zY7ð Þ mB2

~ 13 Y2zY5zY8ð Þ mB3

~ 13 Y3zY6zY9ð Þ

C mC1~ 1

3 Y1zY6zY8ð Þ mC2~ 1

3 Y2zY4zY9ð Þ mC3~ 1

3 Y3zY5zY7ð ÞD mD1

~ 13 Y1zY5zY9ð Þ mD2

~ 13 Y2zY6zY7ð Þ mD3

~ 13 Y3zY4zY6ð Þ





sequently, the design process for the frontal struc-

ture of the vehicle has two steps. First, the bumper

system is designed while considering pedestrian

protection and FMVSS part 581. Second, the crash

box is designed to satisfy the RCAR test, at the de-

sign of step 1.

Figure 7 presents the overall design process of the

frontal structure, which is proposed in the present

study. First, a detailed design of the newly proposed

bumper system is carried out by using RSAO. A new

plate structure and springs are added to the existing

model. The design variables are the thicknesses of

the plate and the bumper rail, and the stiffness of

the springs. The mass of the bumper system is

considered as the objective function and minimized.

The conditions for pedestrian protection and FMVSS

part 581 are used as constraints. Simulations of both

the lower-legform impact test and the pendulum

impact test are performed to generate the response

surfaces. As mentioned earlier, acceleration at the

upper tibia is measured in the lower-legform impact

test, and the intrusion and deflection are measured

in the pendulum impact test. The measured prop-

erties are used as constraints in the optimization

process. Since the two impact tests are carried out

in the time domain, the acceleration, intrusion, and

deflection should be considered with respect to all

the time steps. A response surface is generated at

each time step: thus, the number of constraints for

each property is the same as that of the time steps of

the analysis.

When the optimization process is conducted by

RSAO, an optimum is obtained; the function values

from the response surfaces could be different from

Fig. 7 The flow chart of the frontal structure of the vehicle (ANOM, analysis of means)





real values. Therefore, a confirmation experiment

should be performed. Both impact tests are evalu-

ated again at the optimum. If the test results do

not satisfy the regulations, another bumper system

should be proposed again. Otherwise, the design pro-

cess for the bumper system terminates.

After completing the design of the bumper system,

the crash box is designed for the RCAR test. First,

a new type of crash box is proposed, and its

detailed shape is determined by using DOA. It is

difficult to perform mathematical shape optimiza-

tion with crash analysis because of costly sensitivity

analysis. Thus, shape design is carried out in the

discrete space by using DOA. Design variables are

the shape of the crash box and the thickness of the

crash box. For this purpose, the design variables

should be discretized. The objective of the RCAR test

is to reduce the repair costs. As mentioned earlier,

the strain energy is considered as an objective

function because, if the strain energy is maximized,

the impact energy transmitted to the other parts of

the vehicle would be decreased. It leads to lower

repair costs. After designing the crash box, the de-

sign process for the frontal structure of the vehicle

terminates since the stiffness of the crash box does

not have much impact on pedestrian protection and

the bumper test.

4.2 Design of the bumper system

4.2.1 Proposed bumper system

As defined in section 4.1, a bumper system is first

designed to satisfy both the regulations of pedestrian

protection and FMVSS part 581. A stiff bumper on

the market can typically manage the pendulum im-

pact (FMVSS part 581); however, this stiff system does

not satisfy pedestrian protection. Many previous

studies proposed soft bumpers in order to meet

pedestrian protection; however, soft bumpers do not

satisfy the pendulum test. In general, the frontal

structure of the vehicle needs sufficient space to de-

crease the lower leg injury (pedestrian protection),

but it is difficult to secure enough space in the fron-

tal structure because of the styling of the vehicle.

Therefore, a new bumper system is needed to meet

the two regulations.

