n Mtrils Enginring Strss ntnsit tor of n ntrf Crk in Bon Plt unr Uni-Axil Tnsion No-Aki NODA, Yu ZHANG, Xin LAN, Ysushi TAKASE n Kzuhiro ODA Dprtmnt of Mhnil n Control Enginring, Kushu nstitut of Thnolog, - Snsui- ho, Tot-ku, Kitkushu-shi, ukuok, Jpn E-mil: no@mh.kuth..jp Tokum Collg of Thnolog, Gkuni, Shunn-shi, Ymguhi,Jpn Astrt Although lot of intrf rk prolms wr prviousl trt, fw solutions r vill unr ritrr mtril omintion. This ppr ls with ntrl intrf rk in on infinit plt n finit plt. Thn, th ffts of mtril omintion on th strss intnsit ftors r isuss. A usful mtho to lult th strss intnsit ftor of intrf rk is prsnt with fousing on th strss t th rk tip lult th finit lmnt mtho. or th ntrl intrf rk, it is foun tht th rsults of on infinit plt unr rmot uni-xil tnsion r lws pning on th Dunrs prmtrs, β n iffrnt from th wll-known solution of th ntrl intrf rk unr intrnl prssur tht is onl pning on β. Bsis, it is shown tht th strss intnsit ftor of on infinit plt n stimt from th strss of rk tip in th on plt whn thr is no rk. t is lso foun tht imnsionlss strss intnsit ftor < whn ( + 2 β)( 2 β) >, > whn ( + 2 β)( 2 β) <, n = whn ( + 2 β)( 2 β) =. K wors: Elstiit, Strss ntnsit tor, rtur Mhnis, init Elmnt Mtho, ntrf Crk, Bon Plt. ntroution An intrf rk in n infinit on plt unr intrnl prssur in ig. () is known s th most funmntl n wll known solution for intrf rks. Th strss intnsit ftor is givn in Eq.. K + ik = ( + i )(+ 2 iε ) π, =, = () Riv 6 Nov., 29 (No. 84-) [DO:.299/jmmp.4.974] Copright 2 JSME t is lso known tht th intrf rk unr rmot ixil tnsion s shown in ig. () is quivlnt to th on in ig. (). n ig. (), = is th rmot tnsil strss in th irtion, n x, x2 r th ons in th x irtion so s to prou th sm strin in th x irtion ε x = ε x2 long th i-mtril intrf (). As shown in ig.2 (), ntrl intrf rk in on plt hs n trt in th prvious stuis (2)-(4), n som notil rsults r provi in Tl. As n n sn from this tl, thos rsults lmost oini with h othr. Howvr, th limiting solution s in Tl hs not n isuss t in th prvious stuis. n Tl it is sn tht imnsionlss strss intnsit ftor os not pproh unit lthough s. n othr wors, it is onfirm tht th solution unr uni-xil tnsion in ig.3 () is not quivlnt to Eq. (). 974 974
() G, ν 2 2 () 2 2 = x x2 K + ik = ( + i)(+ 2 iε ) π, =, = G2 G2 x2 ( ) x 3 2 (3 ) κ2 G κ κ G κ = + + + ig. nfinit on plt sujt to () intrnl prssur n () rmot ixil tnsil strss. 2 2 G, ν () G2, ν 2 () G2, ν 2 ig.2 Bon finit plt with ntrl intrf rk. Tl Dimnsionlss strss intnsit ftors of ntr intrf rk in on plt (s ig 2, Pln strss, ν = ν2 =.3 ). G2 G / Rf.[2] Rf.[3] Rf.[4] Rf.[2] Rf.[3] Rf.[4] 4..2.986.5.98.5.986.5.5.9.5..5.9..2.943.96.94.96.943.96.8.7.8.8.9.8 () 2 2 () 2 2 = ig.3 nfinit on plt sujt to () intrnl prssur n () rmot uni-xil tnsil strss. n this stu, strsss t th intrf rk tip will lult ppling th finit lmnt mtho. Thn th strss intnsit ftors r trmin from th rsults of th rfrn prolm n givn unknown prolm (2) using th sm finit lmnt msh pttrn. Hr, th most funmntl ntrl intrf rk in on plt in ig. 2 will onsir with vring Dunur s prmtr, β. Thn, th ffts of mtril omintion on th intrf strss intnsit ftors K, K will isuss. 975 975
