Journal of Highway and Transportation Research and Development Vol. 7 ,No. 1(2013) 105

Lightweight Design of Car Body Structure *

ZHANG Guo-sheng UKOO)ft) I * * , LI Jing-hong (*Dn) 2 , SHI Hui-qi (���) I ,

DAI Wei-liang (1-t1=j:J �) I

(1. Research Institute of Highway, Ministry of Transport, Beijing 100088, China:

2. Shanghai Dianji University, Shanghai 200240, China)

Abstract: The body-in-white finite element model of a type of domestic car was established. The effectiveness and the reliability

of the numerical simulation model were verified by comparing the results of prototype vehicle's stiffness, modal test and finite ele­

ment analysis. On this basis, considered the static and dynamic mechanical property of the body comprehensively, combined light­

weight research with manufacture, mass distribution of the thicknesses of body parts was optimized, and dynamic mechanical

property was essentially kept. The total mass of the optimized body reduced by 7. 84% , the torsional stiffness increased by

1. 54% and the bending rigidity increased by 30%. A practical analyzing method of optimizing body structure was provided.

Key words: automobile engineering; lightweight; FEM; BIW; stiffness

1 Introduction

On the back of the mcreasmg shortage of energy,

people around the world are mostly concerned on energy

consumption in order to meet the sustainable development

requirements of the automotive industry Companies aim to

improve fuel utilization and reduce manufacturing cost,

thus lightweight automobile design has become the main­

stream design of automobile enterprises. As the compo­

nents of a whole car structure are important, having a

lightweight body structure plays a decisive role for a vehi­

cle; the vehicle must not only have a lightweight design,

but also adequate reliability and absolute safety. There­

fore, the lightweight design in the automobile industry at

home and abroad has become an important research sub­

ject.

The present study uses China-made cars as the re­

search objects. Based on the finite element method and

experimental test methods, the body structure, light­

weight research, and actual production of vehicles were

considered. Meanwhile, in order to select the type of ve­

hicle tests-measured values as body structure optimization

design constraints limit, the body structure, lightweight

research, and actual production of vehicles were also

considered. In addition, to select the kind of vehicle

Manuscript received August 25, 2011

tests-measured values as body structure optimization de­

sign constraints limit, the establishment of a body-in­

white S-T was proposed to achieve the purpose of having

a lightweight body structure and to optimize the design

model when the performance parameters of the body

structure is not lower than that of the original car.

2 Optimization design theory

The mathematical formula for the car body-in-white

optimization design problem must be accurately de­

scribed, including the evaluation design performance

merits of the objective function according to the design

goals. The design variables must be determined and the

various performance requirements established in the form

of equations or inequalities constraint equations must be

met.

2. 1 Optimization design model

Optimization design uses the mathematical programs

theory to determine the optimal design, and a mathemati­

cal method is used to describe engineering problems. The

mathematical model can be expressed as follows:

mm F(x), s. t. g(x):::::; 0,

hex) = 0, (1)

• Supported by the National Technology Support Plan Project of China ( No. 2009 BAG13 A04 )

• * E-mail address: gs. zhang@rioh.cn

J. Highway Transp. Res. Dev. (English Ed.) 2013.7:105-110.

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106 Journal of Highway and Transportation Research and Development

where, x refers to the design variables; F ( x ) is the ob­

jective function; g( x ) is the inequality-constrained func­

tion; and h ( x ) is the equality constraint function.

X E R", F:R" -R.

The objective function, constraint functions F ( x ) ,

g ( x ) , and H ( x ) were obtained from the finite element

analysis of structure response. The selection of the design

variables is dependent on the type of optimization. In to­

pology optimization, the design variables are for unit

density; in size optimization design, the variables are for

the properties of the structural unit; and in topography

optimization and shape optimization, the design variables

are in linear combination with the factor of shape pertur­

bation [I J. Auto thin -wall body parts were used for shell

element discretization. Therefore, the thickness T of the

selected parts of the body of each of the thin-walled

member as design variables, and each design variables

and their corresponding components were selected to es­

tablish a connection relationship.

2. 2 Stopping criterion

At a certain point, negative gradient direction of

the objective function is the fastest decline direction,

with the negative gradient direction as the direction of

the search. For the decline in the objective function to

occur, there must be a termination criterion to stop the

iteration. The iteration termination criterion is as fol-

lows:

( 1) When the distance between two adjacent itera­

tive points is sufficiently short:

(2)

(2) When the value of the function of the two adja­

cent iterative points decreased sufficiently small:

(3)

or

F(Xk+l) _ F(Xk) I (4)

F(Xk) (3) When the iteration point gradient is sufficiently

small:

(5)

where, 8; (i = 1, 2, 3, 4) is given as the convergence pre­

cision, generally takes 8; to 10 -5.

