..1摘要：為了研究連續(xù)型拓撲優(yōu)化理論在實際工程中的應用，該文給出了一種多層鋼框架支撐體系連續(xù)型拓撲優(yōu)化設(shè)計方式。基于靈敏度分析，探討了連續(xù)體結(jié)構(gòu)在多工況荷載作用下、同時受應力和多位移約束的拓撲優(yōu)化刪除準那么。為保證拓撲優(yōu)化結(jié)果的合理性，提出了設(shè)計區(qū)域平均厚度的概念。在該文給出的優(yōu)化設(shè)計方式中，首先在不考慮位移約束的情況下對無支撐鋼框架進行優(yōu)化設(shè)計，然后在有位移約束的條件下采納漸進結(jié)構(gòu)優(yōu)化算法和刪除準那么對支撐體系進行連續(xù)型拓撲優(yōu)化設(shè)計，并將獲得的支撐最優(yōu)拓撲構(gòu)形轉(zhuǎn)化成相應的桿件。經(jīng)過一個3跨12層鋼框架支撐體系的拓撲優(yōu)化設(shè)計實例驗證了該文給出的鋼框架支撐體系連續(xù)型拓撲優(yōu)化設(shè)計方式的有效性。關(guān)鍵詞：鋼框架；支撐體系；連續(xù)型；拓撲優(yōu)化；漸進結(jié)構(gòu)優(yōu)化弱的受拉區(qū)的強度。耐用，配置鋼筋后，能夠作為任何結(jié)構(gòu)體系的主要構(gòu)件。根底，大體積混凝土水壩或者繼續(xù)延長已澆筑完畢并且已經(jīng)凝固的混凝土等。對待梁、柱、墻等構(gòu)件，當模板清理潔凈后應該在其上涂油，鋼筋外表的銹及其他有害物質(zhì)也應該被去除潔凈。澆筑根底前，應將坑底土夯實并用水浸濕6英寸，以免土壤從新澆的混凝土中汲取水分。一般情況下，除使用混凝土泵澆筑外，混凝土都應在水平方向分層澆筑，并使用插入式或外表式高頻電動振搗器搗實。必需記住，過分的振搗將導致骨料離析和混凝土泌漿等現(xiàn)象，因而是有害的。50°F縫，這將有損與混凝土的強度，同時也會影響到水泥水化作用的充分進行。配筋的面積，鋼筋的應變和混凝土的應變，鋼筋的應力等等。因此，在選擇混凝土截面時需要進行試算并作調(diào)整，依據(jù)施工現(xiàn)場條件、混凝土原材料的供應情況、業(yè)主提出的格外要求、對建筑和凈空高度的要求、所用的設(shè)計標準以及建筑物周圍環(huán)境條件等最后確定截面。鋼筋混凝土通常是現(xiàn)場澆注的合成材料，它與在工廠中制截面，因此設(shè)計時第一次采納的數(shù)值將導致一系列的試算與調(diào)整工作。當試算截面選定后，每次設(shè)計都是對截面進行復核。手冊、圖表和微型計算機以及專用程序的使用，使這種設(shè)計方式更為簡捷有效，而傳統(tǒng)的方式那么是把鋼筋混凝土的復核與單純的設(shè)計分別進行處理。1935唯一可靠而又最新的資料能夠從制造廠商處獲得。獲得最好的方案。拉鏟挖土機。推土機和正鏟挖土機都能做到這點。拉鏟挖土機的工作半徑最大。推土機所推運的圖的數(shù)量最多，只是運輸距離很短。拉鏟挖土機的缺點是只能挖比它本身低的土，不能施加壓力挖入壓實的土壤內(nèi)，不能在陡坡上挖土，而且挖。卸都不準確。挖土機最適用，但其卸料半徑比起裝有正鏟的同一挖土機的卸料半徑那么要小很多。裝滿，助推拖拉機就回到開挖的地點去協(xié)助下一臺鏟運機。8mm3430機坐在前方卸載，因此有時被稱為后卸卡車。標準的主要目的是提供一般性的設(shè)計原理和計算方式，以便驗算結(jié)構(gòu)的平安結(jié)構(gòu)的破壞概率〔危急率〕成反比。確切的話來說，把破壞看成是結(jié)構(gòu)已經(jīng)到達不能繼續(xù)承當其設(shè)計荷載的“極限狀態(tài)〞。通常有兩種類型的極限狀態(tài)，即：〔1〕強度極限狀態(tài)，它相當于結(jié)構(gòu)能夠到達的最大承載能力。其例子包括結(jié)和爆炸的敏感性?！?〕使用極限狀態(tài)，它對應著結(jié)構(gòu)的使用功能和耐久性。器例子包括結(jié)構(gòu)失穩(wěn)之前的過大變形和位移；早期開裂或過大的裂縫；較大的振動和腐蝕。依據(jù)不同的平安度條件，能夠把結(jié)構(gòu)驗算所采納的計算方式分成：〔1〕確定性的方式，在這種方式中，把主要參數(shù)看作非隨機參數(shù)?！?〕概率方式，在這種方式中，主要參數(shù)被認為是隨機參數(shù)。〔1〕容許應力法，在這種方式中，把結(jié)構(gòu)承受最大荷載時計算得到的應力與經(jīng)過按規(guī)定的平安系數(shù)進行折減后的材料強度作比擬。〔2〕極限狀態(tài)法，在這種方式中，結(jié)構(gòu)的工作狀態(tài)是以其最大強度為依據(jù)來到一些有用的計算方式。通常采納下列兩種計算方式：概率方式，這種方式采納極限狀態(tài)。將這些隨機平安系數(shù)組合成確定的平安系數(shù)。概率法取決于：〔1〕制作和安裝經(jīng)過中材料強度的隨機分布〔整個結(jié)構(gòu)的力學性能數(shù)值的分〔2〕截面和結(jié)構(gòu)幾何尺寸的不確定性〔由結(jié)構(gòu)制作和安裝造成的誤差和缺陷對作用在結(jié)構(gòu)上的活載和恒載的猜測的不確定性；建筑物的重要性和建筑物破壞造成的危害性；〔2〕由于建筑物破壞使生活受到威脅的人數(shù)；〔3〕修復建筑的可能性；〔4〕建筑物的預期壽命。所有這些因素均與經(jīng)濟和社會條件有關(guān)，例如：〔1〕建筑物的初始建設(shè)費；〔2〕建筑物使用期限內(nèi)的折舊費；〔3〕由于建筑物破壞而造成的物質(zhì)和材料損失費；〔4〕在社會上造成的不良影響；〔5〕精神和心理上的考慮。就給定的平安系數(shù)而論，所有這些參數(shù)確實定都是以建筑物的最準確本錢為依據(jù)的。但是，應該考慮到進行全概率分析的困難。對待這種分析來說，應該認識活載及其所引起的盈利的分布規(guī)律、材料的力學性能的分散性和截面的結(jié)構(gòu)幾何尺寸這些實際困難能夠采納兩種方式來克服。