FINITE DEFORMATION ELASTO-PLASTIC THEORY AND CONSISTENTALGORITHM.pdf
针刺机底座钻孔组合机床设计含开题及5张CAD图
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针刺机底座钻孔组合机床设计含开题及5张CAD图,针刺,底座,钻孔,组合,机床,设计,开题,CAD
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A cTAM Eo删ICAs0LI【)ASf N I C A ，V oI14，N()1，M arch200II SSN08949166PubIishedbyH U ST，W uhan，Chi naFIN I TED EFO R M A TI O NELA STO PLA STICTH EO R YA N DC oN SI STEN TA LG oRITH MLi uX uej unLiM i ngi uangw enbi nt A 扫p“以M echnn洒wo妇s。pChi H 。A gcuI Hm U ni憎r s曲tEan(m pHs、，B喇i 孵100083， i m )A I sI R A cTByu甜ngt hebgarith州cstr ai n，t he“n；tedef删tionpl asti ct hr y，删nspondingt 圯innnl t esm 】alpI ast lcthH 了，i seg七abl i s州successi veiyTheplas廿cf 1越St朗talg嘶tm l w ith矗r stoI deraccLlr 8cyk”t 11en11i ted哪Lm et hod(FEM ) 诹devel opedNtlf ne打calexam pl群盯epr髓eIned1l h瞒atet heval ldl t y() ft het hryandeffec咖enessoft heal godt hr nK EYw 0RD s矗cddnent，S面tedef om 姐r j 锄，dasnp】as“阢oDn画3t 朗tal g谢t hmIINrnt 0D U C0N( kner all yspeaki ng，t herr letalrnat eri alw mkeepi t s 、Ium eunchangedi nthcpl ast i cst 札e，kcor dingl yt he矗rsti nvaanL1oft hest r ai nt ens orw i llbezeroi nt hei nf i 血t esi malpl ast i cth印r y，W l 】i lei nt hennj tedefor m at i on山c。ry，thefi rstinvar iant() ft hecom nl onIyusedG r een。Lagr angi an8t rai n，fl =O，knotequi val ent t ot hezemdil at ati onThi sw i llbri nggreatdif ficLIl t yt ot hefi ni t edef0啪t ionpl ast i ct heoryButi ti sinteres廿ngt onotethatt hefi rsti nvar iantoftheIoga“t 蛆i cst rai nfuIfi U s t hi srequir ernentexact I yTher ef or et hei ogari thm icst rai nIneasur eisadopt edandt hei 11fi ni tesi m alpl ast i ct heor vbt ranspl ant edt oestablisht hefi ni t edeform at i (mpl ast i ct he07yweal sorefoH I lt hei nf i ni t esi malel ast opl ast i ccons ist enta鼢it hmpr esen【edi nRefs11，2t ofom lt hefi nit edef onaLi onel as t o-pIas Li cal gori t hm1H EST RA INM EA SU REA N DITSW oRKo叭UG A T匿DS田R正 叠 洛TEN她21TheLo明ri t hm i cStr ainLetXbet heposi t i onvcct orofanar bi tr ar ypoi ntt obestudi edi ni tsi nit i al耐1f igur at ionandxbeit s。0rres p。ndingposi tionvect orint1ecur rentc。nfi gurat i onAss咖ethatx=x( x)andit sconl p。rl entfo丌nz，=嚣(X ，)D ennet hedefonnat i ongr adientt ensorF=ax门Xandt hec。m p。nentR)mFu=az。，axi ktt hepolardecom posi donofF=刚U =V R ，谢1er eRi sauni torth【 籼altellsorr印res肌t ingt herotat ionw hil eUand，areposi t i ve野m m et ri ct ens or sr epr esent i ngt hepl l redef0卜叫t 疏【，andycanbe(=aedt heri ghtandkftst retcht en80r，respect i vei yThel ogar 油m i cst rai nt cnsori sdefi r l edas8=ln(u)D ecom poeu嬲u=Q 1D uQ ，w hereQi sauni to卜t hogonal m aLri xa11dD u=diag(U 1，u2，乩)U l ，u2andu3ar et heeigen_val ues。