CIIO~~M~I - Massachusetts Institute of Technologyradovinsky/papers/01.pdf · cnpoeI(TklpoRaHHor0 no...

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MEXAHNKA L'OJ7NMEPOB, 1975, 5, 822-828 K OllPE,Jl,EJIEHAK3 PAU,MOHAJIbHOB @OPMbl 6E3MOMEH8i'Mb1X ObQJI09EK BPAUEHIMP, M3TOTOBJIENHblX METOAOM HAMOTKW M3 BblCOKOMO,II,YJlbHblX MATEPMAJIOB On~oii ~3 I-1arr6onee 14ru-epecr-rbrs sa~as, no3r~1~11<arou~~s B cnnsri c B03h40iI<- IlOCTblO ynpaB.qnTL, aar-130~11on11eB MesalwrecKkis CBOI"ICTR n rcor1cTpyrzunns 113 I<O~~~O~IIUI~IOMI-I~IS narepplaLnoB, RnnncTcn onpeneneHbrc cservibr apn4trpona- HI.154 PI ~~UCIOI-~~~LHO~~ CIIO~~M~I 0 6 0 n o q e 1 < BP;IQ€!Hl.IR, 1 1 3 ~ 0 T O B j l e M H b I X MeTOAOM IraMoTKa. M~B~CTH~I~ peurewnn pacc~a~pasae~oii aanalrn octrooallrbr rnan- HLIM 06pa30~ ria rrmo~esas ciceTsaroro a~an1~3a>>l,~, ~orna XOHCT~~I<UMFI paCCMaTP1,IBaeTCR KaR HMTRHaR CEICTeMa. B ItaYeCTBe KpPlTepFln 0IITMMa.Ab- HOCTM I7P1,II-IMMaeTCR COBnaAeHMe HMT~~; C T p a e l < T O ~ P I H M P i MaKCH&laJlbHMS rJIaBFlhTX ~anpn>tte1-r1,1~, a 3aKOH YI<JIBAI<B nPIIrII.IMaeTC51 reOAe3IfseCKJ3M. B pa- 60~e~ nono61- an sana~a peuraercR c yxleronr cnnsyrorucro. ~~M~TI,IM, ZITO B nocnenkrenf cnysae anTopon4 r-te n p o ~ e ~ e i - J a1~1a.n13s IInnpn>#eHr-roro COCTORIIIIR a nonyqeHHaR I<oHcTpyrzurrn OILI~~O~HO I-I~OB~H~ ~~BI-Io~~o~I-Io~~. Haxe npennarae-rcn cnoco6 nonyserwt paBnonposHLrx 06onoqe1< Rpa- ueFIuR npn OC~CM~IM~T~MZIHO~~ ~arpy31<e. P~CCMOTPHM OCeCBMMeTPUYI-IYFO A~@OPM~UIIIO OGO.AO~I<~I BpaUleHPJR, Ha- MOT~HHO~~ nOA Yr-TOM cp(r) K 06pa3ymurei (1113~. l). ,4n~ KOblnO3MUHOI4HLIS MarepManoB, y r < o ~ o p b r xo2n"'2>snP"2, onTi.IMa.nbMoe r-ranpnn.rre~kre BOJOKOH c0BnaAae-r c HanpaBneHnnMn rnaBHbIs ~anp~>r<err~+fi". ~ O ~ T O M ~ , npennonaran OTCYTCTB1,Ie CABMrOB MelKAY tIMTRMIl (s=O), 3anllLUeM CBR3L k,Je>KAy M~~~IlAIlO- I-I~.ALM~I~.I M KOJI~U~BLIM YCII~TIIIRMH TI PI T2 B 060~10ZI~e c npononb11b1~ M nonepewtrM ~-ranp~x<e~n~~a B neaTe: TI = h (GI cos2 cpf oz sin2 rp) ; Tp = =I2 (ol sin2 cp+02 cos2 q), rne h. - nepeMeHHan ~onur~-i~ra 06onor1kt~i; o,, 02, s - r-ranpn>l<er-rMR B neeTe, nefic~syrour~re cooTBeTcTneHHo ~ n o j r b ~rr~er"~ oc- Honbr, nonepeK I-IHT~W ocr-IOBLT, M r<acaTenbHbre Ira- npnxeHnR B cnoe. 3a~e~nn4, YTO, T ~ K KaI< pac- CRlaTpMBaeMaR o6onos~a FlBJIReTCR CTaTHseCI<M 0npe~eJIki~0~1, yCFiJIH5I TI PI T2 HaSOAnTCR He3aB1.1- cn~o OT xapa~~epnc~n~ ~a~epnana. C npyroii CTOPOHLT, CBFI~~ M e x n y ~epan13o~anb~oE rr KonL- ue~ofi ge@op~auFi~ivki B 060310we M e~ c fie- ~ O ~ M ~ ~ M R M I I BAOJIL II nOnepeK HFIT~~ &I Pi E2 Fi CABrirOM Me>r<Ay FIHTnMN elg ZaeTCR C ~ O ~ M ~ A ~ M I ~ 7; EI =ex cos2 (F-I- eR sin2 a; F.?= E~ sin' cpf E~ cos2 (p: E12= (E~- E?) sill 2~p. B nOCJIenAMS BLIPaX<eIIIIRS yLIHTblBaeTCR, YTO CTpyI<TyPa oGono~~r<r~ RBJIneTCFi ca~~e~pusrrofi, n npkrr-rFiiMaeTcn, YTO B c e CJTOA ne- PUC. I. @O~MM~YIOTCR 6e3 npOCKa.flh3MBaNMR. He~pynl-ro

