ÉCOLE POLYTECHNIQUE DE THIÈS - Institut de recherche ...
125
RËPUBUQUE DU SËNËGAL ÉCOLE POLYTECHNIQUE DE THIÈS c , PR 0 JET nEF I·N D' E T UDES EN VUEDE L'OBTENTION DU DIPLô-v1E D'INGÉNIEUR DECONCEPTIQN . J TITRE CALCUL DE COQUES PAR ELEMENTS FINIS DATE: 7. jUiN 1986. AUTEUR· .. : YVES HA61&FRANtl) DIRECTEUR ': HOlJ .. AI1ADOU 11. CO-DIRECTEUR :
Transcript of ÉCOLE POLYTECHNIQUE DE THIÈS - Institut de recherche ...
RËPUBUQUE DU SËNËGAL
ÉCOLE POLYTECHNIQUE DE THIÈS
c ,
PR 0 JET nEF I·N D' E T UDES
EN VUEDE L'OBTENTION DU DIPLô-v1E D'INGÉNIEUR DECONCEPTIQN. J
TITRE CALCUL DE COQUESPAR ELEMENTS FINIS
DATE: 7 . jUiN 1986.
AUTEUR· . . : YVES HA61&FRANtl) KON~TE
DIRECTEUR ': HOlJ..AI1ADOU 11. N~IA'If
CO-DIRECTEUR :
REMERClEMENTS
~ 'eJ1onS/"wr e!I;uho W'Q ffJ)1J Jlov~fo'pha Nf)/A YE,
, P," ~JJl»~ 1 po ur- CJ.I/~/ro.c~ .J,' Jo d/nl el,'o" du
prcJe J.
l'er,}:>e ·de fec-hn/i';e/?~ (l/J. -I~J,n/u~"~
'dv û~-1r-f" dfl. Ca lev. /
cfiiJn'n'.wl'
'cD/la bP ra fi'df'),' . ",
." .'
. .~, . .~. . ,
'" ,.......
',' .
•...t
:>OMMAIRE
Ce 0 ov ....og e es J.. Ill. Y'0l'P0r:1- ciPr. 11'0 lIa/ / Il,# t.i""" ~ ,
do"} /.R. bvl- d 'RiJObPt'Qr ....ur- /e::!i"c.r~/ dll ca/cp! dl/. UJrA/e~
at- d« plo?..» fl,J. ;X" la Mgr/At:) ck '(Ù.J Il'/emJ'''f~ /fI'VJ"
AprQJ---V" ~jf'll"'o tLu c.1-1"n tf<P' rion~ /ed Y"c::UlDn~ ~
e,hD;/( du J'1I~~'CDWltyl~ ~:Vè). de';"" c:i ilutle.~ rt.!}VJ
t:lI/OrtJ pro u' d.J' c(" la prll~"rQ 1-/"" ~ dJ#~~rt J...1 -1h-l~
./tPla ~/J '~:/a yr;::: ~:k; f, ~n do . jp.:J / c, '.t I, .e o -'" ",'.r fa ,.. Je
~r ..& <.pI.;. '.fJrdf,'re. et. ~rJ 'é!I~/,.e'cr:;l/p".J J' ~ a,,ta;4cf,'.
r: /U)~."f~i,t<'~nl ·cI 4~)I d /~ ~'Il&' eU lu e ~ Itu"h
f N J ) . .e r ~~àhi0flr dt.. , fUJ G(I,1 a Il<AI' rLe.r ÂW!' p r» a4~'-~ "MA
-Ih.f 'Ina "<F): II A '0'9 if .RI" tft,u'.J.t ri, lb .lfu1>A/t "du (J:J~
~I- de ~ 'f> la ~.f~ d;;t1.1 )a~!14, 0,... _/n!rtJt!W'j. rJ),.e k:'"\.1J,tvol,'on:> do" f f\.?~ ~f"\DIid' tp/ofin ,rlC:i"J .LPfr.;,.h~1tV Ik~
Cft ~fU'eA"" ,rb'v-lkl'P~ lM fo/llYWk. f1J~I.JC(J~ a( /~1101JD .
Y(il-/o~ ,rJvj!Jjl'ClLlo
" "
, ,cl~ft'rrul'j--u I/(p 1 ~f.1 fJ~', t ~LuJ '~';1"r'Q ~
'.R.xt'jft ".AJt'I, .;'//~~j:' -/r~o~;rlOJ,/u,et'-1r!>-'J rue» ~"~r>~h~
a \ ~ ',' pm rre-Is ", "
, ~ ~'no {ytA~J .)U~j;'a 1)': -Ia:'1 /UJWlh';' ~'~irv:k
du ~/J/CJ'i-/ d-4ct'~fJo o-.i,onJ. )U/~ j./~ a f~n .Pk;:>!D/
-ft'.f/on/o /rla/léVJ~tAAI(J"JI 0,", a. ~.'w·f '--6 rneJ/()~nA!
. l'rtf" Ir du ~ft' C/I.J; ~" rn;/trv ~ -f.e j . rum~', ~ : ~cPùo ~ ,r' ~ J.!>",J.- ~ ~,' ~rM.~., '
••J,L
, ~,
3·4 L e vo/h /'rt/r, t.t 5(;
'3·5 J<eJo/v/-'Q/'"l rkJ ~rt:J/-/~A,j ~I cp/~/
des ,c...o,,-/rOJn leJ "2.
4 PP.ESENTI;\TIOiV. bUL DGIC/EL
le . .A Lec.6u,n_ ~ :> do n ~~
~ -2. Co,/fP /:rh· la'c!roJ.f. ~ i,~J~ria/.e:J
.4·~38o~·r,·{; d~~tSIGu) ~'rb';lUêA ·dM., ..'
.ifr/tnl!nh. .. " . .' .
l... 1... Tra'" /~m..M h 'r1.R.~ YE·j. J"-lY",lt J e J... ... ,.d~ éP IJ?po'~ 'I/o~ b~
., ~. 5 ·;30t(c..il· riej' ~S df. ~hG".f~~f)J.. G,g
L.- G,' . A/.90 r/-iA~ ~ f'rOJri:;~hU :/J~~'nc/p~ 1 . C'
.R'E FEREN:C;€.· 5 . "····lIpp~nr!/~ .... •
: .'IIJI/'n) :~ /:>~OJ(o.mir.l.f
;'·I~·6.)1.~5'r(;~h;' t:;".: .
'. '.
····CONCL·USION.. o
e "
• • l'....
. '.
, ..
-.
, ~ .:.'.....
'.:.: ... '. /.. '.
. '.
, "
. "'.
s-Ô: •
. ..' .' . '. .~.
.""V
,... . .
. ' .
l N T R\ 0 DUC T ION
C~IAPJTRE 1
. PRESENTATION DELA
METHODE DES ELEMENT5
Fi Nl5
se fJ ropOJe de c.onlt}uh'onne.,- o» 10#Î
d'analyJe r h.! ~/a?.p.e~ el- /.e.1 Voi/E'J
Ol?
Dep(//~ 'lu e/?ue~ al1n~e3 d(ja') d~~ f".avaux (()n).
ire" eo frejJ r/!> (/ / ~'eO/f j> o/yf~cf,.n'fve. de TA/e~ f> OV r: th~·
ve/0l'P er 10 con c-f,P).,'on a ~~;s le'e ptar ord/nafevr C CA.0.) )
do,." le domtJ,i?e de J~n(iIY,je des slrvc,tvre:.. C'es» 41"J;
que. efevx J0!J/c./e/~· on J. él-e' r(/a//.u~:
/ ~n pov r /'tJ,nt17.se avl-ornah?pe lIeJ ca dr es
, y/a" d e~ //n e 'a/re J el-. ~ )
1 ::.w 1re. . 'pov r / ana /yJ e . c/es mor:~ ,/.>a,- él.e'",-r" 1-
fn,'CeUe onn,û?
,/
CI'el 9.AM' perme/Ira
m/n ee s (ZI') 1/..ex/o/1 . ·
la lorme C?J. /es c.ond/}/o"J d a"e,Pv~~ dt2S ,D/a9.Mf.s
"'elJ~n-lrû.s dan J J~ ma)'o r/ -le l rifl~ pro &/(ù>?(:> ;>rQfl? VIJ
rendeo]: citl/'C/'kJ /!,vit'/t'Ja I/on . de~ mélj,odn e.--/a s 1.' fu e", .'
la me'lhr!>de. d es .sér/e::, dov"/t~ cil. IVt7IV/~r' el- CL/~ tle~ .s;,,~
;lnlnl'/eJ de. Le'v.!! So"J..• hin,.Ie5J,:. ao.k 'p/af..Me~ ret-j.a"'!J""/e'/r~:..1
fanrif:S 9,A,Ae. )~ m ~fJ;it) de de ~ d'j/t'r&t U~ /riu'e~ c,onna/J. des.
cbl/'eu lié:, lo,...1 ole Ja. rflpr:'Hn I-a f/on .<h~ con ci.,-}, "".1 Clc,Ax /J~' .
..j.(l.~j c..~ .Jo"). la 1 J~ ra,t'JonJ.~ c-/io/« cie la mllhoae de~
e'/omt?l,J., tru~., tt/IR. e~J. Ja seule m.tlhoa( AVJ~h"bÛ. cre'r~Jo~ dre. ~anJ f}rojJf:~ . dt/lr'w/I~'.s Ie~ proltt~~J 01.(. F>/a1v~
e"J- de... c.or~,j de .rrmu ~(tIC.pn1.A~~ .
f)al'J r;ofre éiu~.1 n.cV,J o/'pI/1"M.f.r()n~ Je:;:; ffM~ )"/t' dp~
p la.tp(,) rn/nc.(~.J· Je) dY/-tx/~".s Jo,,1- -/a/6It.J elDn n{jA'~
foo tje. Ja dfjforJh'o" ete la J ec.J./on a.,..oih. so os /JYktn ~
art) ~rl-~ -Ir~nc-.hQ"J~, C€.s wl'f'otrii/on~ rrmt/)). a,vJ 11
/e~ bases a'fl. lA IlIe'or/e d(l~ vo/1e:> j7)/n C-Q,$.I' la- a't;tje"ren-
ce SVj';Ok "".(/llairt'. ~'~'ic. (/,,"J I.e c.o/Ylpo.,..1IhJ.(n). ~~ /"J~
re.J el- deJ CDjAIl.; AOVJ l'~J. t/l'A ~a'Yt.J ~xfer/~rl'J
alorj 1.pf. II ef"/~are ,Jft:/ftt;..M< (/~n~ p>/afA-< Â'" In';Jtmf
(/e~ c-A(Ar.:Jf.~ /afe~a/e.J es,/. pOH,'61..e ;Jrat..I.... QI lae-J./on o'fJ
mOfY'l.(nl-,j d.e. lors/on et de II~x"o" J ttUÎ?h' '/,.;(.(( ~J /"rc..e4
ole tuia.iI4h1.K/l)/ Je..J c..ore.~,.(V"t .!J-é/J:ra! SDnt ~a~.$ ~
-!ranJme.!)re le.! ~a':JvJ a«. Jvr/au. ,PCfr- /-R. !J/"aI".J œ(~
(U)"lya,,'nleJ m.e.rn~ranairej ~' a!J/SJt.n} j:>QI'"alle'A,m-ll1) t:UI
p1~n fat"'.1~11). 6t 1 un p.o/n). . donn"e' lk Ja JV~ Ge m.f.'d/tJI-
n~
J
elu 6 l'v" ,.la IftR'cJ.Nf. œf2J m.f/n~ra/}.(> el- ch ce-/~ tYtJ
en -/It;vi:;n /a/r 4 <!W'jf. ~ \ ~flA. ;or.eJ/f)I-~ n~" <if. la
rb.J ~~~"}..J f~'.1I'· e- 'eA~ a/"r; F n.tJVJ "cro tJl'd(
a t ) ~~ bo}la ,ili.,,, du J~/~e0' ~ la ~a.1Jl ~/rhU'..au-tq
/t. -FoRTJ<AN 77.
Nov 1 .(JUl'po~ro"'~' ~ <4 tyla 1R.t-Ja...u ,fth'/t'.l.t' fi 1- homo
qe'n.e ~ .,fJC) frope ,~ da..rl-/~ ,/hua,M"" naos tu. 1/€nrLrDn~
'pa4 n»n p tu) COlt?P -je a!e4 C.oI71'r~."'n I~ Jéfti.rt. 'tJ P e:t/l ~ Vtll-
../l./af.,'on,J 'dt. -/ernplZ'ra fpre 'n./ c6. td~s tkC4 d ri el/e» bn/, )
/e-J de.l'rm(A~onJ ~n.,j./a/JU.
