CAE-Based Design Optimization - jsme.or.jp · CAE-Based Design Optimization Dong-Hoon Choi [email protected] Director, the Center of Innovative Design Optimization Technology (iDOT)

CAE-Based Design Optimization

Dong-Hoon Choi

[email protected]

Director, the Center of Innovative Design Optimization Technology (iDOT)Professor, School of Mechanical Engineering

Hanyang University, Seoul, Korea

September 1, 2006

2

Brief Introduction of iDOT


Sequential Approximate Optimization

Outline

Applications

3


Automation

Integration Optimization

Cost Reduction

Shorter Design Cycle

Improved ProductQuality

MultidisciplinaryDesign

Optimization

Development ofComputingTechnology

Advance inOptimizationTechnology

Why MDO ?

Motivation

4


Research and development ofResearch and development ofmultidisciplinary design multidisciplinary design optimization methodsoptimization methods

Transfer of promising MDO Transfer of promising MDO technology to industry technology to industry

Train industry designers and Train industry designers and educate students on MDO educate students on MDO methods and design proceduresmethods and design procedures

MDOMDOResearchResearch

IndustrialIndustrialApplicationApplication

Training andTraining andEducationEducation

iDOT InternationalInternationalCooperationCooperation

iDOT Mission

5


The Center ofinnovative Design Optimization Technology

Selected as one of the Engineering Research Centers of excellence by Korean government in 1999

Located at Hanyang University in Seoul, Korea

Supported for 9 years by the KOrean Science and Engineering Foundation (KOSEF)

14 Professors from 7 universities4 Research Staffs4 Computer Programmers2 Administrators

81 Graduate Students

A research alliance with ASDL since 1999

6


Research Topics

Computing Infrastructure

Integrated Design

ApplicationTechnology

Design Process

Management

OptimizationFormulation

MDOMethods

ApproximateOptimization

GlobalOptimization

MDOKernel

PIDO Tool

“The Ultimate Design Machine”

DB CAD

ElectromagneticAnalysis

Fluids

Dynamics

Structures

Users

Optimization Methods

PIDO : Process Integration and Design Optimization

Research Areas

7


DOE Module(s)

GlobalOptimizer(s)

Resources

Visual Modeling

ScriptManager

Other Resource(s)

PROCESS Manager

Component Manager

Optimization Schedule Template Manager

DATABASE Manager

USER INTERFACE

ScriptParser

CO MDF IDF …

MDO Kernel

Message Manager

I/O Manager

Com

ponent Abstract Layer

LocalOptimizer(s)

Non Linear Analysis

Crash Analysis

Experimental Results

ApproximationModule(s)

Com

ponent Abstract Layer

EMDIOS Architecture

8


AerospaceAutomotivesBiotechnologyElectronicsInformation TechnologyMarine TechnologyMaterialsMechanicalMEMS DevicesNuclearRailway Vehicles

2152

13226

26222

Applications (2001-2005):74 Design Optimizations

9


ResearchResearch& Development& Development

PIDOPIDOTechnologyTechnologyTransferTransfer CommercializationCommercialization

& Maintenance& Maintenance

FRAMAX is a spin-off company of iDOT,having the world-class PIDO technologies

(Founded in June, 2003). Developmentof PIDO Tool

Customizationof Design S/W

EngineeringConsulting

FRAMAX: a Spin-off Company of iDOT

10


Outline



Applications

11


SOFTWARE

Higher

Efficiency

DistributedDistributedParallelParallel

ComputingComputingTechniqueTechnique

SequentialSequentialApproximationApproximationOptimizationOptimizationTechniqueTechnique

HARDWARE

How to Enhance the Computational Performance?

Motivation

12


Before Schmit and Farshi (1974)

ExactFunction & Gradient Values

New Design

Iterative Numerical Optimization Loop

After Schmit and Farshi (1974)

ApproximateFunction & Gradient Values

New Design

Iterative Numerical Optimization Loop

High Fidelity Model Low Fidelity Model

High Fidelity Model

Decouple an Expensive Analysisfrom Iterative Optimization Process

ExactFunction & Gradient Values

ApproximateOptimum

Approximation

Why Approximate Optimization ?