Transcript of CIIO~~M~I - Massachusetts Institute of Technologyradovinsky/papers/01.pdf · cnpoeI(TklpoRaHHor0 no...

M E X A H N K A L'OJ7NMEPOB, 1975, 5, 822-828

K OllPE,Jl,EJIEHAK3 PAU,MOHAJIbHOB @OPMbl 6E3MOMEH8i'Mb1X O b Q J I 0 9 E K BPAUEHIMP,

M3TOTOBJIENHblX METOAOM HAMOTKW M3 BblCOKOMO,II,YJlbHblX MATEPMAJIOB

O n ~ o i i ~3 I-1arr6onee 14ru -epec r - rb r s s a ~ a s , no3r~1~11<arou~~s B cnnsri c B03h40 i I< -

I lOCTblO y n p a B . q n T L , aar-130~11on11eB M e s a l w r e c K k i s CBOI"ICTR n r c o r 1 c T p y r z u n n s

113 I < O ~ ~ ~ O ~ I I U I ~ I O M I - I ~ I S n a r e p p l a L n o B , R n n n c T c n o n p e n e n e H b r c c s e r v i b r a p n 4 t r p o n a -

HI.154 PI ~ ~ U C I O I - ~ ~ ~ L H O ~ ~ C I I O ~ ~ M ~ I 0 6 0 n o q e 1 < BP;IQ€!Hl.IR, 1 1 3 ~ 0 T O B j l e M H b I X MeTOAOM

I r a M o T K a . M ~ B ~ C T H ~ I ~ peurewnn p a c c ~ a ~ p a s a e ~ o i i aanalrn o c t r o o a l l r b r r n a n - HLIM 0 6 p a 3 0 ~ r i a r rmo~esas c i c e T s a r o r o a ~ a n 1 ~ 3 a > > l , ~ , ~ o r n a X O H C T ~ ~ I < U M F I p a C C M a T P 1 , I B a e T C R K a R HMTRHaR CEICTeMa. B I t a Y e C T B e K p P l T e p F l n 0 I ITMMa.Ab-

HOCTM I7P1,II-IMMaeTCR C O B n a A e H M e H M T ~ ~ ; C T p a e l < T O ~ P I H M P i M a K C H & l a J l b H M S

rJIaBFlhTX ~ a n p n > t t e 1 - r 1 , 1 ~ , a 3 a K O H YI<JIBAI<B nPIIr I I . IMaeTC51 r e O A e 3 I f s e C K J 3 M . B pa- 6 0 ~ e ~ nono61- an s a n a ~ a p e u r a e r c R c y x l e r o n r cnnsyrorucro. ~ ~ M ~ T I , I M , ZITO B n o c n e n k r e n f c n y s a e a n T o p o n 4 r-te n p o ~ e ~ e i - J a1~1a .n13s I I n n p n > # e H r - r o r o COCTORIIIIR

a n o n y q e H H a R I < o H c T p y r z u r r n O I L I ~ ~ O ~ H O I - I ~ O B ~ H ~ ~ ~ B I - I o ~ ~ o ~ I - I o ~ ~ . H a x e npennarae-rcn cnoco6 n o n y s e r w t p a B n o n p o s H L r x 0 6 o n o q e 1 < R p a -

u e F I u R npn O C ~ C M ~ I M ~ T ~ M Z I H O ~ ~ ~ a r p y 3 1 < e . P~CCMOTPHM OCeCBMMeTPUYI-IYFO A ~ @ O P M ~ U I I I O O G O . A O ~ I < ~ I B p a U l e H P J R , H a -

