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Un modèle géométriquement exact de jonction de poutres

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(1)Un modèle géométriquement exact de jonction de poutres Henri Chajmowicz. To cite this version: Henri Chajmowicz. Un modèle géométriquement exact de jonction de poutres. [Rapport de recherche] RR-3372, INRIA. 1998. �inria-00073317�. HAL Id: inria-00073317 https://hal.inria.fr/inria-00073317 Submitted on 24 May 2006. 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.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Un mod`ele g´eom´etriquement exact de jonction de poutres Henri CHAJMOWICZ. N ˚ 3372 4 F´evrier 1998 ` THEME 4. ISSN 0249-6399. apport de recherche.

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(170). . . 4. G.  G. *. G.  G. . . G. *. . G    . G   . . \. . G. \. . G * '.   . G * '.  . . Y[WZŸPUOXGIYoU”“:UWZRP^!dITˆSadIRPSX^K—ÒTVOXU^LA  G  4 } .  G ' \ G a G \ G '   v  v @    G 4 G G G G ' \ \ a G G EWZRP^TI|jWZYP^ b WZYPdo“ bœ To] h\G\F ^mSQT b G3z š&YPOXUOXWZY b G    *   \“PSXG\^ h G\SQTVUOXWZYP^FA G 4 } G G  G G  G \ \ 2  . ,  G a  G a  G v ^WjOaU A G G  G G 4 }. \ G 4  G \  .  v G\U b WPYPd A G G  G 4  v }   ¢ GH©GI H7G A G 4 G G G a  G  vovo  G G G G ; 9 ; g WZR h UWZRPUmOQY b Oad\G A b ToYP^ , } *3@v 2Z“jWZYed\WPYP^O b GF h G  * *  *  Q  @ * N G :C E   G\UEWZY OQYjU h W b RPOaUKS œ WZ]+G z h TVUGIR h A  G  G K   4 }  G  G K * G a G  * G a G   G  G K * G * G     FW R tG\^U5R:Y ]:T h ToH G\F U h G h G\z G\S1| G z h O˜š&ToYjU  L} ¡ ¢ œ Tj] hÂG\F ^SXGmU D G\z W h\GIF H›G b G\^TVd\d h WoOX^^`GIH7GIYoU`^"š&YPOa^G\U"S œ D c†]–WoU D1G\F ^`GB }I  \“\YPWZRP^µT”|oWPYP^ŠS œ G\z ZTVSXOXU†Gz A  G  G K   4 G G  G  G K * G a  G  * G a  G   G  a  G  G K * G a  G  * G a  G   G   .

(171). . .  .     . . .  .  . . . .  .    .  .  .  . .  .    . .  .

(172).  .  .  . . . . . . . . . . . . . .

(173). .

(174). . . . . . . . . . .  . .  . . . . .  . .  .  . . . . . . . .

(175). . . . . .

(176). . 687FM96;:.

(177). . . .

(178) v}. 

(179)          !"   #   "  $% '&  ( *). W R F G\^U5R:Y’]:T h ToH G\F U h G h G\z G\S1| G z h O˜š&ToYoU  L} ¡ ¢ œ Tj] hÂG\F ^mS œ D c†]–WoU D1G\F ^`G  }I~  \“PYPWZRP^]:WZRP|oWPYP^!GIY b G z b RPO h GSTtHeTˆikW h TVUOXWZY'A   G  G`K   L    av  9  ; a ; a  ; a ;        ; a ;    Œ1GH›b GIH{Ÿ b h G b G b h WjOaU`G b Gb S œ OY+G\z ZTVSXOXU:Gz ] h G\z h d&G z b GIYjD UG!G\h\^F U!OQYjU:b G\z  h ToŸPSXGB]:T hÊh D c:]:WoU D1b G\F ^Go“oG\UmOQY F b G3z • ]–GIY ToYoU  G G 1¡ h  Yn@ ]–N GIG RPU b WZYPd{To]:]PSXOX‘:RPG SXG7U G\z W GIH7G G7STwd\WZYj|oG oGIYPd\G WZH›OY+G\z G TwSQT ^_RPOXUG ^_R :G\U WZYP d A G GK GK  SXOQH  ,   <  2  G G T G K G G G GK G G G GTK 4 ,  G  * *    a  G  * *   2   G } G G K G G G G`K G GK G G GTK 4  SXOQH ,  * a  * a    * *   2    G GK G G GK  G G 4 G  G   *     * *   \   *   SXb G\^ b b G3z —ªW h h HeTˆUOXWZYP^ b G3z š&hhYPOXG\^e]:T b h  so \“ žJP !h ^_R h SQT ]–WZh RPU h G h }  h G\^3} ]1¡Švo ©G\z U_ToYjUOY b GIz ]:GIY b ToYjUG\^ G\^ G3z —ªW HeTˆUOXWZYP^md\W G\^_]–WZY ToYjUG\^!^_R STw]:WZRPU G{v’ G\^_]1¡  \¡ . . . . . . . . . . . . . . 