第一種方式對材料和荷載采納不同的平安系數(shù)，而不需要采納概率準那么；第二種方式是引入一些而簡化假設(shè)的近似概率方式2Abstract:Tostudytheapplicationofcontinuumstructuraltopologyoptimizationmethodstorealengineeringstructures,anoptimizationmethodforanoptimaltopologydesignofmultistorysteelframebracingsystemsispresented.Onasensitivityanalysis,anelementremovalcriterionforcontinuumstructureswithstressandmulti-displacementconstraintsundermultiplelateralloadingconditionsisproposed.Aconceptofmeanthicknessofadesigndomainisprovidedtoensurethereasonablenessofoptimalresults.Intheproposedoptimizationmethod,theoptimaldesignofanunbracedsteelframewithoutdisplacementconstraintsisperformedfirstly,andthentheoptimaltopologyofabracingsystemforthe multistorysteelframeconsideringdisplacementconstraintsisobtainedbyusingevolutionarystructuraloptimizationandthegivenremovalcriterion,andfinallytheoptimalayoutofthebracingsystemisinterpretedasbracingmembers.Anexampleof3-bay12-storyplanesteelframeshowsthatitiseffectiveforthegivenoptimizationmethodintheoptimaldesignofbracingsystemsformultistorysteelframes.Key words:steel frame;bracing system;continuum;topology optimization;evolutionary structuraloptimizationReinforcedConcretePlainconcreteisformedfromahardenedmixtureofcement,water,fineaggregate,coarseaggregate(crushedstoneorgravel),air,andoftenotheradmixtures.Theplasticmixisplacedandconsolidatedintheformwork,thencuredtofacilitatetheaccelerationofthechemicalhydrationreactionlfthecement/watermix,resultinginhardenedconcrete.Thefinishedproducthashighcompressivestrength,andlowresistancetotension,suchthatitstensilestrengthisapproximatelyonetenthlfitscompressivestrength.Consequently,tensileandshearreinforcementinthetensileregionsofsectionshastobeprovidedtocompensatefortheweaktensionregionsinthereinforcedconcreteelement.Itisthisdeviationinthecompositionofareinforcesconcretesectionfromthehomogeneityofstandardwoodorsteelsectionsthatrequiresamodifiedapproachtothebasic principles of structural design. The two components of the reinforcedconcretesectionaretobesoarrangedandproportionedthatoptimaluseismadeofthematerialsinvolved.Thisispossiblebecauseconcretecaneasilybegivenanydesiredshapebyplacingandcompactingthewetmixtureoftheconstituentingredientsare properly proportioned, the finished product becomes strong, durable, and, combinationwiththereinforcingbars,adaptableforuseasmainmembersofanystructuralsystem.Thetechniquesnecessaryforplacingconcretedependonthetypeofmembertobecast:thatis,whetheritisacolumn,abean,awall,aslab,afoundation.amasscolumns,oranextensionofpreviouslyplacedandhardenedconcrete.Forbeams,columns,andwalls,theformsshouldbewelloiledaftercleaningthem,andthereinforcementshouldbeclearedofrustandotherharmfulmaterials.Infoundations,theearthshouldbecompactedandthoroughlymoistenedtoabout6in.indepthtoavoidabsorptionofthemoisturepresentinthewetconcrete.Concreteshouldalwaysbeplacedinhorizontallayerswhicharecompactedbymeansofhighfrequencypower-drivenvibratorsofeithertheimmersionorexternaltype,asthecaserequires,unlessitisplacedbypumping.Itmustbekeptinmind,however,thatovervibrationcanbeharmfulsinceitcouldcausesegregationoftheaggregateandbleedingoftheconcrete.Hydrationofthecementtakesplaceinthepresenceofmoistureattemperaturesabove50°F.Itisnecessarytomaintainsuchaconditioninorderthatthechemicalhydrationreactioncantakeplace.Ifdryingistoorapid,surfacecrackingtakesplace.Thiswouldresultinreductionofconcretestrengthduetocrackingaswellasthefailuretoattainfullchemicalhydration.Itisclearthatalargenumberofparametershavetobedealtwithinproportioningareinforcedconcreteelement,suchasgeometricalwidth,depth,areaofreinforcement,steelstrain,concretestrain,steelstress,andsoon.Consequently,trialandadjustmentisnecessaryinthechoiceofconcretesections,withassumptionsbasedonconditionsatsite,availabilityoftheconstituentmaterials,particulardemandsoftheowners,architecturalandheadroomrequirements,theapplicablecodes,andenvironmentalreinforcedconcreteisoftenasite-constructedcomposite,incontrasttothestandardmill-fabricatedbeamandcolumnsectionsinsteelstructures.Atrialsectionhastobechosenforeachcriticallocationinastructuralsystem.Thetrialsectionhastobeanalyzedtodetermineifitsnominalresistingstrengthisadequatetocarrytheappliedfactoredload.Sincemorethanonetrialisoftennecessarytoarriveatthe required section, the first design input step generates into a series trial-and-adjustmentanalyses.Thetrial-andadjustmentproceduresforthechoiceofaconcretesectionleadtotheconvergenceofanalysisanddesign.Henceeverydesignisananalysisonceatrialsectionischosen.Theavailabilityofhandbooks,charts,andpersonalcomputersandprogramssupportsthisapproachasamoreefficient,compact,andspeedyinstructionalmethodcomparedwiththetraditionalapproachoftreatingtheanalysisofreinforcedconcreteseparatelyfrompuredesign.EarthworkBecauseearthmovingmethodsandcostschangemorequicklythanthoseinanyotherbranchofcivilengineering,thisisafieldwheretherearerealopportunitiesfortheenthusiast.In1935mostofthemethodsnowinuseforcarryingandexcavatingearthwithrubber-tyredequipmentdidnotexist.Mostearthwasmovedbynarrowrailtrack,nowrelativelyrare,andthemainmethodsofexcavation,withfaceshovel,backacter,ordraglineorgrab,thoughtheyarestillwidelyusedareonly afewofthemany methods.Tokeephisknowledgeofearthmovingequipmentuptodateanengineermustthereforespendtinestudyingmodernmachines.Generallytheonlyreliableup-to-dateinformationonexcavators,loadersandtransportisobtainablefromthemakers.Earthworksorearthmovingmeanscuttingintogroundwhereitssurfaceistoohigh(cuts),anddumpingtheearthinotherplaceswherethesurfaceistoolow(fills).Toreduceearthworkcosts,thevolumeofthefillsshouldbeequaltothevolumeof