Schema volumes finis : Estimation d’erreur a posteriori hierarchique par elements finis mixtes. Resolution de problemes d’elasticite non-linearie Hicham Souhail To cite this version: Hicham Souhail. Schema volumes finis : Estimation d’erreur a posteriori hierarchique par elements finis mixtes. Resolution de problemes d’elasticite non-linearie. Mathématiques [math]. Ecole Centrale de Lyon, 2004. Français. �tel-00005418� HAL Id: tel-00005418 https://tel.archives-ouvertes.fr/tel-00005418 Submitted on 22 Mar 2004 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. 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P(K) + P(K) 1 0 , ºµ ß * Z? * + * Z? * * ? * ß Ü * Z? * * ? * ß , ]Y(U % !"#>% U= Y [email protected] Y Üß Üß µ¶Á »%& µ ź Ñ µzÑ é º Î Å µxº ¸ µ ¾ÀÁ* È·.Õ · »Ê» º · ÏÜ + Ñ é" ¾Pµ ¾ÀÁ » µ6 » Î ÞÁ µ- º µ Ü 'ßfÜ ' >* ß , Ü 'ßfÜ ' >* ß Y(e !f%VX`L%UZ#n#$% [email protected]$Y ?Y iO\^Y(U`[email protected]!fY Üß + µ · ߧ0 Ü x § yz ß .. ^P(K) 1 Ç Ñ Î Å µ¶¾PÁ ¾ »! µ ÅȺ Ñ Üߧ ± º Ñ Î Å µ À¾ Á7¾ 6 Ô»%& µ ÅȺ Ñ µ Å » Ò* Ú Î µ Ø'0 x » Ñ º» Î Á Ü ß Ü ß 4 Ü ß x § ]Y(U % !"#>% U= Y [email protected] Y iO\^Y.U`W0!fY Üß { x, { x {+ B Ü x § yf} ß X3L+s:=<>7 1 3]/ H3 E6 [email protected]?M -03 7 O3]/[email protected] EY.U Y GvY.e U ?Y i># LYb5Ye ¨ ·" »! µ ÅȺ Ñ ÜßäÈÑ µ# Á » µ È ·Õ 3 % C 3 ¨ ·" »! µ ÅȺ Ñ ÜßäÑ , µ Á » µ®Î5 Î Á7µ µ È·.Õ Ü ß Ü ß Ü ; ß , Üßä¾ µKµ# Á " µ ·" Ü ß ä ÃÜ´¿' ¾ xfxL ß » Å , ÅȺ Ü ß '" ) , Ü ß '" ) , Ü ß Ü) ) ß '" ) , Ü ß Ü ' ' ß '" ) .Y e !fV `LU#$#$% [email protected]$Y, Y iO\^Y.U`W0!fY Üß ¨ "· » ! µ ÅȺ Ñ .. .. * * * * = * x §y *+ +* * Ç Ñ Î Å µ¶¾PÁ ¾ »! µ ÅȺ Ñ .. .. Üߧ Üß ? Üß 4 Üß 4 Üß ]Y(U % !"#>% U= Y [email protected] Y iO\^Y.U`W0!fY Üß ¨ ·"0 * , Á 7ä »Êº Ñ 0 "'" º ¶ÒÑ ÞÁ ¾ · º µ¶µÑf¾( º ¸ , § B ± µ®³ ÑÁ ¾ µ º µ µ'ÞÁ"'" µ ź 3 2 1 4 (x ) Ü ' ß , x § z ·Î3 #Á º Á ¾ 6 µ³ º Ñ µ · ÑÁ º Ø » ¹§ x Ü x Ü ' ß¶ß x [Ü )ß Á x Üx , () *' (' {x ) Ü ß ß Ü x § yf~ ß ]Y(U % !"#>% U= Y [email protected] Y iO\^Y.U`W0!fY Üß ² Á º Á Ü x «ßä » µK³ ÑÁ7¾ 'µ · »P» µ®µ# Á" " µ ÅȺ Ü ' , ) ß Ü 'ß Ü )ß , Ü ' , ) ß Ü) ß Ü 'ß , Ü ' , ) ß Ü 'ß Ü )ß Á Ü ' , ) ß Ü) ß Ü 'ß , B " " " Á » µ®³ ÑÁ7¾ µ º µ ÔÅȺ Ú ##ÁÁ Ú #Á Ú #Á Ú " " Ü ' , )ß Ü [Ü 'ß Ü )ß , Ü 'ß Ü) ß ß , ÜÜ '' , ))ßß ÜÜ [Ü Ü') ß ß ÜÜ ')ßß , [Ü Ü)'ß ß ÜÜ') ßß ßß , Ü ' ,, )ß Ü Ü) ß Ü 'ß ,, [Ü )ß Ü 'ß ß Y.e !f V `LU#$#$% [email protected]$Y, Y iO\^Y.U`W0!fY, Üß Üß µ¶Á »! µ ÅȺ Ñ µÑ é º Î Å µº ¸ µ¶¾PÁ* ·.Õ6Þ· »P» Ü + µ ·" ߧ«NÑ é"¾Êµ ¾ÀÁ » µ f » Î Á7µ- º µ µ ·¾À¿ º Á7µ Ü x §z ß Ü 'ß , Ü 'ß Ü )ß , Ü )ß , Ü 'ß Ü) ß + + x§ º¿Ñ Y.e !fV `LU#$#$% ?Y iO\^Y(U`[email protected]!fY Üß " " " " " " " " " " " " pÑ µ¶¾ ¸ Ô» º Ñ Î Å µ ¾ÀÁ7¾ 'Nµ ·¾À¿ º Þ Á .. .. . = + ... Üß Üß Á Üߧ Üß Üß Ü ß ]Y(U % !"#>% U= Y [email protected] Y iO\^Y.U`W0!fY Üß Üß µ¶Á »%& µ ź Ñ ¶Á é" Ø º» º ¸ ÜßÜ ³ ÑÁ7¾ 'µ ÜßHº ¸ Î,Ò " · »Ê» ßä Á) Ñ é" ¾Pµ ¾ÀÁ » µ³'ÑÁ ¾ µ º µ 'Ü 'ß + Ü 'ß x ÜÜ '' ))ßß 'Ü) ß + Ü) ß x Ü x § z(x ß Ü ' )ß 'Ü 'ß 'Ü) ß Ü + [Ü ' ß x ßfÜ + [Ü ) ß x ß B x §} Ç Ñ Î Å µ¶¾PÁ ¾ »! µ ÅȺ Ñ , , . 243657382 oZPZ , , uv|ls[)yle®'cux| \ w zs[ #% , 4 ! Ã!"#%$ &(') +*- , /)-01$) :9<;>[email protected]?;BACD;FEGCIHKJMLNO9JPCI?/QSR/9"QTAVCIU =XW+?R;>9 +C # \[P]_^ `5%ab\cedgf\h7Z `5ji F k Pl m] !jn8i l `poqi r ! r its ulwv r"yxmz ]] v r" ] & r - n l n8ito jn8i j k l ZMo nurPZ aK zz F" ha{Mz , zqh c &)( & P l Y Z + a|{Pz t , } z~h ji &) ! 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L&@/9JML>[email protected] C U JCIQ N v r lw o ] l" Z o i jn h E G >F Ha.I , I 6 BF>H/a.I , I\h6E ' i % o l] `5 i v r Z rimZ " ]w] j Z " ] o ni o i Q * o ]l i M ;[email protected] JPL8NO9JC ?/Q i aA , hji aA , hjn8io n8nur 0 ZMo ] !0+ l n8i rB+ 8C98D z j ia 6E h7i ]w] n v r + Y AC ` ji4)( c M n l ^ ] yZ #\[P]_^ `5 a& , h ZMo a& , h [ Y o nWi ] ri l ij _a` z'k ] M j;i [ i l ntjgi r YZ G >F H/aJI , I h , IK3 zL ON +6P ] !jn8i l ` oi l ) nim` 7 o rP sLRTS sLU o iWV i ] n r,+ " ] l nu Fi` 0Pl k j` o ul oi l _cbz z , - Fa I zqh , d ]a I z , _ bz he - a f zqh , ] ] d a _ ` z , f ] z~h ] P [ _ ] ^ l Z<lmi nj`on%a>b"!h\h+ZpnrinrqAjsn tl lWnnWi rPn _a` z z , Z\^] a _ ` z , Ij zqh _ `z _ `z Z ] o$# o ]o ]o % n8i o i n Fi n l i n8ZMo nX l `5 o l [Plw]l ab cg!h h % ilu`unwv \ i I z z , j z O z f ' _ ` z P _ ` z x( z , _ ` z ( ] ol l oi l ] i j<j n ] n k sn ri\rPZ ] sn ] nv ( ] njn k nr,+ ] Z W l i [P]_] n^ `unn YZ _ ` z 3 a.8 h , _ bz ^ ja:8 h , [ \Z ] BF>H/a _a` z , jI zqh d F>] HaJIz , _cbz hy ] d >F Ha _ ` z , ] f zqh ] - F>H aJIzqh , - F>H a f zqh , z Ijz3 a.8 h , f z^ a.8 h , ab cg! h nji _a` z ] a a_ ( ` z #% &"y)#%$ )( ] ( z , , Izqh -a.Izqh , Iz'3)( <" ) ab cg!gh z T /4" #%$) ) &$m 243 its @/=X9"AQMCINOC @ 382 li l ;[email protected] ?/Q * ul o ZPs<n)ij luo ZPZpn ]] n ] q na+ Z<lmnnun l ij k n k ojPn ] n&ZPolto * lto ZPs n b"h, c Y nwlBjsn nur ] i ojPn tn1ZMoluo lv r<n k ij<j tsn n tsn il lWi\Zpi\n JTAC ijb\cb\c !#"%$&$('*),+ 1M'*3!)KT xz.-0/ +12)43!5768)9+2:;=< x z a{Mz t , } z~h _ xmz a|{Pz t , } z~h4E a {%{Mz " < <83!U / +2;>;?+2:;@ - '8A6 - <CEB+ DF$3C<G68$H1 - 6JIK;?'L'M123!)N3O'*$QPGR!P*S _ ` z " <83!U V - '*;?1W3 - +YXZ3[12),+\<+2:8X^]'*$H12)O68$),+1`_ +2)a_ ] q nn8i l ` oi njr<l k q ntlmlWnr l(s l tsn luolu s lwv < r n w l l oin8r ojginjn8ir<j nBo k o Zt i oi ij k n ] o < _ bz )9+ -!- +1bc:+T } z } hZ d _ E axz a{Mz t , } z~h agz ha{Mz Ijz F< nurPZ hjiOk f eNf2g <83!U , Ijzqh ha 68U8+] l _ y _ ab +2)o_ lnm h l N p Zq a_ bmsr , b~h l mh , a>b ' : t l S l 1M'*$) - +1^]'*$H12)O68$)9+1o3!$vu>wO12:MLxL'*:; - +1y+1,LH6]+1{z z S zc| +2)}z z S zc|~ } K _ S _1M'*$) - +1=]'*$H12)O68$)9+1<+ - 6]'*$)43!$:3!)+7 B <+1%uv'*;>5+1oAc3 - 3!$\cB+ 683!;?+1@ - '8A6 - +1 a& , h 2+ ) gz a& , h~Kr +12) - 6o]'*$H12)O68$)9+ <+}F68:]\]68;>)[uv'*;>),+\+2$)4;?+ - +1W+1,LH6]+1z z S$ zc| 68U8+ ] - +KL;?'c<8:3!) 1M]06 - 683!;?+` +2) l m b +12) - 6J]'*$H12) 68$),+\<+ 1c68)4:;Y68)43O'*$.68U8+] - 6$('*;>5+ K R *n c i l l br Y qlj k l oi j n r<l k q ntlmlWnr l ] i o ] j n n8i xH a|{Pz t , } z~h k jsn k<j k lw o j n x'z a|{Mz t , } z~h l ZMolv _a` z H ( x H ' H Mg f _a` z H ( _ bz H , ab cg!\f h ( a|{Mz t , } z~h0 *'*$ 6 - +5&2¡+ 5+;B+ 12: - ) 68)KL'*:; - 6{1M' - :)N3O'*$ 57683[11c68$H1 - +£),+2;>5+\<+ -0/ +2;>;?+2:;\<+]'*$H123[12)O68$(]+cR a|{ z Gh i S i }¢z h <8:{L;?'8A - 2t+ 5+ ab f b h 3>= 243 ;C M jo ] * z H 9JPL>[email protected] HKJMLN =X9"H , Iz h a{Mz V U8+] _a H H a|{Mz H ]06*1 @`+2B $+2B ;06 - S'K: t i l l dc H E , Izqh _a H z H a& , h 1c68)43[1Euj683!) T h {Mz F" a H I z F" H <83!U H {Mz H <83!U H +2) _a H y h h , Ijz , H +12) - 6J]'*$H12)O68$)9+<+ - 6 uj685}3 -!- +W; +0B @8: - 32t+ ;?+£<+£57683 -!- [email protected]+1 <834685 2t+ )N;?+W<8:]+2;?] - +W3!$H1M]2;>3!) | R k 7 nji8i n1`po miltoi l i j ]i {MzpaZ<lm! i mnFi l ij k n" lw # A9 / @ H v h 123#+12)JcB+ bc:3 - 68)2B+ ;Y6 - [email protected]/HLHKJP9 / @ =XC AC ?;>9<L>QMC - 6 uv'*;25+£Ac3 - 3!$cB+ 683!;?+ h @ ] itoimnur l ojgi&a nlBsn n8r E JPQ L>9 ;Wm=X9<;LH 9JML>W @ ACD;[email protected] ?/Q CXJ o ] l `%Z ]lwv r n nur l ] o` n zqha<ijo ( miluoi l ij o v *\] i n P nrj [ o ] lWnj`pol a:8 ( a H H E a H h0 v rMojgi <G68$H1 - + h H z H h qz v r<n *$%$4&4 .N(' / +2;>;?+2:;\<+]'*$H123[12)O68$(]+WUK2B+ ;>3 D%+ n8rPZ h g G ef a z iOk f H H hja|{Mz , I zqh Iz F " <83!U E aa H H gv f) d h , {Pz ( z , 68U8+] ) 68U8+] _a H o ] qo c a z H +* hja <+ - 67IK;?'L'M123!)N3O'*$ PGR43^+2) h +2) *n _a H H l n ^ n Z H * a.8 ] o&Z<lWi\Zpi\n l i l ha{Mz , Ijzqh6E 9;: 8 he a:8 h ., -0/ (57, 6 1 , H21 *+<>[email protected]?BA a:8 9 , } qz hG d H , z b h 9;: 8 8 k l( H 9 ab cg! d\h , ij < Z lBsn psn k ntjgiWnij(o v _aC H h {Mz F< _a H k I z F< l( H D {Mz , , Iz ( a.8 h , ilun H gv f k qi a z H H hja|{Mz , Izqh6E H gv f h {Mz F" k H lw I z F" k H lw E , , Ijz' {Pz r^ n8rPZ hciOk f eOf>g G a gz ha|{Pz Iz F< k lw , Izqh E aa H gMf _a H Ah {Mz < M j $ Z i\nmn ) H _a H &h {Mz " f k l( H , k lw H hZd ( z , T njixijo H {Mz h 1 H H a|{Mzqh H 1 H a|{Mz h E a h ,.