Automotive door design using structural optimization ...

Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering http://pid.sagepub.com/

Automotive door design using structural optimization and design of experiments Kwon-Hee Lee, Jung-Kyu Shin, Se-Il Song, Yung-Myun Yoo and Gyung-Jin Park Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 2003 217: 855 DOI: 10.1243/095440703769683261 The online version of this article can be found at: http://pid.sagepub.com/content/217/10/855

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855

Automotive door design using structural optimization and design of experiments Kwon-Hee Lee1, Jung-Kyu Shin2, Se-ll Song3, Yung-Myun Yoo3 and Gyung-Jin Park2* 1Department of Mechanical Engineering, College of Engineering, Dong-A University, Pusan, South Korea 2Department of Mechanical Engineering, Hanyang University, Kyunggi-Do, South Korea 3Korea Automotive Technology Institute, Chonan, South Korea Abstract: Currently, the ultralight steel auto body ( ULSAB) concept is receiving more attention owing to various bene
ts in automotive body design. One of the tasks of the ULSAB is constructing a door using tailor welded blanks ( TWBs). In TWBs, two or more gauges of steel panels (parts) are welded together before the stamping process. In this research, the domains and thicknesses of the gauges in a front door structure are determined by a series of optimization methods such as topology, size and shape optimizations and design of experiments (DOE ). The door is designed to have better performance compared with an existing structure in terms of sti
ness and natural frequency. The
nal design is discussed and compared with the current design. Keywords: ultralight steel auto body, tailor welded blank, design of experiments, structural optimization, automotive door Wj, Wj ini

NOTATION f BASE, f TWB P, S, v

i

R

R new ˆ R X

{XYZP}

i

dBASE , dTWB j j


rst natural frequencies of the current and the improved TWB model respectively penalty function, the scale factor for the violation and the constraint violation of the ith constraint respectively response or characteristic function values from experiments using orthogonal arrays new response considering the constraints for the estimated value of R new optimum combination vector for size design variables (thickness) or shape design variables (magnitude of perturbation vector) ith perturbation vectors for shape optimization deection of the current and the improved TWB model at the location of the jth loading

The MS was received on 31 December 2002 and was accepted after revision for publication on 5 June 2003. * Corresponding author: Department of Mechanical Engineering, Hanyang University, 1271 Sa-1 Dong, Ansan, Kyunggi-Do, South Korea. e-mail: [email protected]

Y, Y

1

strain energy of the inner panel for the jth load case and its initial value respectively
rst natural frequency of the inner panel and its initial value

ini

INTRODUCTION

Recently, there have been two approaches in reducing automobile weight. One is by using material lighter than steel [1], and the other is by redesigning the steel structure [2]. Since steel is not costly and is recyclable, the automobile industry is trying to use the latter. Lightweight steel structures can be achieved by improving the performance of the structure or adopting new manufacturing techniques. One of the e
orts is the ultralight steel auto body ( ULSAB) concept [3]. The ultralight steel auto closures ( ULSACs) are of particular interest [4]. ULSAB suggests several main weight reduction techniques. In this research, the TWB technique is utilized for lightweight automobile body design, and a design process is proposed for application of the technique in optimizing the automobile structure. Although an automobile structure consists of many components, the capability of the proposed design process is applied to lightweight automobile door design. The TWB door is made from a laser-welded tailored blank with di
erent thicknesses. The aspects of welding are beyond the scope

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of this research. Thus, the design process is applied to the stamped material. Initially, the reinforcements of the inner panel of an existing front door are removed. In the TWB, the role of the inner reinforcements is transferred to the thickness distribution of the tailored pieces. A
nite element model of the entire door is constructed and the design is conducted on the inner panel. In conceptual design, topology optimization is performed to determine the path for the sti
est structure without the reinforcements. From the topology optimization results, the designer determines the number of parts and the rough welding lines. Then size optimization is carried out to calculate the thickness of each part under various constraints. The thickness of each part must have a standard value from an existing design code for manufacturability. That is, thickness should be determined in a discrete design space. Various methods have been developed for the discrete design [5–8]. In this research, orthogonal arrays and their analysis schemes are adopted for the determination of available thickness of each part. Finally, the welding lines are
ne-tuned by shape optimization. The proposed design process for lightweight automobiles uses various optimization techniques such as topology, size and shape optimizations. Since the commercial software, GENESIS, has all the capabilities, a single
nite element model is commonly used [9].