2.
f1
1,1
Cen} an~ 0l'rfÜ /','.J-~//s.sth'lt.n~ ~~ bt:t~ es u'.< )17/)4....,!y~ e sIr.NtJ~r4./.L 1.) Jf) C-OI?J D //dt:J 1;'0"" d.(~ ;!)),fo'/e} Jv r-
Ia 1/(x/o'7 QI- la l.orJ/on de~ .p ov/ru d"'f"IJ/) J. /t:t)Ji
rio dt et~ IISO a' .A96'0) /tl. choh'j) ci a),'pl/("d!,'on ch l~nt4
/yJe iQ~ S7r(/~"Y~~ Je //m/J.a,,'j- -I0VJovr~ et' ;1,lvrk at~
SYJ -I(lm(~ v",.tI'~~n,.,'o,,~ to/),I/I~t.> ri ~k.m~"J.~ ;:JD"I,..~ ef
fy~/IA".); 7OUh/o/.J e» Igo9, AITè t:W~.j. -/rovl// UI\.( m./lh~d(
p(J/JJa"";~ u't. res D /",~'o') 'Y/rD~; ~J 'pro6 1.e;"' ..(.l ott /a m t'~t1I
"'f.ue. o'~ m;h't!.w< conl,',w,>;, eall.. l'hA.tkd.,. (.cnhJJeu·j. 4'1n/"'"
fYllie.,- .."ûn !o"e/i'pnndlt., 1/'...,,,- ~ '- ~h lA'U. /onu/cn cit /-o"e),j>tJ l' /l ~1'1'0l'1- é2Q1(. .A;'con,",~ ••: Iv -r"'~/o"'.) ~ ,./.J4) c::I' / eJ)t:ZI'
e J.taJ'tll)- dc.J;" C4)"'W es Il' o't.c/tIU',,..J. ve l'''/t è-r J~~ cor» â/f/,uu
frf)n-ht,..t~ d/,6 j)ro6/(/hA.j c/«JJ. er» <!.I pD/"). ~(. rtiJ,,'t/t1û·;'
la ci#'ef,/Ie' cU ~ tn:ll,pr ot ~"':.s. En Ig43,1 CovRANT /4
Ct", ';0V"" 4 tVP t,11I7IJ,'JJ(J'.J. pIU.l7'eI#·~ /one.he,,.J> hi'll.it..,,·r~.s ~.
~~ rftl/fA,lM Jo d~ I/~"fv Iv UJn d/I-/t:1n,J ?c"itiru 4V'...un nDh'
bre. t'n,,' dt. poin}J ln"A,I~J ~,. la lronf,ih j mtb~ /..(9"4;&.,"
n.t'J",l>rt t:J "fvt:ll"Dn~ a' 1r4l'-I~ o'~VclV~ a,.,.tt,.,. J, ~1111/t'p
pttmt"J. af. c.#1l. mArYn"ct'a a' / '~~.
~" ItJ50,l ~"t<.. l'elvtt.'nAhtfnJ. de. 1 ~"'dvJ f,./c Ut. 1a;,.cn.....),·
1""(" 0" dt.l/f l(Jp~tA .,Nn i/~tnJ. .J/,..,ud-..u r't' 1 taC dw~ rl/mu)
htO"~ t'.fll'n cl ~""h",.e,. J~ r/glrJlf.e' c1f4 :W~/n.(A)..J <:1 f/N hl,,,,braru.. r on ÂL//tf"U·;' Q.,U/C -Ira. fI,'f.(b"~J ~trU~)..l vn,.rJ,w./V)J,'o"Nl
En l''CO 1 ClOU(;H v)/J,Jq 'pour Id ~rfl.In""c. /oh h.•-Ierln.( c/tJJ'.(n) /In.,' rJ4n,J ADn fr"..(ft'V/rc. _,on li iu/.R' \' r he 1/
1
Il Jnilt ~/I"..(Jt; m «1},. d ~." p/""" llr.J~ Q,'f(~I!l1n'lI ": 11I'4 /n,'1h41
3
//e' au d.e.c/'t4pl>~Mtn) d(/J or""
f,.~'If!,""n). fWfYV.'"re. a':U,., 9 n1" "
dl. (!.DnlW co» gr'an.d Â1J~et.S
nafwr.> tF' pertnt /lcuèl>r le
l'1Dm 6re. aopfraI/on~ ,
J)e no~ J'ou rs 1 Ja rn-l'Ih~rI.t.. a'e.) e1Un(/)}.J. ""N.J ILl, 1
..P h h'Joe d~n~ I:H!.(W coup c:I a.c.e Irf~ o'Dh>41n..u tf«f. eeLtu' d< J!R
nalyu Js"..u()-.,uro/.- e"I,alu..,." m~IUA'Uf.M" 0""\ l/u,.tIe~ '" mt~
rl.i~ rft~ AD/J,I /;;!d,.D!P!Jt'C,l eé «: - •
-1.2. LA STRUC.TUAt" .sY.5TEME PHV.5JOlJEA RE~OlJDAE.
Da",> la .eon~-/r»cJ/o,,~ /t Ybk jlr/nclpQ! ~ /~~.(r/tp~ 6~J.
dt pro dt/t..,. 0' !'ontA'Ju. des J1rMc.r,uro en v~ 0'" leu,. tU'
mll.nJ/on""mt.ni-/ /(l.~·J-Ir.;UcJ-...ur6 ~n~f/l.Ntnj. cle~ Jy) {ùnl) "phYl1'
tfMe.> .dDn;'· ) dn~ ~~ . n I~>J p":> ~ -Ioud~u"J la dh/ o'-J,.bn .sy"c .
.Jelh.t ph!fJ-,''JM' es 1- eAr~c.J.e'r".Je 'f>a,. ..,;Un U'1Jll.m 6Le de a/dr/a III,
r« c/tlj;fnc!e.,,;' dL.;··~O)l.dDf)rut,}.J/Jaj./(Jfk:, el- diA Irmp.J/ clanJ le
Ûl~· ou' te> '.'tar/a6!t..) No. deptndVlJ. ,JOd) de,. -IempJ,I /'! J!1J-I~ht.(.
sz.vf. et'J " fa h"on na/re .=..:....::.:...-:._....:.=~.
~rh:tif1R.J. vor"a'ltj . .3on,1- CDIVWf/4 a' /Jr/oY",:' J/ ~~,.J. ~
l'r'opr/Q,fli. '),c9t'J"r ~ du a,'nund-/'o,,;. du lIJ 1e~ ~ ~J ~4'U';<!JJ./D
df.~ eor: dA'/-/ons. OMx -&inile~ ,1 (!;t,.. . / cJ~l"...) va","aélu U par CD"
-In Ao"~ .Ane,DnlLûf.1 ... ciep/Q.utrl.tnl-.),1 ~,:IYa/nlf.J~ ,e}c.. • .,,' // é'Jp
pa,.a.tJ .,;It/hfN'rAà/fln.tn). tJP(. /-1. ",,.Obk.'m.r, rev/e» 1- 0' eon,lr.,uA'
t"e tl 1'aA'cI~ du 10//0 ph!f.Jùl.ML.J 1 .An m~'N!e[k mta Ih~mo j.,.~
./tR//(J,.1- ...fA e Id 11'1,0 .An UJ /) /'WtI tJt.u G #et/t'ap '-" nu ~J. @ ,,1-
Jdl ré:.olu 1-,'0,., donlU ra. )a c/'a /t..et,. d~ damp ,.;i·n '~"MA .Le no", hn. ail d~f}re, rh. //heY1e' rJ!P" J!lJ 1e.'tn.C f>f,!I,fr'9~
,sI- k /t,g/rl bre riR pdYtrlI IYÙ "r(~ rJ..u.~JQ/'U pou~ de.~Ï'u·~ A
4
cho".,c .,..t.4 ,,(~n insJ.onl- é rfDnN'/ I..t 'J/~M.t .uf. dljc.re).
17/ pOJI.I/.'riL ~n n,p",bH fiu° 0'.( d.t.1ytj <i2 A'éerlt.'/ tl;,n~
h (.d~ CDn I""./"c 1 .r/ u 1- ct,'J. t!.Dn htw: une. s-lr..#c,f..u r( .e~ j..
»o» JYJ-hJ~ eD"J.I/tM· ea r ...l/ pf)JJ~(tit. .AJn nD/1?.orc _.in/'N" ai
j)oinl-~ 0of.:'rJii peu J. at.jiv'r hl e"I,~htp~ tiu rre..t~" h c.A.,ht"o,l
r!1J' um,l,.a,./"Io. J <Us rL:~JaClhllnl-.J JJ1. du c1~rJna~o"J.
Aloo ~ ~ t:DlY'pO r/,ml/)J. floP" J!lJ/.fhl.( fl,J crel- el!- cI~~
(JU'l- par..un AyJ It'rn.e li ~~a j,0()I'.} 4 (jt'i"1~J 1 dO") )~
.!U.J.s,w J./on ptwl- tir.. /allt. 6tV(.c:. /e» /l'')·/lhDritA ~"'m~~/~~l,
iL. e.Dlnl'0r}.nun). li A/'t .iyJ .),~ eo»)i~ ~ 1- al. 'cM';, ;:>et r ~n
AYJ.Jllfruo al_~~(//j/o,,~ ~)< d~'r/lIté.) ~t:J,.)/(J.IIt~ aJSoUf<~ a.u~
CD,.,dA·j./(),,~ ~Jc l!liru'/u J ° f!DIY'P.J( ..J.fM.-t rh. )~ cptn'p!.t..;d';"J
dA ~ U'h rJ,,·J./on~.J ee4 ~fPaj./t1"~ ~ pbJv(.n;' ;OtA,J -IP'tJ~ur.J
~j,.tNJI)~(.j d/rfl.e-J~hl.ln).; ,..li tA/- ttl.t.R~UU'r~ ~)~ cilj(/l./f,Ju
e: 'e4-J-- a'. ""'rc ~ I~ rfVh,t'lo cu- fJt:lr tû~ ~4 J./on 1 t::l&~'~Y/
tJMt J ; )a Jowh"" clA.th pro"nw rb J/r.-uc,}..-urc ~~)- i'hhvJ..t ADUJ /-Er1hA litA y,oQJ./t1 n ",,1& ~ t.. é4 f .. al. ~r( v-> peu). .e~
pY/tn,lra \ laltÎf. ·dt.~ h?~IIJ~rI.e~ ~~r96',J./~Il~-rLt )~ IlUteJAI'
9M.e. rkJ rn a /,~/~X v-> 'L,( 1'on e J/ol'J Mile PNP cl ..,û ru LI~
l.eu r: ~fal-"o"(tdVA.e ; la IY\.I!/h()œ,. <Y.t.J eÏR'ht~"h r-iv~ -€J 1- PlU
tru<fhpd" fW'I1'U"'~ qf. h"o!Nf/oIJ 4'pP"DC~~ ~J ,a r o (({p/N,-J
rit. Jahop 1--"" tJf2Vvtn)- A 'tJxpr/htlr AovJ rrm.c vtVl"ah~n-
. "tLIUJ
.A. 3 JNTE R PRE TA tt.ON PH y SI a VI;. ,
La m'-Iho rIR. rie::; e/« Me" JJ f'''''~, J
gel),rQ / 1>i"n CDnllA.f de'1n'gfU' par-
5
E'~ 1- 6",~ i. ~" /~ p,./n
) é">Ort JoWO" « 9o / n9
l'rom ,Da,./- ';0 who/t .....,/ el/Il. eDPJr1".l/e ph!l~/9 (,f (m~n). (;l'ec/)
sirl.crer I~ m"//eAA l'h9d'1°1,Mf. t!J:'IfImt."Q" aS~th'tIl1.1.( a'~ p/"'
"eu'~ l',,}/Iu ,Delflù~.. /e» élihl-tnJ..s .j?nJ'.J. L4 Jlr~d-"r<.
"fUI- .JvlJ tU"v/:Jeé ,qI'J un' l')Dm!J,(, rAt" tir. tel.J eltm~/J).1,hf~
l'ta,. .A" n.o/1't~r#l ~"I'u. et~ t!.D/)tI,°;'/o"'J, ~ eD,.,J.,'n",/16/~ .e)cl"r/
m.t'.i ,.I2n Ct.rl-a/"~ ,t>o/nJ..) comIhU"~ a' jJ/U"J"e,ur.J ;'Am~,,)~
It.J "r,eurlJ. ,e.J 'c.on d/J./o",. 'Jhp~ltlJ) l 'ejq//Ie' tI~" "'.'4mi/ru de s rt,i/er~ cJ,~""P~ av/( nawâ.A CDm",,,,n.J"
1
,On, "' In·h. r,.c.'u~,!," au : eomporlfm;f)J. ethf't .1IW / e'hin~A).
tpull. ;/:,,, l/ova.rfA/f., .e.it.l'r/tn.tl.r -en /cn(;.}/on o'~ Jt.1 !!~p•
m.l'lJu'e.~f cie. .Je) FJ,opr/e'les ~;'!?hrc.~ / (/n prldUlnt//I
oN'" c..lt:lp'p 'cU ,de~/QUhUO)..J dO~J.,.un, iA'm-t4~ ...,il .td} pt1,J
$ri61e en}~ j."/i~a,.f, /es . -Jiu brll..lN4' .e~'.1/J'9M.fJ cl ",. l'''-t r
"aru m'~IYic.e ~ rej/an Jo. '/t'.\ ', rr(.~J 'no cio /e» aux qeplau. -
. lY1~f)}~ 'I)\D ~,.t'~ '/ '~~~I)"'/,~-;" en, Y"flUo.JJ1- -An.f ré,1t:, h;,,,
m()f/Lù./f!/!J.Jfruro/~: al'plt',ea~' a\·n/inpD./rlt. ,~~./ ;'ltk,,;.
ds: Ja" str» {,/:"ur~ ,e"!:er,, ° ~ /YIq/r/u ~ .:z.1tm,n).J (//mM
,u.s €1rJ. f}~ft/l'"flé.2n a/'l"h~4hl- ;,uru. ·,Ie,(;,i'~.,~ ,j;"IJ(",B1,~
. ,l" r'f.fJre.i.e"l-a J./o /") , ril;r» mt'//eM Con J,'n.u, pc. r cI~) ~~N~
.41".pUP r'«N~ , t:1i1J,f1t' 61.6'~, T" kJ.f ~(J(j l'ttD(.il1t/Â / .e/It a 'd~4 ' eh
~/"///u'e. aa-nJ la 1'f'I~//'orit.; dtJ" '~p/fAum.in),J Pt1u,. 14,J d)eutl.