Figure 8 presents the configuration for the pro-

posed bumper system. Figure 9 illustrates the finite

element model for a pendulum test of the entire

bumper system. The finite element model is utilized

for non-linear dynamic finite element analysis us-

ing LS-DYNA3D [19]. The finite element model for

the bumper system analysis consists of 33 645 shell

elements, 3476 solid elements, and three spring

elements. Finite element analyses for the bumper

system are conducted for the 200 pendulum test at

a speed of 8 km/h (5 mile/h) and the pedestrian

legform test. Table 3 shows the material properties

for parts of the vehicle front structure. As mentioned

earlier, a thin-plate structure is connected to the

bumper rail by three springs. The plate structure

helps to reduce the impact to the pedestrian in a

vehicle–pedestrian crash, and it also protects the

vehicle in a low-speed impact. Because of the plate

structure, a certain space is needed between the

bumper energy absorber and the bumper rail. This

space could have a negative influence on the vehicle’s

styling. To compensate for this increased space, the

crash box is shortened afterward. Figure 10 illustrates

the new plate structure. The initial shape of the plate

structure including a reinforcement bead is deter-

mined by trial and error. The detailed design of the

new bumper system to satisfy pedestrian protection

and FMVSS part 581 is carried out while the mass of

the system is minimized.

Fig. 8 Configuration of the new bumper system and design variables for optimization





4.2.2 Design formulation

In section 4.2.1, a new bumper system is proposed to

satisfy the regulations for pedestrian protection and

FMVSS part 581. As mentioned earlier, the number

of target points for impact should be more than

three, including the centre and the side of the

bumper. In a pilot study, the lower-leg injury is the

highest at the centre of the bumper among the three

targets. Thus, only the centre point is selected for

the lower-legform impact test. GTR for the lower-leg

injury has three requirements: the dynamic knee

bending angle, the knee shearing displacement, and

the acceleration at the upper tibia. These conditions

should be considered to reduce leg injury. Previous

research has found that the design to meet the

dynamic knee bending angle can be obtained by

adding a lower stiffener and modifying the lower part

Table 3 Material properties used in the analysis of the front structure of a vehicle

Part name

Material properties

Material name Density (kg/mm3) Young’s modulus Yield strength (MPa)

Crash box Steel (SAPH440) 7.856103 210 230Rail Steel (SAPH590) 7.856103 210 480Plate Steel (SAPH370) 7.856103 207 235Energy absorber Foam (EPP) 87 48.3 3.1

Fig. 9 Model for finite element analysis of the frontal structure

Fig. 10 Shape of the plate





of the bumper cover [3]. Also, if a design meets the

requirements for the dynamic knee bending angle

and the acceleration at the upper tibia, the design

would meet the knee shearing displacement [29].

Therefore, this research only considers the accelera-

tion at the upper tibia.

FMVSS part 581 has two tests: the barrier test and

the pendulum impact test. In both tests, the target

points are the centre of the bumper and the side of

the vehicle. In the pendulum impact test, a vehicle is

hit by a pendulum weighing as much as the vehicle

and located between 0.4 m and 0.5 m (16 in and

20 in) height from the ground. In the pilot study, an

intrusion and a deflection are highest when the

pendulum at 0.5 m (20 in) height hits the centre of

the vehicle. Thus, only this condition is used in this

research, and the intrusion and deflection are used

as constraints in the optimization process. The

intrusion and deflection are illustrated in Fig. 5.

The intrusion is the distance from the front bumper

cover to the leading edge of the hood. The distance is

measured as 75 mm. If the intrusion is less than

75 mm, the leading edge of the hood would not be

damaged by impact. The deflection is the distance

from the rear centre of the bumper rail to the

radiator. The distance is measured as 35 mm. If the

deflection is less than 35 mm, the radiator would not

be damaged by impact.