2

ULSAB CONCEPT

An ULSAB consortium was formed to answer the challenge of automobile manufacturers around the world. The challenge was to reduce the weight of steel body structures while maintaining their performance and a
ordability. To achieve this goal, there are three main techniques such as holistic design, hydroforming and the use of TWBs [4]. Among them, TWB technology enables the design engineer accurately to situate the steel within the part precisely where its attributes are most needed. The bene
ts of TWB are to improve performance, to achieve weight reduction and to reduce the dies needed for part stamping and the corresponding costs. An

Fig. 1

example of the TWB door is illustrated in Fig. 1. The panel typically consists of two blank pieces of di
erent thicknesses (parts 1 and 2). More pieces can be used according to the designer’s choice.

3

DESIGN OF TAILORED PLATES USING STRUCTURAL OPTIMIZATION AND DESIGN OF EXPERIMENTS (DOE )

3.1 Topology optimization Consider a linear elastic structure subject to body force f in domain V and boundary traction t on boundary C respectively. The structural optimization problem can be de
ned as follows [10] Minimize l(u) =

P

uTf dV +

W

Subject to a(u, v)=l(v),

P

uTt dC

(1)

Y vµV

design restriction where u is the displacement
eld to de
ne equilibrium of a linearly elastic structure, a(u, v) is the internal virtual work by an arbitrary virtual displacement v at the equilibrium de
ned by u, l(v) is the mean compliance of the structure and V is a subset of the Sovolev space [10]. Additional design constraints such as displacement, frequency and mass can be considered for design restriction. There are two methods to solve equation (1). The homogenization method
nds the optimum material distribution by using the sti
ness–density relationship obtained by the homogenization of a microstructure [10]. The density method uses an energy approach for the approximation of the element Young’s moduli [11]. Recently, these methods have been adopted for commercial software systems such as OPTISHAPE [12], OptiStruct [13], ANSYS [14], GENESIS [15] and CONSTRUCT [16]. As mentioned earlier, GENESIS is used in the research, and thus the density method in the system is adopted [11, 15]. Minimizing the mean compliance implies
nding a

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structure with the smallest displacement. That is, topology optimization can suggest the sti
est structure with limited or constrained material quantity. Details of topology optimization can be found in references [11] and [15]. The door of the ULSAB concept should be designed sti‚y without any reinforcement under the given test loadings. Therefore, the adaptation of topology optimization is quite appropriate in the conceptual design stage.

3.3 Discrete design using DOE DOE orthogonal arrays (OAs) have advantages [20]: 1. When there are many factors (design variables) to be considered, a small number of experiments can be carried out, while the e
ect is equivalent to that of a full factorial experiment. 2. Since the arrays may be set up with available discrete design values, it is applicable to the discrete design space. A ow of the design methodology using OAs is illustrated in Fig. 2. The sequence of the ow is explained as follows:

3.2 Size and shape optimization Generally, a structural optimization problem is de
ned to minimize the objective under given constraints. The objective is usually the weight of the structure, and the constraints are imposed on the structural responses such as stresses, displacements and natural frequency. The standard formulation of structural optimization is as follows [17] Minimize W(X )

857

(2)