YeJ "cID,,1- JJZJ ,~/.eRùn).J ' on J..,.,u~' "(!,4 ra c.J-e're. ',~n"·dlme"lni:",,,,1t
F.I".M JJ,A"~ /.or/tVL,) ~ 64,.ru. lb,. con ).rl. J / :"".a'4~ noucu/te
est-, 1 'g'/f/n.,n) l'n,', a.' ~ '.Df.f -!roù rU°'Vt-trnnon~ 1"""'· ,P~'"
fN,!- fic r(!'p'or/u,."" ~ /a?"pI.üJ ~aC!e ~ ;o"o.p.N·,/~~
phfl.h~eJ tU. eo")/1aM 'f'" J/ rillliJ,f. °
6
......
A.4 PROCEDURE D'UN CALCUL PAR ELfMENlj FINI)
e/,4 CDmpor--Ie. Je~ é ).4P es ,ju/YIJ/nle ~ :
.~/d,â /ùQf/Dn el- dt:Seréli~o,j."Dn dt. h:, ~7r~e.fu,.e.
eVIl/tI(I ;"0'1. de~ l'Yo,ay/'t''~ cff!~ e/fÎn'nJ~
t'esowJ./Dn de Id ~i".A.JeJ..p,~ d.<scr"~·U(
4. 1.,.4. ] rleAJ,JII!Jf."~n el- rJ,j w/St:/h'pn cl ~n& slrveJ.uY"(
C. le~J, 1 ~.H",6â afl.~ ,!)fJtro}"/)"~ tt" ~v""",,. 1'0"'"
~'jtAbJ/,. 1< ~'('It frtQI/'~'md)'1..Me. d( <!4/iJ,U/ re,are'~,,,f4'nJ.
a.u ""'/ftI"I la ~/y..ucJ-,,,··e. rée/II.,. e//lJ porfe.nJ. s or- /e.s t:iw;r
a~plld~ Py,'nt,'paIJJt (/" pro 6ki-f.c. fJra l'9.Ae .· /(1 fO~Ç1/I?.!J/e
(gc'pmt'I,it el- cAa'-jf.J) ft} la rh~'p!J,.9/fl (/Jl..mal,r,'l.Ul)
/ ;'(j,a h'Jo;,,.,,n ~~P"JII;'{f. e.t' ra Ifa Je~ I~ ~f,.» eJ-AH-(
Y'~el4. 4f
.Al n m.o~'4. ~"'n.v a'.t )a m~u.,'U~c ~Jmalp'
r/dA..,,: ~/K de )a Th.ll.O"./C el- dé.s ~éll'/tu'J eDnJ)/~J./I/(~
cJ,é,.;l/Q"f. k !'f'alt;','au.i '~ pp/nI- ai 'lN IDPPIPIJ/tJMll,.ll./aMf..·
_ 'rahlUur- la slt:.ucJ-.,u,.( (l'.sa Jll.rDhll-l,,'c er» ~i"'JJtI"J.
.W P !t,,,,,\ (parD/~ ~v fJ/aru,J) ou cUI """,r,,'u~ ~WJ~ (CsI,iMtJ)
_ ~iG1'~ J. lluo,,'t )a plM.J apl'rD~~:' a ( eclle 9~~P'N'
ûli&'-'" leJ e.t:Jn tI/f.'-Ph!# d ;'p~.~" (l} Il.\ cl'~lA.
Au pcl"J. rk vu /llufJ49/~Il.l J1lauf:
e.A.DI'"'' Ill.) IDI) ~f7J}"I.Âj",,/.eJ rio /i'tlllel-,'ONIt U.
fifi V,'hJl""',. )(~ eo»J hfl""f) r: aY"""JJln j. ce J l~l.J ..
~ rlJJ cr-e'f/Jo},'p" tl31- / Q,.Jem/' a a.(,j op;rt:lj./pn~ p,.tjJa
rQ l DI"tt-U a ( la. re.'sp W J.,Df1 #cfi.x. cf.f.. Id J Ir.,,{;4 cJ-...t.Ire. 1""-mai)l.(Jt1,fflJ, _,t'chal/SIc" el6. t..Dnd7'.JIf... d.NflA ptAl>J. dt' a'téDIoC.
7
jJer lèh;'.(l/Yt(,,~ Ja sf,.udvrl (ln q'/.fj",~n}J ~n."p~.J ftf tllwl,.~
jO""/. tA#/~'" k &)'t cû t:(J ek;"""}J,' 1"(Jfll"uIIh~,,1; aile
,-'rape flA 1- gu/rlei fJ(Jr /a 7DpD/J:Jg/e.
JI.,.Impo rte rk nt'~,... 'l"".a. l '..J(I,;' /'',Jer/''"" -: I~.J -Ilub"/'J
f>rop()U~j .sonk :J€N:..a/~~,,1- .A"mpC1r/a,Ie" ... /JI' J/en ?U~ /es
"..e~u/';(J;,J /?Il J D"J- correeé«, 9P.e don..1 A te1 tire. tI.e ees .
.,A·cl.tiJ /,',st'J 1-/0":> .
.' ,
4. 4. 2. E.v"/~o;',.()" dfl.J E.,.o~r/e'leJ (/~~ (lle;"'enJ.~
la "o';~ c.".eh:~ el j./oJ')oI.#t..e.P~e~.1 /1. (!,.J1",v/e,. J. de
~( '('(Jppll/.e,- 9M( :. ,,;~/(J.s .i/~mU);".s ~NJ oS on/- ~·m/./~~J
tftl,,, eo« pa,,-. cle~ ~ //gne~"'(I'.p",: /.~ ~/~fn.('»},)
lÙ"'J '1,,1);).0" ~,. d,e::' "'fdt!Jn~ (p.!>u, "/,,L~ ,;';.t'me~f. -/.N'ti/hW,
~·t:J,.,ruJ) }; ;ela"J err Ig('~, 'JMA I~JJ fmlJ /",< et~ ~f/ehJ
d!J; j. . . r'eco» s f; I»u~ ,Ie:ë ,~,{r•.tl(:.f.v".(. "'.tuA 10" J. .en~:ef'.-C; ~ J&>n, .
i (!.JJm,co~ Ifme"~ c er f(,/"e~ p r.Î.'a.v};(),.~ oI",l1e!») ~fre. jJr/J 1/,.
da"~ ,4. ~"r,d(?~" pr:Dpr,,'e'ld.s.; ole 1 ehmenJ r"";' (!.~J)
pouytjP0' " o,?"dp';J.< ..A ~J:)f' cu' dt ';'f1J;:J-tc..J"". A.)~,. ~'hg
au./Von le s :' '. ;, , , " .
_ {)ndf}i~ 'Q.xpdlY'er, h (!.D,.,,~a;'·6"~'.,I,~' ~~ ~.p"'-u
/'1J-tnh Ou ./~~/;'i)l·e d~s '/Q,.,eel. 1o,,/. ,,1, '&'''.1 o'~~ /'''''
-I-lerl., j #;CorQI'IJ. .Ie.) i~;"'rJ,..I~" S!-~ 'nDn· pa~ en ~eI~.cJ
pD;~J..> d~ 1'o,..t.,,.~ ~&A n&eutiJ ",.t;tN~.(NtfnJ/ /-f. /(/I"I'J.
dIL /ev1lJ'" el' ttel<. ~)cJ9U1tlJ1. . A.c Ira rit..u''''4J.j. pt:t'- ~) (!,pn
(!i!lrl'D"~n,) c:4 CU'nl,.,(2,I''',4..\· éUAK #?.ll(!.C,ftt'-, (VI- dv-s a,jt:-/ln
"''n.c4''-I,~ ~ dep/acel1'el>J.:, elo CJN'tlrtU'"/~~ .ç"{'e /1.3 nJJIWrI,.
, 1
1
_ I,,j ID" cJ.,DI"':' atc..r/vQ/>f /es (.,1ftf#b'J/J~ de ~'
f>11Ic.em~/)J.J t:1~ al. (!.#n Irtfi//-> *~ a~JI'.1 /es e'h/nen j~ /t'n/J
n 'R 'j.aflf. P"~ 'OIU1~fl~ el',o ,./or/, on dD;/' la""e q~~ />yj>D
ih/JtJ sor C.6~ l'o"'cl-/(),.~..
7 ov i- e-ho/'n,D g 'etçp,"ht.f. qn /.pn e.1/l'ln cl~l' u,.ftY'l"I
"/1".6re dll parfl mti,.~ ~'~~~;,-/n;AU. ~pn /. ~"e"J.I;;'''S.
tb~ ."Ine,p"n..uu n» rlal.ej / J.L t~l»'p Il~) c..~, '.,' dt 1'~<4"
dt ( re.sp.tJ.er ~ /YII~ /'0 ~n dt')/eJn~ o'.t tUllI"l"t:1hol// -k '
Ou t/'p'/J·J,.e le /1)1'1.1 de~ -/,,,,,t~;"t~ hé:1"j /e..s ".R!V~
/,,~ rne,hiJ"J ae tr'Ïlan}."un ~C1P'~ .",nconA-U ADn'/' npr
"ru'/Rm~" /- ~ l'.Ç1ne.~D".s p"tf/nJ'm.t~ d-e. o'Y"~' _"/Y~N~'
fDt.J~ 1";.1, &1" ~ ,P"",I- ..p/'/~;'e" r~ et~ ?"~'4") 'p.D(yf1~f1l.t "fi dt!l,e' r""~' ..ll dppartVoJ ~.( c.elle. -IrDn fltliPr(
~el-e }tI//!' l'',u.à!''f) cle~ r e:rI;l I ( t:1 }.s " e I~} 1'~lA1't~",; C'i
(.on aJ-"on~ fis,,.,,f"/- ,3oJ,...sleu;.e a \ "';,~ e ,.,;lc~t.& 1 tJtJlLlr""/-)et
. eP" VR':9f~CIL dt la JD/I;I J/D" Q'pprD c~6t .lt.n la .,JoW},'tf,,-.
ekac1a,
SUùla,.J. la ~rtl'" rJw,. so r la~Jl'/f. Dn l'a//- 1" ~l
d.A.tn ~J,(J"'~ (JI- J1;U'f!tJ,../- le.s ~tH,dlhD",.} ~Il. u c:AC1"',D
rruplle} e'~ ID,., J. el \ 1:,,-,..1, ',./twr ~( Jv,. la rfJ,,:://ere c(.c /'#
I/lPUI'II-, .&'f't p(!p1- ~t.,. a,//.I're";'~ trttP t/';'/f"J d ~ ~/J,..,I) /-,)
/'.",~" W"'J,'I;'" (J,',J)/ngve k~ ~/.m.lf)h rlJllolaUAU/l). Ill-
/~~ .11111""1))1 4~~·~re.
l~J e1..f/rttn}.l· ~~ /tJUlfttl)) SDnJ. é/~"Drtlj ~',l}e",~
li,. d.:un cft(Jh"p dfl ~p la am",.)." ex~ a-,\J-fhUn ).,/ h.s éAiN"
rlejJlo CJl/l?.u>; 1't.JI"J, JD,.I- tel.J ~( /t~ rlt;laGli",th),J .jen).
cp,,/ùw.) da,,~ 1.'Amen). (t1JJhlpah'/n'j,-.,It' ",'nle rru) eJ-tl);,,,
e'!eln<o) tll','/.{hUP) ~/:.t?n {(!.#lY'pt1i·ldP~' dr Irtfll/-<"~ Id
/'lJnl"/frf/.)/ l'or UJn-/rt 1.( cAtJhtiP ~ c#"-friUnle 'JP~'"
",(Iw'/- ~ tJwj&'( ~a~ u~ C&Jm~a 1//)///;,' el /.tJ e,,;,rt
rJ/h'f)"J cl "fu///Jye . Jon). v'/o/.e~.) par Cl'~ mt:'tlll~.J; ~. la
t:.sJ,"fJa I,./n'l;/t ' a 1 -IrQ I/,t,'~ Ja rDn.pQ,e. 11) 'f~ J. pasJ 1I('0'R;,,
~n Q -un .e:/I 'm~nJ. oIllf> la umfPJ. nP" ~~".J
fou,. l.t.) Uf.hUpf.J· .e.~·t·I>,(. ,.,;/.J .J Dn). D.6/f'IN.J
a' pori,',. rI:.un d,,':"p cie cD,,-Ireunft,J 4)c"'U";'thttl)~'/1'.Jl',.op./U'e'l~ c6> de,Pla ethJtlJh fJPV' II~ eif'h.~I)}.J cf~lt:I CA -
ht-tnJ. ..ID"} 'mfV'lrlflu~nl- 1/(:JltI~ p~ûr /e4 ~"lrdV',,-I~, ~f/n
lIe.r.JIlmtnJ. ceI!etJ·-' ~ '; can-lrainlf!/J,' potJr ,/4~ o'~~/tRClm.tn).J,
10 ,, If' fJanJ ~l"e ,:.e'l..v.rit / tzgtt.}. .AA h'I;) on*, . ~.le-,4M'b~ ..
d.tp laCllntnJ./,' IL;" /0" ttl:/o.'n~ 1 c1é1/J:>." CA ~4d", Â-D"J. .t:2/,P1"6.J
-rn e: t/o,.. ~ ~~ !Q CAm..t p'J..s",' ... e/I(J ..J'0.1)). , //I~.). ae.t Il#m J;.c
c1';';-, ~nlWf~ .(clt)plau~n).J) .. 'fit. /éte.hùPj.· .. . "·.;.An 'I..NII
pD~J~Id.e" n .d8p!aU/h,lnj.,j ,..l/rva,',,(tntf'l). -",'na'e;'.l'nrldn·/~", ÇJ~
e,~/th' f cP~~ I-o/A l'ni "j.., ~", .on Uh't l'tt ' rit rl'i?~·O."J ~t!/'" J.
a,(.. /01-0 1 ,., para m,/J",tU ,'-"'°nCO/'l/1A.lJ:/,/.tJo: ~/I~,e.) d~ ~~
ve.ty~n 'u'~ e~-' C6,/J/(J/))., tAZlUre,. J~rt J. ..