(180). . . . .

(181). . . . . . . . . . . . .

(182). . . . . .

(183). . . . .

(184). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g G T h bG G z h OX|/TVUOXWZY b G¨—ªWZYPd\UOXWZ9 YP^nd\WZHe]–Wo^:G\z G\^©; • SXWoOX^OQŸPSa9 Go; “dIT h bœ To] h\G\F ^  v @  \“ESaG\^ ™— WZYPd\U`OaWPYP^  *  m^WZYjU b Gd\SQTV^^`GS b G  G |jG h ^  @ * N G <C E  3“:WZYtWPŸPUOXGIYoUA G G ; G G G G ` G K G G G    *        G * G   \  * '   4 G 9 ,  G  * *    a  G  G8K * G * G   G 2 G`K       voso  . . . . . Ñ. . . .  .  . MLM JNOOQPR. . . . . . . . . . . . . . .

(185). .

(186) vov.    

(187) . ¢ œ Tj] hÂG\F ^md\G‘:RPOŠ] h G\z d GF b Go“PSaG7] h WZŸPS GIF H›G|/T h OQTVU`OaWPY:YPG\S   :] GIRPUK^G h G1z G\z d h O h GFA . CŠh WPRP|oG h  G * G   Q  U`G\S‘†RPG A@b  G * G '   Q   ` G * G   :A G G ; K G G G G GK G G G GK ,  G  * *    a  G  * *   2 G 9   ; ; 9 9 @ 9 ; ; a ,”d\Wo^/       a¨^OQYŠ      @  <2 \ ,Id\Wo^I  9   '   N 9  a¨^OQY"  9   '   N 9  <2 9 9 ; ; a ,Id\Wo^I   9     N 9  a¨^`OY"  9     N 9   2 \ ,Id\Wo^/  ;   '   @  a¨^OQYŠ  ;   '   @  <2 ; G G G`K 4 \ ; N;   ? \ a G 9 . .  . . . . . . . . .

(188). . . . .  . .  . .  .  . . .  . . . . . . . . . ¢ œ jT ] hÂG\F ^SXG\^ h G\SQTVU`OaWPYP^[ v }  \“ ªvjvo KG\U7SaG H7W b G\F SXG¥ªuo \“1WZY¨]:GIRPUeToRP^`^OeG\z d h O h G d\G ] h WZŸPS GIF H7G ^WPRP^!SQT7—ªW h H7G A CŠh WPRP|oG h  G ; G , ‰ G 9  . . a. . .  . ,. . . .  . . 4.   Q  `U G\S‘†RPG A@bµ 9 *  9 9 G G G G`K \ G a . \   G  2 G.  . *. ;. * ; . ;.  .   Q   `  G. G *.   :A . . ”d\Wo^/  ;   ;   @  a¨^OQYŠ  ;   ;   @  <2 \ ,Id\Wo^I  9   9 '   N 9  a¨^OQY"  9   9 '   N 9  <2 9 9 ; ; ,Id\Wo^I  9     N 9  a¨^`OY"  9     N 9   2 \ ,Id\Wo^/  ;   '   @  a¨^OQYŠ  ;   '   @  <2 ; G G G`K \ ; N;   ? \ a G 9  9. a. *.  .  . .  . . . . . . . . . . 687FM96;:.

(189) vjs. 