-0/ C5 , 6 a H } , hA , z o j n H a k qi r^ 243 ] a:8 * h a.8 * d h h a:8 * E h , ] i oqic nlBsn nur 9JPL>[email protected] HKJMLN 3 AC [email protected]/HLHKJP9 / @ =XC ;[email protected] ?/Q A9 / @ HS;>C =X9"[email protected]= JP9 @ ?;>9<L>QMC M jo * z ] E H ] itoimnur l ojgi&ac+co l i nlBsn n8r - 6 uv'*;25+£Ac3 - 3!$cB+ 683!;?+ , Ijzqh a{Mz N 68U8+] _a H e h lWnhv H H +2) E , Izqh a|{Pz H z _PaC H Zq p H a& , h 1c68)43[1Euj683!) T h I z F" H , H {Mz H , H <83!U , Iz' {Mz ( a:8 h , R <83!U H S]'*5}5+ <G68$H1 - 6£IK;?'L'M123!)43O'*$yPGR438S'*$^'8Ac)43O+2$) H _a H hy h z U8'*3!;"!,P 3$# |~(- 6 1M+25}3!w,$('*;>5+ +12) - 6WA2'*$$(+K5+12:;?+ z {Mz H &%(' z a{Mz , Izqhy H a{Mz , I zqh , Iz' a:8 h,| R ( # *$%$4&4 .4 ' / +2;>;?+2:;\<+]'*$H123[12)O68$(]+WUK2B+ ;>3 D%+£T V U8+] - 6$('*;>5+ * ef nurPZ g h iOk f {Mz F" agz hja|{Mz Ijz F< <83!U , Ijzqh E aa ) H gvf H hGd , {Mz' a h&10 ( a)mh , 68U8+] 68U8+] _a H e h * n lBjsn nur ] i n k c Y r N q l j sn * ) H o ] r ] +2) H 1 , o ] l , i sn nWn na+o ji 8 6 _a H h } z F ,3254, S +* 1 , 4 a , 1-, 4 a 6 h& H , 1-. H 7 h 6 8 1 F LH68;+YX+25 L - +cR i lmi ]] o l ml nb\cwbenFi k sn `uijgi lmnti ` `un tn ]w] n k r 7 k n {Mz H nrj % ijji l ij k nnmnuo ritn k n } z\c d ab cg!! h / ] q n0+Z lWnn8n l i j k n ) H ! " $ # %'& % .!/!01 2 b , )(+*-, 243 1 12!576 9:8 2;!0 / 2 , ? [email protected] C A? HBA HKJDCIC NOC 3FE W @7JQ L:G?JML>[email protected] 9 C ;FEGCIHKJMLNO9 > W ;?JPLW @ 9<RR/[email protected] =< 243 7382 JPCI?/Q S,i a IH li ] o lw]] o z/r<j ` nj<i\` [ lWn k n * n i l l oj * i i,jsn n k r ` _ `z ^ lBsn nmi\r r ] o l lWn i r lWnjjitoj * r ] o l lmn ] n Z<lmi [P]_nj^ `on o l w ] ] * ] w l o o nh nn8i nn8r o jgiv 3 ( ] a a_( ` z 7 i\`%`onXX( [ Y lWiia z ( z _a` z J ] ( z , , Ijz~h -jaJIzqh , Iz3X( h ] n Z<lWi [P]_nj^ `on%a>bg! gh6nni lWi ia zqh 1 z J1 , z k lmn k nito l]w] n ab cg! \h v r lw o ] nrjgi ; o^ v sn z( , lWiia ab cg!QP\h MLzqh 4 q 4ON , Lz' z ( 0 c$4 ESR *UT $Y ab"! ghWVXZY\[ +^] ]B_ a a ^ a a: Y o % ijPFi l ij z njn8i k ij<j rsn n/ZMol z a : ` L i r aML h nn8i ] o [ o nWnj<i k o ] n k n ] q njnuZMotn ` 1 1 @b z c ijP l] % o rixlBjsn nWi\r k lWn ] nZ<lmi [P]_n^ `un d Zpi\r<l7i lmi\r ntl _ ` z o n ( b ] ( 9 9 9 9 J J a aML h aMLdch 4 q 4ON h1=e cfe nFi d a> {Pz lWiiaML h 4 q 4gN h1=e e K K ` ` 7 i\`%`on ] oV` oi l l rnih nni [Pl ntj rij k l i l ij<j rsn nxij Zpnr i ] qeo ZPZ lWi s<ntl ZMol nto k l o * ijMo ] n nFi h 6 c lmi i tijPn l k tsn lmntl d h\j k 6 d ri\` `uno ZPZ lWi + l ` oi l ij k n _ ` z z d d M ] l * ]wl 1 ( ( ( \ j o nn j sn K a1 zqh i,sn n v o b a j k6 Y q njn8i l ` oi j n r<l ] i h @l H o ] ] ( K Ma Lzqh 4 q 4ON {Pz ] d h j k6 d E _ `z ] ( ( njn8ik9jMo ] n`untjgi l H , k jsn k<j 6 h d d E a ,, H ,, H m ,, h njixijo H gv f l H h d ! j k6 /h d h j k6 d . l ZMolv H g / H 9 jb a k6 d d , , ab c %\h =< 243 73>= @ R/[email protected]HLW # $ ]G $+R H[email protected]=XW / @ A A? 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A h0 9 2 8 L+2:U8+2$)72¡+ )4;+£;?+25 *4\68$H1oz9PGRP |- +1}]'M+ ]23O+2$)!1<8:{)4>L+ - +1uv'*$(]2)43O'*$H1\<+11M+2: - +1}]'*) [email protected]+2$),+1\<+1\[email protected] - +1cR =< E ol k ]o nur l i * ]n lmnjitoj \ r [ o nmn k n {$ c M j luo k b i l]wl nmn ZPZpn ]w] ojPn ] n o n IaEq h , ]o L - 6] B+ 1 LH68; H 1 9, g / 2 * nXlmnFi oj * o lw]] o !4c"b\cwb % i oi l jKrP` tsn lmi v r<n7{Pz n k q r<j(` { !"#%$& @ '# RyW n ij1r 9H a b IaEq h8h a>b ij k nn!nWi\`%`onFitnnFi % o tnjn k n ] o zt , a|{Mz hG{ , o n , a|{Mz he } , Fn i 1 r ] o l lWnnmijgi'v , b { 8 5 , N h a nji b { abm v r<n a . . . . . h+y N h8h 11 9 3 12 6 2 13 1 hx − 16 hy 5 7 h+x 4 − 15 14 ! )( b cwb % M jo u ` ijgi lB sn or(ZMolto * luo & 7 o ] jr ] ] S < r l ZPs<n h , d ] ij k nn sn ] sn `untjgitn g/ k n d a % o tnBb~hv qAsn ] jsn `onrjKi)8 , a ] -, qAsn ] jsn `onrjKi o ^ ] q "n8i qAsn ] jsn `onrjKi)8C =, d k ijP a|{ l n l jPn F n iXil l nrjgi oi l i , a|{Pzqht { a , h = ,H p d k n/.!h = , ha p , hy / 1 H = , hja p , hy 8 H v r<nov b cg! c"h , a{ S < r l i oqi l tsn lmi rP` =, a|{ a|{ k ijP = , ha p , h b = , ha p , h % 10 2 h h b , ij k njn+*Pr,+ i < r l % ijPji l i jn ] n n 8 10 o ri c 7 i\`%`on+{ a { i * ijMor,+ { nmijgiXil8its M j < Z lWi k n k n!` n `un/Zpi\r<l n^ l H l` ,g/H l H h n @8 8 [email protected] h C, , d , ,C, h * a * > >uh a 1 H ( a h 1 1 a a h 1 0 1 a k sn Zpntj k k n!bch!nuo [ i l nrjgi ] n nxn0+Z 1 81 h 0 h ( 1 1 2 h lWnn8n l i jPnv 2 0 0 +P li } tz Wn i riun 0 nji)ij;i h h 1 0 1 o ]j n r<lun k n P ijpontj n nFi } z a * h 1 81 a 0 * 0 * h h a 1 0 1 * b f h b f h b f #0 1 0 1 h ( 0 0 h 2 > * 6 nFi 0 H [email protected] 6 h f 0 h f b h 0 0 h 9 9;: jsn nWi ] ri l Ja lWnjnuZ ij k rZ Wl i [P]_n^ `un ] i o ] aGnur<l r j:i l l oj *\] n 8 h ntj 9 9;: cIa f h h k n ] q njnuZMo nmn a.lmnn8Z cX zqhv L a _ ` z h h /a _ bz h a _ ] `z h ] ] Pb a } a z~h ri lw]l ntojgi h 2 2 ] n n 0 Lh ab c h ab c 8gh 2 0 ab c h 0 6 1 81 2 6 f b 1 1 b a a h * h 1 6 1 8 h * a * 1 6 1 * H nji 0 a H a H > h > a 0 0 h ab c gf h S8 F 2 !!01 1 , , b ! # %'& 3 2 i6 b ( , 2 E ! $ 1' @ '# a.I h z * a 1 1 6 b h 1 6 1 8 a "* l i k9jMo ] n `untjgi H > > q n0+ < Z lWnjnun l i j k n d 6nni lmnn % o tnjn k n8 a * i 1 1 >y [email protected] lmi MnWi H b H k n H a P H a lH oi j n r<l 8 d q njn8i b ] 1 81 ori b d a * ]j n n d Y b d =, o^ % ijPji l i jn k n [ onWn ab c \d\h i ; r ^ a n i) } z h F h nWijgi a ja _ J a H a:8 ( 9 I gc { h8ha 9 9 h J a ]j n nri,il nWijKi h\hc Y o tijgi I f l[ r i l l o^ ij ON h1=e fc e 4 ] ql j k l i f k ¢ C J H o ] j n n8i C h a d h a H L nji ] ] rPn i < r lmZ * E ' 68U8+] 1 9 ( 9 } z 9 9 254 b h 4 q 6 b J h Ih i l l Xj<j<n0+ nh ] 4 q 4 2 g4 N % ijji l i jPn k n ] n n h j [ o nmn k n ] q njnuZMotn ON 4ON 4 jsn iWl lwv r n n l ` q gN 4 q>sn ] sn `untjgi'8 ah J a 9 I H c I l[P] n nyna+ Z w] l l i,rsn nn nrlun 2 o j n Da J ] f f _ bz H ( ] L/a _ bz h 2 h a:a } z h H 8 J ] v [ i l ntjgi H o l ] n k n k jsn i a h a_ b z ] a _ ` z hyD q _a` z H ( ] ( 9 9 b h 4 I k 9 c e 4 4gN =e Z ojPn ] q h j j<na+,n q h1 k ij<j tsn n!ZMolv H La _ bz hy H a 5 , k n l l tnjnn&R oi 9 { "aua{ z I { , } J H h a _ ` h a _ ` h z z f k ( ¢ d ij3lBsn nWi r k ] nZ<lWi [P]_nj^ `o] n%a>b dgh6] ij;i nWi l i S 9 1 Ma` l oi j n r<l ] 5 , 9 H J } tz , [ ol&R tntjgiWl lv r<njn 9 q 4 5 , ;9 : 8 J } tz , ;9 : 8 9 hyD k ij j6tsn njn 9 c l k H a 9 h1 aua _ } zqhyD 4gN =e e =e cZe q 4 k ij<j sn nZMolv q 4 q 4 a _ ` z huh ON 4 ON J 4 h H H H f c 4 9 c e 4ON =e Z q h 2 ] J f 9 f f q 4 q 4 ON 4ON 4 c +1£3!$\0B+ @G6 - 3!)+B 1 12:3!U*68$)9+1 1M'*$)KUK2B+ ;>3 D +MB +1WT _ `z H ( ] _ b H z ( ] S " b E ¢ H f5% +2) 4 f k b % E t6 H H ¢ f k C h H C h H d a d a ( ( ab c 2 H 9 a ;9 : 8 H H % % 4 1 9 Gh 0h - 6WL - :G1 L+2)N3!),+ H68:)9+2:;\<8:^)4;>[email protected] - + 8 L! 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H ! H li l 2 F h Fh 2 P h H x H gvf ] l nunmijPno lmi pi\n F } z huh Mol H x ] ) %$4E * N ) 2 } z~h H gvf H H ) h F n # q ntlWlmnr<l iWn k n!rijPn l n8itojPrn Molv PLh$ 2 ! H $ F h a H gv f } z o |{Pz <lmntjMojgi)ntj t i tsn l l k9n n i |{Mz x-- |{Mz h tsn il n un g!\h s H nni oBtijgiWl l ri onmiWl l ) oj * r o l m l nXnFi 7 ilWi njii i ll _r` z H h H _ bz H f k ( ( ( 2 ¢ d ] ] l ij i o n k n :q nrlWlmnr<l k n&tijPn l n8i ojPtn i l l 7 i lmi o l lmn $i < r l o l lWn gh pi\r<l n o nxlWnjji oj * r o l lmnh 1,yj po mitl ojgi ,ij(o;v } z~h 2 n k q nrlWlWnjr<l v H $ % f k ¢ d C*$ _ bz H ( ] P $ H ( H p Zq 2 $i r<l nlWnjjitoj * n &,+.- 0+ 4 v R - 0 0 ]Z M $ - *$R-]Z %+M&;]Z $4 ]Z BM!4&0/ $4 E 1! 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H ) vZ * 1 1 1 1 8 1 1 1 1 0 F ?G ¢ 1 8 1 C*$ %& H ! f# k d 1 N % % 1 9$ Btij % [email protected] H ;9 : 8 1 9 2 l i j 9 9 ' N ) 1 &+- 0+>N M R - 9] M / E$ 4 n> $ j n C lmn j<:$ 9 lWn El i l 6ilWi 9 lWn $5"h ,yjlWn:lWi$ <j H ) * ) rij tsn lWnrj n k ) n 0 ]Z H 1 7 q ntlWlmn<l $ 1 l i j @ P H ) <lmi rsn n v ! H P ) j ij" v i l H 1 $ ! % $ H * $ $ H 1 9$ % [email protected] $0 $ $ 1 6 1 * pi$<l 94j? 1 6 1 8 * 1 8 1 1 1 $ tsn lWi i j 0 6; $ 0 $0 P;$ A$ @ El 5 n 89$ k ij<j sn El . q n <lmn ij ij pn ntl $ $0 * * 1 1 1 1 1 1 1 1 3$ 0 $ 6 8 8 8 H H % $ $ $ * $ 0 0 * 1 1 1 1 1 1 1 1 0 6 [email protected] $ $ [email protected] *$ %& H $ P0G$ $ 5 H !