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Optimization of Laminate

Composite Structures – RecentAdvances and ApplicationsBy Warren Dias on October 13, 2011

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The use of fiber-reinforced composite material entered a ne era hen

leadin! aircraft O"#s too$ an unprecedented step to desi!n and

manufacture essentially full composite airframes for commercial airliners%

&omposite structures offer unmatched desi!n potential, since the laminate

material properties can be tailored almost continuously throu!hout the

structure% 'oe(er, this increased desi!n freedom also brin!s ith it ne

challen!es for the desi!n process and softare technolo!y%

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)n recent years, *ltair has de(eloped a comprehensi(e frameor$ for

composite optimi+ation% The process consists of three optimi+ation phases%

hase 1 focuses on !eneratin! ply layoutshape concepts throu!h free-si+e

optimi+ation. hase 2 further refines the desi!n by determinin! the number

of plies for a !i(en ply layout defined by hase ), usin! si+e optimi+ation

techni/ues. then hase 3 completes the final desi!n details throu!h ply

stac$in! se/uence optimi+ation, satisfyin! all manufacturin! and

performance constraints% This three-phase process desi!n methodolo!y

has seen increasin! adoption amon! aerospace O"#s, amon! others, as

demonstrated by the Bombardier application process described in this

article%

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Three-Phase Laminate Composite Design Optimization Process

Figure 1 illustrates the different phases of the optimization process.

i!ure 1%

 Phase 1: Concept design of material orientation and placement through free-size optimization

The optimization prolem can e stated mathematicall! as follo"s#

 

$here represents the o%ective function& and represent the j'th constraint response

and its upper ound& respectivel!. M  is the total numer of constraints& NE  the numer of

elements and Np the numer of super'plies( is the thic)ness of the i'th super'pl! of the k 'th

element. The concept of a *super'pl!+ is introduced to allo" aritrar! thic)ness variation of a

given fier orientation at a given stac)ing location. T!picall! onl! one super'pl! is needed for

each availale fier orientation. ,uring this design phase& responses of a gloal nature are

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considered for oth the o%ective and constraints. T!picall!& compliance or )e! displacement

responses are used to formulate the design prolem so that the overall structural stiffness is

optimized. -anufacturing constraints are important for composite design and need to e address

right at the eginning of the concept design phase. A couple of commonl! used manufacturing

constraints are the percentage of a given fier orientation in the overall thic)ness and the total

laminate thic)ness.

 Phase 2: Design fine-tuning using ply-bundle sizing optimization

The free'size optimization descried in hase 1 leads to a continuous distriution of thic)ness for 

each fier orientation. A discrete interpretation of the thic)ness defines the la!out of pl!'undles

"ith each undle representing multiple plies of same orientation and la!out/shape. The pl!'

 undle la!out can e simpl! otained ! capturing different level'sets of the thic)ness field of

each fier orientation. The default method provides a good alance et"een the true

representation of the thic)ness field and the comple0it! of the pl! tailoring. These pl!'undles of 

different fier orientations are then stac)ed together so as to e uniforml! distriuted in the

gloal stac).

n this phase& the design variales are optionall! discrete thic)nesses at unit pl! thic)ness

increments. Also at this design stage& all detailed ehavior constraints& including pl! failure&

should e considered. -anufacturing constraints& such as orientation percentage considered in

hase 1& are carried over during this design phase.

 Phase 3: Detailed design through ply stacking sequence optimization

Though the design achieved in hase 2 contained all pl! shapes and stac)ing details& it is li)el!

that detailed manufacturing constraints or pl! oo) rules are not satisfied. Therefore& the stac)ing

se3uence of individual plies is optimized during this phase to satisf! manufacturing constraints

"hile preserving all ehavioral constraints. mportant manufacturing constraints include# 4a5

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limit on consecutive plies of the same orientation( 45 pairing of 6/' angles( 4c5 pre'defined cover

la!'ups( 4d5 pre'defined core la!'ups.

Draping modeling

$hen shell surfaces have i'directional curvature& fier orientation flo" is rather comple0 and

needs to e determined ! draping anal!sis. Often cuts& called darts& need to e placed to

eliminate e0cess cloth "hen a pl! is placed over a curved surface. An e0ample of draping is

sho"n in Figure 2. n such cases& a correction of fier orientation and thinning needs to e

considered in the F7A model. The ,RA7 card is implemented in OptiStruct to accommodate

this correction information otained ! draping anal!sis soft"are.

Zone-based free-sizing

This design/manufacturing re3uirement "as driven ! some commercial aircraft O7-. Their

design process re3uired constant pl! thic)ness for each zone& defined ! intersected stringers and

ris. 8esides simplif!ing pl! la!out& the main reason for the re3uirement is to accommodate

legac! design criteria "here each aforementioned zone is a panel unit for strength and stailit!

evaluation. Therefore constant thic)ness "ithin each panel is re3uired for accurate calculation of

its properties. An illustrative e0ample is sho"n in Figure 9 "here free'size results "ith and

"ithout zone'ased pattern grouping are compared.