3 Lightweight example

3. 1 Body structure finite element model

The present study takes a car under the research

and development stage as the research object, as shown

in figure 1. The CATIA built CAD model is converted in­

to Hypermesh for simplified reconstruction. The model,

through finite element discrete treatment, handles the in­

terface of the connection between the parts. The finite el­

ement model of the sub-assembly and the entire body-in­

white design were built. In the modeling process, the

door assembly in the body-welding assembly is ignored;

the engine cover seats and trunk lid have little effect on

the body as the whole bending and torsional stiffness

parts, mainly considering the beam space of the basic

closed-class structure pieces and board class inside and

outside panels [2J. The sheet metal parts of the unit are

divided into quadrilateral element CQUAD4, transitional

unit with triangular element CTRIA3, and controlled

within 5 %; after the completion of the finite element

model, the units meeting the warping degree, length-to­

width ratio, Jacobi, skewness requirements, and solder

joints using CWELD units to simulate were verified. The

vehicle model has 383 536 units, with 377 016 nodes.

Fig. 1 A car FE model

At present, domestic and foreign needles on car

body stiffness and modal analysis have been studied ex­

tensively[3J through the trial production prototype stiffness

modal experimental research and finite element analysis

of contrast[4-5J• The validity and reliability were verified

by the computer numerical simulation model, as shown

in figures 2 and 3. The mechanical parameters of the car

are shown in table 1. The body structure completely

meets the body structure perfonnance requirements,

while the total mass reached 196. 1 kg, which has poten­

tial in achieving lightweight design.

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Z HANG Guo-sheng , et al: Study on Lightweight Design of Car Body Structure 107

Fig, 2 Stiffness characteristics test of the car

Fig, 3 Modal characteristics test of the car

Tab. 1 Comparison of simulation and test

Mechanical feature Simulation Test Error

parameters results results range (%)

Bending rigidity (N . mm·1 ) 9 223 7 876 17.1

Torsional Stiffness (Nm . rad -I ) 693 053 750 000 7.6

First torsion frequency ( Hz) 35.915 95 35 2.6

First bending frequency ( Hz) 50.191 81 50 0.38

3. 2 Optimization model

In the present study, based on the finite element

model of the body-in-white structure, the Nastran solver

S01200 module [6 -7J was used to optimize the design and

analysis. From the car body structure features and de­

pending on variable constraints and objective functions in

the optimization process, the thickness parameter con­

straints variable sensitivity and the ratio of the size of the

sensitivity of the objective function were calculated to de­

termine the optimal design of the design variables and

implement the actual sense of optimization [8J• The pres­

ent study refers to the body model and BOM tables j the

available design variables total 237. Based on the experi­

ence of performance to avoid collision and local stiffness

of key panels, the beam space of basically closed-class

structure pieces and board class inside and outside pan­

els, and the ability of anti-twisting property" box-shape"

structure of the panels were considered. Taking into ac­

count the possibility and efficiency of the analysis of the

actual operation, targeted screening based on the objec­

tive function and the state variables of the sensitivity of

various design variables, 49 plates were finally selected

as the optimization variables. With torsional stiffness,

bending stiffness, and modal as constraints, and the

minimum quality of the body-in-white structure as the ob­

jective function, the stiffness and modal of trial produc­

tion models test results are considered as the extremum

condition of the constraint functions, as shown in table

2.

In the body optimization design process, its objec­

tive function and state variables of the DMAP parameter­

ized set design are determined j parts of the source codes

are as follows [7J•

Tab. 2 Objective function and constraint variables

Objective

function

State

variables

Name

Total mass

Torsional stiffness

Bending stiffness

Torsional frequency

Bending frequency

DESOBJ (MIN) = 1

Initial

value

196.1 kg

3.591 595

5.019 181

$HMNAME LOADSTEP "MODE"

SUBCASE 1

ANALYSIS = MODES

METHOD (STRUCTURE)

DESSUB = 101

$HMNAME LOADSTEP 2 "tor"

SUBCASE 2

LABEL = tor

ANALYSIS statics

SPC = 2

LOAD = 4

DESSUB = 201

1

$HMNAME LOADSTEP 3 "bend"

SUBCASE 3

LABEL = bend

ANALYSIS = statics

SPC = 3

Minimum Maximum

permissible permissible

value value

1. 7 mm

0.2 mm

35 Hz

50 Hz

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108 Journal of Highway and Transportation Research and Development

LOAD = 5

DESSUB = 301

9) OPTIRESPONSES Data

DRESPI 1 obj WEIGHT

DRESPI 1001 FRE003 FREQ 2

DCONSTR 101 1001 35. 0

DRESPI 1002 FRE003 FREQ 4

DCONSTR 101 1002 50. 0

DRESPI 2001 dis003 DISp 329336

DCONSTR 201 2001 1. 7

DRESPI 3001 dis003 DISp 700854

DCONSTR 301 3001 - 0. 2

3. 3 Optimization calculation and results analysis

To ensure each constraint condition, six rounds of

iterative convergence optimization analysis were done to

finally come up with the convergence process of objective

function, as shown in figure 4. After the optimization of

the quality, the vehicle's weight becomes 180. 64 kg,

down by 15. 37 kg. This accounts for 7. 84% of the total

1.4 1.3 ]' 1.2

�l.l ::l 1 ] 0.9 :E 0.8 I-< 0.7

2.5

E 2 S

2

� 1. 5 r--Ic-7-""",,­" -'" u :.c I-<

... Left threshold panel --- Medium stringers -><- Threshold inner panel -.-Rear wheel cover ... Reinforcing plate

3 4 5 Iterations

(a)

... Stringer reinforcing --- rear stnnger -><- Rear shock absorber

-.- Empty plate ... Front stringer

6

0.5 L--_�_� __ �_�_� I 2 3 4 5 6

Iterations

(c)

... Left threshold ___ Left wheel cover -><- Bcolumn and threshold -.- Bcolumn reinforcing ... A column reinforcing

2 3 4 5 6

quality and shows a clear lightweight effect.

