Hybrid (Bolted/Bonded) Joints Applied to Aeronautic Parts: Analytical Two-Dimensional Model of a Single-Lap Joint

Transcription

1 Hybd Bod/Bondd Jon Appd o Aona Pa: Anaya To-Dnona Mod of a ng-lap Jon E Paon *, Ma ao, Jaq H, and Fédé Lahad In d Gén Méanq, Too,, FRANE Th hana bhavo of hybd bod/bondd on nvgad. Th on nd dy a baand ng-ap on, and an a bhavo of h aa ad. A fy paa anaya o-dnona od, bad on h Fn En Mhod, pnd. A pa Fn En Bondd Ba n opd n od o a h bondd adhnd. Th aon of fan and hogh pna and na appoah. Good agn a hon. Nona ffn N. - of h png n h don ongdna ffn ffn N. - of h png n h y don anva ffn ffn N. of h png aond h z don bndng ffn E f Yong od MPa of h fan E p oa pona ngy N. E Yong od MPa of h adhnd E Yong od MPa of n h adhv F fo vo G oob od MPa of h adhv I on of na of h adhnd I b K, K ffn a K BB ffn a of h Bondd Ba n L ngh of h ap on M a on N. n h adhnd α aond h z don N α fo N n h adhnd α n h don Q β noda fo N appd o h nod β n h don R dng a R β noda fo N appd o h nod β n h y don adhv png MPa on of h adhnd b β noda on N. appd o h nod β aond h z don T adhv ha n MPa V α fo N n h adhnd α n h y don b dh of h adhnd aa ph bn o o of fan d ngh bn h nd of h on and h na fan hn of h adhnd hn of h adhv * Ph.D. dn, Dépan d Gén Méanq, Eo Naona pé d Ingén d onon Aéonaq,.paon@na.f. Pofo, Dépan d Gén Méanq, In Naona d n Appqé d Too, a.ao@na-oo.f. Pofo, Dépan d Gén Méanq, Eo Naona pé d Ingén d onon Aéonaq, aq.h@na.f. Aan Pofo, Dépan d Gén Méanq, Eo Naona pé d Ingén d onon Aéonaq, fd.ahad@na.f. Aan In of Aona and Aona

2 f fo N appd o h n h don h gn fnon ngh of h ba od h ap gn nd n nb of fan q, q dpan vo ngh of h ongdna ph bn o n of fan α dpan n h don α dpan n h y don ngh of a Bondd Ba n φ da of h fan α gn bp hh f o h ahnd α β gn bp hh f o h nod β ν Poon ao of h adhnd ν Poon ao of h adhv ν f Poon ao of h fan α anga dpan ad aond h z don,y,z d ohonoa ba I. Inodon HI pap da h h oad anf n hybd bod/bondd ng-ap on. Th on of v aaf a T nvgad. Th f nvgaon a h ongdna on of fag. Th on a opod of an h and an bo. Th dvopd hod, hh pnd n h pap, ha o appy o h oh on on aaf. Hybd on a bod/bondd on, hn aoang a d anf od h a onno on, ah on bongng o on ffn. Th bod on d anf od gna a hgh ov aond h ho of h fan hh pda o h fag an. Th bondd on onno anf od ao a b dbon of h anf; hov pn a pa aoodaon hh pda o h a ngh n h ong. In h doan of aaf aby, h hybd onng od b nng ba od d h oad anfd by h fan n od o pov h fag f, h nng a ngh nd oad. Th da o dgn h hybd on n od o ha h oad bn h adhv and h fan n a ab ay. Tha hy h nfn of h on goy and h aa pop on h oad anf nvgad by an of dvopng ffn dgnng oo. Anaya appoah a h pvgd. On-dnona hod fo h aaon of bod on and no o-dnona hod fo h aaon of bondd on. In h pap a paa anaya appoah fo h aaon of hybd on by aoang bondd and bod hod pnd. Than o h anaya od a apagn of anhd n od o vada h anaya od and a a a paa h-dnona na od n h doan of h dy. Th na od ha n paa h aby o pov h od of fan n h anaya od. Th od vadaon a a dfnng h ffny doan of ah od. onqny h dvaon of h anaya appoah ao o pn pna and na appoah. II. Anaya Mod fo Bod Jon Th oad anf n a bod on a d anf od. I an ha bn ah bo, o on ah bay, h f anfd oad onan. Th fag f of bod on an b opd fo h bo oad anf. Th oad anfd by h fan an b oband anayay by n f o by ng an anaogy h an hng., Th fan a δ ay ad by png, hh a ondd o o by hang. Th an paa h gdy of h Fg. Bhavo of a fan. hang png. Th bhavo of a fan n a on a dff δ f Aan In of Aona and Aona