M O T ~ H H O ~ ~ n O A Yr-TOM cp(r) K 06pa3ymurei (1113~. l ) . , 4 n ~ KOblnO3MUHOI4HLIS

M a r e p M a n o B , y r < o ~ o p b r x o2n"'2>snP"2, o n T i . I M a . n b M o e r - r a n p n n . r r e ~ k r e BOJOKOH

c 0 B n a A a e - r c H a n p a B n e H n n M n r n a B H b I s ~ a n p ~ > r < e r r ~ + f i " . ~ O ~ T O M ~ , npennonaran OTCYTCTB1,Ie CABMrOB M e l K A Y tIMTRMIl ( s = O ) , 3 a n l l L U e M C B R 3 L k , J e>KAy M ~ ~ ~ I l A I l O - I - I ~ . A L M ~ I ~ . I M K O J I ~ U ~ B L I M Y C I I ~ T I I I R M H T I PI T2 B 0 6 0 ~ 1 0 Z I ~ e c n p o n o n b 1 1 b 1 ~ M n o n e p e w t r M ~ - r a n p ~ x < e ~ n ~ ~ a B n e a T e : TI = h ( G I cos2 cpf oz sin2 rp) ; T p = = I 2 (ol sin2 cp+02 cos2 q), rne h. - n e p e M e H H a n ~ o n u r ~ - i ~ r a 0 6 o n o r 1 k t ~ i ; o, , 0 2 , s - r-ranpn>l<er-rMR B n e e T e , nefic~syrour~re c o o T B e T c T n e H H o ~ n o j r b ~ r r ~ e r " ~ oc-

H o n b r , n o n e p e K I - I H T ~ W ocr-IOBLT, M r < a c a T e n b H b r e I r a - n p n x e H n R B cnoe. 3 a ~ e ~ n n 4 , YTO, T ~ K K a I < pac- C R l a T p M B a e M a R o 6 o n o s ~ a FlBJIReTCR C T a T H s e C I < M

0 n p e ~ e J I k i ~ 0 ~ 1 , yCFiJIH5I TI PI T 2 H a S O A n T C R He3aB1.1-

c n ~ o OT x a p a ~ ~ e p n c ~ n ~ ~ a ~ e p n a n a . C npyroii CTOPOHLT, C B F I ~ ~ M e x n y ~ e p a n 1 3 o ~ a n b ~ o E rr K o n L -

u e ~ o f i g e @ o p ~ a u F i ~ i v k i B 060310we M e~ c fie- ~ O ~ M ~ ~ M R M I I BAOJIL II n O n e p e K H F I T ~ ~ & I Pi E2 Fi

C A B r i r O M Me>r<Ay FIHTnMN e lg Z a e T C R C ~ O ~ M ~ A ~ M I ~

7; E I =ex cos2 (F-I- eR sin2 a; F.?= E~ sin' c p f E~ cos2 (p: E12= ( E ~ - E?) sill 2~p. B n O C J I e n A M S B L I P a X < e I I I I R S y L I H T b l B a e T C R , YTO C T p y I < T y P a oGono~~r<r~ RBJIneTCFi

c a ~ ~ e ~ p u s r r o f i , n npkrr- rFi iMaeTcn, YTO B c e CJTOA ne- PUC. I. @ O ~ M M ~ Y I O T C R 6e3 n p O C K a . f l h 3 M B a N M R . H e ~ p y n l - r o

Torna, ~ . ~ c n o ~ r ~ , s y n s a r < o ~ T y ~ a ol= 1 k2 ( & I + ~ 2 ~ 2 ) ; 0 2 = -

1 -V1W2 I -V1.V2 (&2+1'1lEl) ,

n o n y 9 e ~ e b l e @ 0 p ~ y ~ b l C O B n a A a f O T C ~ p H B e n e H F l b 1 M H B'. H ~ T ~ Y ~ H O B M n e T b