(190)          !"   #   "  $% '&  ( *). Y[WZ] GF h GKGIYP^_RPOXUGeR:YPGOQYjU:G\z  h TVUOXWZYt]:T h ]:T h UOXG\^5]:WZR h WZŸPUGIYPO h A C"h WZRP|oG h  G * G   Q  UG\S‘:RPG A@bµ 9 *  9 9 * ; *  ; ;   Q     G . . ;.  ;. G 9. ‰ G. ,. .  . . G. . . G.. 2 \ G. G G G , . a ?2 \  . G.  ` :A . GK . . ;. . *.  . . G G G`K \ ; N;   a  G 9  ? \ ; ; 9 9 9 ,Id\Wo^V  ;     @  a¨^`OY"  ;     @   2 \ ,Id\Wo^I  9   '   N 9  a¨^OQYŠ  9   '   N 9  <2 9 9 ; ; a ,Id\Wo^I  9     N 9  a¨^OQYŠ  9     N 9  <2 \ ,Id\Wj^/  ;   '   @  a¨^`OY"  ;   '   @  <2 ^WjOaUEGIYPd\W h Go“GIYt^G^G h |/ToYjU b GSQT h G\STˆUOXWZY¥ } JZ :A C"h WZRP|oG h  G * G   Q  UG\S‘:RPG A@bµ 9 *  9 9 * ; *  ; ;   Q    G * G  ` :A a. ‰ G 9.  . . . G. . G G  . \   4. \ G a.  . . . . ;. ,. G. . . . . G. . 2 \ G. . . . G. . .  .  . ‰.  .  .  . . G G G , . a ?2 \ . . G8K 4 @. . .  .  .   G\U!WPY h G\U h WZRP|oGKST›—ªW h H7RPSQTVUOXWZYt|/T h OQTVUOXWZY:YPG\SXSXG b G\^©G\z ‘:R:TVUOXWZYP^ bœ G\z ‘†RPOXSXOQŸ h G’ªuo \¡ &   W%8  T ' 

(191) "!. EWZRP^TVSXSaWPYP^BH7WPYoU h G h SXGU D G\z W h\GIF H7GLA G * 0 „ ƒ ® „I ‰ „ 0 1 ) 

(192)  *)   " ) *      )B, ? 2 G  9 ; ) $ ' <  &? <   )  )G3 34,

(193)  ) ; G G

(194)  *   L&$&?3 <  

(195) * *) & " G  9  9  @ * N G :C E =   " 

(196)   )'

(197)  &   ,*

(198)  =33  

(199)       ) 

(200)    8. G 9. . . . . . .  . . Ñ. MLM JNOOQPR. . .

(201) vVJ.    

(202) . ¢ IG z H7WZYP^U h TVUOXWZY A Œ1G] h OQYP d\OQ]:hG b G!F SQT b F GIz H7WZYP^`h U h TVUF OXWZY%G\b ^U SXG!^3RPOa|VToYjUFAoWPY{bH›œ WZYoU h Gm‘†RPG!SXG] h WZŸPS GIF H›h GÊ|VT h OQTVUh OXWZYj• bYPG\O /BS G z  h GIYj^UGOXG\SXSXToG H G\GIUKYPWZG YnTToR:]:Y ]PSX] OX‘†WZRPŸPGeS GISXGeH7UG D G\z GKW h\H7GIF H7OQYPG OH›b OaG^3TV¥GUOXWZ\OXY G h ^U R:h YPTV^GE^e—™WPž|oYPWod\OUh OXWZ& Y:YP® G\‡ SXSa#G' ^3:R ° ;R:(YP„ GK*|/T ³žO3³QG\z„:U†² G z  ­ . /  }I~jo#   \¡ .

(203).

(204).

(205). EWZRP^KOYjU h W b RPOX^WZYP^R:YPG{YPW h H7G^_R h? A ;  G G    G  ;    a =  G  ;     ;  *   4  vVJZ    CE G 9  9   CE. G\U5YPWPRP^ b GIz H7WZYjU h WZYP^+SaGSXGIHeH7JG A (¹„)‰¨‰ „ 0 G )  $)

(206)  )

(207) > &    ) )       

(208)  8 "

(209)  *)  & ($  )    J  )')   &  ' 7 G * G    4 9 ,Id\Wo^/   ;   ;   @   a¨^OQYŠ  ;   ;   @  <2 \ ,Id\Wj^   9   9   N 9  a¨^OQYŠ  9   9   N 9  <2 v H    ; G G G G GK \ ; N;    *    4 G ? \ a  v 6o  9  )         34,