fuand锪嚣辩销墨2盎“& 1“。曲“d口“8N01977297332A ( j T AM EC H A N ICA90L幢l ASIN I CA200Icanbecal l edt hem ainsnt chesThust 1el o髓rit hm icst rai ncanbe cal cul atedas8=1n( 【，)=Q 1diag 1n( u1)，In(u2) ，1n( u3) Q=Q7di ag(1，e2，83)QThent hedi lat ationr at i o，t hem easur eof t hev01um echaf lge，i sJ=l Fi =Dui =u1己，2U 舡sum ethatt hem eta【rnat e渤lkeeps砥v0Ium eunchangedi nt hepl as t i cs七ate，i e=1Thef ir sti nvar iantoft he109ar it hm icst r面nt ens ori s11=8瑶=8+622+633=l n(U 1)+l n(U 2)+l n(U3)=l n(ul U 2u3)=l n(J) =l n( 1) =0Thereforet hefh缸i nv商antoft heIogam hm km ai ni s吼mt hem eaSur eoft hedil ati onduri ngt henni tedefo邢at i onSi m i l arl v，t hedeviati onoft 11el o寤ari t hfl l icst rai nt efl Sori s8d7=8i一8v(麒)3=。一(13)占ul n( 1uI)=e一l n(1u113)Thedeviati ont ensorcant husbeexpressedaSs7=1n( Ufu1，3) ，whi chdenot est hedi st ort ionpartexdudi ngt 1ev01ur rl echar 培eI tist henpos时bl et ouset hesum l at i ondecom posi t i onoft heinteorenergyi nt ot hedi st oni onener gyandt hedi lat ationener gyviat hede啪posit ionof工ogari t hrni cst r ai nint ot hedi St oni onandt heddat at ionpart sI nthi sw ayw ecant ransplantt herrespondir堰infi ni t esi m alpl as t i ct heo。yt ot he矗ni t edef or nlati onpl as t i ct hryw i t houtchangeobvi ous l yt hesu“m l at mde咧nposi t i on0fe=f+扩i sn吼val i danyH 10r e22皿eW orkC删gat edS吣sThesLr e8s，w hi chi sw oTkconj ugat edt ot hel ogar i t hm i cstr ain，hasbeendiscussedi ndet ai l i nRef3w ew i l l j Ll st w “t edow nt her鹤u1招w i tkutp耐 Let(A： ，m)and(： ，N：)bet heei gen_pa豳ofVandU ，r espect i vel yThenw ehave。=A ：and雄，=R N ，Let 仃bethecauchvst resst enrTheK i r cl hoffst r esst el l sorw i llbef；加D ennet her ot at edK i rdhhof st Tesst enSorT=Ro氓 The跏ponenti oH nd血eK i Tdl hdi 吼re翳t en3。randt her ot at edK i rchhoffst resst sorcanbeexD ressedasf=r 俨。0_，r=功M 圆M(1)Ingener al ，t hest resst ens orw hi chi 8w orkconj ugat edt ot hel。garit hm i cst rai nt ensorcan_D eder lot edas。3一=U N I 圆N JQ 1Fr om Ref535，t heponent Sof w hi chare珊=砌=罴 焉 溉 ，(J乱 桴 (3)Inthespec甜c舒eofis ot ropicm et alm at eHal ，whi chisusedw i del y，t hest res st ensO r面ugat edt ot heIogari t hrIl i cst r ai nt erl s。ri sshpl yt hem t at edK i rchhoffst r eSst ensor_j 41：o=T=R7德(4)I nt hef。ll aw ingw ew | 11al waysas sum et heIm t eri alur lderst udyt obei sotm pi cw hi chw mgreat lysim pl i fyourdi scus si onTHEFIN砌DEFoR M 7I卫0NPLA SCTIl EO R YA N DTH ECO N S| 1卫N TA L G oRr I 田IThefi ni t edef onll ati onpl as t i c t he。