3 pob and h dnaon of fby povd no d and foaon.,- Th bhavo of a fan an b dfnd by a v fo-dpan of h on. Th na pa of h v povd h gdy of h fan Fg., qod. Th va opond o h nga dpan, hh opod of h dfoaon d o ha, bndng and bang oad, of h fan n h bod on. III. Anaya Mod fo Bondd Jon No pbaon nvga h bondd on. Th ng-ap on a fy nvgad by Von n and ad o h dbon of h adhv ha ngang h oa qb qaon of h adhnd and ang h adhv by an nfny of hang a png. Hov, h ag dpan of h on d o h ny of h oad pah hav no bn ondd n h pvo dy. In, Goand and Rn G&R oo no aon h ff of h ny of oad pah and dnd h adhv png and ha. Th adhv a ad by an nfny of n and hang a png, b h hn of h adhv a ondd nggb. In h Ha-h, povdd a vono o on bondd on ondng h ng and dob-ap on onfgaon, h baand and nbaand onfgaon, h a and a-pa bhavo of h adhv. Moov, Ha-h dd no ng h goa ff of h hn of h adhv on h and oad fnon n h on. Th adhv a ad n h a ay a h pvo on. Hov, h aon of h adhv do no ao o vfy h adhv f a a h nd of h on. Oh aho, povd anaya foaon hh ho h adhv f a a h nd of h on: h a of adhv ha o png no o a h nd of h on b dpad n h ap on and hgh. In h pap h appoah of h bondd on opond o h appoah of G&R, n h o a a dvopng an ay o and ob oo fo anayzng h hana bhavo of h hybd on. Hn h oa qb qaon hh a ondd a Eq. : dn T b d dn T b d dv b d dv b d dm V.bT d dm V.bT d Th aon bn dpan and oad a gvn by Eq. fo h gn nd α qa o and : dα Nα d Eα d α M d Eα I dα α d α α α, α, Fnay h adhv o n h a doan and ad by an nfny of png: G T E Aan In of Aona and Aona

4 Th aon gvn n Eq. o a h ba qaon d n h anaya appoah of hybd on, hh pnd h. IV. To-Dnona Anaya Mod fo Hybd Bod/Bondd Jon Th anaya appoah bad on donno hod d fo ppdon. d Th da of dvopng dgn oo han o a oop poga pad. - Th Fn En Mhod FEM adapd o h da. Th FEM d fo dvopng h o-dnona anaya od of a hybd baand ng-ap on. Th Ba En Ba En pnd appoah n h pap an b Bondd Ba En appd n h on-dnona a and povd h a a h hod bad on h d ngaon of h oa qb qaon. Moov h of h FEM fb n dffn bonda ondon an b appd Tanaona png ay. Tha hy h FEM appoah Rgd Body hon fo h o-dnona dvaon. y En Th hypoh a: a onan hn of h adhv aong h ap on, an a Roaona bhavo of h adhv and of h png adhnd. Moov h go and hana paa and h nb, Fg. Mhng of h hybd ng-ap on h odnona n. qod n, of fan a f. Hov h pnd on a baand on n od o pfy h ahaa dvaon of h od. R R Q Q Q Q Fg. Dpan n h Bondd Ba n. R Fg. Noda fo n h Bondd Ba n. R A o-dnona appoah qd n od o ond h ff of h bndng on h adhnd, d o h ny of h oad pah, and h ff on h adhv png. Hn, h ng-ap on hd n o-dnona n a hon n Fg.. Th pa od h ap a ad by ba n hh hav o nod and h dg of fdo by nod. Th fan a ad by gd bod of hh boh nod a onnd h h oh nod of h by h pan png. Th n fan a png h ap on n n pa pnng h bondd bay. Eah bondd pa ad by a n n ad Bondd Ba BB, hh hav fo nod and h dg of fdo DoF a nod. onqny, h BB n pn h adhnd and h adhv a h a. Th fo nod of h n ao o a no aon h av dpan of h adhnd and ony on BB n qd fo ah bondd bay of h ap. Th a of gdy of h BB n ha o b dnd. Aan In of Aona and Aona