$f # k 1 1 1 1 ¢ d 8 %9$ @9 tij l ij# iC n n q n B q7<j&B ;:n ClmlBsn .n il =?<n H n<l k H $ k n rij j<rn n k ij<j tsn n H n C k lWi6 sn n k ij<j tsn n Elv ! n> 1 8 $0 $ * 1 1 1 1 3$ 0 8 H % $ $ * 1 1 1 0 1 0 @8 8 $ [email protected] H ; H $ % ; % % ¢ !$f # k d $ %& H 1 H * $ 6; 0 2 1 1 9 9 8 9 ' 9 H H H H n> n @ n k ij<j sn ) @ 4 [email protected] n k ij<j sn El 9 '$ [email protected] ,yj [email protected] 8 n j n nrl3un j >sn : :0 n il = n H ! H i n k n rij l i j R 7 ]Z C+v ;]Z $E7]Z $ - * v 1 9 ) ' 6; ) H* ' 9 * 1 8 !$f # k 1 ¢ 1 1 1 $ d %& H $ 1 1 1 % 1 $ 1 1 1 8 1 1 $ 1 8 $ 1 8 1 $ 1 1 0 $ 2 1 *40 '6<83 +2B ;?+2$(]+£+2$)4;?+ - +1W<+2:8X +12)N3-3768),+2:;?1}z9PGR-,. | +2)Cz9PGR-, | +12)<¡: +t6 -0/ +12w )4-3 3768)N3O'*$J<+ -0/ +2;>;?+2:; <+ ]'*$H123[12)O68$(]+S +2${+ +2)<G68$H1 - + ]06*1`)N;>[email protected]: - 683!;?+ - + ]068;2;B+ <+ -0/ +2;>;?+2:; <+ ]'*$H123[12)O68$(]++12) 376 v'*; MB+ +KLH68; _ H ' <83!U & H SK< / 'K: t -0/ '*;0<8;?+ H RK$ ;?+2U*68$(]+S<G68$H1 $ - +]06*1£;?+]2)[email protected]: - 683!;?+S%+ -!- ++12)4376v'*; +MB + LH68; _ H $ ' & H $ S < / 'K: t -0/ '*;Y<8;?+ )%$ R v "%$&6 (' %& H ) 21 1 L'*:; - +]06*1£)N;>[email protected]: - 683!;+z ;+1,L(R ;+]2)[email protected]: - 8 6 3!;+ | R *4 1 $ 1 8 z ;+1,L(R 2 1 1 1 1 8 &z 4 *4 ' / +12)N3-3768),+2:;J<G68$H1 - +{]06*1=;+]2)[email protected]: - 683!;+y<'*$$+yB <G68$H1 2¡+ )4;+ @C2B+ $\2B+ ;Y6 - 3[1+B uj6]23 - + 3 +2$)Jt6 4 ) R 4 ! nrj<tnntj M qA>sn = <lmi $i ij ;j ! hM| S L+2:) ) 0 2; 01 /! , , , , , n i ij k n <lWi n u n )$5 Gh$ n $5 9; '$ n <lBrsn n El , lWn $$ 1 n v , $ $ H _a` ' 4 $ E _ _a` ' 2 _r` ' $ 2 2 * E ' +1£1M' - :)N3O'*$H1 _ ` ' _ b' +2) J_ ` ' _ b' & <+1`L;'8A - t+ 3+1£U*68;>3468w &' ' 2 2 )43O'*$$(+ - 1W<83[1M]2;?+2)!1 $5 Gh +2) $5 1M]'*$)J] cB+ bc:3!U*6 - +2 $ )9+1<G68$H1 - + 1M2+ $H1£'K: t 3 - +YXZ3[12),+W<+1\]'*$H12) 68$),+1 _ E _ +2) _ 3!$<C,B+ L+2$<G68$),+1W<8: 378 6 3 -!- [email protected]+ D' )9+ !- - +1bc:+\T % % ) $ $ 8 ;9'$ 9$ _ $ _a` ' a_ ` ' 5E 2 ] ] <83!U ] _a` ' ) 2E _a` ' <83!U _a` ' ] 2 ] ] P $ $ _ b' ] _ _ `' _ `' d 5 2 # ! # 8 ] ] ] ] *n M j uij lWn _ ) N [email protected] :q n n untj 8 ij k n _ 6 n ui j sn k ntj n .n% n ; GR SLU l Vwnrj lWn n n k sn $nrj k k n 8rij j n k n q j sn :0 sn k n k n> n E tn <l _ [email protected] _ @ _ H i l h % pi$<l k n k sn _ h H gM f ) tn _ $ %$ H =? l $ l m ' 2 n _ %$ ' ) <lB>sn n k n k j ) 2%$ %$ , %& H E : 9 j k6 . n> _ ] ) _ ) %$ H ' ' 4E 2 p q _ ] ] OP h iOk f _r` ' & % & H ij $ I>' ' k ) h$ k j %$ 2 _ I' & iC $ $A5 &% n k sn <j _ b' % & H 5 5 H ' ' 2 _ 2 ) v l H n El 2 ' :q j k n><l k q ntlmlWn l H gM f 9 j k 6 $ . ef g $ "! F M H n k i j<j sn El k j n k n l j<: n ( i; ij q n 8 ij k q nrlWlmn<l j n v H ' ' 2 C*$ !;f # k F 8 ¢ d n El;:l <<n $5 G5 [email protected]<j<i; K 1 ' %(' l ' %& H a H gv f q n 8 n<l rsn il =?<nKn ntj $i j ij v q $#_ 2 %$ l m$ r p l N K 1 ) _ E # ! # H ' ' 4E 2 Elv q <l n 5 n _ ! # =?<n $n n6=?<n k q <ln n D tsn iln un G l ' $ d @E=?<nj<i$ ' & F k M j l _ b' 8 2 5 n C k n lmn j<: n , . iC n '%$ ) l H 2 q j k C n l k q ntlWlmn<l ] H ' h l n B mil ij l j : n n 9ylmi l j _ ` ' & % & H _ b' %& H 5 ] ] ij & %& H @ _ b' %& H @i l yl W i $i k j n nC k ] n lmn j<: n n <lmntjEj nrjti ij v F 8 ' k n ntl on _ ` ' $i ij k j] tij j<tn @9ij3l pn n =?<nj<i$ M "! H q n 8 n><l ¢ d n C k n q ntlWlmn<l k n ! H $ F 5 _ N h H vg f ] E k ij<j sn Elv ! Jil3unntjv *$ %& H ! f#k n H :q n B n l k n _a` ' & %& H t ij ] j<tn k ij<j sn El n ] 6ilmi n k n lmn j<: n . ) H* n lmn H ] H ) 2 # _ b' % & H El B>mil ij @ H :q n 8 ij k n q ntlmlWn><l k n ml n $5"h k j $5 n k n l j<) : n n n 6ilmi k j ] # *4 "%$ <`+ B 3'*$)N;?+ uj6]23 - + 3+2$)bc:+ _ ) _ ) S'*$L+2:)7]06 - ]2: - +2; l S l - +1 ]'*$H12)O68$)9+1 3!$vu>wO12:ML7L'*:; - +1£+1,LH6]+1\z & ' S & 'j| +2) z & ' S & 'j| ~r- 6o]'*$H12)O68$)9+ <+F68:w %& ' S ]C]68;2)[ uv'*;>)9+C+2$)4;?+ - +1 +1,LH6]+1 z t6 +2B )% B+ ]06 - ]2: - +MB + & 'j| 68U8+] - +L;'c<8:3!)1M]06 - 683!;+a s V V V 12:; - +=<+ 3}3 ]068;>; B+ :$3!)W B+ LH68; R ]]H6GA2S R @'*:ZM6 - S HR 68;[email protected]+2;y+2) R R 683!)N;?+ !,P #y+2) l m +12) - 6y]'*$H12)O68$),+<+1c68)N:;Y68)N3O'*$.68U8+] - 6$('*; 3+ R i ! # !;0 47 0 2 , n uno i k n n;@=?<nj<i$ tij k Y [ k K $ n lWi \ M Eq ) Eq ) i$ l 2 2 n N$ % N$ E 2d$ % ! Eq N P 2 ( % 2 % ) 2 P q ) ) 4 2 5 ? ) ) ) % ) !q % 2 ) 2 ) ) ) % 2 N$ % Eq "!$#&%'# !)(+*-,/. 1' 020 n n k ij<j sn Elv @ ) n lWlB6 sn <j sn @ @9ij<i N$ ? !q 2 N $ ? !q 2 N $ Eq $ 2N K n k i B j<n k n C tsn lWij k ij<j rsn n 2 N$ N % 2 ) 2 ( % P 2 ) q ) ) ) $ ;j n v 43 $ d 3 $ $ j 3 q $ ti d 3 3 ri 4 3 q $ ri d 3 N $ 2 Eq 2 N 43 ti 4 3 q $ ti d 3 N $ 2 !q 2 N $ j 4 3 q $ ri d 3 N $ 2 Eq 2 N $ '5% @ k n JlWij nrlWn 2 P 2 P P$ 2 N$2 $ 5 2 !q 2 2 N$ ) 2 ) 5 n un )$5 PQP9$6n k ij<j tsn n Elv !q $ ) j 4 3 q $ ri d 3 N $ 2 Eq 2 N $ ) 5 2N M j rij k nr lWn <j<n k ij lBsn :$ nr lWn k q7<j 8 9 :n k n k sn El HD'9 n 8 9 :n j " ij i ntj? ntj k >sn ti$ <j E = n sn asnu ntj ntj. i$ sn asnuntj 6n lmn nrj k ij< 8 rij l lWn k n B ;:n k ij n < ij k ij j6sn <l 0 ) h . @ i % ) n n < j n n;0lWn <lBsn nrj n:q il k lWn k n&:q nrlWlmn<l k . n# i ij $i$ l n k )tsn lWnrj E k n#8 9;:n j rn"C i ij n ; n k <lWi @ B ,ylWlWn><lxntj % 6 h5 % 6 G5 % 6 ;5 2 Gh $5 %Lh 2 8 5 v?G G5 Gh 6; 2 ,ylmlWn l)nrj # & ! ) H* * n> ) 1 1 *$ d ;?+2)N3!;B+ - +1"3¡+ 3+1;+ 3768;Ybc:+1cR l H ) H* l H ) 6 P' % 6 9' % % 6 1 1 % 1 $ 1 1 $ 1 8 n $n 1 8 1 1 l % 1 9$ @,ij ij =?<n 9 $ l i j 1 8 1 $ 1 1 0 $ 2 1 tij "%$ :)N3 - 3[1M+ - 6B376v'*;Y68)43O'*$^12:3!U*68$),+\T ¢ H ' ) 6; ) * ) 1 $ # \68$H1\]+bc:3a12:3!)!S '*$]'*3[123!) H ¢ !$f # k ! 1 $ %& H d 9 ' $i$ l rn B ;:n ClmlBsn *4 M j $i n 1 ! f#k 9 1 8 % # i ' 6; P9' M l k lWn k n :q nrlWlWn><l k n 9 n k q7<j 8 9;:nDlWlBsn .n i l ? = <n H iC n k n :q n 8 n><lD Wl i6' sn n i j j6tsn n Elv k j & H 1 8 %& H ) ) d ) !$f # k (' $ lmn <lBsn nrj n :q j k C n<l ) +' %& H 5 ) ' d ) +2) '*$6 n 1 1 $ 1 H ) ¢ d R '+ 3&¡+ 3+)9+12) 6 2B+ ) B+ ; cB+ 6 - 3[1 B+ 68U8+] $ 1 1 1 1 iC <lmi 6sn $ k # n q ntlmlWn E %& H 1 % 1 $ '2 1 8 1 1 8 1 1 $ 1 8 1 $ 1 1 % % $ 0 2 l k n"tij j<rn k ij<j sn Elv 1 $ 2 %6$ & ) & H ) +' %Lh$ %& H 5 ! i$ l r i <lWnrl :q j&*E<nrj<tn k n 9tij l ij & H k j q n 8 n><l H @ E nrl tn n t ij l ij pi$<l k )rsn lWntj E [email protected] 2 <@ k )n 8 9 :n ) 2 L & 'h * 2 ; 6; k ij< E , 0 $&1' G $ ' ( i$ lBsn ntj ij ; 2 , 0 * k j tn =? ? <j<n Cl n k n n><l i sol k n pi$<l n< & H ) k n B ;:n 4.0602e-07 3.65418e-07 3.24816e-07 2.84214e-07 2.43612e-07 2.0301e-07 1.62408e-07 1.21806e-07 8.1204e-08 4.0602e-08 0 PROJECDEF_local ! ch $ i n><l .n i$ l % ) E , 0 & 3 nrl un %9' < % 5%5% % $&1' G $ ' ( i$ lWn ; ,0 * # k n B ;:n ) pi$<l ) hKn 2 G $#' <lBsn ntj ij k j & $i$ l ) 2 ) . rn = ; % 2 k n ) & H $i;<l ) 6; 2 * 2 8wj<i$ ij lmn8l=? "sn =?<nuv ; 5 5' %8 % 6 pi$<l ) 2 8 [email protected] ) & $ , <j<n"l . 20 $& n k n i sol -* , -0 0 ! n><l k n q n 8 n><l" i j n 8.2315e-08 7.40835e-08 6.5852e-08 5.76205e-08 4.9389e-08 4.11575e-08 3.2926e-08 2.46945e-08 1.6463e-08 8.2315e-09 0 ESTIMA_local % ! $ i n><l k #n q n 8 n<l i l .n i$ l ) ; lWn < QP h5% # k n B ;:n ) $i$ l ) % 6 2 j * 2 8wj<i$ % l 2 [email protected] Ghn ' n ntl on ) ij ) ;5 & $i;<l ) lmn 8l=? " sn =?<nuv % 6 pi$<l 6; 2 ) 2 8 E , 0 ,0 * $&1' G $ ' ,yj pi$<l n @ej i$ ) <lBsn ntj ij 6; 2 2 $ ' . $& , <j , . $ n><l n l n k n 8 i sol k n i ri n ! q n B n<l 4.0602e-07 3.65418e-07 3.24816e-07 2.84214e-07 2.43612e-07 2.0301e-07 1.62408e-07 1.21806e-07 8.1204e-08 4.0602e-08 0 ESTIMATEURT_local ! v $ i n<l k &n q n B n<l" iC$i$ l % .n ! i$ l ; 9' lWn $5 % < 6 % # k n B ;:n ) pi$<l ) hKn 2 G ) 2 ; * 2 8wj<i$ ij lmn8l=? ; 55 ' %8 % 6 $i$ l [email protected] 2 % ! sn v ) 2 *4H 3 +12) ]'*$H12)O68$)9+LH68;3'*;?]