Finite Element Based Structural Optimization

by GENESIS

2

Outline

!Design approach!Numerical Optimization

"Advantages"Limitations

!Structural optimization in GENESIS!Examples

"Composite panel design optimization subject to crack propagation constraint

"High Speed Civil Transport Wing Problem

!Optimization Errors

3

Design Approach

! Defined design goal" Minimum weight design: Given load, required strength

! Analyze proposed design, for acceptability ! Change one or more design variables to see if any

design improvement can be obtained.

! OK, when the design is a function of only a few variables

! More systematic approach needed: Numerical optimization

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Numerical OptimizationAdvantages (Vanderplaats)

! A major advantage is the reduction in design time –this is especially true when the same computer program can be applied to many design projects.

! Optimization provides a systematic design procedure.! We can deal with a wide variety of design variables

and constraints which are difficult to visualize using graphical or tabular methods.

! Optimization requires a minimal amount of human-machine interaction.

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! Computational time increases as the number of design variables increases. If one wishes to consider all possible design variables, the cost of automated design is often prohibitive.

! It can seldom be guaranteed that the optimization algorithm will obtain the global optimum design. Therefore, it may be desirable to restart the optimization process from several different points to provide reasonable assurance of obtaining the global optimum.

! Because many analysis programs were not written with automated design in mind, adaptation of these programs to an optimization code may require significant reprogramming of the analysis routines.

Numerical OptimizationLimitations (Vanderplaats)

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Structural Optimization in Genesis

! FEA for the initial proposed design! Design cycle starts

" Sensitivity analysis (gradient computations) for the responses included in the objective function and the constraints

" High quality approximation for the original problem and optimization of the approximated problem

" FEA for the new design" Convergence check, start new design cycle if necessary

! Improved Design/Optimum

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!DOBJ: defines objective function!DCONS: defines constraints!DOPT: defines optimization parameters!DEQUAT: to implement equations in

GENESIS!DTABLE: to assign values for parameters in

equations

Structural Optimization in Genesis

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2 ay

x

z

PyN

20"

20"

5"

0°

(45/-45/90/0)s

t45 t90 t0skinstiffener t45 t90 t0

Structural design variables

0.005 ≤≤≤≤ ≤≤≤≤ 0.025 in.

PyN

Composite panel design optimization subject to crack propagation constraint

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Low Fidelity (LF) Model

Stress intensity factor in the 0° ply

Far-field stress in the 0° ply

aK fLF πσ 00 =

LF Direct OptimizationImplemented in GENESIS via its equation utility0.10

0

≤Q

LF

KK

10

LF optimization2a= 4.0 in., h= 2.5 in., Ny=2500 lb./in.

skint45

skint90

skint0

bladet45

bladet90

bladet0

0050.0 0050.0 0217.0

0050.0 0050.0 0250.0

0250.0 0250.0 0250.0

0250.0 0250.0 0250.0

W= 5.700 lb

K=64,642 psi√√√√in

W= 2.127 lb

K=99,986 psi√√√√in

0050.0 0050.0 0249.0

0050.0 0050.0 0050.0

W= 2.047 lb

K=105,927 psi√√√√in

0050.0 0050.0 0213.0

0050.0 0050.0 0250.0

W= 2.112 lb

K=101,000psi√√√√in

Cycle 0 Cycle 1

Cycle 2 Cycle 3

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a r

1 2 3 nb elements

yσσσσ

1yσσσσ

2yσσσσ 3yσσσσ

bynσσσσ

ar 125.r≈≈≈≈0.125 a

High Fidelity (HF) Model

rK

y πσ

2=

HF Direct OptimizationImplemented in GENESIS via its equation utility

0.10

0

≤Q

HF

KK

12

HF optimization2a= 4.0 in., h= 2.5 in., Ny=2500 lb./in.

skint45

skint90

skint0

bladet45

bladet90

bladet0

0050.0 0050.0 0192.0

0050.0 0050.0 0250.0

0250.0 0250.0 0250.0

0250.0 0250.0 0250.0

W= 5.700 lb

K=61,935 psi√√√√in

W= 2.014 lb

K=99,982 psi√√√√in

0050.0 0050.0 0240.0

0050.0 0050.0 0050.0

W= 2.007 lb

K=104,643 psi√√√√in

0050.0 0050.0 0187.0

0050.0 0050.0 0250.0

W= 1.995 lb

K=101,440psi√√√√in

Cycle 0 Cycle 1

Cycle 2 Cycle 3

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! 250-passenger ! 5500 nmi. Range! Cruise Mach speed of 2.4

High Speed Civil Transport Wing Problem

cv4 +x

z

Location of maximumthickness (fixed)

Leading edge radius(fixed)

Outboard LE sweep (fixed)

xy

cv2

cv3

Wing semispan (fixed)

Nacelle locations(fixed)

cv1

! Root chord length! Tip chord length! In-board sweep angle! Thickness to chord ratio

Configuration variables

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Alternative to empirical weight equationsStructural Optimization

! Structural design variables" 26 skin panel thickness-plate" 12 spar cap areas-rod" 2 rib cap areas-rod

! Objective Function" Structural weight

! Constraints" Stress allowable" Buckling

Wing skin panel

Spar caps Rib capsShear webs

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DESIGN CYCLE HISTORY

! DESIGN OBJECTIVE MAXIMUM CONSTRAINT! CYCLE FUNCTION VIOLATION

! 0 79050 91.3%! 1 103380 0.0%! 2 100334 1.4%! 3 80670 32.0%! 4 106566 0.0%! 5 106414 0.0%

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Optimization Errors

! Modeling! Trapped in a local optimum

" Initial design" Round-off errors

! Convergence parameters

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Config. 2

PC WBMW (lb.)

70371

Alpha station WBMW (lb.)

90138

Config. 7

PC WBMW (lb.)

60286

Alpha station WBMW (lb.)

56808

Repairable Numerical Noise

70800 lbs.

Perturbed initial values

55835 lbs.

different optimization method

Optimization ErrorStructural Optimizations: GENESIS

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Optimization Errors

0.0001

0.001

0.01

0.1

1

10

100

0 5 10 15 20 25 30 35 40 45configuration

%(P

C-U

NIX

)/PC

objective functionWb

E PC

-UN

IX

0.0001

0.001

0.01

0.1

1

10

100

0 5 10 15 20 25 30 35 40 45configuration

%(P

C-U

NIX

)/PC

objective functionWb

E PC

-UN

IX