13


High Fidelity Model

Optimizer

Low Fidelity Model

High Fidelity Model

Optimizer

Exact Optimization SAO

High Fidelity Modelrequires 2hr per analysis

Low Fidelity Modelrequires 0.05 sec per analysis

40 x 2hr = 80 hr

4 x 2hr

40 x 0.05sec

24 hr6 sec

x 1=8hr

x 1=2sec

x 2=16hr

x 2=4sec

x 3=24hr

x 3=6sec

Efficiency of Sequential Approximate Optimization (SAO)

14


f

xx

f

f

x

Quadratic Simple Cubic

Using Quadratic Function

real function real function

real function

SequentialSequentialApproximateApproximateOptimizationOptimization

ApproximateApproximateOptimizationOptimization

AO vs. SAO

15


Local/GlobalOptimizers

UL

f

xxxxhxgx

00

Min.s.t.

hg ~,~,~f

x

xApproximate Model

Manager

Approximate ModelDeveloper

Analysis orExperimental Data

x

hg ~,~,~f

SAOManager

Define approximate optimization problem

Convergence Checking

0~0~

~

xh

xgxfMin.

s.t.

xx0

SAO Framework of iDOT

16


Approximate ModelDeveloper

One-Point Approximation

Two-Point Approximation

New Two-Point Approximation MethodSTDQAO

Linear, Reciprocal, Conservative

TPEA, TANA, TANA1, TANA2, TANA3

Typical Local Approximation Methods

Typical RSM based on Experimental Design

Alphabetic Optimality CriteriaD-optimal Design

New RSM based on Experimental Design`Augmented D-optimal DesignSubspace CCD/SCDPQRSM

KrigingRBF (Radial Basis Function)SVR (Support Vector Regression)MARS (Multivariate Adaptive Regression Splines)

Quadratic Approximation ModelingCCD, SCD and BBD

Approximate Model Developer

17


1x1Lx 1

Ux

2Lx

2Ux

0kx

2x: Trust region

*kx

k

1x1Lx 1

Ux

2Lx

2Ux

01kx

2x

: New Trust region

1k k

: Previous Trust region

Approximate OptimizationApproximate Optimization

STARTSTART

1determine

Build Approximate ModelBuild Approximate Model

Converge ?Converge ?

STOPSTOP

Update Trust RegionUpdate Trust Region

Build Approximate Modelin the new Trust region

Build Approximate Modelin the new Trust region

k+1 k=

Evaluate the exact function valueat the approximate optimum

Evaluate the exact function valueat the approximate optimum

Yes

No

k=k+1

SAO using Trust Region Concept

18


0 *k kk0 *k k

f x - f x=

f x - f x

k

k

k k

if 0, approximation is badif 1, approximation is excellentif > 1 or 0,1 , moving in the right direction.

Trust region ratio

0

1

* 0 s

2 * 0 s

1 2

= 0.25= 1

2 if x - x ==

1 if x - x <

= 0.25, = 0.75

R. Flecher, Practical Methods of Optimization, 1987

0 *k kf x - f x

f

originalfunction

approximatefunction

*f x

*f x

0f x0f x

*x0x x

,,

k k+1 k1 0

k k+1 k1 2 1k k+1 k

2 2

1 2

if 0 < , =if < =if =where, 0 < <

Trust radius

0 *k kf x - f x

Trust Region Concepts (1/2)

19


* 0 k

0 1 2 * 0 k

2 if x - x == 0.25, = 0.75, = 0.25, = 1.0, =

1 if x - x <

1 = 0.25 2 = 0.75

2

1 = 1.331

1 = 4.000

excellent goodgoodbadright

directionright

direction

k+1 k2

0 *k+1 k

=x = x

k+1 k1

0 *k+1 k

=x = x

k+1 k0

0 *k+1 k

=x = x

(reject)

0 0

k+1 k0

k+1 kx ==

x

1x

2x

0kx

*kx

2x

0kx

*kx

1x

2x

0kx

*kx

1x

2x

0kx

*kx

previous trust region

new trust region

1x

2x

0kx

*kx

0 *k kk0 *k k

f x - f x=

f x - f x

Trust Region Concepts (2/2)

20


START

DOE

BuildApproximate Model

ApproximateOptimization

ModelManagement

Converged?

