麻省理工学院：《Multidisciplinary System》Issues in Optimization

Issues in Optimization Jaroslaw sobieski NASA Langley Research Center Hampton Virginia NASA Langley research Center A LaRC/SMCIACMB Copyright NASA, Jaroslaw Sobieski, 2003

Issues in Optimization Jaroslaw Sobieski NASA Langley Research Center Hampton Virginia NASA Langley Research Center LaRC/SMC/ACMB Copyright NASA, Jaroslaw Sobieski, 2003

How to know whether optimization is needed

How to know whether optimization is needed

How to recognize that the problem at hand needs optimization General rule of the thumb there must be at least two opposing trends as functions of a design variable X f1 Analysis 12 f2 f2 X

How to recognize that the problem at hand needs optimization. • General Rule of the Thumb: there must be at least two opposing trends as functions of a design variable Analysis x f1 f1 f2 f2 f1 f2 x

Power line cable tout cable slack cable h Length(h) mIn · Given A(h ·| ce load Volume(b)A self-Weight small h/span small tout h slack

Power Line Cable tout cable slack cable h Length(h) • Given: A(h) • Ice load Volume(h) • self-weight small • h/span small A L V min tout h slack

Wing Thin-Walled BoX Lift Top cover panels are compressed .Buckling stress f(t/b)2 thickness t Wing box weight Cover weight min Rib total weight many rew ribs ribs

Wing Thin-Walled Box Lift •Top cover panels are compressed b thickness t •Buckling stress = f(t/b)2 many b Rib total weight min few Cover weight Wing box weight ribs ribs

Multistage Rocket drop when burned rocket weight segment mIn junctions weight 23 number fuel weight of segments More segments(stages)=less weight to carry up=less fuel More segments=more junctions more weight to carry up Typical optimum: 2 to 4 Saturn v

Multistage Rocket drop when burned number segment junctions weight rocket weight 2 3 min fuel fuel weight of segments • More segments (stages) = less weight to carry up = less fuel • More segments = more junctions = more weight to carry up • Typical optimum: 2 to 4. Saturn V

Under-wing nacelle Placement Wing underside drag shock wave nacelle Inlet ahead of wing max depth max shock wave impinges on forward Range slope = drag weight Nacelle moved aft=landing gear moves with it= larger tail (or drag longer body to rotate for take-off more weight fore nacelle aft

more weight fore nacelle aft Under-wing Nacelle Placement shock wave drag nacelle wing underside • Inlet ahead of wing max. depth = shock wave impinges on forward slope = drag • Nacelle moved aft = landing gear l drag weight Range max moves with it = larger tail (or onger body to rotate for take-off =

National taxation max tax paid on earned revenue collected incentive to work 0% average 100% tax rate More tax/last $=less reason to strive to earn More tax/$= more S collected per unit of economic activity

National Taxation tax paid on $ earned revenue collected max incentive to work 0 % average 100 % tax rate • More tax/last $ = less reason to strive to earn • More tax/$ = more $ collected per —unit of economic activity

National taxation max tax paid on earned revenue collected incentive to work 0% average 100% tax rate More tax/last s=less reason to strive to earn More tax/$= more s collected per unit of economic activity · What to do ·| f we are left of max〓 increase taxes If we are right of max= cut taxes

National Taxation revenue collected 0 % max tax paid on $ earned incentive to work average 100 % tax rate • More tax/last $ = less reason to strive to earn • More tax/$ = more $ collected per —unit of economic activity“ • What to do: • If we are left of max = increase taxes • If we are right of max = cut taxes

Nothing to Optimize Rod P Newton A cm2 · Monotonic trend · No counter-trend N/cm2 o, allowable Nothing to optimize A

Nothing to Optimize Rod P Newton A cm2 • Monotonic trend σ • No counter-trend σ allowable N/cm2 • Nothing to optimize A