5 A. Ma of gdy of h Bondd Ba n Th f p o dn h dpan n ah adhnd fo h bondd on onfgaon. Th p gvn n Fg. pn h ondd dpan n a BB n. Th fo nod a qod,,, and h BB ngh qod. Th Eq. o ao o dn h na y of dffna qaon. Th y an b ovd ng h na aon gvn n Eq. fo h gn fnon h: Th na y of dffna qaon hh oband gvn n Eq. : h h h Dh h h d D d D d d d d d D D d d d dd d d d h h onan, and a gvn by h Eq. o : G E b G E I be E I Th oon of h na y, ng h foong qong gvn n Eq., : oh nh nh oh z o z h z z n z z z o z h z z n z h z D h h h D h o a h ngaon onan gvn n Appnd, and: Aan In of Aona and Aona

6 Aan In of Aona and Aona Th fnon D and a oband by dffnaon fo Eq. and pvy. Th ngaon onan a fond h h bonda ondon, opondng o h DoF of h BB n; h ngaon onan a h fnon of h DoF. Th dpan a oband by nvng h na aon gvn n Eq.. h h h h h h h h h h h h α α h h h h h h α Fo h pvo pon of h dpan Eq. o and fo h aon gvn n Eq. h fo n h adhnd a gvn by: E N E N h h h I E M h h h I E M bt h h h h h h I E V

7 V E I h h h h h h bt Fo h Eq. o, h noda fo Fg. an b ddd ng h foong aon: Q N Q N Q N Q N R V R V R V R V M M M M Fnay, h ffn a of h BB n, hh qod K BB, and h z of hh [;], opd fo h noda fo and h noda dpan: Q Q Q τ τ τ R R R K BB,, τ,,, τ τ τ τ τ τ B. Ma of gdy of h Th aa a of gdy of a ba Appnd opondng o h ba od h ap an. Fo n fan, h opod of n nod: ha opondd o n DoF. A gd body n aoad o ah fan. Th gd body opd h pan png, h gdy of hh qod, and. Th fan pad bn h nod and of h. Boh nod of h gd body n a qod and a hon on h Fg.. Hn, h opod of n nod and n DoF. Th paa a of gdy of h fan, qod K and n n h ba ; ; ; ondng Fg. Rgd body and pan png bn h nod and ang h fan. Aan In of Aona and Aona

8 Aan In of Aona and Aona h dpan aodng o ony, ao gvn by: n K ;, Th a aon a oband fo h paa gdy K and K. onqny, h nodon of h n gd bod nd h foong n qb aon and n aoad aon of na na dpndn: n Q R R Q Q ;, n ;, onqny, h z of h dpan vo dang fo n o n, and h ang of h gdy a of h ao dang of n. Th pob ad by h Ma-av hod. I hon o na h DoF, and. Than o Eq. a dng a R, h z of hh [n;n], an b dfnd: Rq q Hn, o: F R q KRq R q F q Kq q E p And fnay, h pon of h oa pona ngy bo: F q Kq q E p h: F R F KR R K Th vo dpan, hh nzng Eq., vf: F Kq A oop poga ao dvopd ng h MATLAB ahaa od, n od o aa h oon of h Eq... R fo h Bondd and h Bod ng-lap Jon onfgaon In od o h h aby of h BB n o a h bondd on, h od d ho any fan, and opad h h gvn by h G&R anay. Th hana and go paa of