Subject to K(X )u=p K(X )y=fM(X )y g (X )å0, j=1, ..., m j X åXåX L U where X is the design variable vector, X and X are L U lower bound and upper bound vectors respectively, W(X ) is the objective function, K(X ) is the sti
ness matrix, M(X ) is the mass matrix, u is the displacement vector, p is the external load vector, f is the eigenvalue, y is the eigenvector and g is the jth constraint out of m j constraints. Size and shape optimization problems can be expressed by equation (2). Size optimization is the basic structural optimization, and the design variables are the dimensions of the cross-sections such as height, width, thickness, area and moment of inertia [9]. When size optimization is applied to the design of an automobile door, the design variables are usually the thicknesses of the di
erent parts. Size optimization
nds the dimension of the structure with
xed boundary nodes, while shape optimization usually obtains an optimum value for the location of the
nite element nodes. That is, shape optimization determines the boundary of the structure. To change the boundary nodes, GENESIS adopts the basis vector approach or the perturbation vector [18]. The perturbation for shape change must be de
ned appropriately in order not to distort the
nite element mesh of the structure [19]. In this research, shape optimization is employed to
nd the optimum location of the welding lines. Various references are available for size and shape optimization [5, 8, 17–19].

1. An optimization process is performed. In this research, size optimization is carried out
rst and the DOE is utilized as a post-process for discrete design [6, 7 ]. 2. Around the optimum, discrete values are selected from available sizes according to the numbers of the levels for the design variables. The numbers of the levels are determined by the designer. An OA is selected for minimum experiments. Each row of the OA represents an experiment. An example of levels and a selected OA (L ) are shown in Tables 1 and 2 18 respectively. These tables will be used in the later example. A detailed explanation of OAs is given in Reference [20]. 3. An experiment is conducted for each row. The experiment is an evaluation of the objective and constraint functions. In an unconstrained problem, only the characteristic function R for the objective is calculated. In constrained problems, R is de
ned to new include constraint violations as follows [6, 7] m =R+P=R +Sä æ max[0, v ] (3) new i i=1 where v is the constraint violation of the ith coni straint, S is a scale factor for the violation and P is the penalty function. In this research, the scale factor is set to a value so that the order of the characteristic value is slightly higher than that of the penalty function. The scale factor is imposed to emphasize the constraint violation. From R in Table 2, a one-way new table is constructed and an optimum combination is selected. Suppose the evaluated optimum values are x , x , x for each design variable, where n is the 1 2 n for number of design variables (factors). Then R new R

Table 1

Levels for L

18

orthogonal array

Factors (design variables) Level

A (t ) A

B (t ) B

C (t ) C

D (t ) D

E (t ) E

1 2 3

1.40 1.30 1.20

0.80 0.75 0.70

0.70 0.65 0.60

0.70 0.65 0.60

0.85 0.80 0.75

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Fig. 2

Discrete design for a constrained problem using an orthogonal array

Table 2

L

18

experiment result Design variables (mm)

Experiment

Error 1

Error 2

A 3

B 4

C 5

D 6

E 7

Error 8

R Weight (kg)

R

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2

1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3

1.40 1.30 1.20 1.40 1.30 1.20 1.40 1.30 1.20 1.40 1.30 1.20 1.40 1.30 1.20 1.40 1.30 1.20

0.80 0.75 0.70 0.80 0.75 0.70 0.75 0.70 0.80 0.70 0.80 0.75 0.75 0.70 0.80 0.70 0.80 0.75

0.70 0.65 0.60 0.65 0.60 0.70 0.70 0.65 0.60 0.60 0.70 0.65 0.60 0.70 0.65 0.65 0.60 0.70

0.70 0.65 0.60 0.65 0.60 0.70 0.60 0.70 0.65 0.65 0.60 0.70 0.70 0.65 0.60 0.60 0.70 0.65

0.85 0.80 0.75 0.75 0.85 0.80 0.80 0.75 0.85 0.80 0.75 0.85 0.75 0.85 0.80 0.85 0.80 0.75

1 2 3 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1

16.61235 16.23040 15.84845 16.26602 16.29297 16.13220 16.31867 16.08821 16.28432 16.26632 16.12322 16.30166 16.23691 16.33354 16.12075 16.37535 16.31405 16.00179

