Une méthode non incrémentale d'homogénéisation de structures élastomères : application aux composites unidirectionnels
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Une m´ethode non incr´ementale d’Homog´en´eisation de Structures Elastom`eres Application aux composites unidirectionnels M. Brieu, F. Devries, J. Erhel. N 3341 Janvier 1998 ` THEME 4. ISSN 0249-6399. apport de recherche.
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(72) TOOMt § $ 7' ) }s71 £t AMt"|~}± z t t|~tlÇ^M(z -Ç Ñ ± M~Az t§ $ ') ' \ # \ [A& 0 4 A R D , ( 0u» 0 ) @² Mt²ÀK|~tt AÁ~}{r s7tJK%Mu}{z{~±\zt )» Râ}´t MUM± tz{t t sut(tt Â=t(|~¡Kt|~Mtt q~~z{ÀK|~t t±}{|~z ÂA~Az ± t» Râ}2t(`z t tlMsÁ~t(|Mt Ns7± qM t tl±}{|~z |~% tØ`t tl~Á~} r(sut Mu}z{M±z{t DRF´|~$(z{t(JM t;At(s7A} ,t K9»~yKz{ÁKÑ=A» °²» KÆ t 2Ñ£¢¤¤ 9ò¥¤ =D OÊ» °²»M%qMt(z{KÁ´} Ñ´£A¢ 7 v 9½>¥ ;>=2ÀR|~z |~ }{t |~§%A±t Kt(KU|~-t(Mt(sxÁ~} t tlsu±;¿ qM t »,szA} ³ t(Mt(sxÁ~} t tjs7± qM tjt;`z Kt j} t,~}{|M,|~z}{z ±t S`S} t,su±;¿ qM t z{t t ØK´t Nt % DR´|~l z{t ?µl t|t(§?t(=t(s7~}{tA» @²t¨R=Ñ OÊ» °²»SqMt(z{KÁ} ÑJ\A¢ 7C 9ò¥>v =D OÊ»½°²»j%qMt z`Á} \Ñ㢤A 9½¥ 7H=Ü»°txs7± qM tt ¿ sut(t(K tN±| t t .~Á~}{r s7tM}{zM±\zt tNǸ> 3z{± Å z{¡t» j7§K t*}FÇ^M(z Mt }} tM9}z{M±z{t | AÁ~}{r s7tµÅzt(\Ñ2 t ts7± qM t*}{z{~±\z t t }} t;¿Ø z | ¡z{z§¨t 2³ |~ z{K t ± § \Ñÿt U± |~U} t~Á~} r(sut}{zM±\ z{t z{Mz Á~t(K| Ñ~|Az ²} ³ ± z{ t l± ± ±tµuM|A¡t\ | | ¡z{z§¨t txt(txM|~¡t }{}{t }|~z{Æt(l tN |MÀK| ³ µF K¡t ¨t ~t» °t²s7± qM t²|~~t(K|~Mt"}z{M±z{z ¨} ÁM} t t$} ³ t Mt sxÁA} t | ~Á~} r(sut» » EUt ¡Kz{tUAt$}{|~z'|~~tsu±(qM t$
(73) TÆ}{t ~ÁA} r s7t%tJ}z{M±z{± § .|AMtNAz tUt(F s7At%z{M(±(sut(`} t |Fq§¨t s7t KJ
(74) T q§ÀR|Mt7zM ± s7t K tq§¨t s7t Kxt $r $t z{ t(¡ `$} ³ |~~z±» °t zJt ~¨t t |~MtF± }|~z{ zM ± s7t KÅ } t t7~ÁA} r s7t"}{z{~±\zt » j· Kt;¿â§ z{tu}ÂÀK|M ¿ }{z{± tu}±(´Mt ± t zs7~}z (z{t(sut(K t7} M~Mt t | §zz ~Mt s7t K | q§¨t s7t K²q~z zâ» N|M ± ¡t } ~´MNz{ z2|AMt$s7± qM t t±}{|Az z ?± t(Kt t~±± t Kt K} ³ z{K±(* 4 lt |~Á~} tÑ´~|~z{ÀR| ³ t }} txM|~l´t(s7t 2³ |~Mt*§ 2³ ±(¡Kz{t( 2³ \¡z{Jµ±| tU t.~ÁA} r s7t tNǸ 3 z{M(± s7t K} t%t( 2³ |~t%§ t}{z{~±\z t(|sz{~zsx|~s } ³ t Mt sxÁA} t t U± ÀK|Mz{M» . . . . . . . . . . . ^[_^. . h o c