+068:X6 - '*;?1 +' %& ) % R'*$(] - 6]'*$)N;>3!w Ac:)N3O'*$ - 'M]06 - +\<+ -0/ +12)N3-3768),+2:;+12)nL - :1 L+2)N3!),+}]'+3 3+ - + 3'*$)4;+2$) - + 1W),+12)E1£$:3 +2B ;>34bc:+1cR E , 0 ( i$ ) pi$<l ,0 * $&1' G $ ' lBsn ntj ij ) 2 * ## 6; j<n"Cl n k n , 0 ' $&20 n><l k n& i tij sol q ntlmlWn><l l i j k n k n tij j tn 8.2315e-08 7.40835e-08 6.5852e-08 5.76205e-08 4.9389e-08 4.11575e-08 3.2926e-08 2.46945e-08 1.6463e-08 8.2315e-09 0 CONSISTANCE_local % ! %' $ i n><l k #n q ntlWlmn<l .n ) i$ l ; h5 % lWn P %0G < % n B ;:n 6 k # pi$<l ) 2 ) Lhwn 2 k n"rij j<tn pi$<l * 2 8wj<i$ [email protected] % ' ) ;5 ij % ) 2 6; 2 lmn 8l=? sn v 6 $i;<l ) 2 8 E , 0 &$ 1' G $ ' $& . ( i$ ,0 * $#' . * $ &20 ## , 0 ' $&20 $" 20 # # iC < i ; n l k n :q n 8 n><l <lBsn nrj i j k j tnB=? 4 j<n l n k n q ntlmlWn><l k n"tij j tn j n ntl on & pi$<l n < k n B ;:n ) 2 ) sol 6; j 2.3735e-08 2.13615e-08 1.8988e-08 1.66145e-08 1.4241e-08 1.18675e-08 9.494e-09 7.1205e-09 4.747e-09 2.3735e-09 0 ESTIMASANSCONSI_local !0 ; $ i n<l k n#:q n B n l iC % l .n i$ l ,* # lWn < ; 5 % P; * # 6 % * ## 0 ) g ) & n ! ) 5 G'5% k n B ;:n $i$ l ) ) ) l g ! ) 2 , 0 n n n ; ghulWn B l sn tn j n n k n q n 8 n>< l v @ @ i & ) : ; ) Lhn 2 lBsn i n ) % 6 ) h5 h '' nrj ! Dh ) 2 lmn 8l=? sn v % 6 pi$<l ) .n pi$<l n l & (' 2 % 6 5 ;'$G 2 8 8 h5"h ' %06 ; 5 0G %06 h5gh (G 2 8 8 '5 ; % 6 $5 ; P % 6 ' 5 ;5% P 2 6; "h , 8 ij Gh j<rn pi$<l * 2 8wj<i$ ij l 5 G 0G' ' $&20 & @ l tij [email protected] % l j ) 2 ; 8 k )rsn lWntj n r ij l ij @ ) @ ) g ) g ) l ! % 6 P5 G ' % 6 %06 h5 QPLh %06 h5('5%; %06 8 % 6 G5 hh % 6 ; 5 Lh % 6 8 8 : i n % 6 $5 $ h G l h %9j k q n u ntl:q il k lmn k n# q ntlWlmn<l [email protected]<ij sn tl v & ) d $ 2 ) C # $ 2 l ) $ 2 ! l ) $n ! ) C3$ 5 9 ) j n n; ) @yij k ij j<n8 n n<l k n 5 @ " ) 2 h 2 pi$<l & @ n l sn $i$ l k n n><l D <rn n k n" ) 2 [email protected]* 2 8 n 2 6; ) ) n ) & 5 8 2 $5 P; 5 ) 2 q il k lmn n<l <lmi rsn n . tij l ij l 8 $5 ! 6; 2 n# unil k 2 5 2 5 # q n 8 n><l C $ lWn n ) 8 9 $5 P; " ) @ 2 6; 5 2 ' $i$ l q n ; 2 P ;9' 5 : i $5 lmn k n =?<n 5 k n rij l i j ) @ l @ & @ l ) ) E! !$# %'# !)( nj<i$ lBsn ntj ij <j Eq rn"C @ i i j i$ l tn6C n ? = 8 n><l i C @rn"= j i$ k n> N$ &n n un n n % ) Eq N$ i k nuv ) 2 $ N 2 2 2 h*q Eq N $ ) 2 2 2 q !q N $ 5 ) N 2 2 n ; n k <lWi n un )$5 PQP96 $ n k ij<j tsn n Elv Eq $ ) q N 2 Eq 2 N $ ) 5 2N tilmlWn $ij k ) % @pj<i$ ij >asn&9 tij l $nrl3 k n"rij< <lWn"=?<n# q ntlmlWn><lxn lBsn pn n 2 ? 2N $ ? Eq 2 N $ !q $ 2N Eq P;h 5 5 n><l : i 8 k n# q n 8 0 uij lmntj n n l 6; 2 ;5 P;Lh q il k 5 n D nC 0 ! k n#:q n B n l4ij j 5 8 2 ij k ij<j<n n n n $i$ l ,yj ) n ti ! l n 0 <@ j n n ; 8 n><l k q ntWl lmn<l : i 6; 2 ) 2 h*q '; 2 !q qn ij k n @h<< @dh Uh:$C @+ <:@+ " 3H+2B ;Y68;]34bc:+cR V LGL - 3O]068)N3O'*$#68:X B+ - + B 3+2$)E1=DF$3[1 P P 9$ Whh:$C @ "$# &% h % &8 "! @ V 3}3 L('*),+.-,/102'3/104-,/1/5'3/6-5),+70-3 % I < %@ !; @ F12)43-3768)9+2:;}< / +2;>;?+2:;6L'M12)9+2;>3O'*;>3 XZ),+1 @ ( B % @ + (G @ P+ ! %'QP QP 8+9'3/yu:'3/<;>=([email protected]'3BDC3E- E 3 -,+GF('H3) ! 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"-2W0J'(*,b#<="6!$2+"05476?#@*J476"H9,/%@#D)32+9,"6)+"0,'(*d%(#@*di " )`- !$-0547H9,* "':9, #D8':"2`- #pG )3#4867#D0J[\'(6!?#@4823'(0L$9 - 47#D23)E9,*"#D)3-*,)E<Z'D*,6)3#4867#D0,[\'(68!$#@4823'(0 "4/9,'(0,0 ? <,)+*, )3'D230tw%('(2+6k1#D<,2;4768 dCJ<1#D67#@I(67#D<J, dL Dy`L )( '& -, +* , ,.( ( * 1, 1, , 32 & 4/ 1, 7* < 65 0/ 1, -, , 7* -, 98;: , : : )( =& 0? @ >5 6A ? @ B C C DC 5EA Ω1 Ω2 Ω Ω3 cwgJL "c9,-*diIR- '(!·` 47623"-L R '(*J6k)3 9,'D!?#D2+0,]6"`4#D0,ID*,)K#[email protected],'D*,_#%D'(0,k-'(0,82+9 " 6: *,0!?#@23)3)3#DI(k[\'(6!· 9J T ;(CJ`4 <='(*,6_)3o9,'(!$#D230,o"'D*,68N=M#%(-.18*,6DCg0,'D*, #%('D0, "'D0,82+9e" 6:M *,0!$#D23)+)K#DID][\'(68!o 9, ; ; <='(*,6k)3<J68"!>23-6k-4c)+ 4768'D2382«"G !> N,)+'[email protected] ^T ;H<='(*,6c)39,-*did2«-G !$HN,)+'[email protected] .,0$9 #D!>")+23'(6"6n)+"V6:" 8*J)+4#47E9,*P#D)+"*,)C(0,'(*J #%D'(0,E*J472+)32+:f *,0>67# $0J"!>"054W8*,2;%D#@0B4E) #iJk9J" -'(!>!$)+!$'(054868)K#M.1ID*,68bcw L1JL ,L A C mesh mesh cwZJL H!?#D2+)3)3#DI(m#D91#D<J4dD L A = x [ :e" !$# E = E E = 1 [23 d " !$# E = [ 456 C = E y C ; = ( x$ ; = ( x$ C ; = ( x* ; = ( x* d ) d ) d ; %"! (&(' C 1, ? C * ? C9A %"! (&(' ; ; =)( x* ; ; ; =)( x* . #Dk48"4 0 ;(L [ \/ [ [ t ¬ Vy C E y C d 'D)3*J4823'(0?48"4 ~ Æ y =J Jt Æ ~ ~ Æ y =J ,t ~ Æ 1 ~ Æ y =J Jt Æ ~ ~ Æ y =J ,t ~ Æ 1 t y± Æ Æ 1 Zt Æ yV Æ 1 t y± Æ Æ 1 Zt Æ yV Æ 1 +-,/. gJL . C E y C9A C C 1, ]V6868-*,6c"0!?#i ]E668-*,6c"0 : = T "! (# ; =)("$ : = T "! (# ; =)("$ y C E 1, 1* d 'D)3*J4823'(0O48"4 ~ Æ =d ,t Æ ~ ~ Æ =J ,t~ Æ 1 ~ Æ =d ,t Æ ~ ~ Æ =J ,t~ Æ 1 1 Æ 1 Æ +-,/. gJL ; C t ¬ yW ¬ [ [ !\ %[[ ; #; A t y1 , 98 : ]V686"*,6c"0!$#i ]E668-*,6c"0 ! (27 ; T %! (27 ; ! (27 ; T %! (27 C 5 A A ; %! (&(' ; %! (&(' ; ; =)( x* ; ; =)( x* d ; ; = ( x* d ; ; =)( x* #Dk48"4 0s L C C C C C C ; ; ; ; ; ; ; ; "! (&98 "! ( &98 ; = ( x$ ; = ( x$ ; = ( x$ ; = ( x$ < t t 8y y ¡ , : Á)5"4R`%:239,-0B4 AB*,E<='(*,6)3-9,"*:io#D47-4 <,6:" =- 9,"0548"C)3V<1#D7#DIDW9J E # G E #D!·" )32+'(68 "'D0,82+9e" 68#DN,)3-!$-054E)K# AB*1#D)+2+4dk 9J_)3# 8'()+*J472+'(0/<,*,2+8AB* '(0?<,#D8_9 *,0Jm-6868-*,6E9,= c ) '(689J68 k9, ; = ( C ; = ( <='(*,6 E = # G ; = ( x* <Z'D*,6 E L_m'D48'(0,W#D*,82=A:*Jm)3#H"-'(0,9,m8'()+*J472+'(0 M Æ 1 "4_N,23-0F#@<,<,68': - #D*J882NJ23"0F#%(- E = AB*, E ¬ L ¬ [ 456 [ \ [& [ Mt yW 4? 1, :e" !$# E = C C $ E = [ :e" !$# E = [ C = C ? -, 98 t y1 : , < t ]V6868-*,6c"0!?#i ]E668-*,6c"0 ; ; ) ; =)( T %"! (27 ; ; ) ; =)( T %"! (27 "! (# D ; =)( ; T "! (27 D ; = ( = ) "! (27 = ) ; = ( ) "! (27 = ) ; =)( ; ( "! (# T ; =)("$ ) T "! (# T ; =)("$ C 5E5 5 5 C A A 5 #Dk48"4 A 5 5 5 A ; =)("$ d ; )= ("$ d ; )= ("$ ; =)( x =( ; =)("$ ; =)("$ ) ) ; A -* ? E \ C E ) ) ; d 'D)3*J4823'(0O48"4 ~ Æ y =d ,t Æ ~ ~ Æ y =J ,t~ Æ 1 ~ Æ y =d ,t Æ ~ ~ Æ y =J ,t~ Æ 1 t yV Æ Æ 1 Zt Æ y± Æ 1 t yV Æ Æ 1 Zt Æ y± Æ 1 +-,/. gJL . C E : = ; "! (# ; %"! (# T %"! ("8 T "! ("8 ; ( %"! (& : T "! ("8 #Dk48"4 0 JL [ [" t ¬ yE C E ]V6868-*,6c"0!?#i ]E668-*,6c"0 d 'D)3*J4823'(0O48"4 ~ Æ y =d ,t Æ ~ ~ Æ y =J ,t~ Æ 1 ~ Æ y =d ,t Æ ~ ~ Æ y =J ,t~ Æ 1 t yV Æ Æ 1 t yV Æ Æ 1 +-,/. gJL . C E 1, -* 0 ,L t 8y y ¡ : , R '(*J6±)3-n#@n47-4 0 ]-4 PtjIR- '(!·- 47623W.18*,6: yn) #D01#D) d 9J"V6:- 8*,);4#@48n-4E!>'(230,- %:2+9,"[email protected] ]V0·Z-4CV9,#D0,/)3?#DP9,Q)3#<,68-!$2«"G 68?8'()+*J472+'(0zt t Æ y/ ; t Æ ~ ~ Æ yb-4 Zt Æ y/ ; t~ ~ 8 y c y 3 ) , < D # 8 8 D # ( I / , 9 # G , 0 D ' , * = < " 8 6 !>-4 9 #@!·- )323'D68"6_)`- IR" 6"!>"054 )3# E E Æ Æ AB*1#D)+2+4d 1 9,/)K#O'( )3*J4823'(0CZ0,'D*,H<1#D8'(0,H"0 = Z-4H9 *, 0J>-686"*,6H9, ; t<; y>#QG *,0JP#D*J476P9, ) '(69,68/9, ; = ( t ; = ("$ y -4o"-"2E<='(*,6H)3-o9J"*di <,6'(N,)«"G !>"47-4L R=)#D( 6b-'(05=)47(6$<='(*,6)3#"-'(0,9, 8'D)3*J4823'([email protected])3c8 " !$#b#D8':"2`/ # G E = 8"!N,)3c!>23"*:iP8_"'(!><='(648"6V8*J6W*J0?9,'(!$#D2+0,f.18*,6:_ AB*, "-)3*,2 '(NJ48"0B*<Z'D*,6 E CZ#D)+'(68mA:*JM<Z'D*,6 ) Á" )3#D4823-2+4dH )+230 " #D236o0J'(*,#%('D0,*,0,/#@!·- )323'D67#@4823'(0 "0F<1#D7#D054m9, E = # G E L . "'D!$<='(648"!>"054c<1#D68#D9,'iJ#D)"4]<="*J4 ` 4768o9V* #>G )3#/4867#D0J[\'(6 !$#@472+'(0OI(-'(!·` 47623AB*,AB*,20 "4_<1#@ #D8 o6:" ID*,)32`" 68 ,L .10Q9J]47-47-6f) 230dh1*,"0J" 9,m)K#b4867#D0J[\'(6!?#@4823'(0>8*J6f)3-e#@)3"*J)3td*,6f) 2+0547"6[j#D"_9,*QN,)+'d; -4]N,)3': CZ)3#>4867#D0,[\'(68!$#@4823'(0<,6:- =- 9,"0547P-49,b")3#D8 ;y`C=0,'(*J]<,6:" 8-0547'(0,H91#@0,])+b4#@N,)3"#D* +-,/. L:JL o)+"W!F- !$- :<='D47g-G 8-f7#D*d[AB*,])3#H4867#D0,[\'(68!$#@4823'(0P9,*$N,)3': ;]-4eb-4e)K#H!F- !$cAB*, <='(*,6k)3NJ)3': C,"HAB*,2-'(686"8<='(0,9p#D*9,'(!$#D230J9,H)K#.1I(*J68bcw LJL QL -? 6C 6C sol cwgJL #P9,-*did2«"G !>IR- '(!·` 47623DL 6C ( A * [ 23 d - !?