2. Anlsis Mtho Th nlsis mtho us in this rsrh is s on th strsss t th rk tip lult EM. B using th proportionl strss fils for th rfrn n givn prolms, strss intnsit ftors n otin with goo ur (5). or xmpl, for mol rk in homognous plts, th strss istriution nr th rk tip n xprss th following qution. = K 2π r (2) t is onfirm tht th rror of EM minl oms from th msh roun th rk tip. Thrfor if th sm msh siz n pttrn r ppli to th rfrn n givn unknown prolms, strss intnsit ftors K n otin from th strsss lult EM. At givn istn r, th following rltionship n riv from Eq.(2). K = onst (3) f iffrnt rk prolms A n B r nlz ppling th sm EM msh, th following qution n givn t th sm istn from th rk tip. K = K A B Hr, n strisk () mns th vlus of th rfrn prolm. B using Eq.4 with strss vlus t rk tip lult EM, urt strss intnsit ftors in homognous plts wr sussfull otin Nisitni t l (5),(6). Although this mtho nnot ppli to intrf rk prolms without iffiult, n fftiv mtho ws rntl propos O t l (2) sussfull to nlz intrf rk prolms. t is wll known tht thr xists osilltion singulrit t th intrf rk tip. rom th strsss, τ x long th intrf rk tip, strss intnsit ftors r fin s shown in Eq.(5). iε K + ik r + iτ =, r, x 2π r (4) (5) ε κ κ ln / 2 = + + 2π G G2 G2 G (6) 3 ν j κ j = ( pln strss), κ j = 3 4 ν j ( pln strin) ( j =,2) + ν j rom Eq.(5), th strss intnsit ftors m sprt s τ x K = lim 2πr osq+ sin Q, (7) r K = lim 2πτ r x osq+ sin Q, (8) r τ x r Q = ε ln( ). (9) Hr, r n Q n hosn s onstnt vlus sin th rfrn n unknown prolm hv th sm msh pttrn n mtril omintion. Thrfor if Eq.() is stisfi, Eq.()m riv from Eq.(). n suh s, osilltor itms of th rfrn n unknown prolms r hng into th sm. x x Q = Q, τ τ = () 976 976
K K K K =, = () τ τ x x Strss intnsit ftors of th givn unknown prolm n otin :, EM K= K, EM (2) K= K (3), EM, EM,τ, τ r Hr, x r strsss of rfrn prolm lult EM, n x strsss of givn unknown prolm. Strss intnsit ftors of th rfrn prolm r fin Eq.(4). K + ik = ( T + is) π(+ 2 iε ) (4) Rgring th rfrn prolm in ig.4, not strsss for ( T, S) = (, ), n T, S = = T, EM, S x, EM = =, T, S, EM τ = = r vlus of T, S x, EM τ = = r ons for ( T, S) = (,). n orr to stisf Eq.(), strsss t th rk tip of th rfrn prolm r xprss s = T + S, T=, S= T=, S=, EM, EM, EM τ = τ T + τ S T=, S= T=, S= x, EM x, EM x, EM B sustituting Eq.() into Eq.