Pi3 BbTPaX<eIiPiR ( 2 ) , 9 T O n J I R 0lITWMZI.lIbMbIX 0 6 0 n o ~ e ~ OTMOUIeHEle H a n p R X e -

(52 E2(l +\'I) H l l h B .TleHTe - = k SfJlJIReTCfl IlOCTORliHbIM M O n p e A e J I R e T C R

G I E 1 ( 1 + ~ 2 ) TOJlLKO C B O ~ ~ C T B ~ ~ I I ? M a T e p H a , r I L l . C ~ p y r 0 c 1 CTOpOlIbI , O C O ~ ~ H H O C T ~ MHOrPlX

KOMIJ03114EIOF1HblX I L l ~ T ~ ~ l l a J i O B COXPal - IRTb J I M N ~ ~ H o c T ~ API.laI'JlLlMMb1 (7-& I l p H

P a C T R X e H B M BnJIOTI-, A 0 p a 3 p y u T e H H f l C O X p a H I I T 3 T 0 OTHOLUeHHe A J R O ~ O J I O ' I ~ K C nOJIOXNTeJlllbAbIMM 3 t I a 4 e H M R M M ~ ~ ~ M O M ~ I ~ T H ~ I X ~ C E I J I H ~ I BI l J IOTb A 0 AOCTH-

X e H M R OnHMhl I13 ~ a n l ) f l } K e H ~ f i (51 MJIM 0 2 er0 M a K C H M a J b H O r O 3 H a 4 e H H R - npeaena n p o L l e o c T I r .

~ < O ~ $ @ N ~ M ~ F I T O R k I! k l n03BOJIPIT C A e J I a T b H e l < O T O p b I e BbIBOAbI. A m TEIIIOB

I < O I M ~ I O ~ M ~ H $ I , y I < O T O ~ ~ I S k l < k , p a c T p c c r < m a w r e c ~ n s y m q e r o npomoiiae~ pamrue pa3pb1~a HMTM, n n R 6onee x s e c T K M x i v a T e p H a n o B c k l > k pa3pyme- H H e KOHCTPYKUEIM ~ P O M ~ O ~ ~ A ~ T 38 CZIeT p a 3 p b I B a H H T ~ ~ lTPN H e p a C T p e C K a B -

m e h . r c R c s ~ 3 y r o u e ~ . ~ O ~ T O M Y , ecnM AJIR M a T e p I j a n o B T a n a c T e r < n o n n a c T m o B

n p m e H e H M e < c c c T q a T o r o a e a n l < a a > > R B n R e T c s B n o n H e O ~ O C H O B ~ H H ~ I M , TO AJIFI B b I C O K O i v l O ~ ~ J I b H b l X BOJIOKOtI n p e A C T a B J I e H H e KOHCTPjlI(UklM B B M n e H H T R H O ~ ~

CI lCTeMbl M e M e e O n p a B n a H O . K p o h a e TOTO & J H paCCMFlTpPIBaeMbIX KOI1CTP)IK-

UIIG M o m e T G ~ I T L n o c T a B n e H a s a ~ a s a C O ~ A ~ H N ~ M a T e p M a n a c x a p a K T e p s c T H -

K8MM k l = k . ~ ~ M ~ T N M T a K X e , ZIT0 €?CAM 0 6 0 ~ 1 0 q ~ a RBJIFIeTCR COCYAOM A a B J I e -

HMR, T O 0 6 p a 3 0 ~ a ~ M e ee N 3 B b l C O K O M O ~ y J I b H b I X DOu'IOKOH AOBOJIbHO IIpOCTO

p a s p e r u a e ~ n p o 6 n e ~ y r e p ~ e ~ m a u ~ ~ . T ~ K N M 0 6 p a 3 0 ~ , AJFI B b I C O K O M O A y ~ b I - I b l X BOJIOKOH @ O P M B O ~ O ~ O ' - I K M ~ Y A ~ T

O I l p e f l e J I R T b C R J J p a R H e H I ? e M ( I ) , K O T O p O e MOHteT 6 b 1 ~ b I l ] l e 0 6 l ) a 3 0 ~ a H 0

Bonpoc n o n y 9 e H M R ~ ~ B I - ~ o ~ ~ o Z I H O ~ ~ KOHCTPYKqMM P e L U a e T C R B ~ I ~ O P O M COOT-