# E = C [ 1 \ [ - E C E E = E E = 1, 1, C C Mt ¬ yV ¬ * ]V668"*J6_-0F!$#i ]E668-*,6c"0 d ) %"! (2' ; T T ; =)( * d ) %"! (2' ; T T ; =)( * ; =5 %"! ( = DT ; = ( ; =5 %"! ( = DT ; =)( d '()3*d4723'D0O47"4 ~ Æ y =J ,t Æ ~ ~ Æ y =d ,t ~ Æ 1 ~ Æ y =J ,t Æ ~ ~ Æ y =d ,t ~ Æ 1 t yV Æ Æ 1 t yV Æ Æ 1 t y± Æ Æ 1 t y± Æ Æ 1 +-,/. gJL C [ !\ [[ ; %"! 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G IH $\FUC#| $qB 3RB | $q*CSMVHo" O > 6k+ 5(F17`!+Y7 -5+r20O(I4 QW "YX V $\ "]X V $ K[Z KZ _^ 4 qr V PH $ 7 K PH $ 7 V P H $ 7 K P H $ 7 " O [email protected] 1 [email protected] ^ " O [email protected] 1 [email protected] ^ " @ [email protected] [email protected] @3 3 " H#Ku1LO 3Q H 1L 1 $ H K 1LO 3Q H 1L 1 $ H [email protected] H [email protected] H [email protected] H K K1 3 QT ^ IH $\7>F5&j$ K 1 3QT ^ IH $\7>F5&j$ H#K [email protected] H H -K Z S K $ PH $\>F Q d4 $ H#K H [email protected] H K $ I H $\>F Q 4d$ 1 `7!+( +`! 6$+1 .(D0)(<!+0+7 -3+0$/ NE IH $\7 " H K K IH $\>F Q EI$ NE IH $\7 " H#K K IH $\>F Q E > G0+`/q0z"1 :1(I.\0.([email protected]> M ^ > ^Y75(-!+Y7 /30$DL 4" IH $\ " H#K -K$ PH $ 7>F&j$ PH $\ " H#K -K$ PH $ 7>F& > t[$$57+$F)[email protected]$ ;)+ 7 iY5(<!+Y7 A30$G z H 7 ["wbL 4 1QL w$ L 4G5(D1 451 ( .\0.(I2zL G5(Y1E451 9(I 0701 +1. 0z w RwF78(`[email protected] <;*u$I3$*7 *7 3+1+`1 fd V$P(78(I7$a1 [email protected]> `+ 1 q 0$0z2++aqr0++5 !$ *< [email protected] 1E2g+^[email protected]^[email protected] !+A9 3S/3" O(7d ! [email protected] [email protected]{\ $5$+$F7 K > 3 ^ > c 3M| "| > 3 > | 23N| V " *!f1> G!+40O(5n P0O(5n G $+ R+0$!+$5A!A1 t[$$57+$`3"+$ " h| ( " 9d * !f1> 90 O(5n P72)(8n G $5++ $ #" &% ('*),+*- ('*),+1032 457678 ^9d, B 9$ .+./ *+ / :% 0 (+A;)+3"+$/+gV @L( I$5 h5 @ 3+1 2zf1 j305I0g0!+%@ [email protected] 7Go+ " |M > " [email protected] $5`7 !7$ I2y+1 @)(Y1EA;*+01 ,(9<! +H1 401 ( 3++;)ft#3056!ft#++H7$$57+$Y!+ 1?t#$5!+$6! q| <3'$ " | > | V -3"+$ " 9d 6G3+1 +z+7-701 +1 YO(-3"[email protected]!+Gr201 !+7$ 1 D([email protected] 7F+9n 1 Yq 0$H 5(97 <0=7*!+/!Y :(I5(94! 2+F1 Gq2!+$/!+/1?t 71 05( (9-1 Yq 0$2d ? .+*; *+ >= / < &= ? ;: ?a > A D & E . > ? <+7!+7ar201 !2(I+3$*7 "7! +O([email protected]@ 7a O(97$ *74>[email protected]> 7P3+OpOn ;)+7D31 +$*q 21 8(IA>r0 $1 Y!.^ [email protected](I+a!ft#+y+1 *<[email protected] @ -y+!+ @ 7 0++71U;)+'9ln 73'[email protected] +:& "BE| $q*C 3RB |$q*C d26h @ 3'5:!73 [email protected] 7O(&)+15+$W((1Yy"$! ^q$ +$7z 1 6^T07GgO0+ .(A!+$,(I:5O(A1 y$7H(A1 :!73 +1 [email protected])(A5+$G1 hy"$!e5+37$ 5 +$G78([email protected]"* Bfz 7r :" |z[|d 3'0+$Y1 /($I0.(I 0fzO(Tfz r I" |9z n |d &3"[email protected] 3+$575 Z .d 7Y9.b 7 O(I 3+Op*;*7H5O(<!++ -3+0$ o"| > 3%| K .( 5"| > | 3M| K z+0(+F;)+ 7F7*b 77O(I<7$5$3"+!+)(jj> +ky+1 *G!+/q00(I+0+ sr$<XYE0$51 .( C FB ld / / uD g N= 0 g N= 0 BDCFE 8 ^*d B [email protected] L.( I$5 6 (I$0( .(<[email protected] 3+$5 fd "!$# &%(')+* ,-/. " [email protected],% 7I* ,% 73CJ'K)3= 1L)M = ')38N9O-?0CP4P4Q0;R) 7>S8%T-?0CP4P4Q0;R)UR12,;7 73CV)31>') K h )3EY8%+-?0CP4P4Q0;R) &%:') ) 73EM)3%kj .D,8\1 0^ 3 0^ " | 9 012)31546) 7')389:7;* <>)3= [email protected],4B8-+) 7 &%DC67 u .D,CP%DEZ7[.D,8\1 )3EM)3%lj )3= ED)q = pf0CPEY.D,815,cdEr)3%DCP1s0I e .D)385.b1) e 7t4Q0O- .D,81 G3e0 " | )3E " GF .D,CP%DEP7I'W0% 7/46)A*X07 " %H,8G7 |]D^ %_)Z`a)3E F .D,81U46)L.b12,cd4f3e) -+)g4BCP%A)d= 0CP1 ) F 4Xhi)3112)38\1 "Q ]Lm )O* <D,Cn9k') Dn" o )3E K " o 9| 0 )3-+)u.b1q);= *3C673CV,%v'W0% 7t46) 7A')38N9_*X07 ] V 0+$& 11 +8(I$$W17&$* +1,(2(&)[email protected]$ ;*77zO+aqr+P571 ( +` [email protected]:y+1F!+`7$y"7P;)+ +<[email protected]:y1 7O(<g+,oq2(r077dxw<+/73'/1 /1+gh!+/1Eh!+$5( H " ; BDCFEd'^9d[ziBDCFEd#^9d c%lz ++Y7+3"`1 1 g6!+D1 H!+$0(I:M" o0 BDCFEd9^9d zkBDCFEd0^*d k(&+`73'D1D1 0+g6!+D1 H!+$5( " H BdCFEad ^9d ^*z BdCFEad ^9zd y%.dcXY7A70+$y"7/^BO(:23+30$0($h1 /!Y73 +1 [email protected](IT+0$54O(01&.( r$5( q2F1 Y0+ ;)+/[email protected] 3"I0O(7F!+k(I77$-!+F7O(I$0 O(7F!+4XD0+O| p {d [c D . 7 A sol_o_k0 sol_o_k2 sol_o_k2_def sol_o_k0_def BDCFE 8 ^9d5B !# "$%' " o " 9z$/" 0.3 0.3 0.2 0.2 0.1 0.1 0 0.2 0.4 0.6 k = 0 et x = 1/2 0.8 0 1 0 0.2 0.4 0.6 k = 2 et x = 1/2 0.8 BDCFE ^'& B ( ") *+,+-/. + 0*+ 210%34.5 -6)7*%"$ H " 8" % " " *z$ " *|k& ; 8 o Deplacement horizontal 1 |9zu " ; 9 Deplacement horizontal 0.3 0.3 0.2 0.2 0.1 0.1 U 0 U 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 0 0.2 0.4 0.6 k = 0 et y = 1/2 0.8 −0.4 1 0 0.2 0.4 0.6 k = 2 et y = 1/2 0.8 BDCFE ^'& B (+ "3) *+,+-#: 54-; <10%. 5=>?*+ %"#0" ?"$%# " " *z$ " *|k& 8 o9|%& Deplacement vertical 0.4 V V Deplacement vertical 0.4 0 " |z$ o o ? 1 |z " ; Composante xy de sigma 0.5 0.8 0.4 SIGMA12 SIGMA12 Composante xy de sigma 1 0.6 0.4 0.2 0 0.3 0.2 0.1 0 0.2 0.4 0.6 k = 0 et y = x 0.8 0 1 0 0.2 0.4 0.6 k = 2 et y = x 0.8 1 BDCFE ^ & ^(B {-0 ->10 4 =2%(0+1 +%2 %*;:81 %4.5 -)6*%"$a " "$%' " |9z /" a "9z$ " 9|k & 8 o . 7 . > A sol_o_k0 sol_o_k2 sol_o_k0_def sol_o_k2_def BDCFE ^ & B !# "$%' " 8 $ Deplacement vertical 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.4 " o " $/" −0.3 0 0.2 0.4 0.6 k = 0 et x = 1/2 0.8 1 −0.4 0 0.2 0.4 0.6 k = 2 et x = 1/2 0.8 1 BDCFE ^'&dcB ( ") *+,+-/. + 0*+ 210%34.5 -6)7*%"$ H " 8" % "u " " $ " *k& 8 o9%& Deplacement vertical 0 V V o H ; o ;y ; 9 Deplacement horizontal Deplacement horizontal 0.1 0.1 U 0.2 U 0.2 0 −0.1 −0.2 0 −0.1 0 0.2 0.4 0.6 k = 0 et y = 1/2 0.8 1 −0.2 0 0.2 0.4 0.6 k = 2 et y = 1/2 0.8 BDCFE ^'& xB (+ "3) *+,+-#: 54-; <10%. 5=>?*+ %"#0" ?"$%# " " $ " *k& o 8 1 " o −3 5 x 10 −3 Composante xy de sigma 1 x 10 ; Composante xy de sigma 0 −1 SIGMA12 SIGMA12 0 −5 −2 −3 −4 −10 −5 −15 0 0.2 0.4 0.6 k = 0 et y = x 0.8 1 −6 0 0.2 0.4 0.6 k = 2 et y = x 0.8 1 !#"$%'&(%"$)!#"$*+*$%-,.%-/&(01!%2()3%20(4&(%5#0(6879:)30("+;<#4*=>6-0([email protected]%BA.CED [email protected](BFHGCEIKJMLNCOPQ#R S%-TFUG.CV [email protected] XI/S8 Y[Z\Y ]_^`^ba>cd^fehgji ' l k m cdn[g l ^ oqp:r.i a>c2e l ats l'uwv ^`^xg mxly{z | .)30(?([email protected])!%~} 0q%~*+%4q*$ 6&(%~#,.,% 626-0(?M%40(.&(,.#"$(%E 62,[email protected]#0q(%4()!)!0q!% ("+%N&(%#(&62"+!620q*=#"+!%&(%[d9#IKI/F;#"$ +dI/S\b %?(!#(*H%- ,.%6-()3"$&5%- K% "+62"5%-)3*+% ,1%2 ,%>} 0q%FH/+SF?#%XI/S8 %.&q,N<"$(%>-% #?<)B3%26-#(0q*=#"+!%#J"$*x#0qB#*+!)?qK2% 6-"$)3%2 *$%-)%-M%-!)~&(%'*$T<()33,N"$#[)!0(*$%62#*$6-0(*&(%-)4¡(0K¢M £¤:<?(?(*$"+}/0#*=3,0(*+%&(%T¥'<0()!)-J1#q"+%2 ¦K§\¨©1ª:«q¬®¦K¨°¯« D « ACEIq± 0h%2q623%#J ¦ §8¨²H³X´T©1ª1«K¬5 ¦ §\¨(µ¶³X´'·B«K¬5 ¦ ¨B¯.« D « A C¸Iq <I % #* 5*+%3 % + + *0 ! '%(& !) +*,-.0/1- K02 3!K) 4*5 K 6/1 K K6207 K !"%$# 8 0 +"30+3 +310% ) 0 1 0 547 + , 31 4/ 1 9&+,/*;: 5"400 " :*,; 7=<>2 & % %>* "$10 -#.*%[email protected] 3%1 .13*:B % +3*+ b 1 3* C [email protected]!GH C KJ$LA*5MON *,MPN + [email protected]*,HT UTVT>/XWY[ZV/]\G/ 2 2 2 IDFE I ID DFE D C [email protected]! C 5_*5MON ) [email protected]*,HT $T`TV/3Wa4ZV/]\ 2 2 7 ID^E I ID D^E D *+4#. " %c2 " 6d "4 fe=% MPN K K *,HT 2 -.gQNS*,HT 2Yh MPNi K *,HT 2 - K QNS*,HT 2 _*,MPN 2 )fgQNS*,HT 2 / % MPNi.A*,HT 2 - K QNS*,HT 2Yh MPN K A*,HT 2 -.gQNS*,HT 2 " k*5MPN K K *,HT I o k*5MPNl.A*,HT I . 1B M Nl K *,HT 2 .gQNS*,HT Y2 h P M N K A*,HT 2 K QNS*,HT Y2 h P 2 K QNS*,HT 2 .gQNS*,HT 2g2 Tnma`T 2g2 TnpVT 7 k*5MPN K K *,HT I *5MPNl.A*,HT I M Nl K *,HT 2 K g QNS*,HT Y2 h P M N K A*,HT 2 K K QNS*,HT Y2 h P 2 K K QNS*,HT 2 K gQNS*,HT 2g2 Tnma`T 2g2 TnpVT 7 j ! #r+q ,#"%3c K %1 K ! o 4 1*+ 104+ '+ +1Bts 4 x* vu / #1u %2 10%3/"6" 0Qz y Q u >>)/0-09&=+0 9�#w ?w/ 7 { 6?5`| +1 0!6 }\GZk~3\Z,"$4=01#" %#1 1 %1^ 4+1wH w ^V~X\GZ "$-1 "%3(w K _*. (_ D& ^ & Z`Z 2 a& H ! " + +!*+310 + )7104|% 0 < %1 .31 "3 2 %60,+,+- 51 ) +*0 " % 4+1 0041 10 %1^'3?51+& { 10*;: ? . %,+1S 31 %3441' 1 *+% *0 +1 "3 -::& : r*$1'*;:+ & 6"$-g1 2 %3 1 +/4+1/'+ 1 %451/=% + e=%1 %316 .1 516*+P e=% 10% 1 +4+*03 % +310+ *+ % $+i1 e=% %31 1 + 3+- 10| * 504. +1+& *+ %" 1 %4.5 - c $ ,1 %" 0% >)1010%30 *. Sf|%30+1 _ #& ^ & Zj\f? '& ^ & ZU; ? #& ^ & Z <K2 & 3441 5%Gd j Oy w Zj\GZ ΓN ΓD Ω1 Ω2 Ω3 ? 