(5) with T=, th vlu of S is otin s T =, S= T =, S=, EM x, EM x, EM, EM T =, S= T =, S= x, EM, EM, EM x, EM (5) τ τ S =. (6) τ τ 3. Strss ntnsit tors of n ntrf Crk in Bon nfinit Plt To xprss th rsults th following imnsionlss strss intnsit ftors, r us. K + ik = ( + i )( + 2 iε ) π (7) Dunurs i-mtril prmtrs, β r fin in Eq.(8). G( κ2 + ) G2( κ+ ) = G ( κ + ) + G ( κ + ) 2 2 G ( κ ) G ( κ ) G ( κ + ) + G ( κ + ) 2 2, β = 2 2 (8) 3. Efft of Plt Dimnsions on th Strss ntnsit tors n orr to isuss on infinit plts, it is nssr to onsir th fft of th plt imnsions on th strss intnsit ftors us th finit lmnt mtho nnot trt th infinit plts irtl. Th rsults of ntrl intrf rk in ig.2 () r thrfor invstigt in Tl 2 with vring = /62, /324, / 648 n =.75, β =, =.9, β =, =.75, β =.2. t is sn tht rsults of < /62 oini h othr n m hv mor thn 3 igit ur. n othr wors, Tl 2 shows tht th rsults for = /62 n us s th infinit plt with lss thn.9% rror. t is lso sn tht s unr ritrr mtril omintion. n th following stions, th rsults for th on infinit plt otin s shown in Tl will isuss. 977 977
= T τ = S x x τ x G, E, ν o r θ x x τ x x2 G2, E2, ν 2 x2 τ x ig.4 Rfrn prolm ( ε x = ε x2 t = ) 3.2 Cntrl ntrf Crk in Bon nfinit Plt unr Uni-Axil Tnsion igur 5 shows th rsults of ntrl intrf rk in on infinit plt unr uni-xil tnsion in th -irtion s shown in ig.2 (). n ig.5, Dunur s prmtr β is fix, n th vritions of r pit with vring prmtr. hn mtril n mtril 2 r xhng, Dunur s prmtrs (, β ) om (, β). Thn th strss intnsit ftors (, ) om (, ). Thrfor ll mtril omintions r onsir in th rng > in ig.6( ). n ig.5, th soli urvs show th rsults of ntrl intrf rk unr rmot tnsion =.Th sh lins r xtn from soli lins us som ss of mtril omintion r iffiult to otin th EM. Th sh lin shows th rsults of tht unr intrnl prssur whos solution is known s = n =. igur 5 shows th vrition of =.882~.36, whih hs th minimum vlu =.882 whn =., β =, n th mximum vlu =.36 whn =.2, β =.3. t is lso foun tht = for th full rng of, β. Thrfor it m onlu tht ntrl intrf rk in on infinit plt unr rmot tnsion of = is quivlnt to tht unr intrnl prssur of =.882~.36. All th vlus in ig.5 r givn in Tl 3 with 3 iml. rom ig.5 n Tl 3, w n onlu tht >. whn ( + 2 β)( 2 β) <, =. whn ( + 2 β)( 2 β) = n < whn ( + 2 β)( 2 β) >. n Tl 3, vlus for =. r mrk unrlins. Tl 2 Dimnsionlss strss intnsit ftors of rk in ig.2 () with iffrnt. / / =.75 β = =.75 β = =.75 β = /62 /324 /648.93955.93962.93982.942.9859.9883.9943.93.9556.9555.9554.9553 /62 /324 /648 2.2-4. -4 5.5-5 2.59-4.28-4 6.42-5. -4 5.53-5 2.76-5 978 978
