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ME-729Engineering Design &

Optimization

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Qualifcation

PhD HUST, China

Mechanical Manuacturing & Automation MS College o E&ME, NUST

Mechanical Design

MS PEAS

Process Engineering !Sc UET Pesha"ar

Mechanical Engineering

Muhammad Farhan Ausaf

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Course Co#e ME $% nstructor Muhamma# 'arhan Ausa Semester 'all %()*

Cre#it Hours +( Pre -e.uisite amiliarit/ "ith MAT0A! Class timings Tues#a/, 12((32(( 45m5

Email2 arhan5ausa6hitecuni5e#u547

Engineering Design &Optimization

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Grade Distribution:

Qui88es9Assignments )(:Term Pro;ect9Presentation )(: Sessional E

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=ou are highl/ encourage#to as7 .uestionsan# #iscuss the course material "ith mean# /our classmates5

No cheating, a>rication, alsifcation,orger/ an# com4uter misuse5 Please s"itch o?94ut on silent /our cell

4hones5

A#here to the gi@en #ate or assignmentsu>mission5

$!ass o!i"#

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-ecommen#e# !oo7s2

ntro#uction to 4timum #esign >/ Bas>ir S5Arora

Engineering 4timi8ation2 Theor/ an#Practice >/ Singiresu S5 -ao

4timi8ation or engineering #esign,algorithms an# e/ 5 De>>

%oos

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Discuss the metho#s an# techni.ues orormulation o #esign 4ro>lems intomathematical orm "hich is acce4ta>le too4timi8ation algorithm

Single @aria>le unction o4timi8ation algorithms Algorithms or o4timi8ation o constraine# an#

unconstraine# 4ro>lems Nontra#itional o4timi8ation9mo#ern

o4timi8ation algorithms "ill >e #iscusse#5 Use o MAT0A! or o4timi8ation

$ourse O'er'ie(

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ntro#uction Design 4ro>lem ormulation ra4hical o4timi8ation

4timum #esign conce4ts 0inear Programming Constraine# an# unconstraine#

4timi8ation Multi@aria>le o4timi8ation Nontra#itional9Mo#ern o4timi8ation

algorithms

$ourse Out!ine

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4timi8ation is #eri@e# rom the 0atin "or#4timusF, "hich means the >est an#characteri8es the acti@ities in@ol@e# to fn#the >estF5

Peo4le ha@e >een o4timi8ing rom ages, >utthe roo# o mo#ern #a/ o4timi8ation can >etrace# to the secon# "orl# "ar5

4timi8ation is oten s/non/m "ithOperations resear"h

Optimization

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Optimization is the act of obtaining the best result under givencircumstances.

Optimization can be defined as the process of finding theconditions that give the maximum or minimum of a function.

The optimum seeking methods are also known as mathematicalprogramming techniquesand are generally studied as a part ofoperations research.

Operations research is a branch of mathematics concerned with theapplication of scientific methods and techniques to decision makingproblems and with establishing the best or optimal solutions

Optimization

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Di)erent *inds ofOptimization

'igure rom2 4timi8ation Technolog/ Cente

htt4299"""45mcs5anl5go@9otc9ui#e94tGe

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4timi8ation 4ro>lems arise naturall/ in man/#i?erent #isci4lines5 n engineering #esign4ro>lem oten goal is to males5

Some t/4ical a44lications rom #i?erentengineering #isci4lines are Design o aircrat an# aeros4ace structures or

minimum "eight

'in# the o4timal tra;ectories o s4ace @ehicles Design o ci@il engineering structures such as

rames, >ri#ges, to"ers an# #ams or minimum cost

+eed for optimization

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4timal #esign o lin7ages, cams ,gears, machinestools an# other mechanical com4onents

Design o material han#ling e.ui4ment, such ascon@e/ors, truc7s an# cranes or minimum cost

Design o 4um4s, tur>ines an# heat transere.ui4ment or ma

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A!! optimization "ases ha'e thefo!!o(ing three things in "ommonThere is an o@erall goal, or o>;ecti@e or the

acti@it/ n a##ition to the o@erall goal there are

constraints that must >e met n all situations, choices are a@aila>le to

meet the goals an# o>;ecti@es

+eed for Optimization

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Pro>lem ormulation Ta7ing statements

Defning general goals an# re.uirements o agi@en acti@it/

Con@erting them into a series o "ell #efne#mathematical statements

Pro>lem ormulation Selecting one or more o4timi8ation @aria>les

Choosing an o>;ecti@e unction #enti/ing a set o constraints

Optimization rob!em

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The ob,e"ti'e fun"tionan# the "onstraints

must all >e unctions oone or more

o4timi8ation @aria>les

Optimization rob!em

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'in# the #imensions o therectangular gar#en o greatest areathat can >e ence# o? Iall our si#esJ

"ith +(( meters o encing

Maimizing Area

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4timi8ation @aria>les 0ength an# Gi#th

>;ecti@e 'unction Ma

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Maimizing Area"ontinued

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A rectangular gar#en o area $1 s.uare eetis to >e surroun#e# on three si#es >/ a >ric7"all costing )( 4er oot an# on one si#e >/a ence costing 1 4er oot5 'in# the#imensions o the gar#en such that the costo materials is minimi8e#5

Minimizing $ost

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4timi8ation @aria>les 0ength an# Gi#th

>;ecti@e 'unction Minimi8e Cost K %(0ength L )1Gi#th

Constraints

Area K 0ength < Gi#th K $1

Minimizing $ost "ontinued

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Minimizing $ost "ontinued

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A can@as "in# shelter or the >each has a>ac7, t"o s.uare si#es an# a to45 'in# the#imensions or "hich the @olume "ill >e %1(cu>ic eet an# that re.uires the least4ossi>le amount o can@as5

Minimizing .urfa"e Area

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4timi8ation @aria>les 0ength, Gi#th an# Height IGi#th K HeightJ

>;ecti@e 'unction Minimi8e Surace area K %Gi#th%L

%Gi#th0ength

Constraints Oolume K 0ength < Gi#th%K %1(

Minimizing .urfa"e Area"ontinued

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Minimizing .urfa"e Area"ontinued

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Design a can to hol# at least *(( ml o li.ui#, as"ell as meet other #esign re.uirements5 The can"ill >e 4ro#uce# in the >illions so it is #esira>leto minimi8e manuacturing costs5 Since cost can

>e #irectl/ relate# to the surace area o thesheet metal so minimi8e the amount o sheetmetal re.uire# to a>ricate the can5 'ollo"ingrestrictions are im4ose# on the si8e o the can5

The #iameter shoul# >e no more than 3 cm an#no less than +51cm, "hereas the height shoul#>e no more than )3cm an# no less than 3 cm5

Design of a $an