(210)  ))Q  8 ¢ GIz H7WZYP^U h TVUOXWZY  b RtSXGIHeH7GJ¡ H   A EWZRP^ b Oa^3]:Wo^WPYP^ b GS œ OQY”i»G\d\UOXWZY©d\WZYoU`OYPRPGA ;

(211)   G 9     @ * N G <C E =      vouo   MPO!SXG\^w—™W h d\G\^eG\fPU†G z h OXGIR h G\^ ; , G ? 2 G  9 ; ^`WZYoU7OQY b GIz ]–GIY b ToYjUG\^ b G\^t|/T h OQToŸPSXG\^  G * G  7G\UtTo]j• ]:T h UOXGIY:YPGIYoU TwF S œ G\^_]:TVd\G G

(212)  9   9  @ * N G :C E =  3“&YPWZRP^]:WPRP|oWZYP^T”§ h H7G h “: h TV d\G TeF S œ OQY”i»G\d\UOXWZY ªvjuo \“P‘†RPGSQT—™WPYPd\UOXWZY:YPG\SXSaG7SXOQY GIz TVO h G<G\^U!d\WZYjUOQYZRPGo“ b WZYPd b O /BG z h GIYjUOQToŸPSXG^3R h? ¡ .  .  .

(213). . .  .  . .

(214). . .  .  .  . .  . . . . . .  . . 687FM96;:.

(215) vH. 

(216)          !"   #   "  $% '&  ( *). MPWoOXU!GIYP^3RPOaU`G  G * G   b TjYP^  ¡ g WZR h UWZRP^ @* 7Q , } *3v*_s 2ÊG\U5]–WZR h UWZRPU G * G    b ToYP^  “ YPWZRP^T”|oWZYP:^ A  9  N 9  Ma 9   N 9  `  \  ;  @  _a ;   @    4 9 G  N 9G   \ ; G  @   G a ¢  *   \  *    9 ; a  N9  \  @   W R[F S œ To]:]PSXOXdITVUOXWZYn³ / . „ ƒ </ „ ¢  G * G   b G3z š&YPOXG^3R ?h  ]:T h A ¢  G * G   A) G * G     9  N 9   \ ;   @ Y  a ;  @   \ 9   N 9   G\^U7d\WZYjUOQYPRPG ^_R h  b G’]:T h S œ OQY”ikG\d\UOXWZY¯ªvouo  ¡ C WZR”ikWPR h ^ h TV d\G T©F S œ OQY”i»G\d\UOXWZY ªvjuo \“ŠYPWPRP^ T”|oWZYP^ G\z ZTVSXGIH7GIYj:U A 9  N9 \ ;  @ L  G G  ;       *   F SQT bG O /BGG z h GIYjUOQToŸPOXSXOaU:G z b G  ^_R h  ¡ !WPRP^BT”|oWZYP^”“:GIY©UWZRPU EWZRP^]:G WPRP|oG WZYP^ b WZYPd7d\WZYPd\SQR h G Te ]–WoOQYoUe *   b G  G\U5]:WZR h UWZRPU * '   b TjYP^  A  {`G  G G* G    \  G * G '   4 9 ; ; ,Id\Wo^V  ;     @  a¨^`OY"  ;     @   2  *   \ ,Id\Wj^/   9   9 '   N 9   a ^OQY   9   9 '   N 9 <  2 9 9 a ,”d\Wo^I   9     N 9   a¨^OQYŠ   9     N 9 <  2 \ ,Id\Wj^/   ;   ; '   @   a¨^`OY"   ;   ; '   @ <  2 G G G G EWZRP^TI|jWZYP^ G\z ZTVSXGIH7GIYjUI“PGIYtUWZRPUK]:WoOQYjU› *   b G  G\U5]–WZR h UWZRPU7 * '   b TjYP^  A G G GK  BG G *G G    \  G * G '   4 ; \ ; N;   ? \ a G 9   *   G G EWZRP^ h GI] h GIYPWZ9 YP^µHw9 TVOQYoU; GIY:TjYo; USQT b GIz H7WZYP^U h TVUOXWZY b RU D G\z W h\GIF H7GJ)¡Ûv+G\UŠYPWPRP^ŠYPWoUWZYP^m *   S œ WZ]+G z h TVUGIR h  * * *   b G3z š&YPO1^_R h  ¡.  . .  .  . .  . .  . .  .  . . .