(75)
(76) hlc]okWcfj
(77) l c6e
(78) l j cfjWkajhmik
(79) l. t±| tu} t "~Á~}{r s7tM }z{M±z{t~± ± t KxM |~z}{z z{ 2³ |~Mts7± q~ t%Muz{~ ±(sut(KÅ}{t z{~zz } t s7t K,|~z}{z ±t M.}{t\ t |M |~t *± } ~}z{ÀR|Mtu¶ð,»S¼' t ¡t tÑ%£¢¢; 9½¥>C=ÜÑA» *»°¨§ Ñ£¢¤¢ 9 =ÜÑ ,»NJJz tÑ´£¢¤A79 v= º(»~'¡K tls7t t²t |~¡Ktt(tlsu±(qM t²z}2t%z{s´Å ` tMt(NÀK|~t" KÅ z{t(sut(K² |As7± q~ t }z{ÀR|MtN
(80) T} ³ t qMt qMtxz{%} t q§sM t ±(~} t s7t K :. #ÅÑSzx} t xq§sM t`ÅzKt #ÅÑ z (z @²®t7~tz z.
(81). . ÷ ö'÷^õ 54.
(82)
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(85) &'$($()* #,+-.#/0* #. ¢. M|M²}{}{M%t qMt qMt z{sx|~}Å~± s7t KU} ³ t(Mt(sxÁ~}{t t ²¡z Á~}{tt tqMt(q§K } tq§s # . # #Å»ÿ |~l t$Ǹ z{tÆss7t M t$§ ± st(²} ³ t =¿ t sÁ~} t D t( t(|At(Mt(sxÁ~} t } ³ t Mt sxÁA} t ²¼ tNq§sM z Ǹz K } t ±ÀR|§z M%M-}z{M±z{t Ñ } ³ t Mt sxÁA} t¼ tNq§sMz Ǹ z `} t± ÀK|Mz{M }{zM±\ z{t » ¼'Æ}{|Az | ~Á~} r(suttuz{|MtF } µÂ} ³ zKt t z{ tut t |= t(A¿ t sÁ~} t » M~ t ± t(sz{Mt( t t.}|~z{ SÑ ±(t(sz{Mtj|~ 2³ Á´ |~MtJ~~£`zÿ sFz )®~|~z{ t }{}{t ¿ðt(|~ $t(`t¼·t U¼·t sut(K 2³ Á~t ~zµ K¡t(¨t(Mt |-~`t |~ÑM}*}{|~z M~M} t S» |~,±\ }{z t } t z ?´±(t KtSz± z{M t%¼F|~ U¼t( t ²¼|A?¼F|~A´M ÀK|~tJ} ³ "A§z t?|~Mt~~£`zsFz
(86) )Ñh ³ tµ z{t?¡± z M§K,} t ±ÀR|§ z M }{z{~±\zt » MtN~~}z \ z ѵ ± M~~z\ÑM± t -SÑ´t(s7t Å tN M|Az{t
(87) ' - #\¡t )» Mt|~t²~~}z \ z ÑM±t -'ÑK´t(s7t Åt(M|Az{t t M|~z{t
(88) (Ñÿz{ su¨t t
(89) § - M¼» ¼ ³ } ¨zq~s7tt ~´± r ÀK|~t} z Å~ t lt(`t t t(Å (t zt » |~~}|M t ± Å z{} |~N} t z ?± t(Kt%Ǹsz{}} t 2³ ~~}z z{M -5 3 - t( } t%(zr t t K¡t(¨t(Mtµxz Ǹ z{tUM|M t K¡£MU}{t²} t t(|~N|}{z¡Kt t$ » ¼ t ¡t tÑ'£¢8¢ ; 9ò¥ C>=Ü» É ')( `«
(90) *,« ` Î ` « + R-Ë , + ! " $# % & " ¼ ³ t(As7t t$±ÀR|§ z MMz|§K}{t~Á~} r(sut ¶ðRº;Ñ?¶ ;RºlzMzjÀK|~t7 t }{|Az tlt } z M t* |~~} ¨t¶¸vKºU |~zµ ± M~~z{}{tlt(Mt(sxÁ~}{t ²¼Ót $¼·ss7t |~z ¶ 7º . ) ' ' E #/ 2 /. 7#0 # # #+(+ H A