16.6123500 16.3690908 16.4603532 16.3674385 16.3630360 16.4278949 16.3302333 16.4522605 16.3825741 16.4316440 16.3262901 16.4072638 16.4406473 16.3762334 16.3429486 16.3974835 16.3918221 16.3911386

the optimum combination is estimated by linear approximation as follows [20]

the number of experiments and the number of levels respectively. 4. It is not guaranteed that the obtained result will satisfy the imposed constraints. To enhance the feasibility, the estimation with respect to full combinations of design variables is obtained in ascending order. Since the estimation is calculated from the approximation, it is not costly. Then, they are evaluated with

ˆ =m + m +· · ·+m
(n
1)m ¯ R (4) x1 x2 xn ¯ =1/N×å N R . If X is the summation where m N i= 1 new of the characteristic function values from the rows where the level for x appears, m is the mean of X . n xn N N and l are Therefore, m =X /(N/l ). The numbers N xn Downloaded from pid.sagepub.com by guest on September 6, 2012

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real objective and constraint calculation according to the ranking until the feasibility condition is satis
ed. Therefore, only basic experiments related to the selected OA and additional analyses for evaluation of feasibility conditions are needed. Using the discrete design suggested in Fig. 2, the optimum thickness of each part can be selected from design standards. It is well known that it is very dicult to include the interactions between design variables with OAs. In the above process, interactions are ignored. When strong interactions exist, the above process can be considered as choosing a discrete design out of systematically de
ned designs.

3.4 Design process of the lightweight automobile Using the preceding theories, the design process for a lightweight automobile is proposed in Fig. 3. At
rst, the design domain is selected. It may be the entire area or a part in the structure. In the conceptual design, topology optimization is performed for several mass constraints to
gure out the tendency of the sti
est structure. The objective could be to maximize the sti
ness under the given loading conditions or the
rst natural frequency of the structure. According to the topology optimization results, the design domain is divided into a few parts which have di
erent thicknesses. The divided rough lines are equivalent to the welding lines. This decision is made by the designer. In the next stage, size optimization begins with the results from the above part selection process. The thickness of each part can be determined in a continuous design space. In many applications for manufacturability, thickness can have a standard value from existing design codes. That is, the available thickness of each part exists in a discrete space. Therefore, the optimized thickness from size optimization in continuous space should be modi
ed.

Fig. 3

Design ow of a lightweight automobile

859

Orthogonal arrays from DOE are adopted for the discrete design. Orthogonal arrays are constructed by setting the discrete value. Through the proposed design process in Fig. 2, the optimum thickness is found. Finally, the
nal welding lines are rendered by shape optimization. The proposed design process may be applied to auto closures such as a door, hood, decklid and hatch, as illustrated in Fig. 4. Among these candidate structures, the automobile door is selected. In this research, the optimum values are determined for the thickness of each part and its boundaries (welding lines) for the inner panel in the front door.

4

LIGHTWEIGHT AUTOMOTIVE TWB DOOR DESIGN USING THE PROPOSED DESIGN PROCESS

The design speci
cations for structural performance of a new door design include frame rigidity, door sag and natural frequency. These speci
cations make the door frame resist the bending e
ect due to negative pressure at high speeds and the sagging e
ect from the self-weight of the door. The natural frequency of a new door design should be equal to or higher than that of the existing design. Sometimes, door design considers some other speci
cations such as door torsion, the check load, etc. This research considers loading conditions for door rigidity and door sag by virtue of the requirements from the sponsoring industry. Nevertheless, the design process will be the same with more loading conditions. The
nite element model of a front door is illustrated in Fig. 5 and represents boundary conditions for analysis, frame rigidity conditions ( load cases 1 and 2) and sag condition ( load case 3). For convenience, the notations of the boundary condition de
ned as 1, 2 and 3 are the
xed displacements in the X, Y and Z directions, and 4, 5 and 6 are the
xed rotations in the X, Y and Z axes respectively. In
nite element analysis, the entire door is included with the outer and inner panels. The material is steel with Young’s modulus E=210 GPa and r =7850 kg /m3. The design domain is de
ned on the inner panel of the front door. The inner reinforcements are removed to apply TWB technology. It is illustrated in Fig. 6.