β=.4.2.98 β=.3 β=-.2 β=.2 β=-. β=.4 β=.45.96.94.92.9 K + ik = π( + i )(+ 2 iε) β= β=..88.2.4.6.8 ig.5 of ntrl intrf rk in on infinit plt unr uni-xl tnsion whih is orrsponing to ig.2 () with /. Tl 3 Dimnsionlss strss intnsit ftor in ig.2 () with /. inits = for ( + 2 β)( 2 β) = ; > ( + 2 β)( 2 β) < ; < for ( + 2 β)( 2 β) > for β -.2 -...2.3.4.45..5..5.2.3.4.6.7.75.8.85.9.95..7.6.6.5 (.3).4.4.3.2..995.988.979 (.966)...999.998.996.99.984.975.963.948.94.93.92.9.896 (.882).4.4.3.2..995.988.978.966.952.943.934.924.92.9 (.886).7.6.5.4.2.7..99.979.964.955.946.935.924.92 (.898) (.36).29.22.2..985.977.967.957.945.933 (.99) (.33).8...99.978.965 (.952) (.22)...987 (.974) (,.25) β goo pir (.2,.3) x/= ( = ) (.6,.4) (.,) (.8,.45) (.,.45) (.,.4) (.,.3) (.,.2) (-.,) qul pir (-.,-) = x/= ( = ) - o (,-.25) - (.6,-.) (.2,-.2) pir x/= ( = ) (.,.) (.,) () Show rgions ( 2 β) < hv no strss singulr t th g x =± in ig.2 () 979 979
(,.25) β (.2,.3) > (.6,.4) (.8,.45) (.,) (.,.45) (.,.4) (.,.2) (-.,) = o (.2,-.2) (,-.25) (.6,-.) < (.,.) (.,) (-.,-) - () Show rgions ( + 2 β)( 2 β) < hv > for ig. () with / ig.6 Th mp of n β 3.3 Strss Distriutions in Bon Plt without Crk igur7 shows i-mtril on plt without rk unr rmot tnsion, whih is us to xplin th rson wh strss intnsit ftor for th ntrl intrf rk. Hr, strss istriutions t ross-stions,,,, in ig.7 r invstigt unr iffrnt mtril omintions. = O Gv, Gv 2, 2 x = ig.7 Th finit lmnt mol in ig.2 () with / igur 8 (), (), (), (), () show th strss istriutions for () =.4, β =.3, () =.6, β =.3, () =.7, β =., () =., β =.2, () =.2, β =. rsptivl. As n n sn from ig.8, strsss t ross-stions,,,, in ig.7 r not unit, howvr, th vrg strss t h ross-stion is quivlnt to th rmot tnsion =. Spifill, =.4, β =.3 is onsir s goo pir sin ( 2 β ) < is 98 98
stisfi s shown in ig.6 (). n this s, it is sn tht = t th fr g of th intrf x=. Thrfor, roun x = shoul lrgr thn whih ls to > whn ( 2 β ) < (7),(8). On th othr hn, from ig.8 (), onstnt strss istriutions of = t h ross-stion r onfirm. Hr, =.6, β =.3 is suppos to th qul pir sin ( 2 β) = s shown in ig.6 (). As rsult, = pprs whn ( 2 β ) =. Similrl, =.7, β =. stisfis ( 2 β ) >, whih is rgr s pir s shown in ig.6 (). n this s, th strss t th fr intrf g x= gos to infinit s. Th strss istriutions nr x = r thrfor shoul lss thn unit s <. This is th rson wh < whn ( 2 β ) >. ig.8 () inits strss istriutions for =.2, β =. whih stisfis pir onition ( 2 β ) > s shown in ig.6 (), n th strss t th fr intrf g x= gos to infinit s, ut iffrnt from ig.8 (), th strss oms smllr roun x=. Thn, = pprs t x =, whih ls to =. Bus in this s, n β stisf + 2β =, onsiring ig,8 () n ig.8 (), it n onlu tht = is otin whn ( + 2 β)( 2 β ) =. igur8 () inits strss istriutions for =., β =.2, similr with ig.8 (), lthough pir onition ( 2 β ) > is stisfi, > pprs t x =, whih ls to >. Bus in this s, n β stisf + 2β <, onsiring ig,8 () n ig.8 (), it n onlu tht > is otin whn ( + 2 β)( 2 β ) <. Thrfor, thr r two lins to ontrol s shown in ig.6 (), on is 2β = n th othr is + 2β =. or ( + 2 β)( 2 β ) >, < ; for ( + 2 β)( 2 β ) =, = ; for ( + 2 β)( 2 β ) <, >. Tl 4 shows th strss t O in ig.7 ompring with of ntrl rk in on infinit