B e T C T B y f O U e r O 3 a ~ o ~ a y I < n a n K M HPITli H a nOBepXHOCTPi . Ann o 6 o n o s e ~ , C n p O - e K T M P O B a H H b I X IlO M e T o n y < < C e T Y a T O r O aF la J IM3a>> , TRKMM 3 8 K O H O M flJ3JIReTCR I ' C O n e 3 H ' l e C K a R I I a M O T K a . A n R 0 6 o n o ~ e l < , I I p O e K T M p y l O ~ M X C R C YEleTOM CBR-

3 y ~ I U e r 0 , ~a1{0l"I 3 a K O H n p E i B e A e H HMIKe. B b l p a 3 M ~ H a I I p R X < e H H R B . n e H T e Pi3

y p a s r J e I l r j R (2) : -

824 B. A. E y t t a ~ o s , A. Jl. Padosiittc~1~fi

1 T~ = ( R b sin an+ 1 / ~ r d r )-,

b

rfie s in ol,= - Y' ; y ( r ) - $ o p ~ a M e p M n M a H a . M3 y p a ~ ~ e r - l u n n a n - [I + (y') 2]''~

.JIaCa I4 Y P a B H C H M R (6) IIOJlyqFIM COOTI-IOUIeHHC

T2 P ' - = r { -------- - T 1

" } . Y '[ I + (Y ') 21"2

(7)

Rb sin ao+ [ p r d r

01 nf Y' k+ (1-k) cos2 (p Rb sin oo+ S p r d r = - [-I;L-] {----I[ 0 [ l -t- (g ' ) 21"' cos cp

dcp sin cp k - (1 -1z) cos2 (p y ---- -- - - - = 1. dr cos rp 1 - ( 1 - k ) cos2 rf (9)

~ ~ M ~ T M R I , q T O n p I 1 H e p a 6 0 ~ a l O U e M C B R 3 Y I O U e M ( k - - 0 ) 3 a K O H Y K J I a A K U n p M - o t 5 p e ~ a e ~ BMA reone3asec~oh nmaM r sin cp=const. M ~ ~ ~ X O A I ~ M O C T ~ secw npouecc I r a n l o T K M no S ~ K O H Y , o T n 1 1 g I m M y OT r e o ~ e 3 ~ q e c ~ o r 0 , BHOCHT H ~ K O T O - p b I e A o n o n H M T e n L H b I e O r p a H M s e H I T r t . T ~ K , a3 (10) C f i e A y e T , LIT0 H a M O T K a TIOA

X yI'JrOM cp= - H e B 0 3 M O X H a , T a K I < a K n p M 3 T O M r+OO. K P O M ~ T O r O , M 3 (9) CJle-

2 k n y e T , TO nptr s ~ a s e ~ u k ~ yma, o n p e n e n R e M o M 113 ycnosm cos2rpm=-

d rp I - k '

n P O M 3 B O A H a R - +W, Y T 0 A a e T MMHEIMaJIbHO B ~ ~ M O X H M T ? p a A I 1 y C I JaMOTKr3 dr

H ~ K O H ~ U , H e K O T O p b I e O r P a H B s e H B R H a J I a r a e T B e J I l l r I B H a M a K C M M a n b H O B 0 3 -

MOX<HOTO OTKJIOHeHHR O T T ~ o A ~ ~ B ~ ~ c I < o ~ JIMHBB H a n O B e P X H O C T B , O I I p e A e J I R e -

Mafl K O ~ @ @ I I U H ~ H T O M T P e H M R n p B H a M O T K e .

T ~ K M M o b p a a o ~ , B COOTBeTCTBHM C I I P E ~ H R T O ~ P ~ C ~ ~ T H O ~ MOAeJIbKJ H O T M e -

rIeMHb1MA B b I U I e O r P a H H ~ e H H R M N ( P O P M ~ o F I T M M ~ J I ~ I - I o ~ p a B ~ o n p o r l F I 0 f i 060- J I O q K N B p B U e H k I R O n p e A e j I H T C R COBMeCTHbIM p e l l e H M e M (3) ti (10). B e n a r l r ~ ~ a n p e n e n b ~ o i i HaTPY3I<M M O X e T 6 b 1 ~ b H a g ~ e H a B 3 (2) n p t r AOCTMXeHHN: O A H O ~ 113 BeJlMqZIM 01 BJIM 0 2 C B O e r O I I p e A e J l b H O r O 3Har IeHEIR .