ryandt hec()nsi st entaIgori t hmarequit esi m i lart ot heinfi nit esi m alpl as t i ct h。oryandt heconsi8t ental g。ri t hm W ew i llf ir sti m roducet hei nf i ni t esi m alonesbri ef王yandt hengot ot hefi nit edef or r nati onpar t sv0114，N o1uuX u白unetaI：FilliLe嘶HnatonElasnplastlcTh00y3331Tl砣Ifini 蛔i m aIPJ豁t ic11l em vI nasense，t hetheoreticalf oundat ionofinfini tesi m al口1astict heor visbasedont w osum rrlat iondepositions0fst rai nT hefi rsti st odecom pose山est r ai ni nt ot hedi stor tionpar tandthed丑atat ion阳rt ItIeadst ot hesuati。ndeposi tionofi nt er i。renergyi nt ot hedi st o卜t i onener gyandt hedi l a诅t i onenergyThesendi st ode咖poset hest r ai ni nt ot heel ast i cpartandt heplasticpartw hi chl龃dst ot hedposm onof t hei nteri or即ergyi nt ot heel ast i cener gyt扩arl dt hepl ast i cenergy矿3211l eInfjnjt esj 脚JElas协pJastjc嘶Is括l蛐tAJ酬t bmThec。m m o“yusedfonllula0fupdati ngt hest re ssi s口(。+”=d(。)+盯rr( n十1)w her e盯=JD 廿dof “?1Ikcause；ti si m possi bkt oi nt egrateitexactl y，t hest resSvaI uecanl l otbecalculatedexact l yItbri Il gsus咖badresult sFi rstly，theequil ibrimequat i onw i l lnotbeexactsot hesol ut i onisnotexactN otonlvcant heer rDrofthesolut ionnotbeest i l at edbutal soi tw i l lbeaccum ul at edw hent hel oadi l l gstepsi ncreas eSe。andl y，i nt hef oH nulat i onoftarl ge眦sti ff nessr r Lat ri xtl est ressvaI uei st obeus edThei nexactst ressw 工eadt oani nexacttaI理entst i ff neSsm at r i x，s0t httheaSynlptoti cquadraticverge士1cerat eoft hepow erfulN ew t oni t erat i onrnet h。dw i l line“tabl ybej ostI n。rdert o矗ndabetterappxi瑚tes。l ut ion，瑚anysdl enl esar esuggeSted0heoft hebeSti st heoonsist enta190r ithm 12I1ebas i cideak：si ncei ti si m p。商bl et ofi ndtheeX actsoIm i onw hil et hefi n“el oadi 。培st epi sused，、vecanpr oposeanapp“) xim at esolutiDnwl 璐eerr orcanbeesti m atedexactly，i ethefi 体torderaccuracyont hi s印pm xi I Tlat es01ut ioncur vew ecal l0bt ain t hef ol l ow i ngs：t heexactst ress，exactequil ibri岫equati onandexactsti ffll essm at ri X 33Tl l eFi niteD efol m at i PIt i cTheor v(、D m 珥m di l l gt ot hein矗nitesirmlpl aSt i ct11哆，thesati ondecon椰i tionof出st or 一廿on arl dt hedi lationi8val i dw hent hel ogari thm icst r ai nm easur ei sadopt edW ecant hentr anspLantt hecorr espondiTl gpar tf m mi n矗nit eS蚰a1t h印ryt othefi ni t edeftiont he。ryw i t houtchangeN evenhel e豁，i nt hefi nit edefo肿at i ont hest rai ncanneverbedeconposedint o=r 十扩W hi Iet hedeposi tionofdef矗m at i ongradi ent F=F酽i snowcoIdyaccepted叫。，act uall yi tis【hedecom posit i on。