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 nacom ，。zbkuang m ail sj t uedu。ca，。Li changpi ngI si nacom 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 hreedi mensi onalcrack probl em s i s constructedandanewm et hodforcal cul at i ngst r essi nt ensi t yfact orsoft hree- di m ensi onalcr ack problem s i s pr esentedW 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 yzedIt 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 ressesThestress andt hestr ess i nt ensi t yfact or ar ecal cul at edatj oint sont hem ainal Tl loft ow ercranesInfl 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 essost rengt hanalysi sin m ai nar tnoft ow ercranesw i t h l ongi t udi nal cl osed cracksm ustbecar dedoutIti 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 ipsM 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 agesM ostoft hemneeddenserm eshesincom put ationsw i t ht hefi nite elem entm et hodsSom em orepreci s eel em ent s，suchashybri dm i xedf ini t eel em enthavem ore preci s eresul t s，but i ti sver ydif fi cul tt ocont rolr esult st abi l i t yTherefore 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 sI n t his PaD er t hel ocalsol ut i onsof di splacem ent f iel dsinfrontof t hreedi 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 hreedi 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 hreedi 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 sW 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 yzedThe 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 cranesI 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 entsTher 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 drespect i vel yK 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 entThent 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 entnodes3,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；Jm w here窑i s t henodal displacem ent ，mi s num berof si ngul ar el em ent s usedM fi s脑i n nodesof t heelem ent boundar y工is Lnodesoft heel em ent boundaryA 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 ixA 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；Jm 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 heret 2i sw hol est udi edzoon，尼i s si ngul arzoonfandare t hefaceforceof regul ar elem entandsi ngul ar el em ent ，res pect i vel ySubst 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 ；22TF (11) w her eQi st he gl obaldi splacem entarrayF andFaret he boundar y forcevect or sint hew hol e zoonst udi edandsi ngul arzoon，respect i vel yKi s t he gl obal st iffm at r i xK 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 entsByvaryi 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=FKN。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 sThel eng血sofcracksar ef rom5m mto500i nnanddepthsofcracksare f r om05m mt o25m m ，res pect i vel yComput at i onalm odeli sest abl i shedandtwentynodalpoi nt3一 Df ini t eel em ent sar eus edFi 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 g1Cal cul at i onl engt hofcracksi s500nl nl Cal cul at i on dept hs ofcracksare 05，10，15，25，30and35m m ，respect i vel yCal cul at i onl oad( 喁) i sequalt o 1700kgcm 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 o05毋Poi ssonsr at i oof m at edalandY oungsm odul usare equal to03andO 07M N m 2res pect i vel yRi ngt ensi l estr esses i ndi fferentr adi alsect i onsw i t hout w el ding residualstressareshow ni nFi g2Ringt ensi l estr esses ofdi fferentaxi alsecti onswit hout w el ding resi dualstressandw i t h w el dingresidual stressare shownin Fi g3andFi g4By t hef orenam edcomput at i ons，t hereal eri ngt ensi l est ressesat thejoint sect i onsoft hem ai nar mint ow ercraneI 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 g1 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 rom0025 t o5m mi sf rom40to 64M N m 32to2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 cracksItcanbese enf r omF培6t hatm axi m umstressi nt ensi t yfact or i s equal to09M N m “w hent hedepthofcracksi sequal to35m 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 32RR：=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 nfrontof3Dcracksal ei nt roduced andanewsi ngul arelem entoft hreedi m ensi onaicr ackprobl em si sconstructed，andanewm et hod tocal cul at estr ess i nt ensi t yfact orsoft hreedi m ensi onai cr ackprobl em si s present ed、qt ht he present m ethodthest ruct ural st rengt h ofw i th l ongi t udi nalcl os ed cracksunderaxi alt ens i onsi s anal yzedIt 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 ressesThew el dingm si dual str essi sharm fulto w el dingm at eri alst rengt hbut 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 ureA 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