Analytical research on impacting load of aircraft crashing upon moveable concrete target

Transcription

1 IOP Coferece Series: Maerials Sciece ad Egieerig PAPER OPEN ACCESS Aalyical research o imacig load of aircraf crashig uo moveable cocree arge To cie his aricle: Tog Zhu e al 28 IOP Cof. Ser.: Maer. Sci. Eg View he aricle olie for udaes ad ehacemes. Relaed coe - Predicio mehod for caviaio erosio based o measureme of bubble collase imac loads S Haori, T Hirose ad K Sugiyama - Normal dyamic deformaio characerisics of o-cosecuive joied rock masses uder imac loads Sheg Zeg, Bowei Jiag ad Big Su - Sudy o Mechaical Proeries of Barie Cocree uder Imac Load Z F Che, K Cheg, D Wu e al. This coe was dowloaded from IP address o 22/9/28 a 2:4

2 IOP Cof. Series: Maerials Sciece ad Egieerig (28) 726 doi:.88/ x/322/7/726 Aalyical research o imacig load of aircraf crashig uo moveable cocree arge Tog Zhu, a, Zhuocheg Ou 2, b, Zhuoig Dua 3, c, Feglei Huag 4, d,2,3,4 Sae Key Laboraory of Exlosio Sciece ad Techology, Beijig Isiue of Techology, Beijig 8, P. R. Chia a zhuog989@homail.com, b zcou@bi.edu.c, c duaz@bi.edu.c, d huagfl@bi.edu.c Absrac: The imac load of a aircraf imac uo moveable cocree arge was aalyzed i his aer by boh heoreical ad umerical mehods. The aircraf was simlified as a oe dimesioal ole ad sress-wave heory was used o deduce he ew formula. Furhermore, aimig o comare wih revious exerimeal daa, a umerical calculaio based o he ew formula had bee carried ou which showed good agreeme wih he exerimeal daa. The aroach, a ew formula wih aricular umerical mehod, ca redic o oly he imac load bu also he deviaio bewee moveable ad saic cocree arge.. Iroducio As a imora barrier o esure he safey of uclear reacors, cocree coaime, oce desroyed, he cosequeces will be exremely serious. Sice he icide of 9/, researchers have iesified heir research o he relaed roblems of aircraf accideal imacs o uclear ower la coaime. As he core of his issue, imac load formula roosed by Riera [] has bee used widely i his field. The core assumio of his formula is ha he icrease of he damaged mass is equal o he roduc of he fligh seed ad lier desiy of he aircraf. I 976, cosiderig he elasolasic characerisic, Driler e al. [2] modified he origial Riera formula. Furhermore Horyik e al. [3] claimed ha he ierial force was overesimaed as he arge was cosidered as rigid so ha a correcio facor was iroduced o reduce he ierial force. Riera [4] summarized he coclusios of oher researchers ad he addiioally roosed a aroach cocerig oblique imac of aircraf. Geerally, i he exerime, he cocree arge is se as moveable arge whose acceleraio ca be used o calculae imac load. Exerimeally, Sugao e al. [5-7] carried ou he Jaaese-America joi full-scale aircraf collisio exerime, he oly oe wih available exerimeal daa all over he world u o ow. I his exerimeal sudy, a lo of exerimeal daa are obaied, icludig he Coe from his work may be used uder he erms of he Creaive Commos Aribuio 3. licece. Ay furher disribuio of his work mus maiai aribuio o he auhor(s) ad he ile of he work, joural ciaio ad DOI. Published uder licece by Ld

3 IOP Cof. Series: Maerials Sciece ad Egieerig (28) 726 doi:.88/ x/322/7/726 acceleraios of he arge a differe osiios, he velociy-ime curves of aircraf comoes such as he egie, he fuselage ad he ail, ad he imac force acig o he arge was calculaed by usig he acceleraio daa of he cocree arge. However, here is o such heoreical wave mehod o esimae he deviaio of imac load bewee saic ad moveable arge while he imac rocess is absoluely wave rocess. As he mos widely used formula, Riera formula, he core assumio of which is quesioable from he oi view of sress-wave heory. Therefore, rese sudy will focus o he descriio of he imac load characerisic for he imac rocess of a aircraf uo a moveable cocree arge, based o he sress wave heory, by which some ovel feaures ad hysical mechaism abou he imac rocess will be ucovered. This aer is divided io four major secios as follows. Followig his brief iroducio i Secio Oe, heoreical aalysis is dislayed i Secio Two, i which a ew formula is roosed. I Secio Three, he umerical resuls for he imac load calculaed by ew imac load formula are reseed ad comared wih boh he umerical resuls calculaed by usig he Riera equaio ad revious exerimeal daa, ogeher wih some ecessary discussios. Fially, some coclusios are draw ou i Secio Four. 2. Sress aroach for imac-load formula I order o obai heoreical resul ad igore he effecs such as geomerical disersio, aircraf srucural characerisic was simlified as oe-dimesioal ole which is used similarly i Riera aroach. I follow discussio, he ew formula based o sress-wave heory will be called as SW formula as abbreviaio. As is show i Fig., whe he aircraf imacs uo he arge, wo sress waves begi o roagae i he aircraf s fuselage i he direcio of he ail, amely, a recursor elasic wave roagaig a he elasic logiudial wave seed c e ad a successor geeralized lasic wave wih he geeralized lasic logiudial wave seed c < c e. Moreover, he sress saes behid he recursor elasic wave ad he successor geeralized lasic wave are geeralized yield sress of he aircraf s fuselage Y ad he isaaeous imacig sress. Here, by geeralized lasic we mea ha he aircraf crushig is o jus a ure lasic deformig or yieldig rocess, which icludes may oher failure mechaisms such as fracure ad bucklig. V C e d σ Y σ>σ Y C d Fig. Wave sysem i he aircraf fuselage A he begiig of he imac, =. The aircraf imac he cocree arge wih a velociy of V. The mass of he arge is M T ad he fricio bewee he arge ad he groud is f. The wave rocess of he imac is showed i Fig.2. 2