fthecon矗gur at i onL etz1andx3bet hei ni ti aland矗rlaLn矗gurat ion，re8pect i vel yLetx2beanint erm edi ate唧f igurat ion，whichi sobtainedf rom 工3byt heel ast i cunl 。adi l l gThe士1，t hedef0H nat i ongradi entcanbew r i tt enaSF=a奶用。1=( az3力工2) (az2舟工1)Fm m 工3t o工2t hedeform at i oni spur elyel ast i candfromx2t ox1thedefom l at i onkpur elypl ast icS0w ehaveax3舟。2=Fanda工2内x1=PItshoul dbenotedthattheintem ediatecodi gurat i onx2m ayn。texi starl dit sreal izati 。n讧notrequi redThusw ef l aveF=r p(5)Letv=v(茹)=出dfbet hespat i alvel 。cit yD enneL=Vv=apax，w hichi st hespat i aldef( m l at ionvdoci t y耵adi ent Thedefom at ionrat ei S守=dFd=d(ax力x) df=a( dxdf)力x=a(dxd)ax(a工加x)=(av用善)F=LFSot hat L=FFThespat i aJdeforrnat i 衄vel oci tygradientw ；Ut henbe34A CTAM Ea州ICASC) L I D ASI N ICAL=膏F一1=( pP十Pp) (p一1P1)=r +(6)w l ere=抑9； 工 尸=F护 矿 一1r一1(7a，b)【kcom p。set hevelocit ygradl enti nt 0asym m et ri cpartandaskewsym m et ri cpa儿d=syl 砌(L)=(L+L7) 2，I ，=skew (L)=(LL7)2(8)W iLhtheassum pt i onthatthem aLer iaIconsi deredw i llkeepit svol ur neduri ngt hepIas t i cstate，w eobt aindet ( P) =1(9)Thereforet hep()lardec。m posit i onoft hedast 沁partofde)肿at i ongradi enti sapplicableduet odet( F) =det ( P) I )P=R 。胪(10)Thedast icl o即ri thni cst rai ncanbedennedasF=l n( )(11)FH ) m ( 7b) w ew il lredefi net hepIas t i cvcl oci ygradi entasLp=FpP1(12)O bvi ousl y，Li ssi m i lart oL。，andbot hhavcLhesam ee追envaIueSSi谢1arl y，t hesyr啪et ri cpar toft hepl as t i cvelocit ygr adi enti s矿=syl m (L9)=(Lp+Lo)2(13)andi tcanbe cal kdt heD l as t i cst rai nveIocit vA cc。rdi ngt oRef10，w ea蝌um etheskewsynunet ri cparti s旷=skew ( L9)二( Lp) 2=O w hi chm eansw =IJ 。(14)Fm mEqs(12) ，( 13)and( 14)，t herat eoft hepl ast i cdefom l at i ongr a出enti s膏p=D 9F9(15)A s sum e廿l atthepl a对i chr deni ng眦) deIi st heki neInati chardel li r培Int roducet i efol l ow i l l gst re蝌tensofs：dCauchvst r essf=，盯K j rchhoffst ressBbackst re ss(16)。=dev(盯)deviati onoft heCauchyst r essS=d一口shif tedst ressdeviat orLkfi net heequivalentsnesss=(导s：sr=(32)1“IsI(17)TheeouaLi (mofvi el d轧uhce沁雪=s矗=0(18)w here是i sahar deniTlRfunct i on乜出scuSsedi nSect i on2，t herotate【1K i rchhoffsr r ess，w hi chi sw or kconj ugat edt or he1口garit hm i cst r ai n，i sT=J R 。厦R =R 。fR 。(19)Ther ot at edst r essdeviat ori s117=佃。口僵8(20)Si m | 1arl vw ecanal s。deI inet her ut at edbackst re ssv。l14，N o1Li uXu自unetal ：F；nj r eD efom nonE1孙t 0_IdastI cThe。ry。35。B=JR。BR。