9 h on nd ondaon a gvn n Tab. Fo h onfgaon, h on fao, hh aad f b L E ν G ν N MPa MPa han o h G&R od, qa o onqny, fo h opaon, Tab. Mhana and go paa. hoo h ngh of h ba od h ap, hh povd h a on fao. Th adhv ha and h png ha a pod and gvn n Fg. and Fg. pvy. I an b nod ha h v a ppod. Th aon of a ng-ap bondd on ng h BB n ho hn a good agn h h G&R hoy. onqny, aonab o hn ha h BB n an b d n od a h bondd pa of h hybd ng-ap, on. In od o h h fan aon h bod, on onfgaon of h od nd ondaon. Th a onfgaon a h pvo on hon, p fo h adhv paa: h av gdy of h adhv..: h ao G/ ha o b a o a, pob fo ap. - MPa. -. An nng a fo h opaon h bod on h fan. In od o opa h, hh a gvn by h od d n h bod on onfgaon, o h aa of h bod on h ongdna ffn..: of h fan n h od a aad o h goba va of h ffn gdy of h fan d n bod on dgn, and an abay qa o N. -. Moov, h anva ffn..: an nfny hgh han h ongdna ffn, n h fan ha no o o nd n oad n h a doan, and an qa o. N. -. Th va of h anva ffn ha no any nfn on h bo oad anf. Th a paa of h fan aon h bndng ffn..:. If h bndng paa an qa o N., a bo oad anf on h bo of h on qa o.% and a bo oad anf on h dd bo of h on qa o.% a oband, and appad a bv fnon, n h a, of h bndng ffn. Th va a h on of h aa bod on dgn. Th ho poby of h bndng ffn va va h dffy of h dgn of bod on. Th pna and na appoah hav o hp ndand h fan bhavo, and o hoo o va of h fan ffn. aba aong h ap on, G&R od D. R fo h Hybd ng-lap Jon onfgaon Th od povd h noa fo, h ha fo, and h bndng on n h adhnd, and h adhv ha and png. Th bo oad anf an b aad oo. Fo Fg. o Fg. h dffn fnon of h hybd on h o fan fo h paa va of h pvo paagaph a pnd. Th nfn dy of h ho hana and goa paa, hh pfod han o h od, f h non nd ha o ay h oad anfd by h fan na hn: - h Yong od of adhnd na; - h hn of h adhnd na; - h ngh of h ap on da; - h oob od of h adhv da; - h ongdna ph bn h fan da. adhv ha, MPa Fg. Adhv ha aong h ap on, G&R v. od. adhv png, MPa,,,,, -, -, aba aong h ap on, G&R od Fg. Adhv png aong h ap on, G&R v. od. Aan In of Aona and Aona

10 adhv, MPa,,,, -, aba aong h ap on, adhv ha adhv png Fg. Adhv ha and adhv png aong h ap on. noa fo, N aba aong h ap on, noa fo n adhnd noa fo n adhnd Fg. Noa fo n boh adhnd aong h ap on. bndng on, N. ha fo, N aba aong h ap on, bndng on n adhnd bndng on n adhnd Fg. Bndng on n boh adhnd aong h ap on. aba aong h ap on, ha fo n adhnd ha fo n adhnd Fg. ha fo n boh adhnd aong h ap on. I pob o add ha h oad anfd by h fan na hn: - h ffn of h fan na; - h dh of adhnd da; - h dg dan da. Than o h pnd od, h nfn dy pfod ay and qy. V. Epna Appoah A apagn of a anhd. Th a a ang, on on hand, h bo oad anf of a o bo ng-ap hybd on, and on h oh hand, h oa dpan of h on a a fnon of h appd oad, n od o aba and vada h fo h anaya od. A. Th Epna Mhod Th bo oad anf ad h an nnd bo. Th hon an gag o a anfad by Toyooy nd h fn FRA- -. Th an gag a qdan fo h ha pan of h bo h an ang of. Ony on o by bo d, and, h poon of h o on h bo h gad o h on ad. An aon of on nnd bo gvn n Fg.. In od o dd h bo oad anfd n h hybd onfgaon, a on a ap, h go and hana paa of hh a h a a h hybd onfgaon, ho bondng b pang h adhnd han o fan h hn of hh abad, pfod. Th gna oband fo h fn ap a ad o pn a oad anf, h a of hh non a gad h appd oad. Th gna oband fo h hybd onfgaon a ao opad h h fn, n od o povd h bo oad anf fo h hybd onfgaon. Fg. Innd bo. Aan In of Aona and Aona