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i!ure 2 ly orientation drapin! on a half sphere%

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i!ure 3 Thic$ness distribution of ree-Si+e results ith and ithout pattern

!roupin!%

 Application example

The three'phase composite design process is demonstrated through the design of the "ing of a

"ide' od! aircraft& sho"n in Figure :. ;ine load cases of )e! significance are considered. n

this simplified e0ercise& onl! "ing tip displacement constraints are considered& "ith upper

 ounds not e0ceeding those of a aseline aluminum "ing under each load case. Onl! the caron

fier composite top and ottom s)ins are optimized. l! orientations availale are <& 6:=/':=& ><

 plies& "ith the leading edge as reference.

 Phase 1: Concept design !ree-size optimization

-anufacturing constraints considered include#

#aimum thic$ness of each fiber orientation 10 mm

456-56 plies to be balanced

7 mm total laminate thic$ness 32 mm#inimum percenta!e of a(ailable fiber orientations 8 109

The thic)ness distriution of the four fier orientations is sho"n for the upper s)in in Figure =. t

can e seen that pl! alancing constraints )ept the thic)ness distriution of 6:= and ':=

orientations identical.

i!ure 5 &omposite in! model of a ide body aircraft under cruise loadin!%

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i!ure 6 Thic$ness distribution of the upper s$in of the in!%

 Phase 2: Design fine-tuning Ply bundle sizing optimization

The results sho"n in Figure = are interpreted into four pl! la!outs for each fier orientation. The

 pl! coverage area decreases as the thic)ness level'set increases. The first pl! undle covers the

entire "ing. La!outs of the second pl! undle of < degree orientations for oth lo"er and upper

s)ins are sho"n in Figure ?. ;ote that t!picall! some manual editing of the ra" level'set ased

 pl! shape is needed. For simplicit!& this e0ample simpl! adopted the automaticall! generated pl!

shapes defined ! the thic)ness level'sets.

i!ure : Second ply-bundle layouts of the 0 de!ree orientation%

n this stud!& the sizing optimization prolem remained the same as in hase 1. For more realistic

applications& this optimization phase should consider all detailed design criteria& such as strength

and stailit! constraints. The numer of plies in groups of </6':=/>< pl!'undles is# /1='9'1/1'

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1<'=/1='1='>/1='1='19/& @B1 "hich can e determined after the sizing optimization. The total

thic)ness contour of upper s)in after sizing optimization is sho"n in Figure D.

i!ure ; Total thic$ness contour of upper s$in after si+e optimi+ation%

  Phase """: Detailed design Ply stacking sequence optimization

This optimization phase focuses on the laminate stac)ing se3uence "hile preserving oth

manufacturing and performance constraints. Additionall!& it is re3uired that certain pl! oo)

rules e applied to guide the stac)ing of plies ased on specific re3uirements. Some pl! oo)

rules that control the stac)ing se3uence are#

 –   -a0imum numer of successive plies of a particular fier orientation

 –   airing of the 6 and – :=s

 –   dentif!ing a se3uence for the core and cover regions

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For this e0ample& the optimization prolem as previousl! formulated in the sizing phase is

retained& and the follo"ing additional pl! oo) rules are applied# 4a5 the ma0imum successive

numer of plies does not e0ceed three plies( 45 the 6 and – :=s e reversed paired. Figure E

illustrates the stac)ing se3uence efore and after stac)ing optimization. Through this proof'of'

concept stud!& the three'phase optimization process has successfull! demonstrated its capacit!

for ma0imizing utilization of the potential of composite material in the design of a laminate

composite structure& "hile significantl! shortening the design process.

i!ure 7 Stac$in! optimi+ation < initial and final stac$in! se/uence%

 Application of Altair’s composite design optimization process to aero-structure composite

component development at Bombardier

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This section outlines application of the Altair composite optimization technolog! to composite'

component design at 8omardier. As part of 8omardiers ongoing technolog! development

initiatives& application of the process "as e0plored at single and multiple component levels. A

description of the process and method of application inside a d!namic aerospace design

environment is descried. -ethods for incorporating structural and manufacturing constraints

are introduced. Also summarized are the interfaces developed et"een design and stress groups&

"hich underpin the successful application of the technolog! in an environment "here design

re3uirements can fre3uentl! change.

 "ntegration of #ltair$s composite design process

ntegration of Altairs composite optimization process "ith the design process and all of the

necessar! interfaces is sho"n schematicall! in Figure >. The main additions to the process are

interfaces accommodating inputs and outputs to and from the design team. ;otal!& custom

responses and constraints are needed to align the optimization "ith strength& stiffness and

stailit! 3ualification re3uirements. 70port of the optimization solution is also re3uired in a

numer of different formats& including CA,'format laminate descriptions& 3ualification reportsummaries and additional finite' element formats.