END

Approximate

Build Approximate Model

DOE

x

xf

x

xf

x

xf

x

xf

: Trust Region

: Design Regionx

xf

x

xf

x

xf

x

xf

Model Management

SAO - Function Based Approximation Methods

21


1x

3x

2x

1x

3x

2x333231

232221

131211

HHHHHHHHH

H

kTk

Tkk

kkTk

Tkkkk

kk yyy

HHHHH

1

111

333231

232221

131211

HHHHHHHHH

H

1x

3x

2x

1x

3x

2x

33

22

11

HH

HH

3231

2321

1312

HHHHHH

H

333231

232221

131211

HHHHHHHHH

H

DO

EM

ath

em

atica

l Pro

gra

mm

ing

Conventional Quadratic Modeling PQRSM

Concept ofthe Progressive Quadratic Response Surface Method

22


: Trust regionx

( )f x

xf ( )f x xf

( )f x

( )f xx

x

xf

( )f x

( )f x

Update Trust RegionUpdate Trust Region

Approximate OptimizationApproximate Optimization

1 n nnumber ofunknowns

Only 2n+1 Experimental pointsare required!!

1 n n n(n-1)/2number of unknowns

At least(n+1)(n+2)/2Experimental

pointsare required!!

20

1 1 1

ndv ndv ndv ndv

i i ii i ij i ji i i j i

f x x x xx

20

1 1 1

ndv ndv ndv ndv

i i ii i ij i ji i i j i

f x x x xx

Make Full Quadratic Approximate ModelMake Full Quadratic Approximate ModelResponse Surface Method

PQRSM

3-points polynomialinterpolation

Quasi-Newtonmethod

Least Square Method

Hessian term

0

11

22

33

H12 13

21 23

31 32

H 12 13

21 23

31 32

11

22

33

H3-points polynomial

interpolationQuasi-Newton

method

+

1x1Lx 1

Ux

2Lx

2Ux

11x 12x

22x

21x

0x

2x

: Trust regionDOEDOE

“2n+1”points

PQRSM Procedure

23


1

1

22221 70sin1.011

n

kkkkk xxxxf xMinimize

1,,2,1,0.1,2.1 1 nkxx kk

Initial Values:

Optimum Values:

,0.1,,0.1,0.1at,0.0 * Tf xx

0

500

1000

1500

2000

2500

0 5 10 15 20 25 30 35 40 45 50

Number of Design Variables

Num

ber

of C

umul

ativ

e Fu

nctio

n E

valu

atio

ns

PQRSMD-optimalCCD

66,91,81196

345

859

316

1201

559

2051

1038

2122

0

500

1000

1500

2000

2500

0 5 10 15 20 25 30 35 40 45 50

Number of Design Variables

Num

ber

of C

umul

ativ

e Fu

nctio

n E

valu

atio

ns

PQRSMD-optimalCCD

66,91,81196

345

859

316

1201

559

2051

1038

2122

Total Number of Function Evaluations

Noisy Mathematical Function

24


1. Gear Reducer Design

2. Rosen-Suzuki Problem

3. Two-DOF linear dynamic

absorber design

4. Elasto-plastic Ten-member

Truss Design

5. Design of a Tracked Vehicle

Performance comparison between PQRSM, D-optimal, and CCD

0

0.5

1

1.5

2

2.5

3

1 2 3 4 5

Problem Number

Rela

tive N

um

be

r o

f A

na

lyse

s PQRSM

D-opt.

CCD

0.27

0.75 0.75

0.170.28

2.61

1.24 1.24

1 1 1 1 1

Test Problems

25


ipii xy

pi is determined to matchii y

gy

g 11~ yy

n

iii

iTPEA yy

yggg

12,

22

~ yyy2,

1,21 lnln1i

i

iii x

xx

gx

gp xx

xg

ixg 1x

ixg 2x

1x 2x ix

1xg

2xg

yg

iyg 1y

iyg 2y

1y 2y iy

1yg

1~ yg

2yg

Fadel et al.TPEA

Wang & GrandhiTANA-1 & -2

Xu & GrandhiTANA-3

Wang & GrandhiTANA

Kim et al.TDQA

1990 1994 1995 1998 2001

Two-Point Approximation

26


n

iiiiii

n

i i

yyGyyy

ggg1

22,2,

1

22

~ yyy

Two-Point Diagonal Quadratic Approximation

Intervening Variable with Shifting Constant ci Diagonal Hessian having different signed values Gi