(21)andtheshif tedI 、ot at edst re ssdeviat ors：Rel sRr ：117一B7(22)Thenthee口uivalentr oLat edst re ssw ll Ibes7=( 32S：S7)1也J(23)Fr onlEq(18) ，di rferent i at i ngt heyi el dfunct i on垂w i t hr espectt ot hem t at edK i rchhoffst r ess11，w cobL ai nthenonll alofLheyi el dsur f ace，or i ent edout si de，N 7=(a垂归T)=(32)12S7(7)(24)w hi chi sauni tvect or U si rlgthet ens orform ，t henst i t ut i vcl aww i HbeT=H ：Fw her eH W =，2(dm d“+d，颤)+ad藏z(25)Theassoci atedfbwr ukoffi ni t edef om l atkmcanbecxpres靴das=sym nl (驴)=口(a西用T1)=(32)陋()=(32)1。斟7(26)啻=( 23)H矿=H 盘s7“Js7)=(23) ”F弧7(27)w her eH 扛Lheef fi ckntofkiner r lat证harde血ngSim i 【art ot heinfi 【dt 郫inl ahhcor y，i ti seasy协p，。vethat矿=卢，where矿=(23) 酩砖)i st hecquiValentpl as t i csLrai nr ateForsi rTl pIi ci t y，denot e廖as卢i ntheR)l l 。w i ngEquat i。ns(5) ，( 10) ，( 11)，(15)，(18)，(25)，(26)and(27)ar et hef undanl en诅le【1uat i onsoft hefi nit edefonnaLi unpl ast i ci t yth舳ry34TheC衄si st entA 190ri t hmofEIast o_plast jcniteD e“m at i仰B asedont heIJ09ar i th-m i cS“锄i nTheess ent i alpar t( )ftheal go“t hm 沁h“wt oi nt cgr aLeD =j lpr1Sim i l art othei nfnLes i m alt heor y，i ti sal i m p(】ssibl et oi nt egrateexact lyInor d盯t ofi ndan印proxi nl at cs0一l ut i onw hi chh出t hefi rst ordcraccuracy，w euset hegener al蚵dp。i ntrul eA ssurnethatt heI】asjcvari abl cs日H )，B(。)，砰。)att i m ef andt hcdi 印l acem ent “( n+I )att i m eo( 一1)areknO w nThequest i onishowt oupdaret hesevJm i abk；eX act l yTheconsi st ema190ri t hm nsist sofrw oparts：elasti cpr cdict ionandpl as t i cc。r rect i onandi sl i st edasfol l ow s：(1)Cal cul 8t cF(。+1)(2)D E 血neLheel ast i cpredi ct ed巧1)=F(。_1)(砰，)1andq：；1)=(巧?i Jl TK：?1)(3)Fi ndthenghtst ret ch听坼p1)=(c)1也(4)Fi ndthem t at i。nRt ：)1)=砰：0I)(碳：，1)1(5)cal cul at etheel ast i cIogari 【hrni cst rai nE：Z)=l n( 吲?f)( 6) Fkm lt heconstit ut ivc1aw，咖structt hPel舐ti c竹ialst ress矸譬011二H ：E譬i1)(7)checkt heyi el dc。ndi t i 。nEq( 18)中“) =sA (矿)O ( 8) Ifycs，leLal It hevari ablcsbe(。)(。+I)=()箸1)el segf est o(9)(9)S。l veTf。+】)，B (。+1)，卢fm mt hef 011( ，wi ll gst h丁eeequat l。ns：( a) usinga1。cal N ew t nni t erat i 。nt ofi nd卢t osat i sfy西”=s一是(扩十9)=0(b) I(。1)=H：(E瞥，1)卢N j 。+1) ，w hereNj。+j sde矗nedi n(24)36A ( i r AM FIAN ICASO L I D ASIN I CA200l(c)Integrate(27)曰j。+1)二=Bj。)+(23)1。删(。+1)(10) FromEq(26)cal cul at et hei ncr锄entoft hepl aSt i cstr ainE1) =胛j)(11)updat et heequi val enLplasticst m i nP。+1)=砰。)+卢(12)updat et hepl as t i cst rain研。+1)=戤。)+蛾。十1)(13)updat et heeIast i cstrain联。+1)=聪i吐)Et。十1)(14)updat et l l edaSti c啦htst ret ch嘶。+1)=exp(目。+1)( 15) I m egr ateEq(12) =p矿，t heupdat edpl a鲥cdefonnat i ongr adi entar eobtair led矸)=eXp(E)砰：；Hnall y，aut hevar iabl esato(。