(217).  .  .  . . . . .  . .  .  . . . .  . . . .  . . . .  . . .  .  . . . .  . . .  . .  . . . . . . . . . . Ñ. MLM JNOOQPR. . . . . .

(218) v6.    

(219) . ³ „ ² ® . ° / . ‡ / °Š„ ƒ „¥ G * G  E V‡ S ¡ MPWoOXU,† G * G <  2 C R:YPG ^3RPOaU`G—ÒTVOQŸPSaGIH›GIYoUd\WZYj|oG h jGIYoUG b TjYP^  ¡VŒT!^3RPOaU`GU,†;  G   <2 G\Ud D TVdIR:YPG b G\^ŠU h WoOX^^_RPOXUG\&^ ,†  G  <  2 C d\WZYj|oG h oG TˆSaW h ^— TVOQŸPSXGIH7GIYjU b ToYP^ G

(220)  9 ;  @ * N G :C E =  \¡ h YPWZRP^5T”|oWZYPL^ A

(221) G ;  9  @ * N G <C E =    

(222) G ;    @ * N G <C E =     v   9 9 T”|oG\dKOQY”ikG\d\UOXWZYtd\WPHe]:TVd\UGo ¡ !WZRP^!]–WZRP|oWZYP^ b WZYPdd\WZYPd\; SQR h G TF SQTd\WZYj|oG h oGIYPd\GE—ªW h UG b GKd D T”• dIR:YPG b G\^5U h WoOX^!^_RPOXUG\^M,† G   2 C b ToYP^!S œ G\^_]:Tˆd\G G

(223)  9    @ * N G :C E =  \¡ ¦ D TˆdIR:;YPG b G\^^OXf^_RPOXUG\^m] h W b RPOaU ,† G   2 C G\HU ,† G <  2 C d\WZYj|oG h oG b WZYPd+—ÒTVOQŸPSaGIH›GIYoU b ToYP^ G

(224) 9 ;  @ * N G :C E 3“od\GK‘†RPO1]:G h H›G\U b GKd\WZYPd\SQR h G TF SQT%— TˆOŸPSXGd\WZYjUOQYPRPOaU:G z b GKS œ To]:]PSXOXdITVUOXWZY  ; G G

(225)  *   b G3z š&YPOXG^_R ?h  G\U T7F |/TˆSaGIR h ^ b ToYP^ G  9 ;  @ * N G :C E  3¡ C </ ³ „ \„‰ / ±² ® . ° / . ‡ / °Š„ ƒ / . ? „ ƒ !/ „‡ „1¡ Œ1G\^ F b GIYP^OXU:G\z ^ bœ GIz YPG h h oOXG G h  G K * G * G   b G3z š&YPOXG\^{]:T h  H  K^WPYoUKd\WZYj|oG\fZG\^”“1‘†R:T b h TVUOX‘†RPG\^”“ G\U T›d\WZG3§ d\OXGIYjU^Ÿ:W Y+G\z ^!^_R C E ¡:Œ1G\^E—™WPYPd\UOXWZYP^FA G * G     G GK * G * G   GK ^WPYoUeTVSXW h ^7d\WZYj|oG\fPG\^7G\; U{d\WPYoUOQYPRPG\^I“ b WZYPd ^:G\z ‘:RPGIYoUOXG\SXSXGIH7GIYjU7— TˆOŸPSXGIH7GIYjUt^GIH7O˜•Òd\WZYjUOQYZRPG\^ OQYj—/G z h OXGIR h GIH7GIYjUI“:^3R h G

(226)  9 ;  @ * N G :C E  \¡ g T h ^`WZHeHeTVU`OaWPY1“od\WZHe]–Wo^OXUOXWZYtG\U bœ To] h\G\F ^ SXG\^5] h WV• ] h O3G\z U†G\z ^ b GS œ WP] G z h TVU`GIR h  G * G  \“PWZYtGIY b G z b RPOXU!‘:RPGS œ WZ]+G z h TVUGIR h b G3z š&YPOŠ]:T h A C <

(227) / . . . . . . .  . . . .  . .  . . . . . .  . .  . . .  . . . .