plt with vring mtril omintion. rom this tl, it is foun tht th strss intnsit ftor is qul to th strss t O in th on plt without rk. This ls us to th onlusion tht of n intrf rk in on infinit plt n sil otin from th strss t th intrf without rk. ()..5..95.9.85 =.4,β=.3 (+2β)( 2β)<.8..2.4.6.8...5..95 =.6,β=.3 (+2β)( 2β)= G =.357 v =.4 G2 =.245 v2 =.4932 x/ = x G =.357 v =.4 G2 =.245 v2 =.4932 = x = (-.,) (-.,-) (-.,) (-.,-),3β = β = (.,) (.8,.45) (.,.45) > (.6,.4) (.,,4) (.2,.3) (,.25) (.,.3) (.,.2) (.,.) - o = (.,) (.6,-.) (.2,-.2) < (,-.25) -.6,3(.,) β = β = (.8,.45) (.,.45) > (.6,.4) (.,,4) (.2,.3) (,.25) (.,.3) (.,.2) (.,.) - o = (.,) (.6,-.) (.2,-.2) < - (,-.25).4..().9..2.4.6.8. x/ 98 98
..2Journl of Soli Mhnis.8.6.4.2. =.7, β=. ( 2 β )> G =.357 v =.4 G2 =.245 v2 =.4932 = x = (-.,) (-.,-).7,β = β = (.8,.45) > (.6,.4) (.2,.3) (,.25) - o = (.6,-.) (.2,-.2) < - (,-.25).(.,) (.,.45) (.,,4) (.,.3) (.,.2) (.,.) (.,).8 ().6..2.4.6.8. x/ () ().6.5.4.3.2...9.8.7..2.4.6.8..8.7.6.5.4.3.2 =.2,β=. (+2β)( 2β)= x/ G =.357 v =.4 G2 =.245 v2 =.4932 =...9.8.7 =.,β=.2 (+2β)( 2β)>.6..2.4.6.8. x/ G =.357 v =.4 G2 =.245 v2 =.4932 = (-.,) (-.,-) (-.,) (-.,-) β (.8,.45) > (.6,.4) (.2,.3) (,.25) - o = (.6,-.) (.2,-.2) < (,-.25).2,= β = - β (.8,.45) > (.6,.4) (.2,.3) (,.25) - o = (.6,-.) (.2,-.2) < (,-.25).,= β = - (.,) (.,.45) (.,,4) (.,.3) (.,.2) (.,.) (.,) (.,) (.,.45) (.,,4) (.,.3) (.,.2) (.,.) (.,) ig.8 strss istriution () =.4, β =.3, () =.6, β =.3, () =.7, β =., () =.2, β =., () =., β =.2 Tl 4 Th omprison twn with /. t x =, = in ig.7 n in ig.2 () β t O in ig.7.2.85.4.8...3.4.995943.98.26..995944.988.275. 982 982
3.4 Cntrl ntrf Crk in Bon nfinit Plt with Mtril unr Tnsion in th x-irtion Tl 5 shows strss intnsit ftors of ntrl intrf rk shown in ig.2() with iffrnt rltiv rk siz = /62,/324,/648 unr iffrnt mtril omintion =.3, β =.2, =.75, β =, =.8, β =.4. t is sn tht ll th rsults oini h othr mor thn 3 igit whn < /62. igur 9 shows th rsults of on infinit plt with mtril unr tnsion in th x-irtion. Th sh lins r xtn from soli lins us som ss of mtril omintion r iffiult to otin th EM. n ig.9, β in h urv is fix, n th vritions of r pit with vring prmtr. Prviousl, it hs n thought tht tnsion in th x irtion os not ontriut to th strss intnsit ftors (). Howvr, s n sn from ig.9, is not in urrnt rsrh. t shoul not tht th strss intnsit ftor is not zro unr x-irtionl tnsion, xpt th s whn ε x = ε x2 is prou long th intrf, n it hs th minimum vlu =.34 whn =.2, β =.3, n th mximum vlu =.267 whn =., β =.45. t is lso foun tht = for th ntrl intrf rk unr x-irtionl tnsion. Thrfor, it m onlu tht ntrl intrf rk in on infinit plt with mtril unr x-irtionl rmot tnsion is quivlnt to tht of unr intrnl prssur of =.34 ~.267. All th vlus in ig.9 r provi in Tl 6. 