(91) C 3 4 D # 57 &., A 73 #*
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(98) + * 3. . \¡t . ¶ð¢Rº. 899. Kt t(z{¡t s7t K ± M~Az %§$¶hº t $¶â¦º. D . G. '. I K M "# KMNX.. ' # G ' $&('*) '+$1 ' ). : 99;. A
(99) C D A
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(104) CBD .*-C 3 <*-CBD A
(105) ,nPQ4< <R 3 DSD ,B( E 8 <X 'd? BA
(106) CBD60 : . 0+ (a * <57, ; &48 # 0 A
(107) C 3 & (+ <* 57,. Í & ª` '^Ë£ª AË ' |~ ±(sFt( } tl~= t|MN-qMz{z{ ssutl~~£`zsFz uz{~zz } t%}x¿ }{|~z Á~t(K|Mtt ÐNKq~rt t?,t(zt? t |~Á§z{M Ñ ³ tJµ z{tJ}U}|~z{ Á~t(K|Mt"t(Æ Mz ±(ÅKN} t z ?± t(KNMz|§KN ssut±(}z ÀR|Mt Ñ~}z{M±z{tÑ | t(Mtt( z{s´K G ' IM» NMUÀR|Mt"t(t"}|~z{ Ñ~M±
(108) Ñ´ ~§¿ z t(KNµ¼» °~§z{ ` ѧz{}' ³ ¨z²t(M|Az{t t M|Az{t µ7§z{ t$}~Mz ¿ M t t »§°t(t" M|M(z{-tǸz{%t( t |A±(Åt t - M¼ U¼ ¶¸z± z{ K º qMzà t - & U¼ ¼ ¶¸z± z{ K 1hº qMzà »U~A}{z z{ - t$¼ M ²¼ ,|A ± M~~z{ . )Ñ'M|MqMz z M"|~MtF ~~}{z{\z zt ;¡t zÿ \}{ t ÑA ³ tUµ z{tl t(}{} t²ÀK|~t ' - & 7 # U|~j\¡~qMz zA t t%A~}{z{\z "\St }} t.tjt(`" 4 s7t s7t Kjz{s~} t 2³ |~zÿ }{z{z Ñ´t x |Az{~±\~s7zMµ t±|~}{$r z{Ǹz{K"ss7t M|M%}{tl¡t ~» ! " ! . . . . . . . . . . . . . . . ÷ ö'÷^õ 54.
(109)
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(114) ) : G 3 99 # 99 .4657,% "= ' G I 99; 9;. ' ) ¥=»U~A}{z z{ - t U¼ ~U¼ ,|A ±(t s7zMt |~x¼ t qMz z{$|~®± t(|~ z{ (Å=¿ ¨t K µ ²¼9|-´zK
(115) ÑA ³ t²µ z{tlt(}'ÀK|~t '- 7 ' K E 2$ / - E UzMz ¶h¥º A&5 ' ' E 2 K / - 9 E M~ t|~¡t(} tq§s )Ò=(z ±-µ §-¶h¥º(Ñjz}%tF } M± tzt t± | t} ³ t Mt sxÁ~}{t t~Á~} r(sut %|~z¡K i(+* 4& R 2 .( *-D3 * 57,4 ')(+*-, .( &. / 3#f D 899 <- ' 4 AUCBD/0 99 ' 6K AUCBD/0 : AUCBD/0 99 ' G K M- . 9 . . . . 9;. 8. A#.5 >D . ö ö6êTS. U. 7 7
(116). #. BC . A
(117) (. #. 0+ & (+ <* 57, 0 A
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(123) (+* # '+$, ' ) ' $& ' ) G i(+* 4& R A
(124) (+*-D .* <57,0'6( *-, ( #2 8 <"= ' ? BA
(125) CBD 4 J ' L I K N M = " BA