+narekor 柳nE(ILIBm uMEQ IJA l l oNA N DCoN S巧TEN T趼羽刚EssM A 佃TheNe咖iterat ionm et hodisuSedt 0l vet hen砌i rl ear6ni teel锄entequat i onsIn0r dert opreser vet heasym pt ot i c卟1adrat i ccor l ver gencerat eofthisITlet hod，i ti sr equi r edthatt heexactt ar培entst i ffnessbefonnul at edf砌mt heequi li bri unlequat i onsI nt hefi Il it edef0玎nationt 哟ry，t hei nt em alvi rtualener gycanbeeX pressedas8w ()=f。P口( a眉x)dVJVw her ePist hef ir StPi ola一心Tchhof fst reSsw hi chi sw oTkc酬ugatedt ot hedispl acer nentgradi e11ta球舟xThevar iati onoft hedi 印l ac锄entgradi entcarlbecalcuIat edf r onl 占( a“归x) =旦口口，wher e旦i st hege0l et ri cm atri xdef i nedbyt hei nt erp。l at i onoft heE血t eel ernentm et 10da11disi ndep即dentoft hedefom l at i on，and口i st heno如ldiSpI acer nentvect or TheeXt em alvi rtualw orki s8w (8) =硒Fr omt hevi nualw orkp慨ipl e涮(i)=dw (川 ，we0bt ai nt heequi l i br iumequati on掣( q)=I，p旦1PdV F=o(28)O bvi ouSly，t hi sequi l bri ull lequat bni se】(act Ndww ew mg。b出ededuct i onoft ar培entstif fnessHlat ri xry(q)=，兰fT(aP胭口)dV-口=K弘qw hereaPa口=( aP用F) ( aF门口)=( aP厢F) 旦herloe坼=I 旦7(aP眉F) 笪dy(29)Theoonsti tut ivel awi snoti nV oI vedi nt heabovededuct i onpr ocess，s0i ti sapp工i cabIei nanycaseS1nceaP内Fhas妇1discussedi nRef【11，w ew il ljustwri拒dt heresult sw i t houtpr00fktD =aP朐Fbet heconsi stenLt angentm odul e，t hecor Il ponentforrn谢l lbeD洲=aPd均 民=占*(F：9u： ；I7)缸T(。+1)曲(Fi户u： ；I“ )曲+(A珏 耐 十Kd拟 州) 矾f(30)w her8A埘=(R喜曾)。(巧9U-即)，恩船L蒯，v0114，1Li uX uejune【a1：Fini teDef舢tiEkH卜pl础t icTh唧37K葫盯=巧警矗)。丁(。+1)席(F：u：；I纠)馆+R锛1)。T(。十1)“乎andM 靠。i sthecornponent for moft ensor M =a(u焉：科)舟(q譬r )1) )，L脚fist hec。m p。nentfonnoft enS0rL=a( 日) )伯( q*j ) )4西i st heponent0f thet al lgentm odul eoft hetensorH=aT( 。十1) 朋(蛾警71) )Theel as一协pl asti cm 。duleisdef inedasI P=d盯d，whi chcanbecalculatedeX act lysi m i lart oRef 1Thet en8ardeduct ionprocess，咖cem i ngt hederi ti veofat en8arbasedfuncti on，willbediscussedi nanotherpaperN owt hefi Tlit edeform at i oneIas t o-pl as t i ct heor yandt hecons ist ental gori t hmhave beenst udiedcom pl et el yAfewnum eri calex锄plesw i【lbepr esentedt oi l l ust rat et11evalidit yoft het heoryandt heef fecti venessoft heal gori t hm1aterV N U I E l H CA L ExA M PL EsIti sassum edt hatt hehardenil l gf uncti on0fal lt heex锄plesgi veni st hel i nearandSat uration1aw sofexponent i alt ype，ie*=(矿) =( d一。o) 1一exp(一矽) +口1矿+。o=K(矿) +。oH er e400，d40，y0areIm teri alcorl stant sExaI npl elE蚍ensi onofastnpw i thaci rcul arhol eForobvioussym m et ryconsi der at i ons ，onl yor l e_quart eroft hespecinlenrl eedbeanal yzedIti sconl put edaspLm l est re sspm bl er nG 即m et ry：L=36O 1，W =20cm ，D =10O ，t hickness=1O c丌1M at eri al ：E=200GPav=03oo=240G Pa。