4. Cntrl ntrf Crk in Bon init Plt Until hr th strss intnsit ftors of intrf rk in on infinit plt r minl trt. n this hptr, th on finit plt s shown in ig.2 () is nwl Tl 5 Dimnsionlss strss intnsit ftors of rk in ig.2 () with iffrnt /. / =.3, β =.2 =.75, β = =.8, β =.4 /62 /324 /648 -.254 -.2539 -.2539 -.2539.75.756.755.754.7962.796.7959.7958 /62 /324 /648. -4 5.53-5 2.77-5 2.59-4.29-4 6.46-5 3.28-4.64-4 8.9-5.3.25.2 β=-.45 β=-.4.5. β=-.3.5 β= β=-.2 β=. β=-. -.5 β=.2 β=.45 β=.3 β=.4 - - ig.9 of ntrl intrf rk in on infinit plt unr x = (s ig. 2 () with / ) 983 983
Tl 6 Dimnsionlss strss intnsit ftor in ig.2 () with /. β -.45 -.4 -.3 -.2 -...2.3.4.45 -. -.95 -.9 -.85 -.8 -.75 -.7 -.6 - -.4 -.3 -.2 -.5 -. -.5.5..5.2.3.4.6.7.75.8.85.9.95. (.267).247.229.23 (.99) (.242).224.28.93.8.67.55 (.3) (.23).87.73.6.48.37.27.8.9.76.63 (.53) (.7).57.44.33.22.2.3.86.7.59.47.37.33.28.24.7.4. (.9) (.42).3.9.9.99.9.82.67.54.43.33.24.2.7.3.7.5.2. -.3 -.6 -.8 (-.9) (.6).7.96.87.78.7.63.5.38.28.9.2.8.5.3 -.2 -.4 -.6 -.8 -. -.2 -.3 -.2 -. -. -.9 -.7 -.5 -.3 (-.2) (.3).22.4.6. -.3 -.6 -.8 -.2 -.4 -.5 -.6 -.8 -.8 -.8 -.7 -.4 -.3 -. -.9 -.6 -.3 (.) (-.2) -.5 -.7 -.9 -.22 -.23 -.24 -.25 -.25 -.25 -.24 -.22 -.8 -.6 -.4 -. -.8 -.4 (.) (-.34) -.34 -.33 -.3 -.27 -.22 -.2 -.6 -.3 -.9 -.4 (.) (-.3) -.27 -.24 -.2 -.6 -. -.6 (-.) (-.2) -.7 -.2 -.6 (.) onsir. igurs n show th strss intnsit ftors for =.2 n =. Th sh lins r xtn from soli lins us som ss of mtril omintion r iffiult to otin th EM. Compring igs., with ig.5, it is foun tht th rsults in igs., hv similr vrition trns lthough vlus in igs., r slightl lrgr thn thos of ig.5. Similr xmintions r prform for =..9 in this stu. Th mximum n minimum vlus of, for h r shown in Tl 7 n ig.2 with vring. Th sh lins r xtn from soli lins us som ss of mtril omintion r iffiult to otin th EM. Hr homois th rsults of ntrl rk in homognous plt, n th prsnt rsults homo oini with si s rsults (9). n ig.2 th rsults r init s th rtios of mx / homo n min / homo. t is sn tht homo givs lmost lrgst vlus of, n th iffrn twn mx n homo is lss thn 4%. On th othr hn, th iffrn twn min n homo inrss with inrsing. igur 2() shows mximum n minimum solut vlus of inrss with inrsing. Spifill, th rsults for G2 / G = 4 n G 2 / G = in th prvious stuis (2)-(4) r plott in ig.2...5 β=-.2 β=.3 β=.2 β=.4 β=.45 β=-. β= 2.95 β=..9 / =.2 () K + ik = π( + i )(+ 2 iε).85.2.4.6.8 984 984
.5.4.3 β=-.2 β=-. β= β=. β=.2.2 β=.3. β=.4 () -. -.2 β=.45 -.3.2.4.6.8 / =.2 K + ik = π( + i )(+ 2 iε) ig. Dimnsionlss strss intnsit for (),() for / =.2.25.2 β=-.2 β=-. β=.2 β=.3 β=.4 β=.45.5. / = β= β=..5 () K + ik = π ( i + )(+ 2 i ε).2.4.6.8 2.5. β=-.2 β=. β= β=. β=.2.5 β=.3 β=.4 β=.45 () -.5 K + ik = π( + i )(+ 2 iε) -..2.4.6.8 / = ig. Dimnsionlss strss intnsit ftor (), () for / = 985 985