, " , ..
en
e,,.;/t.'rt n ! ....d .~" /" -r" t:1-;on . . ~ cle);/a cthlt"J. C~/o~~ ob,'}.
dl"e. le/a ,~~.ru. I)(/~~J. pM . )a~~"h)t~ ~;,n tI.P'>
rz!IqIavnr -&A/i~. ~,\ cDp la C.lm~";..1 ch.ck.,\ '. IU:JltUch Jo" Jo
J(;jl œ/'loUY'/) c.( ri;"" mpU~hUAj. ~ ",.J'p.) "A"j/ tU .-
~ 1> )a rne..I-/Dn ,riA. cDp!aUlY't,.J- ~~"J. 1Ltp"l"n/t,.
cla,"~ ./tfel 4uJo· ~'rl.t.Ïf.hUn). ~t pl'JJ/Jte ,1oI.lï').:e;o;.' .
clr()A·j. fJP.s 9P W& f>~"7YLt/l(
~ IpAtJ ~!.,,"/ J!~,J. .J 0 " "".i
1J''rIR .
~ a'0rh"t;1t~" fi;"" (J./~/n,I>).
jff'~n dt» ~ G"""/' J, tk CD»;O~ ~'
er/Ittre.. "~2.: )d /r-: 04 }a r"eJ/on ~ of,~/tJu
/T'In). do//- l'frtl. dl:J/-/, 'e. -1(.,/if 1"'"~"An" /Ls de» /~ u hl ( ;?)..J
nltlf6411Jc .J DI> j CJJ/njl'Q f/iJ/".J M( e, .;t.I;. ëJ.t:/ 1- d{! o'0 r J1') df ,tl.on
(!,.p"Jhl nie) ÇJn Di)"~/>rw .,/L(e./l.tlt1.ttt) ~ o'Yprh't#,t14.f'\> eP/lS
141t1,~ d4"J -jou) )?e,'tRhv,.,t.: ~ oiulC/'1hJ en'lf!~' ,e& ;.A',yv
~ Jl.k~tn eu du -?t-!êpt,'er./ /DrJ1.AM la laJ/& ~J e-!thVn),
de ér97'~ ..;1 # l'''tlgN ~ CJJn rb·I"~,,..l dP ~/Ol"'" tf1 ho/') CDf)~
Il1'''/t.; ~1 /~ c1r~"J. ~I)c. .e.,"';," r4 p,f/ndre ~..l rn~~,.
Stlf,:J/eujtl"J. au /Jrf.hUër G'''lt~f.~ IndUJ r: -VI Plfh1A "'~
NCJl~·/f"~ "pnJl. i/dfÂ,ldJj':"n du âlr ,.".,ç;j/Q"J ~"'J /~ ~'
hUitJ. t:#IP r~ ~ e. #tA fi,~ " GthV")' '1'tD tIt:w,Je ,deI/');' cpm"ce;
h~"~ 4V~ c. ".tJ n ~.h:, J. d.t oI~r lb a );DI" eJJIl"tJ J.a " ,4...: d'l'NI
fJ#J rk Cl cr;l, 're J Dn ~tPr~ a.u.Jth· cZt er/le.,.( rU. (JfI'"
tdnu ~.. d';'/,//~ preh1lvu
(Â",·.j'}"t fJ! !.. enl,e..hJ e,4~p)J pn ciD,' 1- t!2V.>'I',. ~ t!P,.,,
-flnuJ/,' ~ ....ln e.P""-UCJ .,Qn,,~,nvl)) (....1:.( ~ la CD")'hU"
(lu 1',,,-It'.J /1') ~I- pa4 ~ UJJQ,I',..( )/ tff!W-l't~PJ. di ~ k ?/')~
.ton.) al tI'fJAJ U/IJ{I~J. cb,~~). 4'1,.(. ch""d-7:C~ ~ ~/~ melN~
'F kJ t&rrJl).hD~.& ~JC ••lhlt':I& eu r44 e~wb).J Jo".").
fNê4 (h,'ert ~J.""'c6<{trllV'iv'c~)/ tz"UJ,. Jq cp,.,~·I/o" tit
C4h1,Pd)/J,i//,p'p" q'~ 1~"J;"'ln).
~ (rI6'1A" cfA. rh rej,,/u;','on tmp"J'''é eJl- uI& aU dJ '
/J/au,",/)}"J/ ~/A oIt&u4. du pr/"t::Ipe liA. lIan/a)/lJn ~ 0'
IJ/tl UhLtn),... ,;f !rJ,tf~ 0' "f..P'Q h'"", .DJJ~fW,f l'tII/l /~;P'phttze,.
lùm rb Cf ,D,.lnGl~ ~r"hUZ ,P1YJ/~'hI'~ ./Z" dt,GUn fkJ
net!NrI~ 1 l 'eJJ tllt'Ie ' ab (J'/I),DDJ c;n1es rU œu" '&p,u tU. /.QrUJ
hP rk It.J, ".Wu 1,1tin 1e4 ; ni1'..9 g'j,r.J
-.:....- rLtJ /orUAJ'n leI-/eP 1"1.1 pro r/.w·It.J o'tlM Jo .A fl;gc
-!..u,,_ ,ca,.. j dl rI'Ib'm~ hOl) ~ eJ.
_'c6J -rrtlA. p1'O rÂ,ulf,.l IJqr I.e! AP/)'U")~)/o,,~ .t.1dtl.. -'../U~./I.tJ; , • ~
~ ~Qh'oftJ oilirw~ IrddwJ.tflJ. /~~~~e do ~~
l't 'tu",j/f. ~;"d"J ~~ tlrQ.I-/~,/ dia pnJ. hiu~~ e,1-)~
m~/,"CA ,~ /4ûrJ ~,#'t7",,6 A ~,P~~~ /d' ,".Ir/Ge. r "&1.:d/le" r la .llrJ.,l c.I,pre J' 12'/4' tAl1Ymtm1.pf el, e/J, 4N~,"/-
me J.f.) /0"""4 .err /0" eh;.". cleJ ~) la a,m,~~ .
~ f)fJQ'rah~nJ ''pr/f'\e;,pc:;/t4', c4 !'t::;nQ(ytf( ;pc:;r /0 /1'&4!.' ..
fh4J'rIt. ,ctéd' rit~ /OqAU/>).;' ,4Pn}., ht.. ,d1u'''''''')B4 ~:•
(J). cA.'1"1'h\.I"ru.,. la m" ;1,./ Go' c6 ;/1,9/ri;';" ,tk 0 4 fP-f. ,,~~
1h.t.nl- 'r!~MAn, '1YJI,,~ .,.:rll:.~e ,I),.o,I:)/·f ~' ;;'Ahl4nl- (&N/)
b):, ';rtl".Jr'm~,.. /a'lhalr",,: ,ck ':JrI-I(~ Ipr~/ t:4t 'l/JIe.itw dbJtu !1/PIs/ re/a/Y a r la JI,."",c/~,., c..pm'p/',',4
ft) ~P"~J.t" J~mQI,/U4 ...../,.,rf.,.,,/)'d,ve./&J 'DU,. &J' ..-It"i~ "'(Ji'" (;IJ'''' Ir/a/le , ,}a mQ I,/CA,' et( PfJ/ ;1.//1' rJ, /" ~/,,,,,,, ,-lu ..
r'( cg",,!'~ " ..Jillcl) RIJ.&JU ri,.. l "~ Q J/p " /F] - ,RIl,fI.: fO ~e) ~'!,t:iI'J./,.. du Jo/ul/tfutJ -l'D~t/'') .4 (rLtpltlc.e-
m6nJ.J ~'" nawdJJ ~/(;U/",. /IJ ~1)1r~'nIe-J a.uJt p:t'7,,./J .dt(~:
,rIS.
eft'i;v~ pl/PI') h'tfl/i?I'1>8"). v:J,r", t.Otnllun). .o o cI,!./,rm/n.-t.
Ja l'ntl{r/a ~ rl!J/rb·.p' a': ~arf/,. dt,.. /J"/"~p~ vdr/r.til/""
»e/,
.A. 5 rORnUL AT' ON l) E LA RI SI 1)1TE J>AP. ELEMENT 'FINI
..4.5.1 P.,/" ("/J-c. rit l 'en,~1j P",./p,.)/el/( /nÙW'hJt6 AJ" J Il A J'»o: polpnr/t'/ -/Dlo/ eu 1-l' D/Jc.J/#" aM tU~/a (,lIN,,}
I:,,,.Jr ~'/ 14). o'.t""()I' (DV /I?/n,/ht/~' ) ~elr n:t~r'''ftr av;/( $'
p1tJ Clh'pn}J" e:;1" D !J)/,,,) ~~ o/,ua h"P,,) a' ~~·It"~,-.,· J..e
p"/f)~~ " l'~h'''''/(l plf)~");'/ I1'IN/J,t:Ja .k'/-- 'II' rL,',·o./'fr
le.J .Ilf.Pft:1 j/II"~ J,.41Z~'//J,.t../ 01:''' / a,p~/A ~!JaA~~);IJ'''~
&.Ipt. fi,. 1/a!U;, ;'/11" ct'IJ d.t/J la CI/IV,,).j J .ltf. ~'I .II !..cn;" (,1 (Pllth\.l
~-J:
~~ /brlh/ /DIJ.Jt4 ~ cpn/,j~rq "'',.,''J #1I111J/Â lc.J F"'r
'e!fY"''' "un ~Jlt~ l!1uJ- en .JeJ~VaJ"u;"J. 4 ibn"".f,;"n,J ~N~~ .eJ. /"" CA" """",,,, .. ?I:>~ ~4""'J" ~ ~:,<
.. thc:l""~ rA tJ;, la ct /TIl ",Jo,) ~' .4n /J lu.. t,#O n). ,.dr::I h'J/c:II.Ac/ld .~QI/Dn~ ci ÎF'//bl'<) .ft,n drfJ n ). . dJ:,.-u /~~"/~
pof,";','ellt It::'klft .a;'tll,"'",,~'I't. ~,' u#e VtJ1!e",. ~.I'j,u"
"'''nùt'w'"tI l'I~'A"6,..t. ilJI- dl-f164 ..",>.
J 71f'.f = 0 ('1. 4 )
1~
/"Iertu. 1 DV .e1U';91f. dA. dl~rmQJ/()" lIe.J el- rh. J~N'9/( eJC
lerflll. J DU .q1U~/" /U'ltn)/tlâ. rAJ /t'l'tU ./lJc/c"ÎwreJ" W "
('9. 2 )
,;
U.. e l (J."~
4. S. 2~DrlhV/ahiJ" !J,'IU;o/e rh. /"1>4'''/« po -/",. ;'/e/4
..4. S. 2.'1 E"!."9i,e._ ~'nl!:~
L ~~l'l'rtJ6)'p" fb. l 'g~e~/e .J'n-/,r"" a&A NoXtIM tI~,.,
011'/.1~"J. ul- ..
~/,I' · 'Ci., ~ la rb."•.;,/I' diM.t?'ù rjR ~~"'IhQ J/~" •
(1"10' cI~;'onJ ~,.., CJ)11~..I •c.6. lI\O fNh\.t .,~"U·14~ aw Co p,,"p./U.';':,
(J'I..Jf;~ "'.~ /e«. CD" A-a.,'q 'le., "",).' Il...... oP" oI~,.... -:-h;"'J
pM 4 lo/.J_ cpnJ-IJ·-/.;u )/~J' . (fy'pil. #~DÎ4) -".
•
,Sot' t:/ 'e.t:WJ.( cI.:u,." cchp/iJl UItJ~f)). ~?~'-I<~'~~I, 1ÎNr9/~ l"
lerru (Jf) ey;' (J,u..!tnI".J.e' dA S{}/J ... ' ,0'" a ..-. ..
, -
{~J -:: ~d" lFJ~lj -t\r.l1;nle!JrQ lùn ri.c. J ~ IJ hlJ" cbnAt ..
(of.? C)
1
J)anJ J er(lllo~, LE} uJ /0 htt:J!"/u tI i~JJ/~j/t~' e,/ft
/11D"IN. "'1" ?AM U u-}...un.( r"''''' 9'"Q ofoj,f~ ,
A. S. 2. Z ..f~!!J~·e_ '!:"t.e~~1'"rtrII • Û4J _./ar ,UA .tUeI,,/tw 't,) ~ 0'" rJ"J;/1" .!J lA e .'
_ }<tl /#':.... "" lr.,/arM /111_ lIA !DrUA rh l/G Wh\.I /~1_ ~ r,c.Û con ,,,,.l'Pu .IV' rI.u P~/p)J ~MI;cul/vJ /1>/ .