Fig. 4

Auto closures for design candidates

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Fig. 5

FE model and load cases of an automobile front door

4.1 Topology optimization Topology optimization is performed to determine the number of parts and rough welding lines in the conceptual design. The formulation of topology optimization is as follows Y 3 Wj ini + æ (5 ) Y Wj j=1 ini Subject to Mass åN ä mass frac ref where Wj is the strain energy of the inner panel for each load case, Wj is the initial strain energy of the inner ini panel for each load case, Y is the
rst natural frequency Minimize

of the inner panel, Y is the initial
rst natural freini quency of the inner panel, N is the mass fraction ratio frac and mass is the mass of the design domain (inner ref panel ). To solve the above multiobjective optimization, several techniques have been developed [21]. Among them, the utility function method or weighting function method is adopted, and all the same weighting factors are associated with each objective function. The mass fraction ratio, N , can have various values, frac N =30%, 40%, 50%, etc. Among them, the result with frac N =30% is illustrated in Fig. 7. The elements in the frac dark area are needed for the sti
est structure. From the result of topology optimization, the entire inner panel is

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Fig. 6

861

Inner reinforcements removal from inner panel

4.2 Size optimization In detailed design, size optimization is performed to calculate the optimum thickness of each part, and the formulation is as follows Find X={t , t , t , t , t } A B C D E Minimize Weight

(6)

Subject to dTWB
dBASE å0.0, j j f BASE
f TWBå0.0

Fig. 7

Topology results (up) and part selection of the inner panel (down)

divided into
ve parts. The divided
ve parts are illustrated in Fig. 7. The parts are represented by A, B, C, D and E. It is noted that the divided inner panel can vary according to the designer’s decision.

j=load case 1, 2, 3

X /2X
1.0å0.0, i, j=part A, B, C, D, E i j where X is a vector for size design variables (thickness of each part of the inner panel ), dBASE is the deection j of the current model at the location of the jth loading, dTWB is the deection of the improved TWB model at j the same location of dBASE, and f BASE and f TWB are the j
rst natural frequencies of the current and the improved TWB model respectively. In terms of manufacturability, the thickness di
erence between adjacent parts should not be very large in TWB application [22]. Therefore, the last equation of equation (6) is de
ned not to make one thickness more than twice the adjacent ones. The constraint might be considered as the formability of the TWB. The initial and optimum designs are shown in Table 4. As mentioned earlier, the thickness of each part from size optimization must be changed into an acceptable or producible value according to the design code. In the case of replacement for each thickness to the nearest rounded-up value, they can be t =1.4 mm, t =0.8 mm, A B t =t =0.7 mm and t =0.85 mm. In view of the C D E increase in weight and the uncertainty of the feasibility, a discrete design for a constrained problem should be

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Table 3

Arrangement of the estimators by ascending order Design variables

Ranking

Estimator

A

B

C

D

E

Weight (kg)

Evaluation

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

0.0162894 0.0163056 0.0163097 0.0163106 0.0163116 0.0163116 0.0163135 0.0163260 0.0163269 0.0163279 0.0163279 0.0163297 0.0163301 0.0163303 0.0163310 0.0163320 0.0163320 0.0163329 0.0163338 0.0163339 0.0163347 0.0163357 0.0163357 0.0163395 0.0163464 0.0163466