Tl7 Mximum n minimum vlus of strss intnsit ftors, /, mx Rf. [9],min homo, mx (homognous),min 2..2.3.4.6.7.8.9.36.39.57.89.4.29.336.59.842 2.582.882.848.883.96.959..9.28.432.936..6.25.58..87.34.488.85 2.574..6.246.577.94.867.333.4882.86 2.5776.25.5.75.5.42.8.242.34 7 -. -.23 -.37 -.56 -.79 -.3 -.68 -.272-45.5 / homo mx / homo.95.9.85 2 G / G = 4 2 ( ν = ν =.3) 2 2 G / G = ( ν = ν =.3).8 min / homo.75.2.4.6.8 ().6 /.4, mx.2 G / G =, ( ν = ν =.3) 2 2 G / G = 4,( ν = ν =.3) 2 2 -.2 -.4, min -.6.2.4.6.8 () / ig. 2 () mx / homo, min / homo vs. / n (), m x,, mi n vs. / ( hom : Strss intnsit ftor for homognous plt) o 986 986
5. Conlusions n this stu, strsss t th intrf rk tip r lult ppling th finit lmnt mtho. Thn th strss intnsit ftors r trmin from th rsults of th rfrn prolm n givn unknown prolm. Th onlusions r givn s following.. Strss intnsit ftors of ntrl intrf rk in on infinit plt unr rmot tnsion wr lult vr urtl unr ritrr mtril omintion. 2. Cntrl intrf rk in on infinit plt unr rmot tnsion of = is quivlnt to tht unr intrnl prssur of =.882~.36. Morovr, ntrl intrf rk in on infinit plt with mtril unr rmot x-irtionl tnsion of = is quivlnt to tht unr intrnl prssur of =.34 ~.267. 3. Vritions of th mximum n minimum strss intnsit ftors, in on finit plt r lso invstigt with vring in this ppr. t is sn tht th strss intnsit ftor for homognous mtril homo givs th mximum vlu mx within 4% rror. On th othr hn, th iffrn twn min n homo inrss with inrsing. Rfrns () Yuki,Y., Mhnis of ntrf, (992), p. 2,Bifuukn. (2) O, K., Kmisugi, K., n No, N.A., Strss intnsit ftor nlsis of intrf rks s on proportionl mtho, Trnstions of th Jpn Soit of Mhnil Enginrs, Sris A, Vol.. 75, (29), pp. 467-482. (3) Mtsumoto, T., Tnk, M. n Or, R., Strss intnsit ftor nlsis of imtril intrf rks s on intrtion nrg rls rt n ounr lmnt snsitivit nlsis, Trnstions of th Jpn Soit of Mhnil Enginrs, Sris A, Vol.65, No.638(999), pp.22-227. (4) Mizki, N., k,t., So,T., n Munkt, T., Strss intnsit ftor nlsis of intrf rk using ounr lmnt mtho, Trnstions of th Jpn Soit of Mhnil Enginrs, Sris A, Vol.57, No.54(99), pp. 263-269. (5) Trnisi, T., n Nisitni, H., Dtrmintion of highl urt vlus of strss intnsit ftor in plt of ritrr form EM, Trnstions of th Jpn Soit of Mhnil Enginrs, Sris A, Vol. 65, (999), pp. 6-2. (6) Nisitni, H., Trnisi, T., n ukum, K., Strss intnsit ftor nlsis of iomtril plt s on th rk tip strss mtho, Trnstions of th Jpn Soit of Mhnil Enginrs, Sris A, Vol. 69, (23), pp. 23-28. (7) Bog, D.B., Eg-on issimilr orthogonl lsti wgs unr norml n shr loing, Journl of Appli Mhnis, Vol. 35, (968), pp. 46-466. (8) Bog, D.B., Two g-on lsti wgs of iffrnt n wg ngls unr surf trtions, Journl of Appli Mhnis, Vol. 38, (97), pp. 377-386. (9) si, M., Elsti nlsis n strss intnsit ftor of rk, (976), p. 45, Bifuukn. 987 987