Correction Coefficient

1

g

ix

To define an intervening variable whenthe design variable value is near zeroor negative

11~ xx gg

To match the function at x1

ipiii cxy

0otherwise,1,if

i

Liii

cxcx

iiiii y

gy

gyy

G 21

2,1,21 yy

Curvatures of different signs along each variable axis

1y2y

( )g y

A New Two-Point Approximation

27


STDQAO

STDQAO:Sequential Two-point Diagonal Quadratic Approximate Optimization

28


1. Welded Beam Design

2. Gear Reducer Design

3. Rosen-Suzuki Problem

4. Piston Design Problem

5. Three-bar truss design problem

6. Ten-bar truss design problem Case 1a

7. Ten-bar truss design problem Case 1b

8. Ten-bar truss design problem Case 2a

9. Ten-bar truss design problem Case 2b

Performance comparison between TDQA and TANA3

: Convergence failed

: Prematurely converged

Problem Number

Num

ber

of A

nlay

ses

TDQATANA3

Test Problems

29


Outline



Applications

30


Go

Go

Go

Go

Go

Go

NEXT

AerospaceAutomotivesBiotechnologyElectronicsInformation Technology

Marine TechnologyMaterialsMechanicalMEMS DevicesNuclearRailway Vehicles

2152

132

26

26222

ApplicationsApplications

ABS Controller (Simulink & CarSim)

Air Bearing Surface of HDD (in-house code)

Switched Reluctance Motor (SRM Analyzer)

Hydro-Pneumatic Suspension Unitof a Tracked Vehicle

Automotive Body Structure (MSC/NASTRAN)

Go Drum Washer Suspension System (DADS & ANSYS)

Heat Sink for a 40A-Drive PackageSystem of an Elevator (FLUENT)

(RecurDyn-alpha)

31


Application 1: 40A-Drive Package System

Model : 40A Drive Package System

- Heat Sink (188 x 400 x 60 mm)- IGBTs (46,007 / 42,438 W/m2)- Fan (Model : 3112KL-05W-B50)

Schematics of Drive Package System

7.52

1.5 (B2)

94

537

(t)

2.0 (B1)

Schematics and baseline geometry of heat sink

IGBT_1

Duct Heat SinkReactor

IGBT_2

Optimization of Heat Sink

Numerical Methodology

- FLUENT : Predict Flow andThermal Fields in System

- SQP (Sequential Quadratic Programming Method): Propose the optimal variables numerically

- Batch-process : Integrate CFD(FLUENT) and CAO (SQP)

Objective

- To obtain the optimum design variables

(B1, B2, and t ) by minimizing

(1) the pressure drop (2) the temperature rise, simultaneously

Objective functions

Design variables

32


Application 1: 40A-Drive Package System

Pathlines for understanding the flow fields

Optimum variables ( Temp. rise is less than 35 K)

Results

Comments

- Optimization is strongly needed to guarantee the thermalstability of IGBTs

- It is easily applicable to the other specification of heat sink- As shown the above table, pressure drop increases while

temperature rise decreases. - Note that, in optimum model, the value of pressure drop is

ranged in the characteristic curve of fan.

Comparison with Experimental Data

- For the temp. rise, difference is only 1.2 KGood agreement with the experimental data

Isotherms for understanding the temp. fields

Vortex flow

10.7

7

t

34.93 K ( )

38.66 K ( )

Temp. Rise

43.3 Pa1.52Baseline

1.9

B2

Optimal 50.3 Pa2.6

Pre. DropB1

• Ambient temp. : 318 K (45 oC)• Max. temp. of baseline geometry : 356.66K, Max. temp. of optimization : 352.93 K

Max. Temp : 352.93 K

Unit : [mm]

HOME

3333

Applications

For higher areal density For higher areal density …………

• Reduced flying height (as low as 10 nm)• Complicated geometry of ABS

Application 2: Head-Disk Interface (HDI)

3434

Applications

h*

radius

radius

U

L

radius

U

L

hglide

rotational vel.

halt

radius

Uniform FH (Fly Height) (target FH = 9 nm)Uniform FH (Fly Height) (target FH = 9 nm)