B K a s e c T s e n p m e p a p a c c M o T p r m o n p e n e n e a l r e p a w i o ~ a n b ~ o f i @ O P M ~ I 6 a n n o ~ a A a B J I e H B R , O ~ ~ ~ ~ O B ~ H H O ~ O H ~ M O T I < O ~ ~ B ~ I C O K O M O A Y J ? ~ H ~ I M H BOJIOK- H a M B . B P a M K a X ~ ~ ~ M O M ~ H T H O ~ ~ T e O P N P i 0 6 0 ~ 1 0 9 e K M ~ P B ~ ~ B o H ~ J I ~ H o ~ N KOJIb-

PRP uesoe ycnnnn onpeaerrnrorcn n b I p a x e H w m u T I = -; T*=&[ 2- $1, 2 2

K BMflY:

r y " 1 - ( 1 - k ) cos2 rp - 2 - ---- y'[1+ (y')'] - / :+( I -k) cos" '

( 1 1 )

B b ~ p a n c a n n~~$@epe~uwa .n dr t r 3 (9), T. e. n p t l e e M a n ~ ~ K O H y r t n a A K l I c o r n a c H o

( lo ) , n o n y s n M : I z - ( 1 - k ) c o s 2 c p d c o s c p

dr= - r 1 - ( I - k ) c o s 2 r p coscp

Torna y p a n u e H M e ( 1 1 ) n p m o A w r c R K y p a ~ ~ e l - I B H ) c p a 3 n e n ~ m m u ~ ~ c ~ nepe- M e H H h l M I I

dr k - ( l - l z ) c o s 2 ( p dcoscp y ' -2-+ Y'[I + ( Y ' ) ~ ] r k+( l -k)cos2cp coscp

w ero n e p s b r i i k 1 H T e r p a . n m e e T BEIA:

M H T W ~ ~ J I (13) RBn5IeTCR H ~ C O ~ C T B ~ H H ~ I M B OKpeCTI-IOCTA r = U , I30 ero cxo- AMMOCTb J I e r I<O M O X e T 6 b 1 ~ b A O K a 3 a H a . ~ P O M ~ B O A R 3a M e H y C O r J a C H O (14) , nO.7yqbiM B OI<PeCTIIOCTM 0~060fi TOqI<N

cos cp 3 ~ e c b F = 1 - -.

COS I(aK 6 b 1 n o yXd OTMeLIeHO B b l U e , 0TI tnOHeHH. l e I3MTM O T ~ ~ O A ~ ~ P I ~ I ~ C I < O ~ JIH-

HMN RIO)KeT 6 b 1 ~ b I I p O B e A e H O B n ] l e A e J r a X KOl- lyCa T p e H P I R 1.13 YCJIOBMR TOTO, 9 ~ 0 6 b l I lMTb H e COCKaLTIb3bIBaJla C nOBePXHOCTEI 6 a n n o ~ a n p H I I a M O T K e . T ~ H - r e f l c yrna reonesa.rec~<oro o T r < n o H e w i F t (yma n ~ e ~ n y H o p M a n b m K noseps-

Rn HOCTII 11 H O p M a J b K ) I< uIIIHAI.l H a ~ O B ~ P S H O C T I ~ ) t g 0 = - 1

(me - H o p - R ,-

cl (iJ --r cos rp+sin (p d,. t g 0 = - ----

ry" cos' cp --ty'sin2cp

1 + ( J ' ) ?

l l p e n e n b ~ b r ~ ~ H ~ ~ ~ H I I ~ I V I T a r j r e l J c a yrna reone31~1secr<oro o T l < n o r r e H H n 6 y n e ~ : I tg Onpenl =P, r A e 0 - B e n I J s M H a I < O ~ @ @ M U I , I ~ H T ~ T p e r j u R . nocne Hec . I Ion<HbIx ,

HO r p O M 0 3 A K E I X n p e 0 6 p a 3 0 ~ a ~ l 4 f i (15) M O X H O nOJIYZIHTb C B R 3 b B 0 3 M O X H b I X yrnos H a h q o T r m c ero ~ I ~ ~ Y C H F I ~ M I-la s r < s a T o p e npu

me Cos2(l-2")q,

L (cp) = - [k + ( 1 - lz) cos2 rpI2[1 - ( 1 - k ) cos2 cp]*(I-k)