8 ^ & Z 4( 0% & +1 *%g 12- "" 5jq01 + " *+ -1* :30 +-;52. 4* +1*+," 1 -1 % " +,+20+1 +% # *;:: kZU +1 * "$10 -+1 % 2 10%3+1 *-0 -1 2 %*;: & % 4 ('} Z/ "%31510 1 91 '! %1 "'+ 1 +-31#%e=% -1 *%"$+1 10%3," 5 491 %" 0%09%83?5 401_e=% "$% ('\ +1*+ 40315%Gd(,40+1 + + " *+ =-e=%/*00/1 '! 00 +1 0,"% 4<1 # */ *++1 1 40/3 .4 *e=% 10>" 51010 31/" #43 + %0#% 4 & . 7 7 ! #*41 G% d8,40+1 B nu u 7 \ 10%3)?" 0 10%" 04+% 6 Q u h 7 \610% /" 0#43 + +%30 Q u & &% % :{ sol_o_k0 sol_o_k0_def _ 8 ^ & ZVZ { > 4)`| 440) $ "3$+& 1 0 50 & { +1 .5 4+% 1?4(4|% $0 r 1 10% 710 =? + +1 " 3+%Gd*+%3$+1 )"0 9&+ *+ 0010"$ & )(" 0,:0 +- * 7 V\ ZV/ 2 <(10*+3 *+ 010"$ ( & h " 4*+%3$ %31e=% %(3( 1 10% $`1 *+41010 *+%3 .'4|B & 7 V;3& = Zj\V\ Deplacement horizontal Deplacement horizontal −0.06 −0.13 U U −0.08 −0.1 −0.135 −0.12 −0.14 −0.14 −1 −0.8 −0.6 −0.4 k=0 −0.2 0 0 Deplacement vertical 0.02 k=0 0.03 0.04 Deplacement vertical 0.2 0.03 0.15 0.02 V 0.04 V 0.25 0.1 0.01 0.05 0 0 −1 _ 8 ^ & Zj\ 0.01 −0.8 −0.6 −0.4 k=0 −0.2 −0.01 0 8+ " *+ =01B %"$>10%. 5= 0 0.01 7 >\*,$0 Composante xx de sigma 0.02 k=0 0.03 0.04 10%3"+ +%3> 101 %0 2 & Composante xx de sigma 0.04 0.35 0.3 0.03 SIGMA11 SIGMA11 0.25 0.02 0.01 0.2 0.15 0.1 0 −0.01 −1 0.05 −0.5 0 0 0.5 0 0.01 k=0 Composante xy de sigma 0.02 k=0 0.03 0.04 Composante xy de sigma 0.005 0.5 0 0 SIGMA12 SIGMA12 −0.005 −0.01 −0.015 −0.02 −0.5 −1 −0.025 −0.03 −1 _ 8 ^ &Z!; ," >)1010%30 2 & −0.5 0 0.5 k=0 −1.5 0 0.01 0.02 k=0 1 -1%,10%2 2 %*;:rB %"10%.5 - Zj\`; 0.03 0.04 7 >\*R 1 %" 0% Composante yy de sigma 14 0.05 12 0.04 10 SIGMA22 SIGMA22 Composante yy de sigma 0.06 0.03 0.02 8 6 0.01 4 0 2 −0.01 −1 −0.5 0 0 0.5 k=0 ? 8 ^ &Z < "$15=0B %"$>10%. 5= 0 0.01 0.02 k=0 7 >\*,$0 0.03 0.04 10%" + 04+% > 101 %0 2 '1 -/4+1 *+%3$+1e=% "' *`& +- + e=%}e'%3 19* 1 5%Gd ,40+1 404*;:1 -.02+ 1#"%3 1 ")5*++,+-01> 1 ae=% "%3 1 * "$10 -+1 % "00 ,+ 10%> ) >40*;::3 * 4+1* 1 +% 1 -#.0+ +1 + #" % )#*%"$1 %4.5 - _ 0,10%" 04+% 101 %0*. +1lf| %01c_ &-^ &Zj\#S? &^'&Z <>2 & { ") *+,+-:0 +- +1 0"' 10+- 6 +83+%Gd8*+%3$+1 3-) " +,9&+ 9 +"'+ 1 +-/* *+ "$15=0 1 %4.5 -9) 40 * h Z 2 9) %Gd 9&+,,"' 10+-0 ) 10%,% ") *+,+- 1 % 10%3"+ +%3 #) 101 %0} * "$%*+ #" 5 4 *+%3$#+1 3 #+ *+' +1 *+%3 .'4|?1 2 & :% m ) 7a-)3 -+) 7a*X046*384z7I,%DE_)3= ED)>= )Z`a) *38>) = 7>[email protected]) *M46) 7;* <>)3= [email protected],4B8\-+) 7&%DC67a07 7;,;*3C ) = 7 0 e :t\] ,8W7 [email protected],% 7a1 )3-?01d8>) = d8 h 08tp ,%b'O')>4Q0q7 73812) F CP4O0O8%H)MR1 0%b')I'C `)3= 12)3%H* )t)3%DE 12) 46) 7>* ,8;.D) 7/1L)d= 04BC67 );= ) 7L.D,81/46) 7/')38N9 - )3= EP<D,d') [email protected],4B8-+) 7& %DC67 ( )3E } G\ F %H,E 0- -+)3%DED.D,8\1 46) 7?* ,-/.D,;7d0%DEr) 75'8TE)3% 7;)38\1 ') 7O* ,%DEJ1 0CP%DEr) 7 ') & 08D* < ]! h 0" 0%DEL. 07?* ,-/.b1C67 4Xhi,13CQRCP%H) ') * ) 7 'C `)3= 12)3%H* ) 7 F %H,[email protected],% 7U.b1q)Z= pq)3= 1q)M = %H) . 07t12).b1q) = 7;)3%DEr)31a46) 7I1L) = 7384BE 0EP7U.D,81 : \ ] . 7 7 ! *+ 4031 G% d ,40+1?B 10%3/" #43 + %0## u `u 3& vu 7\ sol 10% /" 01 %" 0%0#3$# u sol _ 8 ^ & Z_^ { > 4)`| 440) $ "3$+& 1 0 50 & Zj\ < h 7\ Deplacement horizental Deplacement horizontal −0.04 −0.02 −0.025 −0.05 U U −0.03 −0.06 −0.035 −0.07 −0.04 −0.08 −1 −0.5 0 −0.045 0.5 0 0.01 0.02 k=0 k=0 Deplacement vertical 0.03 0.04 Deplacement vertical 0.02 −0.0454 0 −0.0456 V −0.0452 V 0.04 −0.02 −0.0458 −0.04 −0.046 −0.06 −1 −0.5 0 −0.0462 0.5 0 0.01 0.02 k=0 k=0 −3 15 x 10 Composante xx de PK1 0.03 0.04 Composante xx de PK1 0.06 0.05 10 PK11 PK11 0.04 5 0.03 0.02 0 0.01 −5 −1 _ 8 ^ &Z? )1010%30 2 & −0.8 −0.6 −0.4 k=0 −0.2 0 0 0 0.01 0.02 k=0 8+ " *+ =01 2* "$10 -H-._B %"$ 1 %4.5 - −3 20 x 10 Composante xx de sigma 3 0% 0.08 SIGMA11 SIGMA11 7 >\}*,$0 Composante xx de sigma 10 5 0.06 0.04 0 _ 8 ^ & Zj 0.04 0.1 15 −5 −1 0.03 −0.8 −0.6 −0.4 k=0 "$15=0 −0.2 0.02 0 .B %"$>10%. 5= Zj\9^ 0 0.01 0.02 k=0 7 >\*,$0 0.03 0.04 + 04+%>) 101 %0 2 & −4 15 x 10 Composante xy de sigma Composante xy de sigma 0.05 0.04 SIGMA12 SIGMA12 10 5 0 0.02 0.01 −5 −1 −0.8 −3 3 0.03 x 10 −0.6 −0.4 k=0 −0.2 0 0 0 0.01 Composante yy de sigma 0.02 k=0 0.03 0.04 Composante yy de sigma 0.045 0.04 0.035 SIGMA22 SIGMA22 2 1 0.03 0.025 0.02 0 0.015 −1 −1 _ 8 '^ &Z?c −0.8 −0.6 −0.4 k=0 −0.2 0.01 0 0 "$10 -+1!z ! _B %"$ 10%.5 - 0.01 0.02 k=0 7 >\k*R 0.03 0.04 06 + 04+% 2)1010%30 2 & !"# 20+1 + 0`%1 0+1 10 00 1 *;:+ %1 .1 *;:31 %2.5 4+%<%$} 7=< " *;:, ) . 5+%3 *0e=% 7 ^ & { 1 *;: + 81A 1 3+ *+,"$ & { +19+ " *+ -1 10- 1010 - +16 +q ,+1ke=% *+%Gd!V +=%1,"$%$ 7 < 0^ + 0. 5*;: 1,*-0 -1 "'+ 10-+- 1 "*1 "4%1?4 "$ -1:e=%7*+%Gd `10 . + 1 %" .5 - & 1 "$%'*+& Xe=% %31 . 1"3'+ 1 +- e=%>+1 *%"$+1 +1*+ =0 4-+1* .4?? &#^ & \ 2 & H y y sol sol _ 8 ^ & Z;y { > 4)`| 440) $ "3$+& 1 0 50 & Zj\ Composante xx de sigma Composante xx de sigma 0.04 0.25 0.03 0.2 SIGMA11 SIGMA11 0.02 0.01 0 0.15 0.1 −0.01 0.05 −0.02 −0.03 −1 −0.5 0 0 0.5 0 0.01 k=0 −3 4 x 10 Composante xy de sigma 0 SIGMA12 SIGMA12 0 −2 −4 −6 −4 −1 −0.5 0 −8 0.5 0 0.01 k=0 500 0.15 400 0.1 0.05 0 −0.5 _ 8 ^ & \ ,"10 0.03 0.04 300 200 100 −0.05 −1 0.02 k=0 Composante yy de sigma 0.2 SIGMA22 SIGMA22 Composante yy de sigma 0.04 Composante xy de sigma −2 0.03 2 2 0.02 k=0 0 0 0.5 k=0 0 -13 B %"$91 %4.5 - 0.01 0.02 k=0 7 V\P*,$0 0.03 0.04 10%" + 04+% > 101 %0 2 & : >1 "$4=01 +1 10+-0+41 51 )2104/%54 1z| 3+1 0 541 1 )24 *+ 4150 %7 d % +1 *+-0 -0+1+& 1 >"$+%3kq r+q ,94 "$-He=% ?, 04. 9 * 0 . 5 & " 5 % * 5 *U+& 2*10 .55064 *+ 4+1 1 *;: + 1 . %,+1Y1 1 +3+0 - "4%1 5"3 1k6& 1"3:+ r& +1'* %d & { +1 `+ G% d 1 %4.5 -1 "' 10+-0+-> *+,"$ 0+,+- 3% ?d 4/% 9) . 5+%3 `3104% _1 * @ 2 @ +/*4 )0 *4 4 "$1' "$%< '?Z2 +/*4 %6*10 4+,+- ,"$1' "$%, , r \ & { "1 40 % ?jd34/% 1 + 8* + +1 " ) 40+1 * 0 | 2 & 31?e=% 9 % 3%( d /%3 1*-0 -1 +1 Z & w Z{ ; Zj\V 0 *0 . < 7 ZVZ 7 >\GZ? Zj\ { { { 3& V\ < 7 > 3& >\ ;> 7 V; V\ 3& >\ Z 3& V\ < 7 >\ Z 3& >\ ;> 7 Z_^V < 3& >\ \ Z 7 < GZ 3& >\ \ 7 0^ < 3& V\ < ; 7 Z < 3& >\ ; ^ 7 ^GZ 3& >\ \ 7 ZjV\ 3& V\ ^ 7 V\ >\ 3& >\ < 7 \ V; 3& V\ ^`; Z 7 < \V\V 3& >\ < Zj\ 7 ^ Z 3& >\ \ ^'& \ { +1 . 5+%301 4+1 "$10 12% ?jd34/% +1 +* =0 4-+1& y y ? Z? \ y 45!6 8 8 9 + e=% e=% 4 ?d 4/% 3+1 0 1 *+ "$15=0+1 @ % 10% *+ q4 9*4 ) 0 *4 ,"1'+ 5& ?d 4/% +1 4 *+ 41'2 1 % c$0 ) 1 10% (#%& ,| & | +1 + "$+ 5= 0 * * \ "$% ) *+," 1 - 2.5 0`4"$% 1 %Gd %3001* "$10 -+1 < A/ ^; "$%2 . ; A/ < "$% { { { { Evolution du max de sigma11 U{ Evolution du max de sigma12 0.35 1.5 0.3 104 MPa maxsigma12 104 MPa maxsigma11 0.25 0.2 0.15 0.1 1 0.5 0.05 0 0 0.05 0.1 Ud 0.15 0 0.2 0 0.05 0.1 Ud 0.15 0.2 Evolution du max de sigma22 104 MPa maxsigma22 14 12 10 8 6 4 2 0 0 0.05 0.1 Ud 0.15 _ ^ & \GZ { . % 3%( d /%3 1* "$10 -+1 0 *0 4 "$1'+ & 8 Zj\ 0.2 . {} { + * 3 { 10 4+,+- . Z? y 45!6 8 ^'& ; { 7 0^ 3& V\ ^ 7 Z!; 3& V\ { 7 >\ 7 >`; y y y \ { & >\ 3& V\ ^ 3& V\ < 7 >\Z & >\ V; & >\ V; 7 GZ < 3& V\ < ; 7 >\`; 3& V\ 7 V;V 7 0^ & >\ 7 V\9^ 3& V\ < 7 < ; 3& V\ 7 V`; & >\ GZ Z 7 < 3& V\ GZ <7 <V< 3& V\ GZ +1 . 5+%301 4+1 "$10 12% ?jd34/% +1 *+ =0 4-+1& 7 Zj\ { < y yy ( +q , 0re=%( d /% +1, 1 *+ "$15=0+1 @ %0+1 +% *0q + 3*4 %*+10 4 =,"$1'5 & ?d 4/% +1 4 *+ 41' 1 %>$ 3, 101 %0 & %|4 & /5| +1 .5 0`4/" %#1 *,"10 -1 3 A/GZ "$% }. 6/SGZ "%3 ^ A/ " % .&% ?*+10 4 = 4 "$1' 1 _\ < 0? g e=%e'%394+1 1 * "$10 -+110 ='* 51'+ 12 1)6r+q ,#" 1040 k 7 >\ tGZ +& ?{ { { y Evolution du max de sigma11 a{ Evolution du max de sigma12 2 10 MPa maxsigma12 0.8 0.6 0.4 4 104 MPa maxsigma11 g{ 1 0.2 0 ?{ 0 0.05 0.1 Ud 0.15 1.5 1 0.5 0 0.2 0 0.05 0.1 Ud 0.15 0.2 Evolution du max de sigma22 104 MPa maxsigma22 5 4 3 2 1 0 0 0.05 0.1 Ud 0.15 _ ^ & \V\O { . %30 % d /%3 +19*+," 1 -1 *+41 44+,+-24 "$1'5 & 0.2 . { 6 A{ 8 Zj\y { 6+ *0 % 8 /"'+ 10-+0 e=%64/, }Z 10 *;: -e=%64+1*+ *%1 6 ' 51'+ 1 %101 "$%4 , S \ & %1 .31 6 " 51 +1 0*+1 ? %01 -0 4+1 3+%Gd ,'+1& % +* +1 +*0312" " `|54 % 1 10% *;:3+0*;:3 10%.5 - % *+ 4U+& 0 6& 0+ 4+ 4+1 'A |31 + `|< +1+& *0U+& >+1 4# % d /% >*+ =0 4-+1& { +1*+-0 4=0+110- * 4*+%+ +1 G% d 5*++11 *+4%1+&v 4>0+1 +% +1*+-0 4=0+1 2 %*;: _& *;: `e=%?