Design variables are determined as illustrated in

Fig. 8. They are the thickness (t1) of the plate, the

thickness (t2) of the bumper rail, the spring coef-

ficient (k1) of the centre spring, and the spring

coefficient (k2) of the side springs. The objective

function is the mass of the bumper system. In the

pedestrian impact test, the acceleration at the upper

tibia should be less than 170g as indicated in the

GTR. In the pendulum impact test, the intrusion

should be less than 75 mm and the deflection should

be less than 35 mm. In the optimization process, the

safety factor is defined as 10 per cent. Therefore, the

acceleration at the upper tibia should be less than

153g, the intrusion should be less than 67.5 mm, and

the deflection should be less than 31.5 mm. These

values are considered as the constraint values. The

values should be satisfied at all the time steps. An

optimization formulation of the design problem is

expressed as follows. Find

t1, t2, k1, k2 ð5aÞ

to minimize

mass ð5bÞ

subject to

ai¡153g i~1, � � � , nð Þ ð5cÞ

I j¡67:5 mm j~1, � � � , mð Þ ð5dÞ

Dj¡31:5 mm j~1, � � � , mð Þ ð5eÞ

where a is the acceleration at the upper tibia, I is

the intrusion, D is the deflection, n is the number of

time steps in the lower-legform impact test, and m

is the number of time steps in FMVSS part 581. The

problem in equations (4) is solved by using RSAO as

explained before.

4.2.3 Optimization results

An optimization design process is carried out to

meet the two regulations by using RSAO. RSAO gen-

erates response surfaces based on the experiments.

An optimum solution is obtained in 16 iterations.

During the optimization, the number of non-linear

finite element analyses is 25 for each impact test.

The optimum solutions are as follows.

1. The thickness of the plate is 1.76 mm.

2. The thickness of the bumper rail is 0.915 mm.

3. The spring coefficient of the centre spring is

56.08 N/mm.

4. The spring coefficient of both side springs is

39.23 N/mm.

Figure 11 presents the history of the objective

function. The objective function values are normal-

ized by the initial value. The mass of optimum plate

structure is reduced by 26.6 per cent compared with

the initial model.

Fig. 11 History of the objective function value





Based on the proposed process in section 4.1, a

confirmation experiment is performed. Both regula-

tions are well satisfied in the confirmation experi-

ment. Thus, the design of the bumper system is

completed, and the design of the crash box is made.

4.3 Design of the crash box

4.3.1 Proposed crash box

After the design of the new bumper system, the crash

box design is carried out for the RCAR test. The goal

of the RCAR test is to reduce insurance costs by

improving automotive damageability, repairability,

safety, and security. If a device absorbs most of the

energy of an impact, it can be expected that the

other parts are not deformed during an accident.

When the energy-absorbing device is removable,

then the other parts do not have to be disassembled

for repair and the repair cost is reduced [30, 31].

Therefore, it is important to have an efficient energy-

absorbing part, and the crash box in Fig. 2 is utilized

for this purpose. In this section, the crash box is

designed concerning the RCAR test. The detailed

design of the newly proposed crash box is performed

by using the algorithm of DOA, which was intro-

duced in section 3.2.

As explained in section 2, a frontal barrier impact

test at a speed of 15 km/h is considered in the RCAR

test. Figure 12 presents a new type of the proposed

crash box [12]. The proposed crash box has a bellows

shape with a rectangular section. The initial shape

of the crash box is determined by trial and error.

The initial shape is determined by the number of

wrinkles, the length of the interval, and the shape of

the section. As illustrated in Fig. 12, the length of the

initial model is 180 mm, which is 50 mm shorter than

the existing model in order to compensate for the

previously increasing space between the bumper

energy absorber and the bumper rail. The role of the

crash box is to absorb the impact energy as much as

possible, and this leads to preventing the interior

parts of the vehicle from being damaged.

4.3.2 Design formulation

A shape optimization process of the crash box is

needed to determine the detailed shape of the crash

box. As mentioned earlier, mathematical shape opti-

mization with crash analysis is extremely difficult.

Thus, in this research, shape design is conduc-

ted in a discrete space by using DOA. Since DOA

uses an orthogonal array, it has the advantage of

finding a solution with a small number of experi-

ments (function calculation).

Figure 12 illustrates three design variables: the

thickness t, the width w, and the height h of the

crash box. The width and the height are defined at

the rear part box because it is difficult to change the

sizes of the front part. Thus, the crash box has a stair

shape. The number of levels for each design variable

is three and an orthogonal array L9(34) is selected.

The candidate values of the design variables are

selected by considering the space of the vehicle. As

shown in Table 1, the combination of the design

variables is made for each row of the orthogonal

array. The first three columns are used. For each

row, a finite element model is constructed.

The strain energy is selected as an objective

function (characteristic function). The strain energy

and reaction force at the end of the crash box are

used as constraints. These constraints are defined to

improve the energy-absorbing capability compared

with the existing model. In other words, the trans-

mitted impact energy to the interior part of the veh-

icle is less than that of the existing model. The strain

energy of the existing model is 7.066106 N mm,

and the reaction force at the end of the crash box

is 177.8 kN. An optimization formulation is defined

as follows. Find

w, h, t ð6aÞ

to maximize

Estrain ð6bÞ

subject to

Eexistingstrain {Estrain¡0 ð6cÞ

Freaction{Fexistingreaction¡0 ð6dÞFig. 12 Configuration of the crash box and initial

values of the design variables





where the candidate values are

w [ 61 mm, 91 mm, 121 mmf gh [ 63:3 mm, 93:3 mm, 123:3 mmf g

t [ 1:2 mm, 1:4 mm, 1:6 mmf g

where Estrain is the strain energy, Freaction is thereaction force at the end of the crash box, and thesuperscript ‘existing’ means the existing model. Asexplained before, an augmented function Y(b) inequation (2) is used to consider the constraints. Theoptimization formulation of equations (6) is changedto the following. Find

w, h, t ð60aÞto minimize

Y bð Þ~f bð ÞzP bð Þ

~1

Estrainzs max 0, E

existingstrain {Estrain

� �h

zmax 0, Freaction{Fexistingreaction

� �ið60bÞ

where s is the scale factor. The formulation in equ-

ations (69) is solved by using DOA.

4.3.3 Optimization results

The shape optimization process is performed us-

ing DOA. Table 4 shows the levels of each design

variable. Since the number of design variables is 3

and the number of levels is 3, the L9(34) orthogonal

array as shown in Table 1 is selected. As shown in

Table 5, each design variable is allocated to the

variable in Table 1. An experiment is carried out for

each row, and the best one is A2B1C3 of the fourth

row. Table 6 is the one-way table for Table 5 and the

smallest values are selected. The solution is A2B3C1

and a confirmation experiment is performed. In

the confirmation experiment, Y of the combination

A2B3C1 is 1.06102 and the constraints are violated.

Therefore, the final solution is A2B1C3 in the fourth

row of Table 5.

Figure 13 presents a comparison between the

initial model and the optimum model of the crash

box. Through the optimization process, the width

and thickness of the crash box increase compared

with the initial model. The height of the crash box

does not change. At the optimum, the strain energy

is 1.026107 N mm, and the reaction force at the end

of the crash box is 169.6 kN. The strain energy

increases by 44.5 per cent and the reaction force

Table 4 Levels of each design variable

Designvariable


1 2 3

A (w) A1 5 61 mm A2 5 91 mm A3 5 121 mmB (h) B1 5 63.3 mm B2 5 93.3 mm B3 5 123.3 mmC (t) C1 5 1.2 mm C2 5 1.4 mm C3 5 1.6 mm