cutsandwhereverpossiblethecutsshouldbeplacedneartofillsofequalvolumesoastoreducetransportanddoublehandlingofthefill.Thisworkofearthworkdesignfallsontheengineerwholaysouttheroadsinceitisthelayoutoftheearthworkmorethananythingelsewhichdecidesitscheapness.Fromtheavailablemapsahdlevels,theengineeringmusttrytoreachasmanydecisionsaspossibleinthedrawingofficebydrawingcrosssectionsoftheearthwork.Onthesitewhenfurtherinformationbecomesavailablehecanmakechangesinjissectionsandlayout,butthedrawinglfficeworkwillnothavebeenlost.Itwillhavehelpedhimtoreachthebestsolutionintheshortesttime.Thecheapestwayofmovingearthistotakeitdirectlyoutofthecutanddropitasfillwiththesamemachine.Thisisnotalwayspossible,butwhenitcanbedoneitisideal,beingbothquickandcheap.Draglines,bulldozersandfaceshovelsandothis.Thelargestradiusisobtainedwiththedragline,andthelargesttonnageofearthismovedbythebulldozer,thoughonlyovershortdistances.Thedisadvantagesofthedraglinearethatitmustdigbelowitself,itcannotdigwithforceintocompactedmaterial,itcannotdigonsteepslopws,anditsdumpinganddiggingarenotaccurate.Faceshovelsarebetweenbulldozersanddraglines,havingalargerradiusofactionthanbulldozersbutlessthandraglines.Theyareanletodigintoaverticalclifffaceinawaywhichwouldbedangeroustorabulldozeroperatorandimpossibleforadragline.Eachpieceofequipmentshouldbeleveloftheirtracksandfordeepdigsincompactmaterialabackacterismostuseful,butitsdumpingradiusisconsiderablylessthanthatofthesameescavatorfittedwithafaceshovel.Rubber-tyredbowlscrapersareindispensableforfairlyleveldiggingwherethedistanceoftransportistoomuchtoradraglineorfaceshovel.Theycandigthematerialdeeply(butonlybelowthemselves)toafairlyflatsurface,carryithundredsofmetersifneedbe,thendropitandlevelitroughlyduringthedumping.Forharddiggingitisoftenfoundeconomicaltokeepapushertractor(wheeledortracked)onthediggingsite,topusheachscraperasitreturnstodig.Assoonasthescraperisfull,thepushertractorreturnstothebeginningofthedigtoheoptohelpthenestscraper.Bowlscrapersareoftenextremelypowerfulmachines;manymakersbuildscrapersof8cubicmetersstruckcapacity,whichcarry10m3 heaped.Thelargestself-propelledscrapersareof19m3struckcapacity(25m3 heaped)andtheyaredrivenbyatractorengineof430horse-powers.m3m3.Specialtypesincludetheself-loadingdumperofupto4m3andthearticulatedtypeofabout0.5m3.Thedistinctionbetweendumpersanddumptrucksmustberemembered.dumperstipforwardsandthedriversitsbehindtheload.Dumptrucksareheavy,strengthenedtippinglorries,thedrivertravelsinfrontlftheloadandtheloadisdumpedbehindhim,sotheyaresometimescalledrear-dumptrucks.SafetyofStructuresThe principal scope of specifications is to provide general principles