11 Th dnon of h on a d by h dnon of h an gag d fo h nnaon of h bo. Th adhnd a anfad fo An H. Boh bo a an bo ANA, of hh h da qa o.. Th adhnd a bondd by a o oponn a poyhan adhv Pogp / by Ahand pay ha opany. Th hana haa of h adhv a pd o b ab o ha h oad bn h fan and h adhv ay. I n an bhavo an b fond n Rf.. Th go and hana paa of h ng-ap onfgaon d n h pna appoah a gvn n Tab. Th on d nd qa-a n oad hh pfod han o a ng ahn Inon h a N oad. Th ahn fy op onod. Th oad and h dpan of h gp a odd by h y. Th n n oad ono. y of nay oad and noad a pfod. Th f o on a n n N and h foong n N. Th v of aa oad a n od o ay n h a doan and o avod daag n h nnd bo. An aon of h pna -p gvn n Fg.. B. Bo Load Man Th bo oad anf ad and ddd aodng o h hod dbd n h pvo paagaph. Mo py, h odd gna of boh nnd bo ao o op h va of h ha an a a fnon of h appd oad and fo ah bo. Aodng o pna o ng h nnd bo h oad no dbd fay bn boh n of bo: on n of bo oadd p o % of h appd oad. Th apagn ao o ho h png pna. Th poaon of h pna daa ao ad fo h gna oband by ng h opd ha an of boh nnd bo. A a, h opd gna oband fo h fn ap ad o pn a bo oad anf of %. Fo h fn ap, o dffn ang of appd oad hav o b ondd. Th f ang of appd oad oad bn N and N, and h ond on oad bn N and N. In h o ang of appd oad h ha an nang nay h o dffn a. Fo h a of h hybd ap, h ha an an b ondd a nay dpndn on h appd oad bn N and N. Th nay vaaon of h ha an a a fnon of h appd oad ho h bo oad anf an onan nd o oad, a hon n Fg.. Fo h hybd a, h ang of an ad opond o h ang fo N o N of appd oad n h fn a. onqny, h bo oad anf opd by opang h a n h ang fo N o N. Th oa bo oad anf.%, and h.% fo ah bo ad. E ν E ν d b MPa MPa... Tab. Mhana and go paa.. opaon h h Anaya Mod In od o h anaya od, h ffn of h fan hav o b ad. In h paagaph a hod ggd. Th hod bad on pna and on h aon of h fan by an a ba nd ha and bndng oad. Th ffn ha no nfn on h oad anf. By hoogny h h foong ffn, pon ay b opd, h n ffn of a ynd, h ngh of hh h dan bn h oa ha an, / Fg. Epna p. appd oad, N fn ap hybd ap Fg. Toa ha an ad fo pna. Aan In of Aona and Aona