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i!ure = Schematic Summary of the )nte!ration of *ltair>s &omposite Desi!n

Optimi+ation rocess ith Bombardier>s *ero-Structure Desi!n rocess%

Composite optimization interfaces

A revie" of the 8omardier aero'structure design process "as performed to identif! the inputs

and outputs re3uired for the composite optimization process. Successful access to the

technolog! in the overall design process is underpinned ! these interfaces "or)ing efficientl!

and roustl!. The main focus areas for the interface development "ere#

i5  Conversion of 8omardier F7- data to OptiStruct format suitale for

optimization

ii5  F7- e0port at the end of the process

iii5  CA, format e0port of final designs

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iv5  Gualification anal!sis reporting in 8omardier format 4spreadsheets and other

digital documents5

Altairs generic F7- and composite interfaces "ere modified to facilitate each of these

re3uirements in the 8omardier design environment. The resulting solution "as a single

integrated platform that facilitated passage of input and output data to and from the optimization

 et"een 8omardier and Altair. Composite specific results visualization and report data could

easil! e shared and revie"ed ! all parties.

%ptimization problem formulation

The optimization prolems "ere t!picall! defined to minimize mass su%ect to stiffness&

allo"ale composite stresses and stailit! criteria. -ultiple load cases "ere defined

and& "here availale& appropriate stiffness targets set for each& ased on the aseline

response.

n addition to the composite laminate sizing design variales for components& shape

optimization of the stiffening memers also "as investigated through FR77 SHA7

optimization in OptiStruct. Ireater design freedom is afforded "ith this approach&

since it allo"s each stiffener height to change independentl! and freel! in shape as "ell

as size. This is often advantageous "here a alance et"een relative stiffness and

stailit! must e maintained. To constrain the optimization to derive designs compatile

"ith the design team re3uirements for some components& zone oundaries "ere defined

over the surface. OptiStruct can constrain the laminate solutions to respect these

 oundaries from the first free'sizing stage. This is often a )e! manufacturailit!

re3uirement and can e loc)ed do"n at the concept stage.

Commonalit! et"een manufacturing constraints "as maintained throughout the stages

to enforce minimum percentages of cloths and uni'directional plies in the stac). n the

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later stages& manufacturing rules "ere enforced limiting the ma0imum numer of

consecutive plies.

The structural constraints "ere implemented ! direct sampling of finite'element

results 4stiffness and strain5 or ! custom calculations developed to correlate "ith

3ualification assessment methods 4gloal and local stailit!& additional strength

re3uirements5. The custom calculations "ere implemented through OptiStructs

,R7S9 functionalit!& "hich ensures efficienc! in the handling of custom calculation

routines and response sensitivities.

 Discussion

The composite optimization process "as applied successfull! in a real'"orld aerospace design

environment& allo"ing efficient e0ploration of designs and delivering "eight'saving potential for 

a range of components and s!stems.

  The follo"ing ma%or advantages "ere found from application of the process#

i5  The free'form stage provided an efficient testing ground for design sensitivit!

to applied loads and design constraints. The solutions "ere not influenced !

 previous designs and provided insight into methods for improving structural

efficienc!. The! provide a ver! efficient method for performing trade'off

studies and rapid assessment of changes in design re3uirements.

ii5  The process demonstrated the value of loc)ing pl! continuit! into the

optimization from earl! in the process. n this "a!& manufacturailit! could e

constrained "ith less impact on the structural efficienc!. nterfaces "ere

developed et"een the OptiStruct pl!'ased output and design s!stem carr!ing

over pl! continuit! directl!.

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iii5  Significant mass savings "ere predicted from application of the technolog!

and a measure of the effect on "eight of var!ing manufacturing constraints

could e 3uantified.

iv5  The input data and optimization solutions could e integrated "ith the current

design practice at 8omardier& facilitating efficient communication and final

design 3ualification.

Application of the optimization approach at 8omardier has led to a repeatale process& "hich

accommodates the composite design 3ualification re3uirements and can e enhanced and applied

at component and s!stem level.

The three'phase design process starts "ith creating design concepts capale of full! utilizing the

increased design potential of composite material. t finishes "ith a final design of pl!'oo)'level

details "here manufacturing rules& together "ith all performance re3uirements& are satisfied. An

aircraft "ing case stud! is sho"n to demonstrate the optimization process. Then& a detailed

description of the application "ithin a real'"orld aircraft design environment at 8omardier

Aerospace is given. t is particularl! notale that customer'specific design constraints on panel

strength and stailit! are incorporated through e0ternal responses 4,R7S95. These factors

demonstrate the versatilit! of OptiStruct that allo"s the optimization process to fit into an

estalished comple0 environment of commercial'aircraft design.

This paper is written in collaboration with Ming Zhou, Vice President of Software Deelop!ent"

? @earn more about optimi+ation solutions from 'yperWor$s

► Explore the Aerospace solutions with Hyperor!s

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•  *bout

 

• @atest osts

Warren Dias

Business De(elopment #ana!er - OptiStruct at *ltair 

Warren is the Business De(elopment #ana!er for OptiStruct here his

responsibilities include increasin! the !lobal footprint and usa!e of

OptiStruct% 'e Aoined *ltair in 2000, and no has nearly 16 years of

eperience in the field of finite element analysis and structural optimi+ation%

'e holds a Bachelor De!ree in #echanical "n!ineerin! from #anipal

)nstitute of Technolo!y in )ndia%

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