~. ~leJJ lA d~m, rb ŒA/J/~cPhI,n;J" QI't a :
f4.f)
, ~~ ~ es]: la fIJ"'!,ju~j./f)" r/u r/,/>~ u tn''')J ~ p~/n)J.,j~
,I«(!e;;'''tm dJ. 1'(/ If ~'9fU. ItIsrlnJ (-) rIA /'tf,tAdh~n 7 JIeJ'J, ~1. ~~ .tk I~·J. ~ lu C;fdh? €Jclw'euAu ~r/,IJ).
" ~r Uf4,1'd cilt. 'a \. ~eJ-...uer fA.,. frewtllll
15
1I"Pe"! ("\Vl~(E] leHl'H~I)!t -toH ~tp.l d'ilu111\1J)
l:--~ 4j iP~ (~, 8)
b' IR /ù'tfrtlhLI cfio/~' 6~"V0w/'l ciI~.:v ..e, (~,",D tvl~/'YaJJ. ao» ~n rP~I"Dn.J ro"~~/ la h\I~ é't a& /~".",..
",'e,A0/",I.'eltt .'h?Ù.,.//nQu, rU ~ ÂIY-hc.J",u.,Al. . ~~ftf ~
N Ik c6 d.t POJlJ""..;<''f!.
. ,(~,.Al.)
(~. Al)
, l,. \
i
i
COIM\J ay~ 1 ri/II au h'eu ~ :Y,IPA1""ur )a in/lA, ~ '" .e'1r (~=:~)I4f)n lJt(; ~t!llvw ~ ~M;""~ ~ i1r1f e» /: d-ùP? r6 Idl:
1~(JJ/eJ" .(.Il) oJ,19/L( .Juj, t:A\ c~~ ~cI./ ~ CP~'
'fNe"J./ pn ,eJ ldo/tAl- J.4f .. \,1c1i =~' 'teJ ~ J~
tÂ-- iol~ -=' " le -1 )~ ~
ch'~" tfu6...h01N, ~/) cle;"J »o, pn Q.'
11"Po. := '1 ~.i~ 1:lc.-11[B.ÙEl[ 8.1.LV' [e-1/il' - ~~ ~fF-1lvLGl tlP.j dot
~ 1 t t- ~ ~~ [e-1 ;,[G] ~ ~jJJ -~()f ~pl l~. .«)
:/'~fu~"( /pr/<n),'r.lte. ~k/(. i., /il Jk..vcl-.p~ U'J /q ~"'h\.l rk
elUl;p,'c.J ~/'lhl,°l/hJ tic J r ~ntI~) ..,
Trp ': . L 771t (~ /SJ
g..o ~t iW). .e. lI'f~" du ~/d Ull'Unh rA~.,A la ,J,J""c
-IM,.e, D" psu;.' .eCr,À.8 a\ ,carl,;" ri< .ft') # (15) ~.,
11"1' =1 1!f~ ([c-11J&JtEJlB.J]th Ic-1)/l1, ' V (~. "J
. -lat}: llc"1~ ((ljp.,~Jv) -/4f~[c.-111GJ11i~rb)-litljil
/~' fF0f.,D"J ri 'q'pw' //Jre. /JI>I" j.. U/&J 1,.,uJ' ~n 1 J(;i~'
A.t 4 uj" '"'h',;/'IÂ :
~1Tj -=- 0 d Trf. - 0 • •• - '?J ne -: 1:> (,A, J/-:::)/ - J ) - '7
~ ~~ ~~
)0 o/Ut1t/~;'J ~~)" t'e/tI'ÂJ ~tU r"h\.( /rlAJ,,'t:,/d& riDn""';/ t.'Iere»7on ,ÂZu'.10 ft.A. .:
A1
~"
(~[c-1~v~J1tJ /!.J dv le-1){"l{ :
J:rle-1110.J ~/ cff,. le -1}Gt/~J"~)'" iP( (~. li)
c,. 20 )
i '". •
'!l ill-= 18 ~ I~/ ~. . (e9' 21). .1 ,. \ •
•'C . .,J' • ,) ,
CHAPITRE II
PRE 5ENTATION DE S
COQUE~ ET PLAQUE.)
2, --i DEFINITION
/:.".r!JQ /'Jo/-/IJ" dDI')J. 0" Gl pt7r/I' dtll'J /t:1 /,rlJ CI 'tu
'r( dt. CP 1(!p1 (J n él/hJM 1- ? '~,,. uJ. fi"'" e:)or' e 'tU. o..JJaire
r!tflf1J te ~ lev/ d.tJ c..PnllI"lr...u "hD"~ o'tl. ~~n;f CI"';/ rie 1o~/(
/'J(JI.A.1'e.,,; u/ap"fTJlJ. d 01/'"'' ---u" me/I/t.AJ, (;r'ere.u rit./ ;'JJ ft? I-/e/ a'il ) (, ',t(;;. ~J con',tU,,*-, ri(JJ ~ t·du a'
-/"/J dt'IJ?'';d'/Ï1nJ aller..: _ /tJ?",.e1J ~" a f0':J'~(JrJ #ai~,
e ~.J 1-: QJ"'" ty",u.A 1~'cIea //JQj/D" 0'~n eer J.eu'" Off';u. cl '.e,&mfh!-J rb, cprtJk,.,uc},~"· tU)n~'f dt 10 n.Df/l()" U
. eD'fWJ/ on d,'j.. au~', ~··a m/ntl.
. En ~j., ~ dt;',- 6, repreHnler ~ Â::i h1.e//leu~c
r,~f) 'pD.JJI'i!.t ~ d'et,. deJ !f:)rc.<J tf"" ·...;nlerl/l~,.n.#nJ. thnJ
/I!.J 'paro/J d,J Jlrp c.r.A,l~(J /e/&J' ~ ArJ !UJe.I't/thÎ"J.,I aJ64,a"J ) JeJ" cpr. ~'/~~' IeJ ~v"e:'0 tL.J 1 (!!oc. • " f1!)VJ ./JntNAI
tflc J.:/ciJ'a-6JQ),'on ;o~r JDh'~ eont,./LU,J (JI"~)c d"iJu"
h'o,.J.; CA ~n). ~J 4v~ (.I,J ,Po r/euHJ .. 9'"" ~ d,,'v>~,,~.en
tftwl! ~/~"r"('~: k tJuI\/dc.c4 ~"';~~J k"''.S~''~tSIeJ DI.#
flJla~J", .et /DJ ",Jur./oUIJ po!,/euJ.VJ ~W'>bJ 0" U)?..~.· UIV ~?."ul. al //fh",I'/-I< 'pah tUuA: ~/beu ~~
6eA 1" ~J .,0 a ":J,~J' .~. J/c.CÜlJ. la 1 l.é,JafJ,J~" cit la tnJ'm,(yttl n.f
. #1 (/aIu'Q 1ft r Ttta,,/, A.tJ~ /tV'~ ~a/) rd,~pÂI- t:War au
-/rt"J cb'mfl/>&lo~J i /~ Ju,,/eJ CI 6't't.v~ t en~ k tU.u k par':t,'JJ
e-J. '1"'"" ~ ,t"J( ~n.~)c ) ;p;vJJ~ r c6 )a ur-' ~ eJ j.
~'p.pt~ t AtI'»~u Au 'dû~ /U;' ...Qru. CJ:J?~ e'j,!J1 ::, hV~~~
,"",,} dl 'vu'./.t ,a~.Aa .dz,I.hr U }ni (UQ~ M PI" ~1"t:U'Neü".
(f~ .4),; )(}. CPW'I~ : rJ,.' AJ ~~ u J'h,.téitOnA of, ~n"<iw~,
J)~ aIR c/.,!';.yi,or. ·rivJ CJ)~ 01 .0" peu ). cJ,;,u auJtJ•
J9
9.,,1,,1:..u1lJ. UfM(. U'J-."tIn.l p/r",uJ..pre F' ~euj. .l!.Ah oih~~
o'f>tJyJ.,., d}Uro /,h~ /YU·nu..1 e» -IrtJIfU/Dr;rttll!') wd~/~~
fr'IPJ'tn en..,uN 4W?r e.t ~ \ #-o'!Y',p ~ oc.e dDV!>tA. ~u!'buAl./
Ji J II' mi;' ~ /~ Iy/o/~ r6 fi,J Ir/bi/on fk U'n
-/rain-l1J el- rLu cif./o~rnt:lJ./~"J <1(,1 l'I''f.MrH ~D"j. vQ/a.(tu
I>t:JlJ r /.eJ t!.DreJ; e» ~d-" a/J'Ad 1M..t le1 ~la1.-l-UA /r4
Va,.I'//(/tJ- .l!J'Jfn ;'/el/",m;,,;'.I!" I-&.~·~"'" 4 CPf..,t.U1 et( /,a/'l. 1- ~
UJCAh lruAt .jrafl,d wu lIenl- fj.~ Il /IVn J. t/.44 !/'MfJ dP M ~
p1(Jn;~ 71d ltVA'b-oru.Jl f~ 2); /es rwll-~"/u rie)
"CI.!. _en_tlf'v~h!.", ~~ fl"-.P~t;Jt!.'cJ,~~
kt! 1.: Jc..Jr~hu;r"'fl"(" ;"6", (d'Jo" ~'IU~'hJ. tlfl (~e
zo
CDn!ra./n!v:> (Jfjt'JJ(;nJ. fJt:Jr()..//,/h",fl)). au,P /t3n ~.!/e" lit Jt:f
(,D1.M( onl- o'f~ CQHtpD.J(J/')-IeJ; I)lJrmah.J a\ IQ ckA?U eJ.
~p~oA';e/)J- 'dfl CA /t'P';' )a p/fIIJ !Jrtlntlll. l'fA/l f ,'( 6. )tJ
C#(J'Ye. (r"aJJ..,n,g~np""'rt ~ Cl ft~.( r6 .Jh-~ cJ-..urf) ,
En ~/Rmll.n;' !,'nJ~ /.eJ a,1I''e.u/';~j -/."J,.,:'<nltJ étU
I"..ai!flml.nl- .aes CD~c!.J ...8té eDnfourfLI~ -eo /,tVJtlnJ.
1dpprOI(/h't:J /-,0". 1,..t,U' c.on<:f7J;'e. d' tfV~pÇ)JV' ~6 /-t ~"'I'Qr
.JtNtI ft). fi~~ ,rJt;Ir~ u. é/ cp(..I17lsvre. con ~'fL,I;4~ peu,J. (,I-~e
C-Dnllenoâktnfn;'re.pr.'lÎf.nlf~/Jar a/w' d~'U d't.u'~e.c ?'mJ't fiA. PJ?;.,.I-J, e./';""ln)J r>/ofJ,,' O~ "'''.JI-o/e ~I( /~
pro 'cima f/Dr> W' cl 'au. fan!- ",~/fleu"t' fMe /Q -Ieu'/IA tté.a
e.te~A f\ JJ rie 'cr 0,.1-{fj.,lA re 3·). .. AI0 ~ J au r on) clon c. Q tira/le r , ~J, e'leinen}J ~ k I J
,.IlA!J"'J~(); rwr» ,feuf'gm.tnJ-." tif. /a //R/I./on "lnaù ~qAII1.I"
du (0'" t!I4 "at:Jf?J !4ur plt:tn , "
i,)
, 2,2 L 'ErA r PL.AN DE.. , CON TRAIN rl;-
,(jt.Jop ri. aRJ' /r> J.Dnra,I' ~f."Mf~~ a ( .on«
~/a'rfl rn/rr cs , dan.s,',J,on proprt. plon,! 1~:t-t:;l- rk CQf'I
lri:v'nle .eé rfR.clllYormal-,on a" 1~."/~""'ù;ur cI~ ja ~/eI?..P.(
(2Jf 0l'I'v/", ~(/, fJ'raf /Jh,;,~.e CJ:JnfhV'n';~'?",/ ul- .é.l-ol
ftl'r ca r a c.,te:,ll-l' »«:: ~, c.Dr>dt'h on,J dt I,.~~ ~1-/k.J ~.
fn,fnf,onJdernJ ., /0 st,;r~c.liDn'7'( ~j. if ) .• ',# • • d
" , Ain:.u N.. forci.' n 'iJ.(J ,,1. t:;I,~ /;~~.,,; ,.Jw 'c/el ,. Jo.3'Au"
Jo IUhr u ~ /Q l'/a~/ ~ cDtnp P.J t:1 " / e4 ,riA CD" -/"41',,-A
t)(,5 ~ ~J' 4u" /(;4 Au!'~ lot el- ~ a\ -!,dA/e,..j /:'~QI'J
Jeu,. riA. 10 p/Q~f. ~ 'anlW!tnJ.~·_,,;I/U ~&,o~ ~.( /fVJ
.J, 1
i:' ~ 1~ ,,'". J
Ô'I~ 11
1 11
1 : 1... •t' •.0 (h)
)(
H~. 3 (Q) Au".·.1,/"!Je. cl ~~~/"}J -Iria"!J/J/QùfJ .,eplf~"/dltJ-
"ru tl..t'~f c1R?, Ih«. Q"IJ,.I,.alrc. (~) ~oo,. o'DnlV~J bf!1;!t4
e~ ~o,."",;~ g/fJ6aj,J pD",. ...un ill/n,,,J. 1"~"J~/e&""'"
22
eonlr(p'n/~· ~I \1j J 'lll#,COb "·dfl"'"".)·I'e'}~ J. dL U''' Ireu'rt·f.f. h'.Df) Irtk èlI ( )4
ft9.A1" S,: ~clt e).. ~ .4onJ Le.J e.on IrtA./·"fo horlrtdt!.eJ ~/J
J(/17 1- )ru,,""'(J n J, 211eJ- J' /fI4Pof. d-, 'iJfmsr»1-J' r~ el' !;~ ,)# r,J·
If; con -1 reu"nlt.} df. &Ja/I/.fth fI) J. F" ().c1/./JMj. ju r: /tJ JJD~
~ el # At4? J.'·II'Hrun J. " U--., <:kM l.i4 rbÀl e-/-/orld ~ eJ at -'Ud.P'"
f,".J( M.In J. :
Cej CDn Irai:, /:J c.~:Jtrl.J~'" 6,,). ao« d~D,.",,,J.IPnJ I~I
flrtru~PJj . t)" (a. :.ÀW'.p.. ~ .ritp/o.UIJV()~ ,.~.!. u~:it â.dn,J lu
d;'ù,!/~n<"e~.+(~.•-;r f:'''''' 6J..r '.~: 1., ...