12 na a of boh adhnd, and h da h da of h fan h E f MPa and φ. : E πφ f Fo h dnaon of h fan ongdna dpan aong h a d o ha and bndng oad, h ha ffn and h bndng ffn a nd by Eq. h ν f.: ν f φ onqny, ony on ffn ha o b dnd. Th anaya od povd h oa dpan of h on: n h h hana and go paa of h pna, p h hana paa of h adhv, hh a an vy o ν. and E. -. MPa. -, n od o a h of h fn ap. Th va of h ha ffn, fo ap, ad o b h on, hh povd h a oa dpan ad dng h of h fn ap. Th va of N. -. Th bo oad anf aoad h h va of h ha ffn.% on ah fan aodng o h anaya od n h hybd onfgaon ng h va gvn n Tab. Hov, h bhavo of h fan n a on o b o opad, and a h-dnona od ha o b hpf, n od o a h ha and bndng ffn fan. VI. Na Appoah A paa h-dnona od qd n od o ndand and o pn aay h bhavo of h hybd on. Fo a paa h-dnona od of a bod ng-ap on dvopd pay fo pvo d abo bod onng ng h AMEF Fn En od, a paa h dnona of a hybd ng-ap on dvopd. A. Fn En Modng Th Fn En od dvopd ng h-dnona b n. Mo py, h adhnd and h adhv a odd h gh-nod n DoF and h fan a odd h ny-nod n DoF. Th h paay fnd aond h ho and n h adhv ay n n h hn of h adhv ay. Th yy aong h ngh of h ap on adopd, o ha h dy pfod on a haf od, a hon n Fg.. On nd of h on apd, ha h oppo nd f o ov n h ongdna Fg. Fn En od of h hybd on n ng-ap onfgaon. don ony. No p-non appd o h bo, and no aan bn h adhnd and h fan ad. Th ona bn h adhnd and h fan ay b na o non-na, aodng o h yp of anay o pfo. A na anay pfod han o h na od AEF of AMEF, ha h nonna aa pop and non-na goy a ndd ng h non-na od MEANO of AMEF. B. Na Appoah of ha and Bndng ffn fo h Fan aon of h Anaya Mod Aan In of Aona and Aona

13 In od o dn h ha ffn and h bndng ffn fo h fan aon of h anaya od, h Fn En od d n na anay h an adhv ay, h hana pop of hh a vy o ν. and E. -. MPa. -, n od o a h of h fn ap. I ffn o pfo a na anay, n h aa appd oad o nogh n od o avod a oo hgh onday bndng of h on on on hand, and on h oh hand, no o hadn h aa. Moov, h ho a na bhavo nd o oad. In h a, h ap ffn gvn by h Fn En od,% bo h on ad dng h on h fn ap. Th na od h ad o pn h good agn h pfod and an b d o dna appopad va of ha and bndng ffn. Th ha ffn ao nay ad by dvdng h oad pad by h fan by h av dpan bn h fan and h adhnd n on d n. Th va fond fo N. -. Th bndng ffn nay ang by dvdng h aon on n h fan by h av anga dpan bn boh d n of h fan and of h adhnd. Th fond va fo N.. Th oad anf gvn by h anaya od, ng h va of h Eq. fo,.% on ah bo. Moov, h appoah ao o a no aon h oa bhavo of a fan hogh h na dnaon of h oa ffn. VII. onon An anaya o-dnona od of hybd bod/bondd on n h baand ng-ap onfgaon dvopd and pnd n h pap. An a bhavo of h aa ad. Th od bad on h Fn En Mhod, o ha a pa Fn En BB n opd n od o a h bondd adhnd. Th aon of a ng-ap bondd on ng a BB n ho good agn h h G&R hoy. Moov, h n povd a, and on n a bay ffn. Th aon of fan opad d o h op bhavo of a fan n a on, and q an aa aon of h oa ffn. To appoah a ggd n od o dn h oa ffn. Th f appoah bad on pna and h ba hoy. Th ond on bad on a na h-dnona Fn En od, hh vadad hogh pna. Boh appoah povd oa ffn fo h anaya od, hh ao povd good agn h h pna, n of bo oad anf. Th od fy paa. A a, nfn d a anhd ay n od o dn h hana bhavo of h hybd on. In od o ha h oad bn h fan and h adhv ay, a fb adhv, n paa, ha o b d. onqny, h od pnd ay b gadd a an ffn, ay o and fa oo of dgn, hn aay abad. Th ay a nd ondaon o onn. Th f ay h dvopn of h baand BB n. Moov, h ngaon of a pfy a-pa and of a voa adhv bhavo n h BB n agnab. Th aon of h fan ha o b dd oo. Th ond ay h anh of fag, n od o vada h aby of h hybd on. Th hd ay h poaon of h na od, n od o ndand aay h hana bhavo of hybd onng. Appnd Th gdy a of h ba od h ap : K ba E I I I I I I I I I I I I I I I I Th ngaon onan a gvn by h Eq. o Eq. : Aan In of Aona and Aona

14 Aan In of Aona and Aona nh n n o nh oh n oh nh o nh n n nh h h h h h h nh oh nh oh nh nh nh nh Anodgn Th dy pfod n oopaon h AIRBU Too and an-naza, Fan. Th aho a gaf o h nda pan fo h adv and ppo. Rfn Ta, M. B., and Ronfd,. J., Anaya and Epna Invgaon of Bod Jon, NAA TN-,. Ro, R. D., An Ea op fo h oon of ha-lag Bod Jon Pob, NAA TN-,.