2 2 2 2 3 2 2 2 2 3 2 2 2 2 2 3 2 3 2 3 2 3 2 1 2 2

2 2 1 2 2 2 2 1 2 2 2 2 3 2 1 1 1 2 1 2 2 2 2 2 3 2

2 2 2 1 2 3 2 2 1 2 3 2 2 2 1 2 3 1 2 3 1 2 3 2 2 2

3 2 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 2 2

2 2 2 2 2 2 3 2 2 2 2 3 2 1 2 2 2 2 3 2 3 3 3 2 2 1

16.17990 16.23040 16.23629 16.20313 16.06437 16.15667 16.04360 16.28679 16.25363 16.11486 16.20717 16.09410 16.12352 16.31620 16.25952 16.12075 16.21306 16.08759 16.09999 16.04114 16.06683 15.92807 16.02037 16.29544 16.17401 16.36670

Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Violated Satis
ed

Table 4

Determination results for the thickness of each part

Initial design (with reinforcements) Optimum design in continuous space with TWB Rounded-up values with TWB Discrete design with TWB

Weight (kg)

t A (mm)

t B (mm)

t C (mm)

t D (mm)

t E (mm)

17.009 16.357 16.612 16.367

0.700 1.318 1.400 1.300

0.700 0.793 0.800 0.750

0.700 0.679 0.700 0.650

0.700 0.660 0.700 0.650

0.700 0.812 0.850 0.850

used as illustrated in Fig. 2. The levels of the design variables are de
ned in Table 1. Note that the optimum thickness in the continuous space is located between levels 1 and 2. An OA should be chosen on the basis of the rule for selection [20]. The interaction between factors is the bottleneck when OAs are used because the interaction should be identi
ed before DOE is carried out. It is well known that identi
cation of the interaction is very dicult and costly. The interaction is ignored in this research. However, it is compensated for by: 1. An orthogonal that has even distribution in columns for the interaction e
ect. Also, the OA is set up around a mathematical optimum. 2. As mentioned earlier, the
nal solution is determined from the list of ascending order. Therefore, the solution of this research does not guarantee the mathematical optimum but rather an excellent solution. An L

18

OA is used since it has an even distribution of

interaction between factors. After each factor (design variable) is allocated in the L array, as shown in 18 Table 2, 18 analyses are conducted according to the L 18 OA. The new response R is calculated using equation new (3). A proper scale factor S is needed to calculate R . new In this research, S is set to be 0.3 times of R . The new results are shown in Table 2. Estimations for full factorial combinations (35=243) of factors are obtained using equation (4). The results are arranged in ascending order, and analyses are carried out until all the constraints are satis
ed. Since the 26th estimator does not violate any constraints, the design combination is selected as the optimum solution. The combination of design variables is 2, 2, 2, 2 and 1. It is shown in Table 3. Therefore, only 18 basic
nite element analyses and 26 additional ones are conducted to
nd out the discrete optimum thickness of each part. From the result of discrete design, optimum thickness is t =1.3 mm, t =0.75mm, t =t =0.65 mm and t = A B C D E 0.85 mm. The weight is decreased by 245 g compared

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863

with the weight with the rounded-up values. These results are summarized in Table 4.

4.3 Shape optimization At last, shape optimization is performed to determine the
ne location of the welding lines, which are the boundaries of each part. During shape optimization, the thickness is not changed. The formulation is as follows Find X={X : i=1, 2, 3, 4} i Minimize Weight Subject to dTWB
dBASE å0.0, j j f BASE
f TWBå0.0

(7)

j=load case 1, 2, 3

4 {XYZ}={XYZ} + æ X ä{XYZP} ini i i i=1
3.0åX å3.0, i=1, 2, 3, 4 i The notations are the same as those of equation (6); {XYZ} and {XYZ} are the coordinates of nodes for ini welding lines and their initial values respectively; {XYZP} means that the four perturbation vectors that i change the area of part E are de
ned for the position of welding lines. The perturbation vectors for the
rst shape optimization are shown in Fig. 8. The arrows of the
gures are represented as perturbation vectors. Careful setting is required to avoid severe mesh distortion. That is, since the inner panel is very rugged, as illustrated in Fig. 9, shape optimization with tightly limited bounds should be performed and new lines can be found by repeated optimization processes. The last constraint of equation (7) means tightly limited bounds. In this problem, shape optimization is carried out 3 times until no

