第四届数学中国数学建模A题DOCWord格式文档下载.docx
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DesignofBackplatecurveinslimlineseats
Abstract:
Thisarticleismainlyabouthowtodesignthebackrestcurveofthehighbackseat,theAngleofthebackrestandthepaddingtomakepassengersfeelmorecomfortablewithoutchangingtherequestoftheinternalstructure.
Inmodel1,whilecalculatingthestaticpressuredistributionofachair,weuseKringinginterpolatemethodanddrawstandardbodypressuredistribution
inSURFER.Thenwecalculateanddrawthecontourofthecurvature
and
.Finally,weusetrapezoidalgorithmofBivariateIntegraltoobtainthecentercoordinates
ofpressure.
WhileestablishingComfortEvaluationModel,weselectCurvature,maximumpressure,averagepressurethreefactorsinspine,hipandshoulderblade,respectively.ThenAHPisused.Weconstructguidelinesjudgmentmatrixaccordingtoexpertassessmentmethod.ThenMatrixnormalization,featurevector,discriminatingcharacteristicroot,consistencyindexandweightsareobtained.ConstructionoflinearmembershipisfollowedusingLinearinterpolationtogetseatcomfortmodel.as
.
Whilewedesignoptimalcurveofthebackrest,theinitialbackrestcurveisobtainedfirstly.Thenusingacubicsplineinterpolationalgorithmtosolvinganypointinterpolationresultsandtheradiusofcurvature.Basedonthemaximumcomfort,thispaperestablishesobjectivefunctionandconstraintswhilePenaltyFunctionMethodisintroducedtosolveMultidimensionalconstrainedoptimizationproblem.TheresultisR（130）=1036,R（500）=551.Thecurvatureandthebodypressuredistributionarenormalizedtoweightedsumandtransformmulti-objectivetosingleobjectivefunction,Comfortis0.8970.933beforeandafteroptimization,respectively.ChangethecurvatureRoftheobjectivetargettoanalysisbodypressuredistributionandcomfortindicestendency.
Inmodel4,withoutchangingthemaininternalstructureoftheseat,backplantangleisoptimizedbasedontheminimumvalueofdifferencesquarebetweenthevariouspressureregionandiscalculatedas
.Thenusingthespacegeometryandelasticstrainenergymethodstoobtaindata,suchascontactareaandmaximumpressuretodoregressionandpartialcorrelationanalysiswiththethicknessofthefillermaterial.Thethicknessofthefillermaterialrangeisbetween102（mm）and54.6issuitable.Finally,thebackrestangleoptimizationfunctionandthefillerthicknessisjointoptimizationwithmodel3,respectively.WeobtaintheoptimalbackrestcurvewithComfortare0.922and0.973,respectively.
1.Introduction5
1.1SittingpositionState5
1.2Bodypressuredistribution5
1.3Comfort5
1.4Thecontentneedtostudy6
2Nomenclatures6
3ModelOne：
Bodypressuredistribution6
3.1Introduction6
3.2Assumption7
3.3ModelBuilding7
3.3Conclusion10
4ModelTwo：
ComfortEvaluationModel10
4.1Introduction10
4.2Assumption10
4.3Analysis11
4.4ModelBuilding12
5ModelThree:
Thedesignofbackcurve13
5.1Analysis13
5.2Thedesignoftheinitialcurve13
5.3ModelBuildingofBackcurve14
5.4Algorithmsolution15
5.5Theoptimizeofthemodel16
5.6Conclusion17
6ModelFour：
Optimalcurvedesign17
6.1Analysis17
6.2Modelbuilding18
6.2.1ModelbuildingofAngle’sChange18
6.2.2ModelofthicknessoftheFiller19
6.3Optimalbackrestcurvedesign22
6.4Conclusion24
7EvaluationandFutureWork25
7.1Strengths25
7.2Weakness25
7.3FutureWork25
8References25
9Advertisingmaterial27
1.Introduction
Becauseofitsfastandconvenience，flightgraduallybecomeapopularwaytotravel.Andinordertoincreaseairlines’profits,theydesignanewtypeofslimseat,inordertofullyconsiderthepassengers’ridecomfort,weneedtomakeoptimizationofslimlineseat.
Itisgenerallybelievedthatcomfortdependsmainlyontheseat,whichcanscaleonthebasisofhumanbodyengineeringconformstotherequirementofhumanphysiologicalcharacteristics,ifwejustprovidesimplesupportseat,itwillleadtopeople'
sfatiguequickly.Sostudyingseatmodeling,thegeometrysizeandthemate-rialperformanceisimportanttodesignconcept.Inordertosolvetheproblems,thefollowingbackgroundisworthmentioning.
