1.Finite Eement Facture Aalysis of the Main Arm of Tower Cranes with the 3-D Cracks.pdf

第38卷增刊 上海交 通大 学学 报 Vol38s up 型兰 12旦 型垒1211坚垒翌里坚垒 垒212型g坚型 墨i 坚 2 2坠 文章编号 1006 2467 2004 S1 0171 05 Fi ni t eEem entFact ur eA al ysi s oft heM ai nA rmofTow erC r anes witht he3 DC r acks Zongji e Ca01 2 a ZhenbangK uan91 5 andC hangpi ngLi2 1 D epart m ent of Engi neer ingM echani cs ShanghaiJi aot ongUniversi t y Shanghai200240 Chi na 2 D epart m ent ofM echani calEngi neeri ng Aeronaut icU ni versi t yof A i r Force Changchun 130022 Chi na 8zj ca096 si na com zbkuang m ail sj t u edu ca Li changpi ngI si na com A bst ract I nt hispapert hel ocalsol udonsofdi splacem ent fi eldsi nfrontoft hree di m ensi onal cracksar ei nt roducedandanewsi ngul ar elem entoft hree di mensi onalcrack probl em s i s constructed andanewm et hodforcal cul at i ngst r essi nt ensi t yfact orsoft hree di m ensi onalcr ack problem s i s pr esented W ith t he present m ethod t hestr uct ur al st rengt h ofw i t h l ongi t udi nal cl osed cracksunderaxi alt ensi onsi s anal yzed It i s poss i bl e for t hecr ackt o pr opagate becauset hereare r ing t ensil estr essesneari oi ntsoft hem ai nar mi nt ow ercra nesunderaxi alpressst resses Thestress andt hestr ess i nt ensi t yfact or ar ecal cul at edatj oint sont hem ainal Tl loft ow ercranes Infl uencesof wel di ng resi dualst r essonstr ess i nt ensi t yfact ors andstr essesar ediscussed K eyw or ds s t ressi nt ensi t yf act or r esi dualst ress si ngul ar fi niteel em ent crack 1I ntr oduct ion Som e t ype oft het ow er cra nesi soneoft hem ost heavy t ow ercranesint heelect r ic pow er sys t em Severalcat ast rophi c acci dent st ook pl ace w hent het ow ercra nesw er ei nengi neer i nguse B ym agneticgaugi ng l ongi t udi nal cl osed crackshadbeendi scovered general l y i nt hesurfaceoft he m ai nalTnoft ow ercr anes Crackscanaf艳ctt hest rengt hoft hest r uct ur es sost rengt hanalysi sin m ai nar tnoft ow ercranesw i t h l ongi t udi nal cl osed cracksm ustbecar dedout Iti sverydif fi cul tf or generalm ethodtoaccur at el ydeterm inet hatcrackshowtoi nf l uence onstr uctur al st rengt hof t ow er cranesbecauset here are si ngul ari t i es i ncr ack t ips M any researchershave proposed var i ous si m ul at i onsandt r eat m entm et hodsL1 aboutsi ngul arf iel dsatcrackt ips Ever ym et hodexi st edhas i t sadvantagesordi sadvant ages M ostoft hemneeddenserm eshesincom put ationsw i t ht hefi nite elem entm et hods Som em orepreci s eel em ent s suchashybri d m i xedf ini t eel em ent havem ore preci s eresul t s but i ti sver ydif fi cul tt ocont rolr esult st abi l i t y Therefore itneedsanespeci al al gori t hmf orengi neer i ngappli cat ions Si ngul arfi niteel em ent shavespeci aladvantagesi nsol vi ngstressi nt ensi t yfact orsofcr ack pr oblem s I n t his PaD er t hel ocalsol ut i onsof di splacem ent f iel dsinfrontof t hree di m ensi onal cracksarei nt roducedast heext ens i onofelasti cprobl em sof2一Dcr ack si ngul ar fi niteel em ent s andanewsi ngul arelem entoft hree di m ensi onalcr ack problem s i sconst ruct ed andanewm et hod f or cal cul at i ng st r ess i nt ensi t y fact orsoft hree di m ensi onalcr ack probl em s i s present ed 田l i s m et hod m ay not onl y save m em or y and com put ati onal t i m ebutal soi ncreaset he accur acyof sol ut i onsfor cal cul at i ng str ess i nt ensi t y fact orsin i nvol vi ng fi nitedom ai n problem s