(228). . . . . . . . . . . . . . . . . . . . . . . . ;. ) G * G    G  9  G  G K * G * G   G K G\^UE^†G\z ‘:RPGIYoU`OaG\SXSXGIH7GIYjUK— TˆOŸPSXGIH7GIYjUK^GIH7O˜•Òd\WZYjUOQYZR[OYj—VG z h OaGIR h GIH7GIYoUK^_R h? ¡ . A.  . . . . . . . 687FM96;:.

(229) vju. 

(230)          !"   #   "  $% '&  ( *). m¦ WPYP^O b G z h WZYP^’HwTVOQYoUGIY:TjhYoU S œ WZ]+Gb z h TVUGIR  h  ¢ œ b G3z š&h\YPF O]:œ T h ªv H   ¡ MPWoOXU ,† G * G   <2 C R:YPG ^_RPOXUG›— TVOQŸPSXGIH7h GIYjF Ud\WZYj|oG jGIh YoUG ToYP^ h ¡ b ToD] G\^!S OQY”b ikG\d\UOXWZh Y d\WZHe]:Tˆd\UG’G ªv  \“YPWZRP^b]:WZRj• |o;WPYP^d\WZYPd\SQR G TtSQT d\WZYj|oG oGIYPd\G›—™W UG G d TVdIR:YPG G\^U WoOX^^3RPOaU`G\^ ,†  <2 C TjYP^

(231) G    @ * N G :C E =  \ ¡ !WZRP^+GIY b G z b RPOX^WZYP^ SQTd\WZYj|oG h oGIYPd\G¬—™W h UG b G5UWPRPUG\^ SXG\^ ^3RPOaU`G\^¬] h W b RPOXU^ b  Rw9 U»c†]–G ,† ;  @   \ 9  N 9   <2 C ¡P¦mG\d\O&YPWZRP^m]:G h H›G\U b G!d\WZYPd\SQR h G TKF SQT%—ÒTVOQŸPSaGKd\WZYjUOQYZRPOXU:G z b G $^_R Dh  “:]:T h d\WPHe]:Wo^`OaU`OaWPY T”|oG\d!S œ WP] G z h TVU`GIR h SaOQY+GIz TVO h G T%F d\WZG3§td\OaGIYjU^!Ÿ:W h Y G\z ^ b G3z š&YPO)^3R h C E ]:T h A. . .  . . .  . . . . . . CE. .  . . . . . CE. d\Wj^/  ;  –d\Wo^I  9   9 ad\Wo^I  ;  :^OQY  9   ; a ^OQYŠ  ;  :d\Wo^I  9   = a^`OY"  ;  –^OQY  9   ¢ œ Tj] hÂG\F ^!SQT b GIz H7WPYP^U h TVU`OaWPY b R’SXGIHeH›G{J¡ H “:SQT›—™WZYPd\U`OaWPY:YPG\SaSXGtSXOY+GIz TVO h G  b G3z š&YPOXGe]:T h  v6o  G\^U d\WPYoUOQYPRPGn^_R h h ^WZRPh ^tSXG\^ h?D  c†]–b WoU D1œ G\F ^`G\^ b R<U D G\z W h\GIF H›b G J)¡˜v:¡ ?h Y< GIY b h G z b RPOXU SQT —ÒTVOQŸPSaG ^GIH›OەÒd\WPYoUOQYPRPOXU†Gz OYj—VG z OaGIR G^_R GS Tj]:]PSaOXdITVU`OaWPY  G3z š&YPOXG^3R ]:T A v ~     G * G    4  G * G    a {` G * G    B G * G    8 ® „ ² / D /Q°"„ ƒ „  V‡  ¡ EWZRP^TI|jWZYP^!]:T h d\WZYP^U h RPd\UOXWZY A ` G * G    G 7G G G ; G`K ! = G ; ! = G ;  G G - = G ; a    v 9 v 9 G 9   9 Œb1G\^ h G\SQTVUOXWZYP^ ªsj !G\U b žJP  5YPWZRP^]–G h H7G\UU`GIYoU bœ G\z d h O h G{SQT h G\SQTVU`OaWPY ] h G\z d1G z b GIYjUGGIY©—™WPYPd\UOXWZY G\^K^GIRPSX^’G\z S_GIz H7GIYjU^ G ¡  G * G G  G   G G ; G G = G  ! G ; ! G          a     CE  CE v v  CE G 9  9 9 * ; * = *. .  . . 9. . . . . . . . .  . .  . . .  . .  . . . .  . . . . . . . . . .  . . Ñ. MLM JNOOQPR. . . . . . . . . . . . . . .