Table 6 A one-way table of the orthogonal array

Design variable


1 2 3

A mA1~ 1

3 Y1zY2zY3ð Þ~2:07|104

mA2~ 1

3 Y4zY5zY6ð Þ~1:28|104

mA3~ 1

3 Y7zY8zY9ð Þ~3:33|104

B mB1~ 1

3 Y1zY4zY7ð Þ~3:45|104

mB2~ 1

3 Y2zY5zY8ð Þ~3:02|104

mB3~ 1

3 Y3zY6zY9ð Þ~2:09|104

C mC1~ 1

3 Y1zY6zY8ð Þ~4:24|104

mC2~ 1

3 Y2zY4zY9ð Þ~5:46|104

mC3~ 1

3 Y3zY5zY7ð Þ~4:34|104

Table 5 Matrix experiment results for the crash box

Experiment

Value of the following design variables

Characteristic function YA (w) B (h) C (t) D

1 61 mm 63.3 mm 1.2 mm 1 1.1061027

2 61 mm 93.3 mm 1.4 mm 2 1.176104

3 61 mm 123.3 mm 1.6 mm 3 5.056104

4 91 mm 63.3 mm 1.4 mm 3 9.8461028

5 91 mm 93.3 mm 1.6 mm 1 4.116104

6 91 mm 123.3 mm 1.2 mm 2 6.236104

7 121 mm 63.3 mm 1.6 mm 2 3.856104

8 121 mm 93.3 mm 1.2 mm 3 3.776104

9 121 mm 123.3 mm 1.4 mm 1 5.116104





decreases compared with the existing model. In

other words, the optimum model is absorbing more

impact energy than the existing crash box model,

and it could lead to a reduction in the repair costs.

Based on the proposed design process in section 4.1,

the design process for the frontal structure of the

vehicle terminates since the stiffness of the crash box

does not have much impact on pedestrian protec-

tion and the bumper test.

5 CONCLUSIONS

Various regulations are related to the automotive

frontal structure. The regulations are pedestrian

protection, the FMVSS part 581 bumper test, and

the RCAR test. In these regulations, the stiffness

requirements of the bumper system disagree with

each other. In this research, a design method for a

new bumper system and the crash box is proposed

to satisfy the regulations related to the front struc-

ture of the vehicle. Consequently, the bumper sys-

tem satisfies the pedestrian protection test as well

as the FMVSS part 581 bumper test. Also, the crash

box satisfies the requirement to lower the repair cost

concerning the RCAR test. Computer simulation is

employed to describe the impact tests.

Analyses for the bumper system and the crash box

are highly non-linear and sensitivity information is

extremely difficult to calculate. Therefore, an ap-

proximate optimization algorithm such as RSAO and

DOE are used in the design process.

A design process is proposed in order to design the

frontal structure of the vehicle while the regulations

related to the frontal structure are satisfied. Accor-

ding to the design process, a detailed shape of the

bumper system and the crash box are determined.

The design process consists of two steps. First, a

new bumper system is proposed to satisfy the reg-

ulations for pedestrian protection as well as the

FMVSS part 581 bumper test. Detailed design of the

bumper system is carried out using RSAO. Second,

a new type of crash box is proposed, and the detailed

shape of the crash box is determined by DOA. Using

RSAO, the mass of the proposed bumper system

is minimized while both regulations of pedestrian

protection and FMVSS part 581 are satisfied. When

using DOA, the strain energy of the crash box is

maximized because the strain energy is the cap-

ability to absorb the impact energy. Using DOA, the

strain energy increases by 44.5 per cent and the

increasing strain energy leads to absorption of the

impact energy. In conclusion, the frontal structure

of the vehicle is improved through the proposed

design process.

ACKNOWLEDGEMENTS

This work was supported by a Korea Science andEngineering Foundation grant and supported by theKorean government’s Ministry of Education, Scienceand Technology, Republic of Korea (Grant R01-2008-000-10012-0). The authors are grateful to Mrs MiSunPark for her correction of the manuscript.

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APPENDIX

Notation

a acceleration at the upper tibia

b design variables

bL, bU lower and upper limits respectively

for design variables

D deflection distance

Estrain strain energy of the crash box

f(b) objective function

Freaction reaction force at the end of the crash

box

gj(b) inequality constraint

h height of the crash box

hi(b) equality constraint

I intrusion distance

k1, k2 spring constants

m number of time steps in the Federal

Motor Vehicle Safety Standard part

581

n number of time steps in the

lower-legform impact test

P(b) penalty function defined by the

maximum violation of the constraint

s scale factor

t, t1, t2 thickness

w width of the crash box

Y(b) characteristic function, objective

function in the design of experiments





2373 structural optimization of the automobile frontal

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