W i tht he presentm et hod t he st ruct ural st rengt h w i t h l ongi t udi nal cl osedcracksunder axi alt ensi onsi s anal yzed The stressandt hestress i nt ensi t yfact or arecal cul at edat i oint son t hem ainarl noft ow er 172上海交通大学学报 第 卷 cranes I nfl uencesofw el dingresi dualstr essonst r essi nt ensi t yfact orsandstr esses ar ediscussed 2The Singul ar Fi ni t eEl em entM et hod Becauset hestr ess si ngul ari t y exist sincrackf ront s iti s very dif fi cul tto preci seexpress i nt ensi t yof st r essf iel dsw i thnor m al f ini t eel em ents Ther efor et o arbit rarycracksshapes ina3 D body l ocaldi splacem entf ield str ess f iel dandstr ainf iel dcanbe expr ess ed ast hefol l owi ngf or m s 盯 Sf K f 1 sf B f K f 2 巩 M fK f 3 w her e Sf Bl and M f aredi st ri but ingfunct i on m at r i cesofl ocalst r essf ield l ocalst r ainf iel dand l ocal di splacem entfiel d respect i vel y K f i st he array of str ess i nt ensi t yfactor s SIF at an arbit rarypoi nt i nt hecrackfrontl i ne w hi chi st hefunct i onoft hepoi nt placem ent int hecr ackfront The quadr i ci nt erposi t i on funct i oni susedt osi m ul at evariet i esofstressi ntensit yfact orsoft he cr ackfrontl ine i nt heel em ent Thent hefoll ow i ngequat i oncanbegi ven K 西 五 五 如 丸 1 k t Ku K X i 1 4 5 6 w her eLi s quadri ci nt erposi t i onfunct i on m at ri xofstressi nt ensi t yfact ors 名i st he array ofstress i nt ensi t yfact ors int heelem entnodes 3 ii st he array ofst r ess i nt ensi t yfact orsoft he i thnodeatt he cr ackfrontl ine i nt heel em ent Subs t i t ut i ngl ocalsol ut i onsEq 1 一 3 i nt oi soparam et ri cel em ent t heelem ent di splacem ent f iel dof arbit raryshape t hreedim ensi onalcracksi sasf ol lows 球 J 口 M tL N M t 工 J如 7 l N q J m w here窑i s t henodal displacem ent mi s num berof si ngul ar el em ent s used M fi s脑i n nodesof t heelem ent boundar y 工is Lnodesoft heel em ent boundary A ccording t ot herel ati onbetw een str ainanddispl acem ent s E V m t he fol l owi ngequat i oncanbeobt ai ned 盯 IBq 耻Jm w her esand口aret hestr ain vect orandt hestr ess vect or respecti vely E1 V i s t he dif f er ent i al oper at or Bi s t hestr ain m at rix 峨i s t he si ngul ar str ainm at ri x Di st heelasti c coeffi ci ent m atr ix A ccor di ng tot herel ati onbet w eenstr essand str ain t hefoll ow i ngequat i oncan beobt ai ned 口 呦 册 量 鲕 9一 口 fl DB q J m 3St ress Int ens i t yFact or sof3DCracks A ccor di ng tot hem i ni m umpot ent i al ener gypr inci ple thefoll ow i ngequat ioncanbeobt ai ned 石 姜饵eo T Tf d口一ow t o w here t 2i sw hol est udi edzoon 尼i s si ngul arzoon fand are t hefaceforceof regul ar elem entandsi ngul ar el em ent res pect i vel y Subst i t ut i ngEq 7 一 9 i nt oEq 10 fol l ow ingequat i on 塑型 圣 鲴 竺生 垦 生 翼 堡 竺 堕 里 也 翌 堕 旦 石 Q 1K Q Q 1F 2TK Q 17K 2 2TF 11 w her eQi st he gl obaldi splacem entarray F andF aret he boundar y forcevect or sint hew hol e zoonst udi edandsi ngul arzoon respect i vel y Ki s t he gl obal st iffm at r i x K N si st hecoupl i ng gl obal sti ffm atri xbetw een regul ar el em ent sand si ngul ar el em ent s Ksare t he gl obal st iffm at ri xof si ngul arel em ents Byvaryi ng tot hei ndependencebetw eenQandA res pect i vel y t hefol l owi ng equat i ons canbeobt ai ned K Q K M i F 0 12 K N Q K l F 0 13 w her e K 置忑 Eq 13 can berew ri t t enas fol l owi ng f orm 五 一K i l K Q 一只 14 Subst i t ut i ngEq 14 i nt oEq 12 t hefol l owi ngequat i oncanbe obt ai