4 IOP Cof. Series: Maerials Sciece ad Egieerig (28) 726 doi:.88/ x/322/7/726 V 3 V V 2 O L 2 L L X Fig.2a X- relaioshi i imac rocess 3 2 o V σ Y Fig.2b σ-v relaioshi i imac rocess Some addiioal assumios are dislayed below: maerials of he aircraf, oce desroyed, will vaish i a very shor ime so ha he elasic wave will o roagae io crushig regio which is he area afer he geeralized lasic wave. This assumio base o he fac ha he crushig regio cao be observed i he exerime which imlies he legh of i is shor eough o be egleced. Furhermore, he srucure of he aircraf is simlified as a oe dimesioal ole, as we have meioed revious, so ha he aircraf will be reaed as homogeeous maerial. Alhough he yield sress of he aircraf is uclear ill ow, we ca calculae a average value aleraively from he daa of he exerime. The imac rocess ca be disseced by dividig i io some sub rocesses. Accordig o he sress-wave heory, he coservaio codiio cross he lef-roagae elasic wave fro is: c ( V V ) () X e Where σ ad σ 2 are he sresses, V ad V are aricle velociies i he corresodig area. ρ X is he bulk desiy of he aircraf. The sress of he area is he yield sress as he imac velociy is high eough: 3

5 IOP Cof. Series: Maerials Sciece ad Egieerig (28) 726 doi:.88/ x/322/7/726 Y (2) ad hece V Y V (3) X c e The coservaio codiio cross he lef-roagae lasic wave fro is: c ( V V ) (4) X Subsiue Eq.(2) io Eq.(4): c c ( V V ) Y X c e (5) O he oher had, he arge is acceleraed uder he imac sress. Thus, he moio of he arge ca be wrie ou by he Newo's secod law ad he velociy of he arge is: M d V f T (6) d A c A c Le he wo revious equaios equal, he a ordiary differeial equaio for deermiig he velociy of he area afer he geeralized lasic wave ca be deduced: dv d ( ) V q ( ) (7) Assume ha: c A ( c ) A ( c ) X c f ( ), q ( ) c V Y X M M c T T e A c Cosiderig he iiial codiio: (8) V v (9) Where, he arge velociy is v a iiial ime =. The geeral soluio of he Eq.(7) ca be wrie: s ( ) d ( ) d ( ) V e C q s e d () The, he iiial codiio Eq.(9) is subsiued io he uer formula o deermie he udeermied cosa i he geeral soluio: 4

6 IOP Cof. Series: Maerials Sciece ad Egieerig (28) 726 doi:.88/ x/322/7/726 C v () Thus, he soluio of he ordiary differeial Eq.(7) uder he iiial codiio Eq.() ca be wrie wih geeraliy: s ( ) d ( ) d ( ) V e v q s e d s, ( ) ( 2) Afer V is deermied, σ may be deermied by Eq.(5). The siuaio i area 2 will be:, V V 2 Y (3) c 2 2 x e A his oi, all he saus durig - eriod have bee ideified. I addiio, Eq.(3) rovides he iiial codiios for deermiig he ex eriod ( - 2 ). Furhermore he velociy of he arge a he begiig of he eriod from o 2 ca be calculaed: s ( ) d ( ) d ( ) v e v q s e d s (4) The mehod used o aalysis he ex eriod is jus same o he revious oe. Referrig o he above equaios, i is easy o wrie he SW imac load recurrece equaio: 5

7 IOP Cof. Series: Maerials Sciece ad Egieerig (28) 726 doi:.88/ x/322/7/726 c c e L L ( c c e ) 2 L c c e Y V V, c X e Y A ( c ) c f q ( ) c V Y X M c T e A c s ( ) d ( ) d T V V e v q ( s ) e d s c Y c e c ( V V ) X P ( ) A ( c ) 2 Y V V c X e, ( ) (5) I is o difficul o achieve he acceleraio of arge i he rocess of aircraf imac from Eq.(6): T dv A c f a ( ) d M T A c (6) The formula shows ha he acceleraio of arge is iecewise coiuous fucio i he SW imac load model. This is also he ieviable resul of decomosig he rocess io a series of sub imac rocesses. The velociy of he arge should be cosidered whe calculaig he imac sress due o he moveable arge, so ha he velociy differece bewee he fro ad he back of he geeralized lasic wave fro i he movig arge will be reduced. This may lead o a chage i he geeralized lasic wave velociy, hereby affecig he legh of he damaged zoe, ec. o he oher had, he imac load will be smaller ha he imac of he aircraf o he saioary arge. Whe he airlae his he moveable arge, is velociy ad acceleraio are deermied by he imac load, he moio fricio resisace ad he mass of arge. Geerally, i he exerimeal sudy, if he mass of he arge is large eough, he daa of acceleraio sesor would o be recise. O he oher had, he imac load would be effeced if he cocree arge is oo ligh. I he acual siuaio, he uclear 6