15 H, J., D a d abag pa boon o v avaan n an, AEROPATIALE Aéonaq O/Ab, Too, Fan npbhd. Unpbhd Rpo of h BOEING opoaon, Rnon WA. f, T., Dvopn of h Fa-af Dgn Fa of h D-, Daag Toan n Aaf, ATM TP, Aan oy fo Tng and Maa, Phadpha,, pp. -. Hh, H., Infn of Fan Fby on h Pdon of Load Tanf and Fag Lf fo Mp-Ro Jon, Fag n Mhanay Fand opo and Ma Jon, ATM TP, Aan oy fo Tng and Maa, Phadpha,, pp. -. op, D. A., and Lay, T.E., Inny Dnaon n Lap Jon h Mhana Fan, Pnd a AIAA, a Dyna, and Maa onfn and Ehb, AIAA -, - Ap, Aana GA. a,. O., Load Dbon n Mp Bo Tnon Jon, Jona of h a Dvon, Vo., No.,, pp. -. Von, O., D Nafvng n Zgbanphn Nvbndngn Konann Lahnqhnn, Lffahfohng, Vo.,, pp. -. Goand, M., and Rn, E., Th n nd Jon, Jona of Appd Mhan, Vo., No.,, pp. A- -. Ha-h, L. J., Adhv-Bondd Dob-Lap Jon, NAA R-,. Ha-h, L. J., Adhv-Bondd ng-lap Jon, NAA R-,. Aan, D. J., A Thoy fo Ea n Adhv Bondd Lap Jon, Innaona Jona of Mhan and Appd Maha, Vo.,, pp. -. Rnon, W. J., and Vnon, J. R., Anay of Adhvy Bondd Jon Bn Pan of opo Maa, Jona of Appd Mhan,, pp. -. Edogan, F., and Raan, M., Dbon n Bondd Jon, Jona of opo Maa, Vo.,, pp. -. apn, W.., and Bao R., To Fn En fo Modng h Adhv n Bondd onfgaon, Jona of Adhon, Vo., pp. -. Aa., and, F T., A Moop Poga fo Anay of Adhv-Bondd Jon, Innaona Jona of Adhon and Adhv, Vo., No.,, pp. -. Ada, R. D., and Ma, V., A hod fo h Anay of An-An Bondd Jon, Jona of Adhon, Vo.,, pp. -. Paon, E., ao, M., and H J., Hybd bod/bondd Jon Appd o Aona Pa: Anaya On- Dnona Mod of a ng-lap Jon, h Innaona onfn of Ingad Dgn and Manfang n Mhana Engnng, - May, Gnob, Fan o b pnd. Tn, M. J., Man, H.., W, R.., Fh dvopn and appaon of h ffn hod, n AGARDogaph : Ma Mhod of a Anay, d. by B. M. Fa dvb, Pgaon P, N Yo,, pp. -. MATLAB, v Pa, V.... Ra, Ag, Th MahWo, n. Ky, G., Jonng of abon Fb Rnfod Pa fo Rnfod Appaon, Ph. D. Daon, Dpan of Aonaa and Vh Engnng, Roya In of Thnoogy, oho, dn,. aov, R., Mhanay fand on: a ng of ng ovap on, FOI dh Dfn Rah Agny, nf Rpo, FOI-R E, IN -, Mah. Eqo, J., H, J., and Lahad, F., Modéaon pa één fn d n abag aéonaq n p an, Pnd a h ongè Fança d Méanq, Pap on D [Pap No. ], pb, Toy, Fan. AMEF, V..-., ah Gop. Aan In of Aona and Aona