'

P e I I I e H I 4 e H e p a B e H C T B a - n I , l a n a 3 o H B 0 3 M O K M b I X yr.JlOB H a M O T K H B 3aBHCI.I - MOCTB OT yrna H a M o T I t r ? H a 3 ~ ~ a ~ o p e cp, n p r ? k=0,1 H P=0,5, 1 PIC. 2 ) . 3 a - n a s a n c b , H a n p r m e p , ( p a = 12" a n p 0 B O n R n p R i v b I e no n e p e c e s e H u R c rpaau- U a M U ~ ~ a n a s o ~ a , n o n y s a e M , s ~ o H a M o T K a B O B M O I K H ~ AO yrna rp=36". 3 a - MeTMM, YTO A I , I a n a 3 0 H MOB<eT 6 b 1 ~ b CYIUeCTBeHNO p a C U I M p e H y B e n u Z I e I + F I e M I < O ~ @ @ H L I M ~ H T ~ T p e H H R , H a n P M M e P y B e J M Y e H M e M CTeI IeHM n O J H M e p M 3 a U M M c~x3ymrrlero B n e H T e n p I i H a b r o T l z e .

A p y r ~ r ~ O r p a H M 9 e H l l e h l n p k i F I a M O T K e R B n R e T C R H e B 0 3 M O X H O C T b o6ecne- X

g e H N R DPEIHRTbIM 3a I<ONObI HaMOTI<EI B 0 3 B p a T a HUTM H a H O B ~ I ~ UMICJI (P=-- 2

r sin cp=ro. (16)

n a p a ~ e ~ p b ~ nepexona ( 0 6 0 3 ~ a ~ e ~ ~ b r e I i H n e K c o M <cn>>) , 06ecnes~rsamm11e ' ~ ~ l ( C l l h l a J I b H 0 R03MO1BBOC l l C ~ O J b 3 0 B B l l l I ~ 3 B K O H B )'iMLinKH H l l T l l (14), CTPO- I ,

I nTCR B (~)YHKUIII.I OTHOCIITCJIbHOTO PaAPIyCL? n O J I I O C H O r 0 OTBePCTMFI

L ‘ I-k - ro cosl' cp,[l - ( I - 1:) COS"~] - -- sin qn, (1 I -k -

COS" qn[ l - ( 1 - k ) COS'? q n ] 2

1'0 H a s ~ r r a n c nepexon~oro panr~yca r,= --- , +opwa 06o.aosr~r-r onpenenn- s in q,

clr y, ( r ) = -+C3.

' 2 - ( 1 - k ) r 0 2 ] ~ + ~ < (17)

r6 1

3 n e c b nOCTOzIHI l aR C3 OnPeAeJIR€!TCR PI3 YCJlOBNR H e n p e p b l B H O C T N C ~ O P M ~ I M e - p M A H a I I a , a C p - I13 YCJIOBNR HelTpe]IblBHOCTkI ee I I ~ o H ~ B o A H o ~ :

P e U I e H I 1 e no (17) hfOX<eT 6 b 1 ~ b YTOYHeHO B OKPeCTHOCTI i nOJIIOCHOT0 O T B e p -

CTNFI no M ~ T O A H K ~ ' , ecna n M e e T c R ~ e ~ a n n ~ l ~ e c ~ ~ i i @ n a ~ e u . r Ipo~ep04~brCi p a c q e T H a n p R x e n H o r o COCTORHMR B 3 o ~ e I - ~ O A ~ ~ M L I ~ C I < O C I H a -

MOTKH n O K a 3 b l B a e T , YTO n J I R 0 n ~ l i ~ a J I b ~ 0 8 060- n o s K n H a n p R x e H k r R n a a a r o T c y ~ e ~ ~ r u e ~ ~ e ~ pa- neyca, T. e. obonosria, n p o s k r a R n p M r=r,, 6 ) ' ~ e T

70 ~ Z ~ B ~ A O M O ~ ~ O Y H O ~ n p r l ro<r<rn. H e o 6 x o n a ~ b i e npI1 n p O e K T H p O B a H M P 1 B e n H -

60 YHNbI M a C C b I ( G ) M 0 6 3 e ~ a ( V ) O ~ O . ~ I O Y K M MOI'YT

.1

f 6 b l T b O n p e A e J I e F I b I no EISBeCTHbIbI 3aBMC1,IMO-

CTRM 50

4 0

30

20

10

828 B: A. 6 y n a ~ o o , A. JI. Padoout~c~uu"

1 --- d r --G=ynfSl=ynf 2 / Y ~ + ( y f ) 2 - .