Limited Pitching (between 250 and 300 Limited Pitching (between 250 and 300 rad)rad)

Limited Rolling (between Limited Rolling (between --5 and 5 5 and 5 rad)rad)

Altitude Insensitivity (80% FH @10k ft)Altitude Insensitivity (80% FH @10k ft)

Fast TOV (80% FH @ra=15 mm/skew=Fast TOV (80% FH @ra=15 mm/skew=--25.54, rpm=2.5K)25.54, rpm=2.5K)

Application 2: Design Requirements

3535

Applications

•• Design variables: S1~S10, recess depth, and shallow stepDesign variables: S1~S10, recess depth, and shallow step•• Using SAEUsing SAE’’s shape function for design variable linking s shape function for design variable linking --> [shape.in]> [shape.in]

Application 2: Design Variables

3636

Applications

2 2max min

min

max

, 1 ~ 8, ,

0.5*( 9 ) 0.5*( 9 )

:250 ,

: 300 ,

:

1

2

3

find

min. nm nm

subject to g rad

g µrad

g

i s i recess shallow

F hINT hINT

Pitch

Pitch

min

max

max

1

5 ,

: 5 ,

: 9 (1 0.8)*9 ,

: 0.8*9 ,

0.02

4

5

6

rad

g µrad

g nm

g nm

where -0.05 mm mm

ALT

FAST

Roll

Roll

nm hINT

hINT

s

2

3

4

5

6

0.020.020.050.050.05

-0.05 mm mm

-0.05 mm mm

-0.02 mm mm

-0.05 mm mm

-0.05 mm mm

-0

sssss

7

8

0.050.052

0.2

.02 mm mm

-0.02 mm mm

1 m m 0.1 m m

ss

recessshallow

Application 2: Mathematical Formulation

3737

Applications

Uniform FH , Limited Pitching , Limited RollingUniform FH , Limited Pitching , Limited Rolling

Application 2: Altitude Insensitivity

20 30 40 500

5

10

15

20

Flyi

ng h

eigh

t [nm

]

Disk radius [mm]

Initial Optimum

20 30 40 50200

250

300

350

Pitc

h an

gle

[ra

d]

Disk radius [mm]

Initial Optimum

20 30 40 50-15

-10

-5

0

5

10

15

Rol

l ang

le [

rad]

Disk radius [mm]

Initial Optimum

3838

Applications

iteration number : 17iteration number : 17total function calls : 221total function calls : 221

Application 2: Optimization Results

0 5 10 15 20-2

-1

0

1 G1 G2 G3 G4 G5 G6

Con

stra

int v

alue

Iteration number0 5 10 15 20

0

10

20

30

40

50

Cos

t val

ue

Iteration number

HOME

3939

Applications

Design PathRoad

Design Requirements

4040

Applications

ABS Controller FRT On Switch ValueABS Controller FRT Off Switch ValueABS Controller RR On Switch ValueABS Controller RR Off Switch Value

Brake Actuator Gain LR & RR

ABS Controller Switch Threshold

Application 3: Simulink Model (Including CarSim S-Function)

Simulink Model

4141

Applications

Initial/Operating Conditions (CarSim)

Application 3: CarSim Model

CarSim GUI

4242

Applications

4343

Applications

Simulink + CarSim

Application 3: Integration

Design under Uncertainty

Uncertainty Analysis

Sequential Approximate Opt.

Optimization

Approximation

Design of Experiment

Parametric StudyFRAMAX

4444

Applications

Multiobjective Problem•Weight Factor(Station) : 0.75•Weight Factor(Yaw) : 0.25

Optimum

Initial

Application 3: Pareto Optimum (1)

Station(m) vs. Time(s) Yaw(deg) vs. Time(s)

4545

Applications


Optimum

Initial



4646

Applications


Optimum

Initial



4747

Applications

Pareto Set

0

100

200

300

400500

600

700

150 160 170 180 190 200 210

Station

Squ

are

Sum

of Y

aw

Weighting Ratio(Staion/SquareSumYaw=0.75/0.25)



Application 3: Pareto Optimum Set

Pareto Optimum Set

HOME

48

Applications

Maximize Average Torque

Torque ripple

Maximum Current Phase

aveT

%20ripT

A6maxI

Switching on Angle

Switching off Angle

Rotor Pole Arc

on

off

r

Design of a Switched Reluctance Motor

Application 4: SRM (Switched Reluctance Motor)

49

Applications

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Angle (deg.)