Figure 5 shows the 49-group iterative process.

Structural modification of the thickness and number of

parts was carried out to ensure that the performance of

the automobile is unchanged under the premise of achie­

ving the purpose of weight reduction.

200

195

185

2 3 4 Iterations

5 6

Fig. 4 Optimization iterations of objective function

The calculation results show that the optimization

model of static torsional stiffness of 431 317. 8 (N . m) ,

rad increased by 1. 54%, and the optimized model of

static bending stiffness increased by 30% to 10 402 NI

mm. The analysis results meet the design requirements,

2 3

2.2 ... Empty plate

... Fender panel ... Left side wall .... Rear stringer below -.-Swing arm bracket ... Rear stringer rear

4 5 Iterations

(b)

E 2 --- Front stringer rear �_-� E 1.8 � 1.6 ] 1.4 .:= 1.2 � 1

6

0.8 L�="::!::::===!::===:!=� 2 3 4

Iterations

(d)

... Tailight mounting plat ___ B conlumn inner plate .... B column outer plate -.- A column and C column ... A column inner I

2 3 4

6

5 6 Iterations Iterations

Fig. 5 Design variables iterative course

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Z HANG Guo-sheng , et ill: Study on Lightweight Design of Car Body Structure 109

thereby achieving the optimization objective, The body

structure improving the performance of the vehicle struc­

ture design has a certain guiding significance,

Figure 6 shows that the dynamic optimization design

results of the first-order natural frequency increased by

7, 5% ; the second-order natural frequency increased by

6, 3%; the fourth-order, fifth-order, sixth-order, sev­

enth-order, ninth-order, and twelfth-order natural fre­

quency amplitudes showed no fluctuation; and the third­

order, tenth-order, and eleventh-order natural frequency

amplitudes decreased by 4%, 3, 6%, and 2, 5%, re­

spectively, The second mode (i, e, , first-order torsional

mode) increased from 35, 92 Hz to 38. 18 Hz, which re­

mains under the torsional mode, while the fourth mode

(i. e. , first bending mode) decreased from 50. 19 Hz to

50. 11 Hz, which remains under the bending mode.

70

N 60 e; ;>, u 50 " " ::l c;r " "" 40 e ::l '" 30 Z

20 2 4

__ Before optimization

---.- Modified results

6 8 Order

10 12

Fig. 6 Comparison of natural frequency before and

after optimization

The low natural frequency sensitivity of the design

variables results from the file jobname. £06 read, as

shown in figure 7. The results of the inherent frequency

sensitivity analysis show that the thickness of parts 4, 6,

13, 19, 20, 31, and 42 components increased, while

the first-order torsional mode frequency value decreased;

the negative sensitivity value belongs to such a situation.

Similarly, when the sensitivity value is of positive varia­

bles, the natural frequency increases along with the in­

crease in thickness. Therefore, for the body structure de­

sign, increasing the thickness of the structure is not nec­

essary to increase the dynamic stiffness of the structure,

which may prove to be counter-productive. Thus, it is

imperative to conduct sensitivity analysis and design opti­

mization in order to achieve a reasonable mix of design

parameters.

Studies show that when the design variables of mass

I

0.1 0.05

e; -0.05 f -0. 1 .� -0.15 " '"

-0.2

-6- Second order

-+- Fourth order

-0.25 "-----'----'-----'----'-------' o 10 20 30 40 50

Part number

Fig. 7 Sensitivity of natural frequency to design variables

sensitivity are large and the torsional stiffness and ben­

ding stiffness sensitivity is small, the quality of the itera­

tive process is reduced. When the design variables of

mass sensitivity are smaller and the torsional stiffness and

bending stiffness sensitivity is large, the quality of the it­

erative process increases in order to compensate for the

reduced stiffness properties. After the optimization design

of car body structure based on this rule, the design varia­

ble that can improve the efficiency of the optimization a­

nalysis is selected.

4 Conclusions

With the quality of the body-in-white design as the

objective function, comprehensively considering the stat­

ic and kinetic mechanical characteristics of the body and

in combination with the finite element method and the ex­

perimental test, the sampling vehicle tests measured val­

ues as the body structure optimized design constraints

limit and the establishment of a body in white S - T to

optimize the design model.

With a domestic car as the research object, the Nas­

tran optimization module integrated into the body of the

static and dynamic characteristics was used. DMAP para­

metric design was realized by optimizing the thickness of

the mass distribution, effectively improving the body of

the static and dynamic characteristics. The torsional stiff­

ness increased by 1. 54%, while bending rigidity in­

creased by 30%.

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