ned 酸一一F 0 15 w her e 笪 K K M gl l K F一 F KN X 1F L 16 17 4N um eri calexam pi e Thet ow ercr anei st russst ruct ure i t sm ai n ar m sareseam l esssteelt ubesf视19x20 w hi ch are2矿steelm at eri al s Thel eng血sofcracksar ef rom5m mto500i n n anddepthsofcracksare f r om0 5m mt o2 5m m res pect i vel y Comput at i onalm odeli sest abl i shedandtwentynodalpoi nt3一 Df ini t eel em ent sar eus ed Fi ni t eel em entm eshofnear danger i oi ntoft hem ain arl nw i t h l ongi t udi nalcl osed cracksi sshow ninFi g 1 Cal cul at i onl engt hofcracksi s500nl nl Cal cul at i on dept hs ofcracksare 0 5 1 0 1 5 2 5 3 0and3 5m m respect i vel y Cal cul at i onl oad 喁 i sequalt o 1700kg cm W ben t he w el ding resi dualst r esstot hem ai n ai mw it h l ongi t udi hal cl osedf low si s consi dered t heequi val ent w el ding residual st ress 国 i sequal t o0 5毋 Poi sson sr at i oof m at edalandY oung sm odul usare equal to0 3andO 07M N m 2 res pect i vel y Ri ngt ensi l estr esses i ndi fferentr adi alsect i onsw i t hout w el ding residualstressareshow ni nFi g 2 Ringt ensi l estr esses ofdi fferentaxi alsecti onswit hout w el ding resi dualstressandw i t h w el dingresidual stressare shownin Fi g 3andFi g 4 By t hef orenam edcomput at i ons t hereal eri ngt ensi l est ressesat thejoint sect i onsoft hem ai nar mint ow ercrane I ti s poss i bl efor f low st o propagat eunderri ngt ensi l e st resses nearjoint sect i onoft hem ai narm Fi g 1 Thefi niteelem entm odelofj oi nt sont hem ainar nl 174上海交通大学学报 第38卷 w hi ch l engt hs ar ef rom0 025 t o5m mi sf rom4 0to 6 4M N m 3 2to2矿st eelm at er i al The m axim umst r essi nt ensi t yfact or ne ar j ti nts oft hem ai nal iai slesst hant het hr eshol dval ueof pr opagati on for si ngl eedge cracks Itcanbese enf r omF培6t hatm axi m umstressi nt ensi t yfact or i s equal to09M N m w hent hedepthofcracksi sequal to3 5m m Them axim umst r essi nt ensi t y fact orw i t hw el dingresidual st r essi slessthant hatw i t hout w el ding resi dualst ress 5Conclusi ons i Fig 2Ring t ensi l esU essesi nr adi alsect i onsw i t houtwel di ngr esi duals tr ess l o j 口 州Pa 艇 饿 1R 911 cm 鬯 2R 950cm i 3R 9 89cm 4R栅101 5R 10 5cm 6R 0gcm Fig 3R i ng t ensi l esl l es sesi naxi alsect i onsw i t houtwel di ngr esi duals tr ess 10 0 重一10 一20 30 4 O 6 5 J一 2515 4踟 l 1R 911cm 32 RR 9 98590ccm m1 4R 101cm 5R 105cm 6R 10gcm 埘cm Fi g 4 The ri ngt ensi l e slr essesi naxialsect i onsw i t hwel di ngresi duals tr ess Int Ili spapert hel ocalsol ut i onsofdi splacem entfi eldsi nfrontof3 Dcracksal ei nt roduced andanewsi ngul arelem entoft hree di m ensi onaicr ackprobl em si sconstructed andanewm et hod tocal cul at estr ess i nt ensi t yfact orsoft hree di m ensi onai cr ackprobl em si s present ed qt ht he present m ethod thest ruct ural st rengt h ofw i th l ongi t udi nalcl os ed cracksunderaxi alt ens i onsi s anal yzed It i s possi bl e for t hecr ackt o pr opagate becauset herear eri ngt ensi l est ressesnearjt i nts oft hem ai nam i nt ow ercra nesunderaxi al pressst resses Thew el dingm si dual str essi sharm fulto w el dingm at eri alst rengt h but m e w el ding resi dualstr essm akes ri ngt ensi l estr essoft hem ai nalTO 塑型 垫璺笪 竺竺 丝璺 里垫垒 呈 翌兰坐生堕坐堡兰塑生堕坠垡 坐 竺垫兰望l垡二二 15 downin t hisst ruct ure A tt he sam et i m es tres si nt ensi t yf act or sdecrease t he saf et ol eranceoft he m ainarmoft het ow er cr anei s i m proved References 2 0 10 0 250500 xl m m Fig5 St ressi n