Fig. 8

Fig. 9

Rugged surface (enlargement of the circle in Fig. 8d)

improvement of objective function occurs. Each shape optimization result is represented in Fig. 10. As a result, the weight of the TWB front door is 16.270 kg. The shape sensitivities are much smaller than the size sensitivities. Therefore, drastic change is not made during the shape optimization processes, and the area only of part A is somewhat decreased. The optimum welding line changes relative to the initial welding lines (illustrated in Fig. 7) are presented in Fig 11. Compared with the weight of the original structure with reinforcements (17.009 kg), the weight of the TWB door is reduced by 739 g. In size optimization in discrete space, the weight of the door is reduced by 642 g. This quantity is 83 per cent of the total weight reduction. During shape optimization, the weight is reduced by only 97 g. Since the outer panel is not included in the optimization process, the weight of the entire door is reduced by 4.34 per cent compared with the original structure with reinforcements, although the reduction rate for the inner panel is 11.72 per cent. It does not seem very e
ective. However, it is quite a large amount because a car has two or more doors, and the proposed design process

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Fig. 10

Fig. 11

Shape optimization results

Optimum welding line (dotted and solid lines are initial optimum welding lines respectively)

could be applied to the hood, hatch back, and decklid. It is noted that a better design can exist according to the designer’s selection of parts.

5

CONCLUSIONS

A design ow using the optimization method has been proposed for lightweight automobile design, and it is applied to TWB door design. In the conceptual design, topology optimization is performed to
nd out the number of TWB parts and rough welding lines. In the detailed design, size and shape optimizations are conducted to
nd the optimum thickness of each part and the

optimum welding line locations respectively. In particular, to consider the manufacturability, orthogonal arrays are utilized for discrete design. The inner panel of the front door is optimized, and the weight of the improved TWB inner panel is reduced by 11.72 per cent compared with the original inner panel, with the structural sti
ness maintained. The main weight reduction is obtained by size optimization, and it is found that the proposed discrete design scheme is very e
ective. The design process is applied to stamped material. Therefore, the stamping process should be de
ned to generate the solution here. It is found that the front door with TWB is a typical industrial example where various optimization methods can be utilized. For a more

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AUTOMOTIVE DOOR DESIGN USING STRUCTURAL OPTIMIZATION AND DOE

lightweight automobile, the proposed design process can be applied to other auto closures such as the hood, decklid and hatch. ACKNOWLEDGEMENTS This research was supported by the Centre of Innovative Design Optimization Technology, the Korea Science and Engineering Foundation. The authors are grateful to Mrs MiSun Park for her correction of the manuscript. REFERENCES 3 Davis, J. The potential for weight reduction using magnesium. SAE paper 910551, 1991. 2 Cho, S. B. Development of a lightweight door considering high safety (in Korean). MSc thesis, Yonsei University, Seoul, Korea, 1994. 3 Song, S. I., Im, J. S., Yoo, Y. M., Shin, J. K., Lee, K. H. and Park, G. J. Automotive door design with the ultra light steel auto body concept using structural optimization. In proceedings of 20th International Congress on Theoretical and Applied Mechanics, Chicago, Illinois, 2000, Technical report 950, p. 51. 4 Opbroek, E. and Weissert, U. Ultra light steel auto closures project. In Proceedings of International Body Engineering Conference and Exposition, Detroit, Michigan, 1998, Vol. 1, Advanced Body Design and Engineering, pp. 41–52 (SAE International). 5 Arora, J. S., Haug, M. W. and Hsieh, C. C. Methods for optimization of nonlinear problems with discrete variables—a review. Structural Optimization, 1994, 8(2–3), 69–85. 6 Lee, K. H. and Park, G. J. Discrete post-process of the constrained size optimization using orthogonal arrays. In Proceedings of 6th AIAA / USAF/ NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Bellevue, Washington, 1996, Part 1, pp. 56–61 (AIAA ).

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