*+4%4 rQrQr ZV/ 777 / D D ; -9 0,?*+4%4+1 4 10 1 10'*+#%3( d /%3 "$ -10% )/30,#+1*+ =0 4-+1 6* Q 2 d * 2 / + 10|>) @ DaD *+#3 6*++4%4 Q=& .* >= { { { ; Q C { * Q B2 { *rQ 2 { @ * 62 7 @ 10%34 0+ 4>%( d % | V 5 & { *^ & 2 y d y P* { 6* Q 2207 { +1 " & 001 ":'10e=%1 10- 1 47* 51 % , & ("!'$#5 % -35-g$ + -F %# *;:: + 16" /16*+'A,*+4+-163 { 5! ! & +16%G!d * 6 *=01610- +%Gd> r+q , 33*4 % '%4&% %| ,& *^Z $ $ *FZ \ $ ~ :/ o 2 h 2 \*FZ Z $ ~ 7 o 2 { , `|+,+-10 0 3%4" +1 Kq +1 7+ 1 0*4 5 & # 1 "05e=% ve=% *+3=e % %>*+4% +1 ,?| + 401 4% 5 %#%3(, 3%&% %| "4%1 "$ & +*+ 1 4 1 %4.5 -('*) '+-, /.1032 B {* Q 2 Z&5476983:98<;>=>80"$;?:@8$AB6DC E F(GIHKJLG"M BA 6N6PQ O " HKR ABSITU Q4Z`/ 777 / DVW H A/6 R A " QYX Z * Q 2 Z * F(G / J[G 2 / J * Q 2 J * F\G / JLG 2 / 6 " Q M AB6N6 Q ;<S "*"]8 M Q S>^ R ;$TI;/_Q ` :]T Q "ba Q :Ucd: Q =-"fe?S QgX E AB2 hiajh Z hickh Z 7 6 " Q M AB6N6 Q = Q 6-A3_]lIT Q _-;$^-8m_]SN_ MYn Q 6 M A3_N_o;$p Q _ Q 6]:qrJUKQBr X E AB) \ &ts<6UTgQ O "uABS]: H ;v ` = n ;o8 M Q M 2 S "Nw3xyQ O _-;{z-AN=BSu_ Q "i|@876908 " M Q O w/[email protected]:};<S M Q O Nl S]: M Q w Q wBx; R 38 :>T Q H = Q R TABl-=-Q ` _ Q "3S983z;<6]:~C h 4.P t7@ xw# y // * & 2 u 3- # u 7 Z!; ;3&oABS>T Q VZ / 7 77 / D H AB6 w?;>=>w3S-= Q * Q 2 Q :t M BA 6N6yQ O R ;$T V* 7 >2 X < & uT-83: Q ` T Q MYn Q 6 M A3_N_o;up Q _ Q >6 : C daY *rQ 2 K / *V'&Z 2 =$; w Q =N=BS-= Q Q " Q T>; Q 6 M A3_N_o;$pgQNO Q H w Q e?S98iT Q z98 Q 6]: ; ` M 8m_[876NS Q T F * Q 2 H "3S98BzI;<6]: F * Q 2h F *rQ 2 ~ c 7 w Q w]8 T Q z98 Q 6]: M AB69w}; ` M 8m_[836NS Q T Z * Q 2 Q : J * Q 2 X & =N= Q T Q 6[\ "]8b= Q 6-A3_]l>T Q MYn Q 6 M A3_]_o;$p Q _ Q 6]: Q "B:q836>|YQ O T-8 Q S>T BA S Q O p>;>=b JU KQ/r X "' *$ +-21 ""3e=% 2 % "0V39+& ,*V 7 2 z%(& w *+ "$ - %c 1^ 10%30 *+ *+% 3 & >\. af|% __I 7 Z3& 10%34 JUKQBr +"'+ 1 +- #3 ##1 '% & 4#?5 + ) % , `|< ( *;:31 a- 7 (c 7 & { +1 *+3441 5%Gd,4 +1<*+310 + 0$+ 1 10- 1 rq 1 e=% 31 4 " 0`|5":t & 410 e=%># 4)`| & { | 4:3 !"!# %$"&('*)(+,&.-/)102&1354.' F\G &14 $ G ',+354768+353:(9& '<;>[email protected]? ( F G A AV;>-~tZ,ACB 1& 4 $ G A 7=<D ;>[email protected]?FEG=H'1IJ0K4L&H+3;M?(&13M6 F(G A 7 AV;> &14 $ G A 7 <D DNPO Z 7 G A 7 < A>\ A$ 1& 4 QA AZj\ V? 68+3R)SEUT I8350K45V9& 68&('W)([email protected]&('[&('14 Z,A B M\ JLG 7 < ^]@_`Sacdfb eUdhgfeUd `Si dfj ]lk dfjSd ka]@m<m<n | dfb dhjhoqp i^[email protected]_ e a>]lk g[s8ptj [email protected] pujUd `vi dfb s ]@it_ eUp ]lkPa fd jSw [email protected]`xnCm 1d & e ` dfj wyDz8jUp e _ dhj a_{m7n e d b ` p [email protected]_R| ]l_ jw `8dhb jUd k e ]lk j [email protected] j}ghd e _ p^j _ pue _k d~g [email protected]` exd a dhj}ptj ] s @n i d _` j a d Z n & g(y n e _ d dfb e n wMd a d i nCi | ]l` pueUy m dw `8dhb g d b a d k e | sol 0.404 0.317667 0.231333 0.145 Lambda _ | \`; b j ] s Cn i d _>`a d Z [email protected] p d & m d up e d b `xn eUp ]lkR| Z!;Z sol 0.404 0.32475 0.2455 0.16625 0.087 Lambda ?cL | \ < b j ] s @n i d _`a d Z B ZVZ p d & m d pue d b `xn eUp ]lkR| sol 0.404 0.354912 0.305825 0.256738 0.20765 0.158562 0.109475 0.0603875 0.0113 Lambda ?cL | \$ b j ] s [email protected] d _`a d Z B;lA p d & m d pue d b `xn eUp ]lkR| sol 0.404 0.364006 0.324012 0.284018 0.244024 0.20403 0.164036 0.124042 0.084048 0.044054 0.00406 Lambda ?cL | \ b j ] s @n i d _`a d Z B ; p d & m d up e d b `xn eUp ]lkR| Z!;>\ sol 0.404 0.367495 0.33099 0.294484 0.257979 0.221473 0.184968 0.148462 0.111957 0.075451 0.0389455 0.00244 Lambda ?cL | \V b j ] s @n i d _`a d Z B V< < p d & m d up e d b `xn eUp ]lkR| sol 0.404 0.372991 0.341981 0.310972 0.279962 0.248953 0.217943 0.186934 0.155924 0.124915 0.0939055 0.062896 0.0318865 0.000877 Lambda ?cL | \ b j ] s [email protected] d _`a d Z BoGZ p d & m d pue d b `xn eUp ]lkR| sol 0.404 0.372991 0.341981 0.310972 0.279962 0.248953 0.217943 0.186934 0.155924 0.124915 0.0939055 0.062896 0.0318865 0.000877 Lambda ?cL | \? b j ] s @n i d _`a d Z oB p d & m d up e d b `xn eUp ]lkR| Z!;V; /..I0B. , . Y) , + 0^ # rJUKQ/r Z \ ; , 0 . 0 , ?03. , , ^ g )u 0, < ZA ZVZ Zj\ jZ \ | < | ; < < | ;u \ | A Z | A | >\ A | < A | ;V; A | Z7 A | ZVZ A | A> A | A < m n|dm dke| I | < {"n s @n ` p n exp ]lk[a_ m<n d p m[_m d k r.]lk g1exp ]lkWa_ k]lm ` d a dfb e n w dfj a d ka]lm 7 Evolution du max de sigma 14 12 104 MPa maxsigma 10 8 6 4 2 0 0 2 4 6 8 10 12 14 Endom _L | ;lA { n s @n ` p n eUp ]lka>_{m<n d p m[_>m d k .r ]lk 1g exp ]lk a_ k]lm ` d a d ka]lm m<n | d m d k e | i dfj a dfj { dhj `8dhb j _i e n exj ] eUd k _ j}dfep iuit_ j e `8dfb j [email protected] j i dfj | _` dfj *5_ `8dhb w ]lk jYdhj [email protected]_ de _ d iti dhj k>]l_ j k>]l_ j n eUexd ka p ]lk jho n & j n s ] p ` _k & itn w ` d m p d & ` dvd1e n & itnWa d _ a p ` dfgfeUp ]lk j e _ pqg ]l`U` dhjYw ]lk>a d k e nW Z!; < | | \; d:w `Y] w d p d& m d | | \? n& _ n | n exp ]@k{a dfj ptjUjYdhg1e ` pughd | 2 o g ]l_ k ` `Um a5nCd kk e jYj hd j j a eUpue ` d a d g d b i1d b m d k exj k ptj * {"n s nCi e _ d k>]l_ j ]lm w @n `Un tp j ]lk o oo dfe ` d m d ` ghp ]l2 k jw k]l_ j n s ]lk j n e _ p k]@_ j ]lk e ]l_`i d _` g ]@iti n g(y d b e _ d i e _ dhj `8dhb j _>i e n exj ] xe d k8_ j n @s dhg _>k g ]8a d dfb e dWb d k s ] z dhb j~w [email protected]` i d b e _ ptwMd a d b o _k [email protected] ` jUpue d b ]l`Un exp ]lk!| _[ | ;GZ b j ] s [email protected] d _`a d Z BZ p d & ` d pue d b `xn exp ]@k!| ?cL | ;>\ b j ] s @n i d _`a d Z B ZVZ p d & m d pue d b `xn eUp ]lkR| Z!;u Z | |[email protected] o + [email protected]&l0K4 )([email protected] 02+3>' [email protected]&l0t'14Z&13R)(&}45&(+?x&:' 0K3 3R+35E 0K3R&[email protected]?v&1EG='14 02)10K4 N ` (g y | n e | dhg(y | [email protected]| ; o ;V;>! < AV; o *FZ7>V 2 | \ | @n ` w d k exptd ` n ` ptd i p o +h6 19& E 0t'[email protected]+3 4! ,9& +? 0 I5& &14 I"19& ? 0 I5& @6 I () +# ;5+? 4Z&7&1354 ,0t',)(+19& EG='14 0 I5&Q6 T(19& EG='14Z+#%&1$ ?x&('H',+ID'',+EKE 02)[email protected]+3>'&>[email protected]?'7+350 I5&(' N)( y dh& Yj d n & i + * k [email protected] ` jYpue d b a p d [email protected]` jUdhp iti d bb o *^Z3$u 2 | ; ^| | p [email protected]`Ui dfe @n ka | fd z m ]lk5n eho-, I8? tE &('Et+0t'F68&*)(+# 5; +? 4L&7&1354 1& 3 19& EG='14 02)10K459& 3R+3. E 0K3:h9& [email protected]?x& N/ | S| | o d ` pud b b ?\ u o < \`; < \ o ^* Z3 \ 2 | < ^| | p [email protected]`Yi dfeho10 EG='14X02)10K45S9& 4X? [email protected]&13>'102+353R&1EKEt& o n jUj ]@k o *F3Z 2 | W ^|32 dhj e _ z ka d ` o4 +h6 19& E 0t'[email protected]+35Q,9& )[email protected] I & 68&('6W0KE 02&1I7 )(+354 0K35ID' o n exy d b m<n exp e _ dhjd1e w>w i pug n eUp ]lk j tGZ o iui puw dfjho *^3Z $Z 2 | )(+,&.-)102&1354 86 &EG=S'10K3<;@[email protected]?10K459& ^|68& 82 EG= hd j ,' e +_ E z I8k4 02a +d 3*` df6 e T IJ3 |8;M2:[email protected]=h]lE>&$_57n o"&<0 &1'1EKE4 00;M 4X0 [email protected] 4XI502+&[3 '1IJ68?& UE 8I T 3&1? ?x+&1I"[email protected]? &1'1? IJ4 [email protected]& &() )(+0K3 o S| =| b(| S| 8 [email protected] zJjYd k _m d b ` p e _ [email protected]? _m d ` ptg [email protected] [email protected] z8jUpujs ]li | Z < o k ; o5w | \`;$ n & \ <D o *FZ3 A 2 | A| 2:[email protected]]@_5n oCB M3 [email protected] ',&D [email protected]& [email protected] 0 5I & &14^35I"19& ? 0 I & 68& I 1& E I5&(' ;M?x+8=hE>&$ 7&('68&EG=V? I,;M4 I8?x& o ( y fd & jUd n( & { E* k pGsld ` Uj pGe d-b F ptd `Y` dvd1e @n ` up d _` pud F [email protected]` pujHG b o *^Z3 ; 2 | a oJI | I d [email protected] [email protected] | I ypueUd m<[email protected] oK, 0K3<;@[email protected]? 0K4X02&(' [email protected] )(+3>'14 ? I5)14 [email protected]& F | 1& 4!5+h` 6ptjY'Ms L [email protected]+`Y?S | 8 d `RQc]@iurXn g(y!o *^Z3 ; 2 | 4 5 1 & K 0 O ? N x ? U & @ = P 4 7 1 & 5 3 4 U ` ] a k oF ghdfd p jfo [2 | | ! n p k dhj [email protected] I E| 2[| Ip i j ]lk oS, 4 [email protected] &13R&1?P; 68&13>'10K4 +TL ? [email protected]=1&1?'