(232). . . . .

(233). .  . . . . .

(234). .

(235) v.    

(236) . EWZRP^T b H7G\UUWPYP^¬] h W/|POX^WoO h GIH7GIYjU!SXGSXGIHeH›G^_RPOX|/TjYoUA (¹„)‰¨‰ „ 0 4 

(237) ! )   "  )    9 )Q"     &  )3!3 "         ' . .   . K

(238)  ".     F   ( "  

(239) 

(240)  K  ; ;  G  ;     

(241)  9  G  ; CE G 9 G 9.   ¢ œ TjRPU h G]:T h U”“†]:RPOX^‘:RPG{]–WZR h UWZRPU G. YPWZRP^]:WPRP|oWZYP^ G\z d h O h G A. *.  G.  G  ;. . . .  . . . CE. .

(242). . CE. . .

(243).

(244). . .  .   b oT YP^  “:YPWZRP^BT”|oWPYP^  ;    4 N G  CE G. . . .   &?    F 

(245) . .  G   ;. 4. . . .  . . CE. .

(246) . NG. EWZRP^KGIY b G z b RPOX^WZYP^ b WZYPdA  G * G  `G  G G G ; G ; ! G  !   a G G - =   G  ;   N G       9   v    CE v   CE G 9  9    C E ;

(247) b œ h    -+Y´U`GIY:ToYoUtd\WZHe]PU`G’GIY<WZRPU G GnS OY”i»G\d\UOXWZY$d\WPYoUOQYPRPG     @ * N G :C E =    “ÊYPWPRP^ G 9 WZŸPU`GIYPWZYP^5SQTeH›OYPW h TVUOXWZY A ;  G * G G 7 `G  G UG G  ; ! G  !      G        , 9  a ?        CE  CE v   CE v G 9 = G G- =  G  ; a  9     C E  N G   9 G ^_ R:9 ] ;  9  G      C E  2 Y[GIY d\WZYPd\SQRPU T7F SQT7d\WZG h d\Oa|POXU:G z b G  ^_R h  ]:WPR h SQT YPW h H7G b G  b G3z š&YPOXG{]:T h  vVJZ \¡ .  . . . . .

(248). . . .

(249). . .  . . . . . .

(250). . .  . . . . .  . . .

(251). . . . .

(252). . . .

(253). .  . . . . .

(254). . .

(255). . . . 687FM96;:.

(256) v~. 

(257)          !"   #   "  $% '&  ( *). ° „ . ²ˆ„&¡ g T h b G3z š&YPOXUOXWZY1“:S œ G\^_]:Tˆd\G  G\^`UG\z ZTˆS&ToR YPWVcZToR b GS œ Tj]:]PSaOXdITVU`OaWPY 5  b G3z š&YPOaG^_R h  ]:T h A 5   G * G    4 ,, G \ G  2 G  9 ;  9 ; =  *3,† G 9 G ;   \ G = } 2  G  9 ;  * 9 @ 9 @  -  *3,     2   9 ; =  * 9  N 9   ;  @  -* ; G   @   9 G   N 9  <2 ^Om   +G\^U!| G z h O˜š!G\z Go“ZG\UK]:T h 5   G * G    4 ,, G \ G  2  G  9 ;  9 ; =  *3,† G 9 G ;   \ G = } 2  G  9 ;  * 9 @ 9  -  *   @   ‡  * 9  N 9   ;  @ -  * ; G   @   9 G   N 9   2 ^Om ~  +G\^U!| G z h O˜š!G\z Go¡ -+Y h TVOX^WPY b GS œ OQY”ikG\d\U`OaWPY d\WZHe]:Tˆd\UG A

(258) G ;  9  @ * N G :C E =    

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