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1、AbstractWebuildamathematicalmodeltodeterminetheoptimalcurveofslimlineseatsontheairplane.Inthefirstquestion,wetaketwomainfactorsintoconsideration,oneisthestandarddeviationofspineequivalentstress,whiletheotheristhedifferencebetweentheseatbackcurveandthenaturalcurveofspine
2、.Weproposeasimplifiedmodelwhichisasystemof24rigidrodand25masspointanddistributetheweightofupperbodyoneachrodsequally.Thencarryoutforceanalysisontherodsandthemasspoint.Basedontheabovediscussion,webuildanoptimizationmodeltofindacurvetomakepassengermostcomfortable-uniforml
3、yforced.Finally,weuseMatlabsoftwaretofigureouttheoptimalseatbackcurve.Inthesecondquestion,weputemphasisonboththepassengers’spaceandcomfort.First,westudythespacewhichisneededtobeleftforthebackpassengers.Thenweassumethatthebackplatecurvecoincideswiththebackseatcurve.Tolet
4、thebackpassengersreceivemorespace,weneedtoadjustthebackplatecurveandofcoursehavetokeepthebackseatcurveinvariant.Thus,wedealwithbackplatecurvealongwiththepadding’sshape.Obviously,thespaceforthebackpassengersgetsbetterifthebackplatecurveisadjustedandandasaresultthepadding
5、willbedeeplycutdown.However,wekeepthepaddingthickerthan5cm,astheminimum,incasethefrontpassengersfeelbadifthepaddingistoothin.Consequently,howtoeliminatethiscontradictionisourmainpurpose.Fortunately,wefindadeepstudyofthemechanicalanalysisandbuildanoptimizationmodel.Witht
6、hehelpofMatlab,wefinallyfigureouttheanswer.Manymathematicalmodellayemphasisontheanswer,whileourmodelfocusonthewayofsolvingthisproblem.Ithasawiderapplication.Atthesametime,weconnectthenaturalspinecurvewiththemechanicalanalysis.Itismorescientific.Indespiteofthis,thereares
7、tillsomeshortcomings.Theweaknessofourmodelareneedtofurtherinvestigate,whichisshowninthepaper.Keywords:optimalcurvepaddingMatlaboptimizationmodelmechanicalanalysisContents1.Introduction......................................................................................
8、...........................11.1Backgroundoftheproblem.........................................................