(126) CBD . . ; G O *- C 3 <*-CBDA
(127) ,PQ4! <RN 3 . DSD+,B( E A#.5 C A
(128) ( 1 # :. , |Al± | tx} t"~ÁA} r s7t"sz (Az ÀR|MtÑÿt(`~}z (z{M²u} z tx s7¿ t(sut(`»§S ± M~~zz{ Ñ~ ' K . . (. '. KMNX. M "= K MNX. . 'JG IK Râ}2¡Kz t(`U}{ . " M "# K M X. "# K A&5 ' K I UzMz' |Â~z¡t|s7z{ ~z ÀR|MtÑ~ z{±| t 899 ! X 'd? A
(129) CBD60 M "= K M X . K A
(130) CBD60 ' : 9. ¶£º. 9;. . '. . . 8 # . 3# D D 5 C AU( . 0. (+ <* 57, 0$A
(131) C 3 (a * <57,. \ ¡t # #Å»K ³ t ~U|~FAÁ~}{r s7tN£¡t |~MtA± Kz{Kt » jT|~z}{z KU} }z{M±z± txtxAÁ~}{r s7tÑÿ z{=¿ |Az{ } ± s7z{z{|Az{¡Kt ' K 4 . ' K
(132)
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(135) (. # #Kl}{|=¿. ÷ ö'÷^õ 54.
(136)
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(141) CB6D 0 0. (+ <* <57, 0$A
(142) C 3 ! (a * <5n,. ¶h¦º. 899 ! X '@? : ' " M X 99;
(143) 8 #. 0. .
(144). K. . . . A
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(146) C D. £. . . 0. 0 (+ <* 57, 0$AUC 3 . (+ <* <57,. ÁMt ¡t tM|~¡t\| ÀK|~t7} t~Á~} r(sut-¶\vKºt"|~ ~Á~}{r s7t}z{M±z{t» jÂ|~z{}z ` t"Å r(tÑÿ ± st}|~z{|AU}{tsKt t MN"= ;»M,MUzMz . ' 4#=E Z K Z #ÅÑ'
(147) T Z #lt"|~MtÇ^M z Á~z{Åzt*ÀR|Mt } ³ z ¨Mt(Å ~E M %}x|~z{t»MU}{
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(151) T D D C . ¶ º. ö ö6êTS. U. 7 7
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(156) ' &48 #. .
(157) . . E. \ E . . AUCBD60 AUCBD60. 0+ & (+ <* 57, 0 A
(158) C 3 9 (+ <* <57,. °tN~ÁA} r s7tN`NǸ(z{} t(sut(KU}{|AÁ~} t Ñÿz{~z'ÀR|Mt}{tAÁ~}{r s7ts7z{ ¿ ~z ÀR|Mt¶h¦ºÀR|~z t|~ÂAÁ~}{r s7t tØK´t$± } z ÀR|Mt\¡t $A± Kz{Kt» U~r } "± }|~z{ t t z ?´±(t K ~ÁA} r s7tJM|M% ~§z{M §z{t }¿ } t(sut(`,} t Sq§sMjsz (~z{ÀR|Mt » jt ?t ? tjqMs7~jMt t(K s~} r;¿ t(sut(` ~K|M$ÀR|Mt*} ÀR|Mtx} t q§sMsF ~z ÀR|Mt l} t*t(K» U±\ A¿ suz{M Ñ=M|~Nssut %t -sut |~t t±| t$}{tl~ÁA} r s7tlsu ~z ÀR|Mt» jÆt ?´t(\Ñ~§ ± M~~zz{- 4' K MNX
(159) K E P E U}{"t ·|~z}{z{K$} t$t(}z M t|~~}¨tut(`tF}{tx± qMt }} t"s7z{ ¿ ~z ÀR|Mtt(sF(Az ÀR|MtÑ~z}´¡Kz t(K E K K M X
(160) - ). ' P ) E |-t M t .