8 IOP Cof. Series: Maerials Sciece ad Egieerig (28) 726 doi:.88/ x/322/7/726 coaime cosidered o desroyed, oherwise, i is meaigless o aalyze he imac load of he aircraf imac. Therefore, i order o be closer o he acual siuaio, he mass of cocree arges should o be oo small. Therefore, how o selec he aroriae mass of cocree arge is a imora roblem i he aircraf imac exerime, ad he aalysis of hese arges rovides a heoreical basis for solvig his roblem. 3. Numerical resuls ad discussios Moveable arge exerime is a effecive mehod o measure he imac load of aircraf imac uo uclear coaime. Therefore, he imac load formula is cosidered o esimae he imac force i boh exerimeal ad acual codiios. Furhermore, he differece of he imac load bewee he wo codiios should also esimable. I his ar, cosiderig he liear desiy of he aircraf, he imac load ad some oher arameers will be discussed via umerical ways. The olerace of he imac load bewee moveable ad saioary is showed by erceage i Fig.3 which is calculaed usig Eq.(5): Fig.3 Imac load olerace bewee moveable ad saioary arge over differe imes of he arge mass As showed i Fig.3, he imac load olerace bewee moveable ad saioary arge icreases over ime. Because he velociy of he moveable arge is a he begiig of he imac. Aarely, he larger mass of he moveable arge(he raio of he arge mass o he aircraf mass)he more recise daa could be achieved by exerime, however he cos ad he accuracy should be cosidered simulaeously. The imac load of a aircraf imac uo a moveable arge which has a mass ha is 5 imes of he aircraf is showed below: 7

9 IOP Cof. Series: Maerials Sciece ad Egieerig (28) 726 doi:.88/ x/322/7/726 Fig.4 Imac load comariso bewee 5 imes mass moveable arge ad saioary arge The differece is cosicuous if he mass of he moveable arge is ligh eough. However, i Jaaese-America joi full-scale aircraf collisio exerime, he mass of he arge is 25 imes of he aircraf. I order o es he ew equaio, he velociy of he arge over ime is calculaed ad also comared wih he exerimeal daa as follow: Fig.5 Velociy of he arge over ime The comariso bewee he exerimeal daa ad umerical resul shows good agreeme so ha he ew imac formula ca be used o esimae he imac force ad also some oher arameers. 8

10 IOP Cof. Series: Maerials Sciece ad Egieerig (28) 726 doi:.88/ x/322/7/ Coclusios The SW formula is based o sress-wave heory which shows more deails ha he origial Riera formula. Furhermore, he SW formula ca also redic he olerace bewee he exerimeal ad acual imac force which is a robus ool for researchers o decide he mass of he moveable cocree arge before he exerime. Refereces [] J. D. Riera, O he sress aalysis of srucures subjeced o aircraf forces, Nuclear Egieerig ad Desig [J], 8 (968) [2] K. Driler, P. Gruer, Calculaio of he oal force acig uo a rigid wall by rojeciles. Nuclear Egieerig ad Desig [J], 37 (976) [3] K. Horyik, Aalyic modelig of he imac of sof missiles o roecive walls, Trasacios of he 4h Ieraioal Coferece o Srucural Mechaics i Reacor Techology [J], 977. [4] J. D. Riera, A criical araisal of uclear ower la safey agais accideal aircraf imac, Nuclear Egieerig ad Desig [J], 57 (98) [5] T. Sugao, H. Tsuboa, Y. Kasai, N. Koshika, S. Orui, W. A. Vo Riesema, D. C. Bickel, M. B. Parks, Full-scale aircraf imac es for evaluaio of imac force, Nuclear Egieerig ad Desig [J], 4 (993) [6] T. Sugao, H. Tsuboa, Y. Kasai, N. Koshika, S. Orui, W. A. Vo Riesema, D. C. Bickel, M. B. Parks, Local damage o reiforced cocree srucures caused by imac of aircraf egie missiles Par, Tes rogram, mehod ad resuls, Nuclear Egieerig ad Desig [J], 4 (993) [7] T. Sugao, H. Tsuboa, Y. Kasai, N. Koshika, S. Orui, W. A. Vo Riesema, D. C. Bickel, M. B. Parks, Local damage o reiforced cocree srucures caused by imac of aircraf egie missiles Par 2, Evaluaio of es resuls, Nuclear Egieerig ad Desig [J], 4 (993)