1'0 cos y '

3 ~ e c b y - n n o ~ ~ o c ~ b ~ a ~ e p k i a n a ; Sf - 0 6 q a s n n m a HHTH H a nosepx- MOCTN. B e n ~ s w ~ ~ a nf M O X e T 6 b 1 ~ b H ~ G - n e H a 113 YCJIOBBR npOYHOCTI1 O~OJIOYI<I . I H a 3 K B a T O p e

I-Ia ~ R C . 4 n o ~ a 3 a ~ b 1 $ O ~ M ~ I ~ ~ J I J I O H O B n a s n e 1 - 1 1 1 ~ , n o c T p o e a l m e c HC- n O J I b 3 0 B a H I l e M HOBOI'O 3 a K O H a HaMOTKM 1.1 y Y e T a C B R 3 y m Q e r O I lpM k=0 ,1 ( K ~ M B ~ R I ) r e o ~ e 3 1 1 ~ e c ~ o f i y e n a A r < u ( K ~ A B ~ R 2) M reone311~ec~oro Gannor-ra, c n p o e I ( T k l p o R a H H o r 0 no r ~ n o ~ e 3 a ~ c c c e T s a T o r o a ~ a n k r 3 a > > ( ~ p r j s a n 3) A n n na-

B ~ I B O A ~ I . 1. I ' l o ~ z a s a ~ o , TITO A n n o n T m { a n b H 1 = I x o 6 o n o s e ~ B p a u e H r r R , PIJ-

rOTOBJIeHHbIX MeTOAOM HaMOTKI? M3 BbICOI<OMOAYJIbHbIX M a T e p M a J I O B , paspy- l r r e H N e HHTM M O X e T TIPOIlCXOANTb P a N b L U e p a C T p e C K H B a H I 1 R C B R 3 y I O Q e r 0 , YTO A e J I a e T BO3MOXI-IbIM C 0 3 J a I l E l e ~ ~ J I ~ o H o B AaBJIeHElR r e P M e T M Y H b 1 X B n J I O T b KO '

p a 3 p y r u e ~ ~ n . 2. npenno>~ee 3a~or-r y K n a A K r I HI IT^^'^, o ~ n t r u a m q ~ i i c ~ OT ~ ~ O A ~ ~ I I Y ~ C K O ~ O ,

o b e c n e s r i ~ a ~ o q n i i p a B H O n P O q H O C T b O n T l l M a n b H b l S 0 6 0 , n o ~ e 1 < .

ro p a M e T p a -=0,2. P e 3 y J I b ~ a T b I

1 . E/ lna~beac~uu' A. H., Bacunbea B. B. Ilposrloc~b IurnrrHnpr.fqeclcMs o6onorlee 1J3 ap- MlTpOBaFfAblX MaTepHaJIOB. M., 1972.

2. Yepe8ayh-~lI C. 6. 0 npOH3BOJIbHblX HllTeBblX 06onos~ax , kIarpy;KeHHLlX naB.Ue- I-IUeM. - B KH.: ~ P O ' I H O C T ~ If AtltlaMMKa aBHa&I?OHHblX nI3llra~eneB. Bbln. 4. M., 1966.

3. Jong Th. de. A general theory of isotensoid pressure vessels. - 111: Contrib. Theory Aircraft Struct. Deflt, 1972, 11. 207-227.

4. Brar~drnnier H . E. Optimum filament orientation criteria. - ctJ. Cornp. hlaterials,), 1970, u. 4.

- G ynfn

1.37 1,30 I ,32

- V .- na3

0,54 0,49 0,14

a p a C Y e T a OTHOCIITeJIbHbIX 063- G n n n o ~ 1 -sr- e M a I3 MaCCbI n O K a 3 a H b I B ~ a 6 -

pat. n ~ ~ q e . 3 a n q e ~ r i ~ , YTO B ~ O C -

G - v - Y On P

P

2,53 2,65 3,OO

n e n H e M c j l y q a e M a c c a y B e n r 4 - I Y M T C R 3a C Y ~ T r e p ~ e ~ m a - 2 UIIM. 3

1,37 1,28 1,3O