.LE 0WVD&X [email protected]&1? [email protected]' NY | \ V o ; < j.; A o *FZ3V? 2 | | | l ] i | dfg(y F yDz8j Z,A | c| n [email protected]` oZ +h6 19& E 0t'[email protected]+3 [email protected] () +# 5; +?14L&7&1354[ ;5&1? 19& EG='14 0 I5& I>='10P0K3R)(+# M; ?x&('('10\=hEt& & i +* k up [email protected] ` jYpue d b 68& '14 ? I5)14 I8?x&('H=8)102&1?. 19& EG='14L+#Q19& ?(&(' 1& 4 @= E [email protected]+3 &f;W19& ? 07&1354 [email protected]& o ( y df& Uj d nQ a p d [email protected]` jUdhp iti d bb o *^Z3$V; 2 | ZVZ F | {"[email protected] dfs d & @d o] ,9& )[email protected] I5&S3R+3 E 0K3Vh9& [email protected]?x&~68&(' '14X? 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[email protected] 02+3>' o | w w 2i | F yDz8j | VZ Z o \! ?>\ o F* Z3 < A 2 | Z S| I | 8| a d k o [email protected]? ;8& 68&!L +?' [email protected]+3 0t',+4 ?x+(;M02)v&1EG='14X02)10K4 \ 3 4!5&S)(+? ?x&[email protected] 02+3 T+ L45&(+? [email protected] &f;5&1? 07&1354L +? 0K3R)(+# ;M?x&('('10\=hEt& ? [email protected]=1&1?'.LE 0WVD&',+E 0X6' N F `U] ghdfd a p k | j ] z | ] gftp dfeLz {q]lk>a]lk ;V\ o j ; o *^Z3>V\ 2 | Zj S| I | 8| a d k o + E I"7& ) >[email protected]?P;8&('7='(',+,)[email protected]&U6 0K4! 45&768&!L +?' [email protected] 02+3 T+ L ? [email protected]=1&1?.LE 0WVD&W',+E 0X6' o | dfg(y | F yDz8j | ]li p a j \ < o >; \;^;V; o *^Z3> >2 | Z S| | pus i p k o [email protected]? ;8& &1EG='14 02) 68&!L +? [email protected]+3>' +TL70t',+4 ?x+(;M02)Z [email protected]&1? [email protected]' \ , +#7&IJ350 I5&13R&('(' 45&(+?(&:' L +?;MI8?x&5+#7+ ;8&13R&(+ID' 68&!L +?' 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[email protected]>a _ g(y a d ` F yDzJjYp # o bbgb ? ; o ZA A>\ o w ` p k | d ` o d `Ui p k o *F3Z 2 | \ < 3 | | G n g(y>d `xnCka o ,9& )[email protected] I5& 68&('KW0KE 02&1I8 )(+354X0K35ID'/&14 [email protected]& [email protected] o ] eUdhj a d g ]l_` jfo i d `Um ]lk e d `U`[email protected] o *^3Z >@ A 2 | Z!;> # "# " h Z , 0,>0B. , # +3 3R+4L&;>[email protected]? !#"%$ N @'& $ N )( *( &14 M,+ (>W .- * 2 / &14 %/0 / $ N @*& $ N )( *( &14 M,+21 (>W .- * %/ I $ Et&('L +3R)14 02+3>'-=hIJEKEt&(' [email protected] ',+354c69& 3502&(' ;>[email protected]? Ni < Z Z'3 NYN < Z Z'3 &14 N 3 < Z Z \ # $"&('~0K3:9& ;[email protected] 0K45(9& ''[email protected]&(' ',+354:c19& ? 0 ,9& &(' Z 54 m*,M7+ 6 2 m</ n d Z *5M8+ 6 1 / 2 / m / p k Z *5M7+26 1 / 2 Z @:9 *5M8+ 6 207 ; u 0, k. I0B. , , . I0B. , > ' 8" , M + 6 bLi dhj e}g ]lkk _ e _ d B @ 3 h = h = = 9 B @: /< <; h = = 3 h = = h = h = , , Z 54 m d1e Z ] _& % " = @ = Q!L - * [email protected] 2 d1e = = o = o = 3 * = >? , 7. 0B. , # ECB I &1E I5&v',+0K4Et&v'10);@3R&V68& 3 +3 =D === A~ , ;2/ 2 Z o Z * h \ h \ = = = 3 2FGE / 1& 4 Z h Z * h \ o \ = = = 3 .2 GE Z rPW9l*5M7+26 1 = = = = ?= h \ ?= h \ H[& ;ME ID''10^+3 = = = = 3JI A [email protected]+?x' Z r Y*57M +26 1 / 2 Z o ? = h \ N 68+3R) Z r Y,* M7+#6 1 %/ 2 \ = E , 0 = = = 3 hHA Z h ? = h \ Z rPW9l*5M7+26 1 / 207 Z r Y*,M7+#6 1 %/ = Z!; 207 / 207 E p = = = 3JI A o ]lk n < ^* Z h \ \ ? \ 2 / Z F* Z h \ Z 2 Z @:9*5M +26 1 / ; ; = Z 4 Gm *,M7+26 1 E p = = = 3 h A o ]lk n ? = / = 2/ Z 2 \ o V\ < h \ o `\ < 7 / = m n p iui n | dhj * dfe jYp i n e ` p [email protected] | _ i n xe p ]@k dhj e _ k d [email protected] p ti i d 8` d b | >_ i p d & ` d a d < Z / / / a]lk g E p = = = 3JI A ]lk n ; n sldfg N 0 8 4 mG*,M7+6 2 . I0B. , Z Z :@ 9*5M +#6 1 / d1e 2 Z *,M +#6 1 /0 * / $ N @*& $ N )( *( 2 G /< A A n [email protected] %/ %/ / 207 B 2 Z 4 mG*5M +26 1 / 2 o a]@k g @ B / dfe M,+#1 / / 267 Z :@ 9f*,M7+ 6 2 / / < Z Z @:9 *,M7+#6 1 / 8 k n / < ^* Z h \ \ ? \ 2 Z Z @:9*5M +26 1 / E p ===3 h A 2/ 2 \ h Z \ 7 %/ < / Z Z @:9*5M7+ 6 1 / Z 5 4 m *5M + 6 1 / d1e / 2/ (>W .- * %/ 267 n sldfg k w ] j [email protected] e '3 dfe 4 +26 1 / ! /0 r r &%' ,+.- / 1d e ( ( *) *) A s Cn i d >_ ` j w U` ] w ` dfj a d k w d _ e m<]lk e ` d ` _ d dfe B j ]lk e a]lkk dfb dhjw [email protected]` 6 6 6 n sldfg 6 o i dhjWs [email protected] d _` j w `Y] w ` dfj a d s Cn i d >_ ` j w U` ] w ` dfj a d #" 9 +#6 1 %/ > 0 $ / / #$ &% '& .- 0/21354 -687+79- ;:=< 69- 3>1 78-6 < )(+*,(+* ! #" a 2 h 3 h a 1 h 1 a 2 3 [email protected])D | FEHG >_ m d b `U] e n exp ]lk a dhj Xr n fg dhj a _ e ` p [email protected]=Ili dJ k n LK M /HN & N M ( *(PO RQ Tn S / &M & M ( *(UO V Q W n S " aYX ] _ S i nWm<n e ` tp ghd Z\^[ ]`_ Z \Z [ Ue Z " % - + " = = = =3 k LK M / a pus / a pus " Z`[pZ k o = = + - ]`a cb a db 3 a db 3 ^] a db .- " n [email protected] - % a =3 n [email protected] *" .- PM M )n + 3 3 = =f - 2g = ji = % - = N mM l ( *(UO RQ Tn S " " " " kq sr h ( *(PO .- " a]lk g 6 k Z\[ Z KM .- " % G _ + " + - K/ E )( *% qk 6 ( &% .- % +S ( &% / / % % ( *(UO ( *U( O & % ' "!$# 2 - " )(+*,( =3 = 3 = 3 = 3 = = = = / Z 4 6 Z [p = e? = / N & M ( *(UO WS Q TS / & M ( *(UO TS Q T S Z\[ Z ] 3 3 3 _ 3 ] 3 3 " 6 b Z [pe Z = k k aYX ] _ S .- .- .- 0 /21354 -687+79- <-, : - 3>1 87 -6 < /.1024356.87 X + :9; <20=0> I 8?$3 I + 02 <[email protected] + $<20=<2.6C-0=B.-DEF/3<2 /.A7HG6.$ IJFKFG<=BL 3 2 1 4 [email protected])D NM b EG + 9BO [email protected] P6$<2FQ7B.RDS 3B. 7 + [email protected] e \Z [ Z 7/<2 I + S K M /HN & N M ( *(UO VQ S " " 5TF3K0=B. N W X9Y6$?$<=3B " - % l 7HO /<=.U FMV`_ U0=B. " KM 7HO /<=[Z/ ? " .- % k KM " 7HO /<=. B / N & M ( *(PO V Q T S " k / FMV 0=B. M 7<=T M _ _ _ NMl _ I 02J M _ _ _ _ ( *(UO sQ S " .- [email protected]/HO.Z6? ] % S I B. O S 0= _ " I 0= " S .- _ G !$# E _ / &% ' % Z\[ Z 7/<> I r / l lM ( *(UO V Q W S r KM B. O _ K/ ( *% qr 6 ( &% +S ( &% / / % - % - % O ( *(UO ( *U( O - .- O ( *(UO .- ^ F #" ! " B .BI + 3 N0=<2/7?$ 7/FLU02. I BO HOB?J?$<[email protected] ?6020 S 02. + M TF3$ + ?K7 BO Z/02 3B9;L . + Z/Z F.$ + /7HO Z /7/BL + ;/7 _M 2 .U335 .I02 I ?$ 7/<2L 7/B.U7HBO Z0> 3B9BL. B. U7/F/HO[Z ? 3 F< $ F< - $ $ q $ _ _ _ + [email protected] 3 _ 3 33 - 0= + - 3 - - 3 3 _ q $ 0$ q 0$ q $ $ q$ q _ +S - W /.$ + ? I/7/ + 3 ?$B 7/[email protected]<=BI. X O 3B?$< _ - [7/ 0= /.$ + ?7B. 7HO DE ?$9;6<=F/. M B .U3B 9;Z F.6C$B. .$ C _ - I ?67/<2CU7/7HO DEF?$9;6$<2F . X O [email protected]<= 02 ?$. - W - _ _ _ _ _ _ - - . - _ - - - - - _ - - _ _ _ <=/.$< _ _ 2 /.R335 .I 0=B.R<=CT6 [email protected]<> L$.R7/ [email protected]/F /HO. Z ? 3 ? ? 7/ /7 ? VJ <2?$3 /B. $? _ _ _ 7/ /HOZ ? _ _ ? $? $? +S k _ _ _ k _ _ 33 7<=T 7<=T k 0=F?$. 7<=T 33 - 3 7/< T k - 33 Pe _ _ _ 33 _ 3 S + < Z ?$9U7/F3[7$? < ? + Z/?$FG0 B9 G/<=7/<29B/[email protected]<2F/B0 M $? _ _ TF/F/.U9; <2L L X0S X O + 6$<2F 7 X O + <=20 <=G/?$ M 3B 9;9 <=/.$<*I F99; " # " % ! " " ! W " " " W [Z?$B9<2? /.$ + ?U7/ <=F0> ? ? ? M 3/3/ GI M I + 0*I M 6? I B?BI M M <=$?$6I!#"%$'&)(+*,$.-%/1032546-%0708-%/109*;:=<>"%$.-%07&?<@07& A &%B- 0C*,0ED A &'F/=-GIHJ:K:LM&?DN*,$O&?<@PQ*,/SRT%B- LS%B- (U-%P=$)"3V#P=&W"X(3&YRZ$.-E"I G + 9;? MI 6 M b _ e " I F^b M M I [+ 0*I M + 7/<=I\H]:=<>"%$^-%07&?<@0%&_-%0708<@0`-E"%$'&)(+*,$.<@0bac<@0bV#P=&)$.-ed,<@LM/1(U-f(U-%$ A <[email protected]"Eg Z Z/02<=B7 6 /B 9;6<=3B. 7 F9Z + 6<=F _ I e _ I `_`_^_ M @ Sh:M GKM ?$F027I M ?$ <&Ijik&YRl-N2m*,P2mP<@PDE<@Pcac<@07(3&)P1noV#P=&)$^-p-%LW-%(U-%P=$q(U-%$ A <[email protected]"srt&)(q:LW-%u (U-%P=$?*,$O&?<@Pgv:=<>"%$M:08<>DE-E"E"%&)P1nw*,P2b-%0708<@09-E"%$O&)(+*,$^-E"Iyx Ezq{ I I I `b e M M| M 20 0*I!}~<@P=d,-CRZ&)$O+DE<@P2,&)$O&?<@P"q*,P2U-CRZ&W"%$.-%PDE-$ A -E<@08-%(;"q&)PbP<@P=LM&)P-N*,0I-%L*@"%$O&?D%&)$'>g 6 My B3 M / 0 M ] I L _ I! F M [email protected] M e ]S M Mv [ /7 M J M 9 <= I H <>"%$^-%07&?<@0%&~070E<@0oj"%$'&)(+*,$^-E*@">-N2k<@Pmq&?-%0C*,08DN*,L*@">-E"I l M G + 9; ? M 0 M[^ _ I 1 eNI! F K M M M [ M5 B <=.$B?I~v<@(U-9H <>"%$.-%07&?<@07&~0%08<@0j"%$'&)(+*,$^<@0E"ac<@0p-%L)LM&|:$'&?D:*,07$O&'*,L 2,& -%08-%P=$O&'*,LW-NF/*,$'&?<@P"I 6 M F9Z M ./I b ^_ Iv ^b e M /7 @ M ? 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