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(175) &'$($()* #,+-.#/0* # 899 ! "= 'd? MN"= K : ' 99; ' ILK MN"& 4 G O *- C 3 *-C DAU,PQ4! R 3 D. . ¶£¤º. . . h¦. . AUCBD AUCB D AUCB D D+,B( E. UMÀR|Mt} tq§ s7M t
(176) ±(ÅK ±\}{ |~}{± Ñ~t~Á~} r(sutt |-s4(sut²ØKt"ÀR|Mt¶h¦ºt N±}{|~z Mtt M§ t z (|~}{±» jN M~ Ñ\|~~t.Ç^z{ t~Á~} r(sutj±}{| Ñ\}{t q§ s7M'sz ~z{ÀK|~t'µ%} ³ z{±(Åz ´t(|~¡t(` 4 t\ } |A} ± s7s7tl|~z{ . . 899. . . '
(177) E : P. ¶£¢º. MNX
(178) - E MNX E P K E ( '(
(179) " $+
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(181) "& ('& + (,J'(
(182) "-% & _a` kal h okalnmpokacfj 6j l m
(183). °s7s7t M|M¡t M~ t%} t ¡z{Ñ} t%} (|~} t%}l± Mt 2³ |~MtN|M(|~tU s¿ ´z{tµNMz|§KSqK`t ± } z ÀR|Mt,´|A,|~~t }}{z{ z{z{ ~M±tÑM± t zt} ±}{|Az tAÁ~}{r s7tNsF(Az ÀR|Mtt(lsz ~z{ÀK|~t|~~} ± lÀR|~zSt |A¡t K ¨± M±(t( tN ~ t\}{ |~}{ z |§z{Ç^ » |~xA`± t µÆ tx± }|~z{M Ñ z}Jt *M± t z{t ´³ t ?´t |~t *|~Mt z ±(zÿ z §z}{t"Å `| ~z{¡t\| su(~z{ÀR|MtxÀR|Mtxsz ~z{ÀK|~t» U|M\¡M qMz zâÑssut$z{}St|M|Mt } t*} tǸzt"t Tsu± \Az ÀR|Mt t sz{}z t(|A-Kz{K|MÑ|~Mt z ±(z{z O§$}su±(qM t t± } ±(sut(K MA~z »SyKzJ}{t7q§ ¨t(sut(`"sF ¿ ~z ÀR|MttxÀR|Mt }{~ÀK|~tÑ,}{t ± Ç^suz{Mz{ |~z{tMtut `"§$~Å `tx|~ } ³ t Mt sxÁ~}{t t±(} ± s7t K t} z ±(z{z su ~z{ÀK|~t t}*|M(|~t» °s7s7t²} t ~Á~} r(sut s7z{ ~z ÀR|Mt ±(´t( t Kz{s~}z zt(sut(` |t Mt |~ ¨Å z t K t ± Ç^sFz su(~z{ÀR|MtÑ´}{t*\}{ |~}ðÑ2µF|~Mt*z± z{ ~M±tÑ t }*sFz{t t"z t |~ t"q§ |A tU± } ±(sut(K M~~z t} z ±(z{z -sF ¿ ~z ÀR|MtM± tzt } ±}{|Az t} ³ t Mt sxÁ~}{t t%~Á~} r(sut %t(}{}{|A}zt » 99;. . . '.
(184)
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variables d'ordre psychologique: soit f.amiliale ou personnelle, soit so- ciale, soit professionnelle, soit une combinaison de ces facteurs. Ce patient a récupéré
For the two coolest objects in Figure 3.6, HD 4539 and PG 1716+426, both at Ta < 27, 000 K, there is a good match between the predicted synthetic spectra and the FUSE data: the
lui inculquer le registre li'lquistioue, les l1abitudes alimen- taires et vestimentaires ainsi que le comportement des bour- geois de Québec. Pierrette Paul doit
La conciliation emploi-famille : des mesures à développer dans les milieux de travail Tableau 4 : Les dispositions favorisant la conciliation travailfamille dans les
Figure 2.4 Predicted (continuous lines) and observed values (filled circles: stands aged from trees with root collar; open circles: stands aged from trees without root collar)
Cette posture permet de dégager deux idées centrales : le poids des milieux professionnels locaux dans l’intermédiation et le transit des idées, modèles et pratiques