..,1
• ,'! • '\ .•' l '
eonlrtAln/~.). l'la,.,) / p/orf. m/n (!.A
~;ge f d"ru A.D" ,d~n
23
~" a . é'lt ':' ~ 1J' = "dV"" «~= ~ -+ ~ ((1. 23 ).~)'\. ~
?J,jI à'n.
lél> [{)t~
e,1- ~ '?J,J
- IJ~
~~
dy
1... rI7tL,II
~IVL"\ .
. ~J.M
eJ:Jl"hU. cr-, -::. 6""3 -:: ~f x:D J fi k'pAU )Q /1,; riA. Ho~ 4.</on t:2 ~ lo/f.d :
\)~ A v ,,0 6tlf~, . E v .A t~- - 0 (e1. 21t)- •.A _V2
~"a1~ 0 0 .A-v r,,1' - ZI~
C---,' uJ.. l~" re,/a /-/f)n . ('.onlr~·nlt - d1Dr m" I-/on.! 1~f?-'" bd J. l' Ie;n. cb. CD" /.rai" If- ). ./EJ t4 J1'" Jf) IYttP Iriu cl 'g 'lai /-/ei ,/,' Cf)r'f'CJp~" tkn '. . .
te'/ ~()f/~(,- ~nrf4,.t )Lt ... l'..tjJtUJu"u,. dt IC3"h~.f.'·
.2..3 LES PLf. QUf~ EN FLEXIO/y
~. ~ . .A F l~)C/onl't~liù: dfJ I!./()~:pj min eJ,~
c Por- .O~I'·o~·h'pn aA,,1~ p~r'D/~ e-j,t!2'::lIl~~ 'a'c:1nJ fwv-
p/fln } · /elJ p/().fG'e1~ ~~"f mttPn lu)an!- clfd/ldJ/ cé4, />,e)\PiU> dI~
ICV'rR/tUI)J. e:;;t" /~,. r'/fln ~jI./n. 'Aln dâ.rr/l/'f.f" 0 toH'U
/DrrrwlfJJ,'lJn ,.ft,t,#Jt:ihVnef)) ,A'/m~6 r6. 0 ~rO~hLC;Dn arl
nul- . ~tfAJ'n.vJ l:f/I'P Ij,t~ eJ ;,m, .t;P~a f,/c.e-J
2.5
! :.
l'!I/!.O fhi.J!!.~ .1. Kir J,.f~/t.)
_ /eJo jD/~~,u APnJ m''''U-J ptfflr r,,/,/,o/1j. ewJc
rI/hI"UJf"!)~~ hon'J ar» I-d/~
/e~ IJ?" l'l'Y/aul{ J::Jn J- l/ruN"'e~
_ l,Jo c.Dn-/rp"n-leJ tf titlDr"'(J f./f/" j J'on f rJ"e,4 .-(
/'i/leJ at 1!JNC~ Jeu;" lnInf: ,A.I =V =t~ -: ~ -= rr:t -: e "~f~
I~ d,;Claum-tn}.J .Jonl-!tv'il'J fJéI y r"l',PtJ"} tA'
/'e.j>oiJJwr .. w U/. ~IIJ. ,/IM'cJtJ n }- J'_ 1es #,,J.J A-f CDn rlA/nJ tk.J av ~jev'//;IrLtfl)-
JD"/- ~JJn()re~
_ "1.èJ. .P!)'" /.-J JIll. !"o'-U/o"J. l'v'" .."u"f. 'UlrNta/#. tUt
I~!/~I.J '"":Y"n a./tlhl- Je. cJl/p " ".." J/",n .4)' Ir./J f,(~J
fo~D ~"'J t:J~'fU' la rAY(),~~).,p"
.1 <,
Alli' Ud ~~fJ,.fUA" I~ p/dF ~ f/.J)pY)/J()rfe t:-DI'J'IIJ\(
'pn .eml";~hJe..:"blit. 1~'I/tl-J cl '.tjJa/JJ~V" -Â~;,,"II~in~ 4 t{fl
~. I-t 7"!)UV~"~ t!.fa eu" U" .ifo;' ,/~~ <lQ c.J)"ln:t.I'"
-/JI. • lb",. rer» d"e pDJh'~ / I~F'A~ Jl,fpn cf 1 pn tlAo'AlJ.:
Ira fJ4 r b Ju," A ifo6. /ILl pl-" 1 i>.J '.J}V> c.e du 'c:'n1reu'"~
-!t;"'.!L"i-,'e/nJ trfJ"'J v-ûJtI lu r"J el- ~J 1 "'41j J:)" (l)n,.,'oi~ 1U~8~a «eJ U4 cie?,..,...QhQf\'J @"re4~"tû;" ~ ,tr':J -=
~J=o
j)i/!."~()!i~J_ (bJ. _c1Jk/a ~hLt"l-~
Co"'/h'rI";'l)nJ J~ dUrjoU hlR~on~ d PfiI tt"o f.AAf It-/-
iVI'pOJDnJ ~ 'elIR c,o"n ",,'a'f aN{t. II/... ~ I()n ~,,~ (;WIH» Jo~
IL(. J.( p~od<.ui-( )a /&/(/01) du( IJ.,U.)< InDh'fnh ~ l'[ptM al'I'J/-
Zb
-p
~I 0(
~ :l.. d9tro -,lf
•
1.0-- ....1-- ')\
(())
ï -"'(dw'1 .
• 1·' 1 ..... - - -/-'I----P
~d~
trn1
i1t1
o
î"?" CPhlPlJmPn-!re',IIA, I(J /,iJ..urt. ,,' rivrol' Jo !fIA /"/C"~"" k!,~rh'(plefJ;' .~" b-fh€"f «(lM 6. fJ/tJn ~cI' AvJ,';U,>1- 6. pL
;;}J rLe.'p/~ U~n~J W {.JU'p-f h dieu !o./;tu ~ ;rt1on }fet (,&..9. "1).1'
(!,.Df'lJ7"cJ, ~()".J pru ~ecf,,'on nPf'/f?t:J/e a\. la ~ lo?",.f. /JI-l' tJ rd 111'[,
a,u' l'Id') ~J ~fj·l,~),· la p.e"A ~ la Âu-'/a~ m,trvê:"u
oI~~ 10 ii,McJ./pn iK 'vJ. ...A~ =~ J"~~
p()!l 6 trtf~ J'la/,JPf'nJnu,. 1-) eJJ,,/6 daM la fi,)u J./~"et M J. ~ "=' èJw
: j ./~~ ~ "po ~] (~. 2S) ,-
1d
•
27-
.l7 D" UlnJ-;r6;... !l?euÏ?I'''tlP/-..p1V rb'NJ/tJrt ~e-/~"?.AM. IP-n
qdfl.-J & fJlt;n 1"j' (fll ".6)) )~ rJ,~r~nu. ~ <iP/P',lr;I~M
rkd dt.u'iPI" h (1Wdl Col" fJ ~ ttJ (}I, (/11j "'
rovr: â/Jer MI;"" r k CD tA!J 1ru,.t.J . rJ,. la ,ju"I!' G( mJ. r1I(:uv rit
jf) t#tJ'f"",e) on ,J.I r(lpp'//.e. ~ 4 o/.&~.~~ W API)J ,cP /..'Ad.,-,
cf,;M ",un ../LI Lad, la t>tn-A etc la JW)~q it4111J"A-f1U ?h4-lt:JJn
?Mil rl.iNcJ.,Dn p~} ~J.. ~.PP.u'( Yda ta' )b,,~ fP-f!tV'!
Je:;; la~,f ,., le. et l la Juhl' t.( daM «/1e dt;u e-J., '0,., @e t. ",#1(1n
"'ttJ; eu'",.." 1 ÂU/'vtlP Jo le; r//,AJ e.I.'~ n ~;' ~. ~ .erJ ~ ~J~,., ~
~lA!t /w".e." a 1~)vJ }a "&n/JUeA.tr' riA. )::v, c. rit ~ e 8, ri ~"t:P 4 "1vJ.- rac.' r1f (~'~. ~)
f
Zg
Of' )(J fp"'PeN" rit J~ e" ~ GII\.~ ~ t:A~'h'W'IC' ÎtI t:J
.v~)\ 2,#, àw 2· -= à~ VA T ~) l' ~ ~')1.
do" t.
1
e ?
J~ - ~w ~ _ _ ~w (2'). ')\ - - d/rt 2- J ~- ~t
J~ 8?jfU (-J m» ,'n.) t:J1',cafiai J. CfAI1 fl"'t:lntl ')t ~~»&,J"j.", di
c!~) )/,tn-A )7.(1 .. ..cPi>uiW f. •d~
.'
5vp,o~~~ 'JPf. ~ If J . ~W]A." t~' ~': n)l -ef ,,!! ~;cn J. ~~'Mt""_4
V'"e/JorJ/J ru r: /1l~6o',;rI.J rb le; 'p/t:J~-t J' :'fJar' Q,,(!JII~,.~ a#Jlf.<
1t;;P{).Jf,.f~R .~ 13 e,fZPw!1,' tu")13 PlC/~" pv~ rÂJ 6d.'~
pr/~m(J l'f;CAeJJ Jt:It~ rl2Û.rt ),YP.D f/t.U-f· hV"h DI> 'YI; dt. ""',R.~
P"?" J. . ci,. 'cP/V. F Ja 1V0 u .nu~Qfl,.( ru 1v"'"/-,lJa4 d~ lb'
Vo"""Qi,on e"t- ~ . lM riJ.,!ar~(JJ.ID";.J ~ I~·/I.(I- t:ft.t. cl
(fj.AD) Inl"cu' c" lacPiftIJ':'u'~ riJ. /~'Ia.. Ih/JUIN. ~nJ. ..
e. ': ?:.f. -= -.zd'tv.. ~. ~I':: 3() := -~~ 1· (29·a)d ~ .: ,. d7d")1} ~ G c/ '~:. ~'l
, p
~n Ir-a/n I~~------/(l~ Üf) 7r-"Ù... -k.l 9"" û~'J/l!Jn œh.t @'K" cl0 ,ht(; h~,.
/t!/ df:> /.ew'//lJ..J .J.PI' J. I~ Ci''' 11'(,&1'''' -lu r: ~n av~'J'-en.,iJ(J~ fJlt,I? da. o"lrtV,,-I,/ -R"', #..eJ. )t:/ ;trla~~ e44 /tV';.uj
el- !.lA /e,w'lleJJ b,.J,. /,./"(.J:! r6 J.t <t~,It'W,. clttlW )(14
rt·~ c./-,'f)ftJ f"/(Jn..lJ ,,' la rel(J f /0" (pn Irev;" l, - cI'r r ,"el 1,:0 n J!4 J.
rb,7C. ull" 0 / ~/ftlJ. plan .CU c.pn/raJ'rt/r (~~J."()", 24)j E
U'J, IJ 1nPrk,/, d t 'IoJI-,'up , e-J.. Y..& CP#'~t'" 1- rb .!c/JJ on.
Ai11
dU111w
~dJ> .'
\~. \1"~n"t
1\
(a) ( b)
30
D'" Q ..
. ,
tll1 -:: .tl (fl1t -t\)r~) à ~~-=~ f~g T y~)"
(~30 )
,(!o,,+/rlJf'o"J ,/YIà/" ';'17"" J. ..e, eA-J 01~nJ FJ!at"e /& th~1
,,~M~ /"'J '-J.~f)~""ItJ a9/JJ -t ;' ;" jJur .....u".f. ~tc,.j/()n parql
I~ a \ J ~)Cf' j ~J ,A"n el, AI'( pel'" rf:IpptU" j. au II; ~kU
7J( J-~ / ~. a c.,-cI (ftJI. u«) ./lifJ re~n le. ,."uN l' a/JJ, ~ rk
I~//II- m,;,u (Abc. 01 (fj."/c) cb~Up~1 l'a". /0 -J-teJ/()"
31
r'pI'.f7~rQi/ .0'-' ~j. rJ,1RrhVn.u- }a -IU'h~n ag/JJdn j..
ÀU" /« lau a" ac.. 1YI~'1> ~ -t?,eN~h~M rit Ja fta
h,NI/ "i ) ~n rI./cpmpo~ ceI/( ICI>.h4" en.."vM c.olY'p oJt:ln-lf
nortn"h Oh d ~IU. cptn,D6un.ft tiR ,û~l!.fhLtl'). 'l" 1: -' ,4, V4!P"
rb tecJ t.t"'I"Dd8n k ~ ~n'V( ~a/l /.u ..e~dSl, #:, "4
or. ': cr,. e..D') 2J -+ "j /n'" 20{
Gné: -4 (~-~~ ),..,'" 20l
d(JM Ùd'fP~11u ri u} .) h"9lt ~~ /tfU't J. !1gnt"4 il hJ
aNte )~}l.tl du 'K (fj}. .AA-4),,' /'d nc9 " oIM)- cPn4->'''''
'./pf;J'~1 .4 ~'/ ~) ;n,fu"" rbJM U PM h,Pral..N.