computationalmethodsinordertoverifysafetyofstructures.The“safetyfactor〞,whichaccordingtomoderntrendsisindependentofthenatureandcombinationofthematerialsused,canusuallybedefinedastheratiobetweentheconditions.Thisratioisalsoproportionaltotheinverseoftheprobability(risk)offailureofthestructure.Failurehastobeconsiderednotonlyasoverallcollapseofthestructurebutalsoasunserviceabilityor,accordingtoamoreprecise.Commondefinition.Asthereachingofalimitstatewhichcausestheconstructionnottoaccomplishthetaskitwasdesignedfor.Therearetwocategoriesoflimitstate:Ultimatelimitsate,whichcorrespondstothehighestvalueoftheload-bearingcapacity.Examplesincludelocalbucklingorglobalinstabilityofthestructure;failureofsomesectionsandsubsequenttransformationofthestructureintoamechanism;failurebyfatigue;elasticorplasticdeformationorcreepthatcauseasubstantialchangeofthegeometryofthestructure;andsensitivityofthestructuretoalternatingloads,tofireandtoexplosions.Servicelimitstates,whicharefunctionsoftheuseanddurabilityofthestructure.Examplesincludeexcessivedeformationsanddisplacementswithoutinstability;earlyorexcessivecracks;largevibrations;andcorrosion.Computationalmethodsusedtoverifystructureswithrespecttothedifferentsafetyconditionscanbeseparatedinto:Deterministicmethods,inwhichthemainparametersareconsideredasnonrandomparameters.Probabilisticmethods,inwhichthemainparametersareconsideredasrandomparameters.Alternatively,withrespecttothedifferentuseoffactorsofsafety,computationalmethodscanbeseparatedinto:Allowablestressmethod,inwhichthestressescomputedundermaximumloadsarecomparedwiththestrengthofthematerialreducedbygivensafetyfactors.Limitstatesmethod,inwhichthestructuremaybeproportionedonthebasisofitsmaximumstrength.Thisstrength,asdeterminedbyrationalanalysis,shallnotbelessthanthatrequiredtosupportafactoredloadequaltothesumofthefactoredliveloadanddeadload(ultimatestate).Thestressescorrespondingtoworking(service)conditionswithunfactoredliveanddeadloadsarecomparedwithprescribedvalues(servicelimitstate).Fromthefourpossiblecombinationsofthefirsttwoandsecondtwomethods,wecanobtainsomeusefulcomputationalmethods.Generally,twocombinationsprevail:(1)deterministicmethods,whichmakeuseofallowablestresses.(2)Probabilisticmethods,whichmakeuseoflimitstates.Themainadvantageofprobabilisticapproachesisthat,atleastintheory,itispossibletoscientificallytakeintoaccountallrandomfactorsofsafety,babilisticapproachesdependupon:Randomdistributionofstrengthofmaterialswithrespecttotheconditionsoffabricationanderection(scatterofthevaluesofmechanicalpropertiesthroughoutthestructure);Uncertaintyofthegeometryofthecross-sectionsandofthestructure(faultsandimperfectionsduetofabricationanderectionofthestructure);Uncertaintyofthepredictedliveloadsanddeadloadsactingonthestructure;Uncertaintyrelatedtotheapproximationofthecomputationalmethodused(deviationoftheactualstressesfrom