Ave

rage

Tor

que

(N-m

)

75.0

80.0

85.0

90.0

95.0

100.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0Angle (deg.)

Tor

que

Rip

ple

(%)

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0Angle (deg.)

Max

imum

Cur

rent

Pha

se (A

)

0.15

0.16

0.17

0.18

0.19

0.20

0.21

0.22

0.23

0.24

45.0 47.0 49.0 51.0 53.0 55.0 57.0 59.0

Angle (deg.)

Ave

rage

Tor

que

(N-m

)

45.0

55.0

65.0

75.0

85.0

95.0

105.0

45.0 47.0 49.0 51.0 53.0 55.0 57.0 59.0Angle (deg.)

Tor

que

Rip

ple

(%)

4.00

4.05

4.10

4.15

4.20

4.25

4.30

4.35

4.40

45.0 47.0 49.0 51.0 53.0 55.0 57.0 59.0Angle (deg.)

Max

imum

Cur

rent

Pha

se (A

)

Switching on Angle Switching off Angle

Parameter Studies of Switching On/Off Angles


50

Applications

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5 6 7 8 9Iteration

Ave

rage

Tor

que

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

0 1 2 3 4 5 6 7 8 9Iteration

Max

imum

Con

stra

int V

iola

tion

0

0.1

0.2

0.3

0.4

0 10 20 30 40 50 60 70 80 90

Rotation Angle (deg.)

Tor

que

(N-m

)

Initial DesignOptimum Design

Initial

Optimum

on off r aveT ripT maxI

22.4 55.7 38.0 0.30 19.98 4.91

25.2 45.1 30.0 0.17 98.60 4.02

Optimization Results


HOME

51

Applications

14 inch

Minimize the vertical acceleration at the CG of the hull

wheel travels during jounce(6)

equally distributed static forces for the wheels(6)

track tension(1)

charging pressures of the 3rd and 4th HSU’s(2)

static track tension

charging pressures of the 1st, 2nd, 5th and 6th

HSU’s

length of gas chambers

pre-load for Belleville springs

choking flow rate

inner diameter of orifice

Objective

Constraints (15) Design Variables (9)

Application 5: Tracked Vehicle

52

Applications

Is the acceleration a nosy function ?

• Gradient based optimization algorithm may cannot be converged.• Function based approximate optimization algorithm should be used.

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Time

Ver

tical

Acc

eler

atio

n (m

/s^2

)

Noise ?

Noisy Cost Function


53

Applications

Optimization Result - Acceleration


54

Applications

Optimization Result – Wheel Travel


HOME

55

Applications

1

z' z y'

y

1t

2t3t

1SV

2SV

Hz

Application 6: Automotive Body Structure

56

Applications

Optimization Results Convergence History

2.98415E-31.37259E+313

3.49547E-31.37245E+312

2.53623E-31.37371E+36.22981E-31.37171E+311

3.77472E-31.37340E+39.90981E-31.37084E+310

1.19377E-21.37201E+31.54264E-21.36953E+39

4.39808E-21.36701E+32.15811E-21.36823E+38

5.50377E-21.36875E+32.94570E-21.36642E+37

2.27294E-21.37600E+33.80981E-21.36567E+36

1.61079E-21.38161E+35.48596E-21.36501E+35

2.35630E-21.38227E+36.08585E-21.36717E+34

3.69611E-21.38771E+38.19064E-21.36478E+33

3.78596E-21.38829E+36.29008E-21.37034E+32

4.30770E-21.38883E+34.30770E-21.38883E+31

Max.Violation

Objective function

Max.Violation

Objective function

TPCATDQAIT

16 kg 15 kg

Application 6: Automotive Body Structure

HOME

CAE-Based Design Optimization

Dong-Hoon Choi

[email protected]

Director, the Center of Innovative Design Optimization Technology (iDOT)Professor, School of Mechanical Engineering

Hanyang University, Seoul, Korea

September 1, 2006

Documents

CAE-Based Design Optimization - jsme.or.jp · CAE-Based Design Optimization Dong-Hoon Choi [email protected] Director, the Center of Innovative Design Optimization Technology (iDOT)