Co,.,,.,' rbtrOfl 1- -ID'" i /,I,J. /eu".lit fJ ana /"9""u e~ a \ a e ri.
.4ur loul. Il;,,aùJe.u' rA j 'a jDhF.f (f,;,-.4/-')) lu 1"" 1
&7'0" ~r"'Q~J ~"" d.D"NnJ. --& ht.Pnvn). /~ G-~j.It:!1n). t:#c!l'Jh~ 1
..duy la ,ue,t,on &f e, cP Ir; l'/a~-t 1 rII,,1- )eI v"Lt~r p~
.A-I/U'/, . rb jp~ e,e.. ,. rte a ( 81'''th/z.
n, -= 1 'JI, -$"dJ (t9- 32-<1)_h/l.
~rJ ;,jNJ .lP"J- e-/&'/1'7J rh r~n a ( C,f""'.R k wleu"
pDn';"1/tW r6 eu h?J)httl,..!:J b /.,,, J. .luP 'CH" -I~ ~ ~tS r: fÛ4
lHcJ-eurJ Udn,J 4 rbjuc..J/!J~.o",,·h~ ~ 1'1. # t) ",#J' /~n
en't/,Io'R la ~Ist ~ Ir~1J CÛJ1,6 riA I(J mtl.fn rt"o/Ie (fj.JI_tA).
32
'par ~'/( CÛJ ~~Ihuu ~ 4J IQ cu c6. /!t'lt.nv"tMJ/,,,·). p10ntnl- rkn;,.J. /q l'A ~./cn rb)Q l' 1t:1~ V ru
peqr/f";' -IOt.Arnu- ~' aP-Io,,~ du (l'X~ 1U"71'4J 11"- n.l..ttn
J~,..; ntJ"""Q~ al /0 .JiV1~c.c .e.:laJl,f.M.A" ...",01~II.c F-tle'.>. cb~"".,(J}/oM . ClÎ4 :?'~tJ parallttu a,.c..)c m U GUfx
t (fj" A~'" tI) ;'~!.MJbJ dC
) 4 ~j;'~" ~ 3. d<, ~n nv~;'", .
A AJtp/!-,°h1Anr paA';" .o
. . ~n' 7. s fi.., t/J- !t::- 3 fI:::nt
f /rt .tA- ft ,prit 4 C?WJ~J ~ le; ,hIr.f6c.c ela4h"
r: dt:JM ~. lJf!(/ftJ .lh.J U- ts .é,.. t!:J rn I:J.;" Q ~ f ~ e >r.pMoh~nJ c:::W'( c je( ~/ ri" Ha t1 ~
l/I- en /l!~or hïn) .. daM' 32 -0) ,!) n . a "
l'tin = ]) (f.. -dtt:-) ~ -1) (~, + V~) (.ri' 33.d)
P?ur !) 6;""/r,,.,uN .,t>c/,rfJJ;;o" J.v rn'Mvn) ~ torho" n'If, aD"
h'cU~t)rtJ )0 fO:'h·D.n ~:Un /dPo/lt.:f ,nt'nU' alxcl rJp"t ~ .
(s) 1, J ·a 6 M-- .t:)' d . AJ.;,.,J.- ptMelllx ~~ a.<I)c d/A;e~~nJ hl ~t-
t J -l-1- '1,;U1"',M. -/NLII/'ot.a c. I~ d!·.tf~ 1) CI d ~ pla n nv'"''cr"
•f'
(h) .•
•(a)
h,2J!.: cI~"".o}/onJ dt: /!:w/~l. ÂUlJOft ~ nU t.
33
P(J"J~{?é la f6~on rb la p1a~ (Ij A2· 4)/ -6 fJ.9'I>I-J
a, b; e, "d ~; cLt~bUl"). e» P' /,'/~ tf"~" I-/"J;, ~;~fll
~ ~ V 4 C#m'p~eU1n-1ed du r6;.,la(l!IV;I)./ "",..../p),,,;, 0/ te.
Œtp!Q unvnl- ~./ DJ',,) a ~â (4"). al ri..4~ )~ rltÀJ el/~I/" rkJ
11 el'J. fi'"~)~ .vi u/iu' rJ., b c/6M /0 rt~ e.h'.o" rk t-
U t V "1" t) tilt i ,cali ~'p rit ~J dt~/Q(JhU"t.J~ ~/ Â-(
,Pr: () dud· -A"I N q"~ r mt:1 I-/Q /) ,Dai'» f':)Il 1.~ n .'
~h t-:. ~ ~.. + d\t. ~ ~f'\
1. -Ie"n'I'''' "'C-I~·/lJnvn). ~"'fJd~,..i~~/~ ..I-(n:~
7" 1;- -- a (à.u -t"~ )4'!- ~"
)'(7 r: )t:ë I?,M. ..A2- b 9"'" fiel';1' tJ.tnif }a ,# C}/ pn ~ /a
Aun~ u .e:.taA/-'~ ~ ....un 1'/t:Jn V'IflJ./~Q/ ~~(;n 1- 'pM I~)(,
rIu~, P" ..;t:?Îf 9'"( ) '0"., il . rit ro fa !/a" fI~" 2'1"ha.-e"i-
P'1 J'I1,,/'''Q IRhlLI') Jo ,eu"',Pl''' eiI(:.t., leuJtt'· ~ a.v p1(Jr)'?J1!:1 ~I
Jl)a 6 al - ~ •. p~ ",.,uJf 1~~ ;. ~'m.,,,) ,4?'iul' Q (. !Qdt; fa rr C( 3 dv ,0/#" nv l6à" ,n, ~'J. ..-û n dJplQ Vm4n).. a'~A4
)tA d/oVÛ','on ~ 1 ~~ / a' "
.p": -3~."lA" fi 41~,.,f'Lf Mt It'f dl n (J 1b~ ~"~~J. au fi,p70 ~""" ~ r::U.
~"" .e6ht.t,,;, de; fI4 la Œ"AJ eJ/~'} .. t 1 ~d / <:il { .'
"_ V ~ - "${::dJ ~ Vc::;I~" oP" tb du/J.
trn t--; d..u ... d li' -= _ 2~ à~~ ()o-n e;1 ~n~~
~~. ~3-1,)..... " .:
. )
2.. ~. 2. CQ~ ~eN.,~1 tIA /!e lC/ O ro t/tl.J ~f::!!..!
.1 'e tu lb' .P"'~U fÛn..Jt. c!pnurllA b. ~ t:Â Iq l'&lfI# r» tiW"l
fJ&. .. ~ p1(J~ /U-oI-d,,?/~J ~K ~.Dj)~ tiI4".,.~~ ~I
IlnJ. . du· 'nv~nh 1'/e./t114nI-J .MNprWUMtl.1'J1- repa,. hJ ,. ,.#~
P()J~ ~ (JuA c.o.s 9~nJrQ/, .:J" NfJ/,JJllra .P" e!4/'ef"'I"N"~ ~/
CJ)n~ vJPrLt rf'''''' ~/fUn~/~~" la ~Q~~;" ~M.~
.ft" fJHnor'l t- rk ".a le':" ~ eJcf' ~pn t/.,"w /OJ/.f1 '" PI' ,Pl"J tJ,:N f.M-l
.A:7W'" ~~ .e-61'N"~"~ 9P'/ePn~ .A'~{,' ~M )ç;o pk~,1 4cpn r/./I-,'o IIÂ plU. ~ rL". k r ~ t ~ J- .."." cJJa':P.I;'J :./~.Jw ~.( ~ htPiNtI
riA 1d~"Of'\ e"f rh. . tor.<h~~" do,d -& V(J/.Û,rJ AP"J. 6n",~ pa!' a.,.Il.PO J,.'O".J '. (32:' ~ ) rvJ- (32- ~ ~ ,4:Jl'b1;' !Up4ft J/~' b /0':1 dA la .ptAt'
fJ~t rb. J~lt MUt p.; ~,.., p/t-fn ciro .bd t6lt C},.OIJ,I ln U t 1 Jljo/u
,,' ~ vj" V or: a-vra .(Ij. 13! -6.1 .e)tpAU~~1\4 A-w'llfS,,)U .'
tI.. •. . . '.
35
f ;
:3vfpOJD",) rnt:U',..-j,,,,o..nJ. r->: c,1,(Jf'!Jf.: Y'fl..FJt:A,f,~ (9,g./JH"j.
pe.~~"rb'eù 1c:u~MI"). ew p1~'" lt\I ~(," d.t la FJ/q~l;" J~" J.
" ,.nJ. "",,'n-j,"ch·./I' F~ et4M L, fa.j t1"N~(J/ pep f ~v
...6iu:U're rN"J. e,,,,/p,, c,;,,,,,, ri... l'7 UoY J' .e» ciJ c,VI'~f1 ~..kt'" ..e Ct
Tn.,t"J, r1J le::; 1"1q,~( ~ rfLu" pa/AkJ Je F'kM pa""14 lt.. 4Ull'
pilnJ ')1J e}!/J'[ fj ..AJ c/ At. ) " on rb '6.u'J. fi,. piAA f la /1-(JJ.'
~ r-> réU~n ~ 1::' eI-/~", d.e 9 ~ ..,,10/ p p"~ œc.,....t:A .4l.I ,..
~ r U4 )a ftrt' !.t4 ~ eu- ~ frV n I-~ IN' " tHN /QINn J. ~ Ir\!) Nit
r 1&~/~n Û rf, -Iofll·,'ol'\ ~ tnt3VJ 4(.f H--' ~ ~Ja taJ k~n e.k"
~".I(Jn;'tf il rlP" t JIU ,)tS fw,~, p44It ...,un//!' rA ID "!JPe.v ... ~
rbfiuê4 ~"'.'
DI' pnJ. Y1A~"?" âJ IJa/Uo f/tUl4 riA 'e1l,J ~J ~J ~ ."e,,,ePrk rbifDpe.t4 J'nIÛU")fd-,'hI Q ~ clM J 1;t" d N,PpD;U· ~~ kt
#rl:J ktJ"ue~/J ~ !I-D n I:J ~ 1Y e-r ~ rJ)c ,0 04H11 J.
pQ/l ~J unlre.,) rb c!l~aV')h' rt~1 -r c.u CÛ4 ..if, ÎNn fJ .
~. &lr) f)M vi- ':J pr'lf 4 #~p IJ ../'p~ /Q ~("l ,#tIM
(.~ f/; ) '" f.A~pf rLa I GI?~ .AS" ~ r",,),·./.,j ~o~~pondtNI"J
lb)
~ -_.-
'.
. '~!f
'3
ç: '
37
/tf/IlIA. la~o dro,ie 1 cbJJ-Q /) /-f dR. d:n qJi. )(Jr u #av c~
,)J.f r:~ f'I J. :
~;}1 + 'd-tf1ll'\ fi". flw -+ d f)~ r"n - n~!, T "dfh,g ri"~ 1 ~) t7' d?n.
..,ï/-e", ~t:1 fi, MiMA~~". lu ,-t'U'J p(J'Ç/~'61 ~ ,d~1? "'cS /-V' kvP~J4"). ~ )ç; (~~ Cf $l'}, /:JD(;;h~ rblll'J Je; tk'
lu cf/o" :J ) J '.tr '1/~ r4 / '~ ~ Il). pVtll't.t) ri ,,~)..,
. lj:=o ='> ?:,ro". jI <;/11 <ljl,n. + 90')<,: o
cl ~'" + d ~M -+ a =0~ _~ -1
ln"...."1"'" ;n ".. ="> -;'':tJ cI"::r -~na ~ <ho +,.li.;. = D
~fVI c.eJk .e~(lh~1t 1 .DI) Q ~j'" -fA WVJINI'IJ. rit la J~ 9el- «4' di: ~ t /q cJaJLI'tIl-/on rb ~ ~'n1'.",,;itvll)J p.t j;k li 9/1du.
~I'Qù'~} / t:h~ •
d,~ tf2p/tt~")J/(J~fù ~ ~nV~ -(- dn~ - ~)I e &> .,
."" t7 -. ~ ~
~ -f~;J.. ,."tlN J.t k.r.'/' e;t:U'~~'" r1tA p/47~ .P~ fiey,po"#
tflpi( aufre-t rb'htI"'d?D"~", en peu/- ~.eiJ6.;a /jf..w- ~ ~ bI-
t ÂIA/) ~ i ~Wt~J tU la /Jlta~ 1 ;ho In '" 1..P-' ,,~) ~JI,}
I)~J g""J.,ftJ.~ ll.'/4.p,M""'·1)1'l du ~~~h'oll4 (3~. a ); el) "" h,.
rru n~:, - ng~ 1 ~,n r6~(k",.) ~ 1I(J Iwn rit ~ e; ~ .e»
/: d>~" et. lA rb/..e Ifl"'" 1AJ •
38
'r!vrfJ"l. ) '~,,(J(yJ.f J ..""'·,r;ul- ..en~A~QI prtlh?"M-( ~ ,.,Ift"Qur
1l.t#J , dlo),'.A-lrkJ ,(Pl?lr(u'n1u AWt .~:~;'~J1eu,. dt I~ pla
~ fJa/I lu ~~)~. "'-;;;:"If/I l'LU. t3,P/';;P.n:~J,( h1pl11.In)J œ/&'11;In.Pl1Uflh rb -/,Ju-,'o" e!:'.'o(#.Pf'h Ir~n~~n.J.J,,l J'JttJV> ...,;(,ANY" rit
)c;lI t.!'CI,Pt)'~;')Q /'~ , 13. '
D,,'pwra/ofA '~/wl..t.r I.ea (/QltNl'~ IntlX//nQ!e4 "-Je;"h-zu'n Ad cf, '!tnt;D".), rLt /!)M'cl'! ..e4- ~. e,I~1Aht.lII). .'