l =O 002M Pa，d=240G Pa=1O GPa，7=0L0adi I：For ce=A 声，声=100N cm ，Aist hek蛆di l l gf actor Thi sex二 ；1： scalculatedit1t hearclen矗m et hod，using21Fi g1m”o。 “ 戚嘲嘲“)11“1dte口(215tldiM H g2Pl嘲icdef ana石。n(cm )Fi g3Thedi 印Iac锄e11tUat耐m Awrsust hel di ngfact or一 一B m，38A CI AM EC H A N ICASO L I D ASIN I CAl oadi ngsteThedef or r nati onshapesatst eps11and21areshow ni nFi g2T曲le1The蛐balaII cedf orceatm bI蜘nIoadi ngsteps卸di椭tionst eps(N)1讪k21m er 吲dua| 印er 盯atdi ff e瑚t蛔di ll gsteps锄dd珊 嗍ti蚰steps(NcrTl)Fr onlTabl eslarl d2，theasym pt ot i cqLl adrat i cc。nvergencerat ei sdear l yexhi bi t edExam pl e2Al oll go。l um nw i t hsquar ecrossSecti oni ssubj ect edt 。mD ressi onatbot hendsThem eshisdi scr et izedt o2230i nXya11dZdi rect i onsI、he8一nodeel em enti susedG 旺net ry：A =1m B =1m ( ：=2mM at crial ：E=( ) 2M Pav=0360=O 001M Pa，01=O 0G Pa，口。=O 00叭M Pa，=O 0001M Pay=0Fig4G 舯pr蹦湎ofa曲咖L0a血培andnst rai nt ：Thebot t omendi sst rict l vcon5t rai rledi neachdi rect i onThet oDendi scorl st rai rl edi nXa11dydi rccti onSandissubi ect edt oD ressi oni nZdi rcct ionN oww ew i l lcheckt heapproxi m at i onoft hesolut ionsol vedf m moural gori thrnI ti sknow nthatnone( ) ft hep【础t icalgor i thr r懈w i thfi ni t e10adi ngst epca“yi el danexacts01ut i onB utever yal gori t hmsm ul dappr oacht ot heexactsol uti onw i t hinnnites蚰all oadi ngst epI nt hefol l ow i l l gw eshal lusevery锄a11st 印t odenot et heexactsolut ion，atl d1argerst epofoural g。r j thmisusedi nm pari sonInt hi sexam I) 1e，t hes01ut ionof10adi ngst。pPl =400Nw i l ldenot et heexactS01ut ion，ont heot herhand，t hel oadi ngst 印P2二25Plohheak料i thmi susedforpari 跳Theresul t saredem onst 豫t edinFi g5Itshowst hatw hent he10adhl gvolH ，N olLi uX u白unetd：Fi ni t eD cfo仃nat i onElas廿pl 积i cThry39sr epi ncreasest o25t i m esbi gger，oural gori t hmst il lpossessesveryhi ghaccur acyInTabl e3theexactsolut ionandt heappr。xi m at eoneaswellast herdat i veerr orar el i st ednunl eri cal l yTable311lcexactandapp邝xi m atesol t i 蚰s000_020加柏川60_o80100120一140160180(m )FI g5CbTnI】an30nbetw 唧thee cactandappraxim ate烈utionU ：T0pdi splact ： ngfact orCO N C LU SIoN S( 1) B yuSi l l gt he109ari t hni cstr ain，t hefi ni t edef ornl at i onplaStict heor yc。r r e印( m di Tl gt ot heinfi ni tesim alpl as t i ct heor y，ises诅bl ishedsuccessi vdy(2)Basedon出efi rst orderappr 0)【i m at esol ut ion，thispaperdeducest hee)(actfom l ul
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