1.1SittingpositionState
Insittingpositionstate,supportforthespine,pelvis,legsandfeetandsoonarethemainstructureofthebody,.Themostcomfortablesittingpositionishipsmoveslightlyforwardfromthebackofachair,madeaftertheupperslightlyupwardsloping,keepingbetweentheupperandthethigh.Atthesametime,thelegthrustingforward,thighandcalf,calfandfeetbetweenalsoshouldreachacertainpointofview.
1.2Bodypressuredistribution
Thebodypressuredistributioninthebackandcushionofthebodyiscalledthebodypressuredistribution.Themostcomfortablesittingpositiondistributionshallensurethat:
mostofthehumanbodyqualityshouldtakealargerbearingarea,thesmallerunitpressuredistributiononthecushionandthebackrestreasonably;
Pressuredistributionshouldberaisedtosmoothlytransition,avoidsuddenchanges.
1.3Comfort
Setappropriatebacktolowerbacktension.Whenhumandorsalspinesinanaturalformthemostcomfortable,toachievethis,itisonlythroughtheanglebetweentheseatsitfaceandbackofachair,theshapeofthebackofachair,toensureproperlumbarsupport.Duetothedifferencesofindividual，thecomplexrelationshipbetweenbackrestheightandshape.
1.4Thecontentneedtostudy
Inordertoaddressproblemsabove,weconcludeforsub-problemstotackleinourpaper:
●Findingoutseatstaticbodypressuredistribution,thestaticanddynamicbodypressuredistributionshouldbeconsidered.Consideringpassengers’bodypressuredistributionanditsderivativefactors,establishtheModelbuildingofpassengercomfort,makingevaluationtothedesignofthebackcurve.
●Underthepremiseofwithoutchangingthestructuremodeltooptimizationdesignofthecurveoftheseatback,getmoreaccordwithhumanbodycurveoftheshapeofthebackofachair,namelytoimproveridecomfort.
●Dynamicmodelissetup,optimizethedesignofthebackcurveandfilleratthesametime,improvingthecomfort.
2Nomenclatures
Bodypressuredistributionfunction
CurvatureofBodypressuredistribution
Comfortvalue
thepressurevaluein
Factorsaffectingthevalueofcomfort
Thecontactareain
region
Thepressurevaluein
Symbolsaremoreinvolvedinthisarticle,instructionswillbegivenwhenusing.
Bodypressuredistribution
3.1Introduction
Theflightisacomplexdynamicprocess，bodysurfacepressureincludinghippressureandbackpressurehere.Weneedtogetairlinepassengersstaticsurfacepressuredistributionbeforethebodysurfacepressuredistributionofpassengersinmaneuvering
flight
conditions.
isactuallytheinitialvalueoftheoverallbodysurfacepressureand
.Iflocal
surface
pressure
valuesandthegradientaretoolargeorbody
centermisplaced,comfortwillbereduced.
3.2Assumption
●Staticmeansweonlyconsiderthecaseinarelativelystaticflightandignoreflightstakingoff
and
landing
process..
●Assumingpassengershadmoderatefigure,andignoringthedistortionofthebodypressuredistributioncausedbyseatsize.
3.3ModelBuilding
Literature[5]showsthateachpressurelineisdimensionlessrelativepressurestrengthaccordingtostaticbodyposturesurfacepressuredistributionofAmericanpilot.Then,asthisarticle,the
Kriging
interpolation
is
selectedafterweanalyzingandcalculatingthepressuredataofthebackandhip.Kriging
interpolationisbasedonregionalizedvariablesusingvariogramfunctiontoobtainestimateswhileguaranteeunbiasednessandminimumvariances.
Assumingregionalizedvariables
satisfySecond-orderstationaryorintrinsichypothesis,theestimatespointPtobeinterpolatedas:
Where
representsweightsofnknownpoints,andsatisfyequation:
。
accordingtoestimatedMinimumvariancecondition:
Inwhich:
:
Lagrangianoperator
Variablefunctionvaluedifferencebetweenknownpoints
Functionvaluedifferencebecomesknownpointsandbeinterpolatedbetweenpoints
Bythis,calculatetheestimatedvaluethattobeinterpolatedpointP.
Figure1:
BodypressuredistributionofBackrestandCushion
Pressuredistributioncontoursandthree-dimenhipsionalsurfaceofBackthatcalculatedbyKriging
interpolationisshowedinFigure.Asshowed,themaximumpressureisinthehip,nextiswaistandlastisback.Asharpdeclineofthepressurestakenplaceinotherparts.
Todescribethechangesinsurfacepressure,weCalculatetheFirstDerivativeofsurfacepressure,aspressuredistribution
hadbeendiscrete:
Fig2:
Thebacksurfacepressurederivative
Accordingtothefigureknown,Lumbarspineandshoulderbladesurfacepressurechangesinthelargertrendinthehorizontaldirection,thesurfacepressureonthewaistbiggestchangesintheverticaldirection.
Withoutconsideringthedepressedconditionofthechairofthecontactsurface,Bodysurfacepressurecan
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