.r#J ~u 1 .,t_Â?~~) ,.1 dM ~ et )/'oI?J (28) el- (34 -a) J,,.A,f:
!!. ~ } 2 (f... ~vp~)7 / ri) (& ~ VFtt)7 = &Th.. L../'-v '1. ,'J/ L . tI.J 7)j.
':', ,, . ,
A-1' s- ~t1) Q !.PM
".
39
,..\
:,' j
:',
..c", •
, ',!
2. t. PLAGUE"~ jU8/~~ANr L'AcTION COn81NéE I>E LA,
FLExIf)/J{ E-ï J)F,S F oRcE~ i)AN~ ..3 ON PLAN
~J'f' '(A' Pr8~"); NJWJ aN~"'.J ÀVI'P oH~ ~ /4 ,,-1tJ
e;u'" .p cA,'J. .s oVJ JQC 1-;10'1 ,d~n..t c../,ta ":9 e J(I le~o It e f 'f~.(
)e.J 16 ~~J ~'oriw'/~~ e'j..(U',;") .,' /a,"~J Fe )q /&X,/t,n
,À't.A 6-; J. p Q r I.t P /Qn "":J"" rit. JQ P'A~ PP" l/d,I ',i ;:h né:'
g-&j(1~ ; ~. ri., ~J) ,."Ii Il'l4/JIt. ~J /~H'a4 ~/JJQ").
lihf'ld lt j1J!on hw'yen cû Ja p1~ f..,tA,f, .e.#.t, rb t,/errrv'Nn)
,..p'lI thl'''' ma f./lJ" ~. Pion./ -fovk /o/J,I 0'" Âl-I~p'pHrq
fP '(1/&.1 .e"~" rJ.r(U'~ œJ l,n.s/()nJ ~'A,pp) /a.,./4t ,lJe:t.h
./1 QfJl'DÂf aA-')C#",rt-ô"J w')'F ./ ~h~~ J:>n ~) ~.ejp'"
l'~} ~ 'e/fpJ ,cI'O ri,.,fi~",J A.tr )q /&XI~n J.t /q /{1tJf~
e,-j. ~ (IIrtA 1Ir-e r- 4 kl1h~" -/.01-(1 lu A ~'ht"N";' 4V-ec.
.,PnA.. tfApprtllx/,.""fliJ" ÀU#jqn-A -e o 4v1f"U'",P',JqAJ. :"lu .Ju,b~\) ..
~t4 c=e( la ~~rma ~~f) tk fI10 f" ~J'" ,/ ~f cdltl ;~tItN~j·.
fW' )q daJt6" 1. ,t,~ f.f •
g; JlX~ "e;,J,p/IIJ ~ . e1'fit&·'t • 9:1 rkiJ r lJ eu JDIAI" 4.1
P"/t:iF ,I1{~'nQn);,1 ~ !'p/lCf,d etc::~ ~"(la" ~ ca./~ 1»'"
lu /'1a~IJ fP't ~~/~" , ~a/)) eh' VeJ I("éd c6 r r:,A"n r1Jp,'" rIttJ nk"l Q,,:/ 0"- rra ~'Jalt,', a.u~' ~ m»~~
ri 4'&~n;/,Îù"./~CI~ c.1:;~n ~ CQÂ C'b -/,yn .Mpt:W~)
d -4 ~l'eÂpA#r ~ Je; ÂUli~.
40
, .
CHAPITRE m
~ .
FORMULATION DE), MDDELES
. PAR ELEMENT5 FINl')
. ... " ."
. . ....
.. ~
....
~ .'
•\
3.A C140,)( a)V CAlAI1P oE 'IJEPI.A CGI7GNï ET /JE 1.. 'EI.EnFNr
/ ~'J;';~, rI;U,., t.PN'J (U-J. .ltnl,e,~)- tlt/,"v' ~ /tl
c!.pnn(Ji~6f) e.t ri;Un NJI'Y' In-c ({,? Iv' ~ (D"'P p"'" -A4 Ju ~/IOIJ
tU.MA 6j!JIt:Ju~n~J~ ~\ I~;, l.th'eu".pu u~~ oI.!N~ ~ed\ t J
~Ju~ ~ l' on -h~r'( al~ 7M... pah f j..b. ~h'p ~';'
'retn"lir )a." dJJC.16U '.tt:.I!1(Jn e..t ~ clrIre rit7uJt:{/4 (~4rk'J./P"
cÎR ~"'fJPJ"lnh'P/ Ot4 cpn/-,'/'UV'/t /~n-/QtN. 0& ~ ma A~) .e,J.
dt ,oÙ hIa/Ai ,tZu.xc.on~'I;~nJ ~N:I(J,
, On,' a vu "9~ '~ ,~".,<' A R",PA/".tU'J. ..en /~"'c.
l,an 'dp" ~rftV'n ,nom6re cl IIt:?/.eUYJ dûc.re.'It.J.I Lu ~/.::l
UIt1l,,).J c~'j,'J, ..(!A1', CA1lj.a.I~J ~t4 A-,'i:M.e'.4' ,h-tr /t:I/~f')h~'
t'{ cA /~/~;"Rn);, J1~x&eno je;; ~tuJ cb#'e,'6,. ~t remp~'
-&M rie /q ~~ 'lUI~D"" J. d~n, ~ ~'tt rhplGumenJ.
pp'" v~ Lt/d.lï- ri ,~~,.e,. la. ePn J/;uu-;J,' fÛ4 rLr.j:11a
œ su»h '-& :.&":J'" et. 10U4 tea fU>/I? Ji .,~·;iu~ ~ ,AI ~ lM/N'n .-h'e;t4/u~n 9" 'a' 'J'laj. f/,. '~ I.:'/rie/);,?'c.Qf/~" rIu rhjJ~ ccr
rru.nYJ ftlt7 dao» ,aux" AW!,sn.œv'~ ~/t)mH"~· ~ .é.&iIu"tJi.' ..
~/..~I- // .,f, h :/' '~ 3' '/A~",' t. l ,c.u' ""'U. v... et\.( 1", (la, CA ,"fC 1
ot. e,~ fYI/> ~ o/Ia CJ /YIII? J. 'du/l. Qif! cl :zu flot /Ja/l f. ,,46i
J./J!euN a.vX"U)nrl./J.,'o'nJ;4Vf>,P!enun r e:u..Al4 ~ ,PI?J. 4 tJv'
. ./..tu..,.4 M- .2.;' ~1 Ju#.)~ tjA-t_ ,U4 rIeu·x. rJu')e4J ./.J!h~")
Mmp.{",:/OU y ~ )0. ~f.M .~'on (9f)cH/)JJ< ~ la ÂP!NJ~')
JZ.,)(a cJ.t , ,~
Fn CP~ clv ~'D~ / Jo ,Sa/v 1-,'0,., ~,o;:>r()'cN€. 7DWlI&/(.
pa'" /G:< 1'rtP'J-/'or:L, du .étt'rnJJ ;?iv~ kn cl L.4U4 I~ ~ fN '
}/9n ~ka cJ.e' .f'" Q n cl on !Az.,ici,',,)) 'Jo( -1O~~UA4 ~ rit"~,, l:
l 4 J-Ir~ c..-fA Ju. ~.t-,..c.. ~ i t . ,4'7" lu . Cf-'n rb'!-/ruJ4 d-f.,vÎltSf' Ju ~n J.,
4'
)
a) lof. c.,.hdhtp u4 COnJ./AM dtfM lA ~h>NAt (diAtil(l~)
6) k ~(/Imp ûlù/a/J l.t4 C!.t)n clrJ./cM ~ >c '&'/1w'-
J<,J ( cpnJ./IIMA".j,' -4 -&~ k 1''''t:Jn.f/~ ck ~''''''''<J
c..) lA. c,~h',D c;nJ./eh} 4 lh.P~ ./U~.~
cl) 6. c-~'"P CD"l'''e,,} ~ /1'V)du /(P~M4 ev
IW>t ~ da.(or Nta).,'o;" U'nA ~t:ln.,le
1 1
POlA ~ !bJ .i&MIl? 6 ~'IU .,J.t;I/J/on) ~ ./l,J4Q cJ. f 1'11I" ).
él" ,1,) t!/- cit*,~ .",-1 Il)t.I·J If I..t ciL/lei, c:1N, é~ P q I-,,~- -/1:4 t '>')
~' A:JI U). 44/lVO"'J.", a41'f,f"~ Jc:f ~n~p""
El? :JR~ 'r<:1' i -' ~ /0,., cJ./~1 C ;&,h'~t::>"''' cb éAI'
M -&' c ~.m,P er» 1~ )./D,., .A&>" ~ cf.t.,~ f:)tyn$hU:J U It;
~rhU.
f()\I!1)= d,... J.,~ +J'!J "?oI4 lt ;' JSll:! '" rJ,~ 2.-+oI~~J
... c{j~:t -+ - _. + ~,...,).r~~~Jli:.)I n'
cU bh t:- 1,.,ut Jo. 'pMMI~ UJ"",'j.,~~ ~ ~~~..,t'J fi,e"'pb,;
Pa!' etA' //tlby ,1 ,,'/ ./ewl- ~'/t" i< c.k;,',. du PD~dhV4 .Â'n
f!.P"?pIt-JJ 1..-':( "',.~ aJ'J-t:tI;"J ..j-f))/JUA (~d.t.J rJ.,.·rt"/4Qme,, t) t4
rb~ 1 .,,'7 ,,'(2(," I1'nQnr'.~j../ e:::uÏWt~ -4 /~u')eJ>fJ'W rJo.,;"""J-
at/fD,'yo foU4 /,u/.tJ,f'ILl,J rh.. cUc?t" .../;,/wèu,.. .e--I- ila 1 at/~/>~
....ft~ .,t'fg~ fk cUMwéd ~c. ~~/)~ .A'"hl1>~f)
tu,n l- dA Vf4 -&4..-Ah ';'f;'~ UJ ,
En CR r: (!P"eth"" .1 ~'d.t..~ e, al/on ./}/r.,,(,loeJ-P,el f:JP'n~
1I4 fJ1a.?,u.(4/ ~'/ u1- 4'..n'r4h). F }~n rbÎ). .,uJ///;.f'" ~
d-t'ttvn)J ..tt4~ eh~ ~'>c ~ du -q,i1M cpnl//Wed,l' I~"
~nJ. /rla"j'V/tVM ~1Y'j(.( -& In(W t6 ~~' ~vr..-M'U
J/-t;Q c)-..ul'C 'JP~/(JJ"1~ j,.,'tJ'hlJnl,'on 111/4./ ""euJ )Q ~/
f'cA,I'f/I "'ey'ev,. /tI:s.,'rA dcul4 1~"'';'f'p''f')fI)/~'' l'h.!lJ'1~ ~
l'''CIÀ du (/~fhAf)IJ; cid60AtI 4 rk;'/tfI~hU"b ~ ~
A&'"J. ;"'ppD~J tj"e ~ ~é la CAnv" j.J /U~!J ~o/''').J (1)1'
"reJppn ~ fi I:t, _cU. J4 J J./W c,I-~ l''t j .e,., (tu'A 1 l.t e.hf#f7'l~ ".~ak& ~ tpnlrc:u" 4 c1PrvJ /: 'hht,,,) ~/f tkf .Ae"'ID /" u'pt/'
~ e.Jf~tA Jl~lJQltn)t4 t:W}c ~rh; etJJ ei'aI'p~'
"/l.n/..vJ 1\1 C9rrtJpo" rk"J. .lUI /Q/,J. a {)Ui,n c2.cA n,~c:w ~
r'0,',..h cp""~p"d(ln4 t6 /4 AJ,...,;Û~ ,A..e.e.l& U- ,4Pnl
rIt,,, c 1 (;)-/ve.-J,
N O&lJ Ivl'pOJ.f"'~"J av n/.tf/~ rit /'U) l"t ..eLA huit). ~
J~;oQitJeur J, lA} U"J}q,,";' tVf ~ -û'n 1VJ Iflh.t c:J ~X.f
.4t!4/ vf le'! ~ 1 ~)\.( JI (J)/"u'dA 4cN., ..& CSJ4'~.J
.4 tv.eurh th ~~ i.", J, )~I{It\I/))( "~·"Ij· .e«),
3,2 FLEnEIVT TI<I/lN(JUl.All<é EN éTAT 1'1.. AN /JE
CON1RAl/IITé
3. 2. -1 ..f.lu~;~ _ ri:! .!q#"y!!,~ ~ _6.k.k !!l'IU~~
En ~tJ'J. p'1t:l n dt cgn frœlnlt" ......G JtI"'JO rit rIA'
, lac.lrntnj. .pJ CPr'J I,.lu,' p~ k rIL~ /0 t.I~" J.J p/t:1n"M
.f/J,- v : Jv1-= [.P,V71:.
P~lÙ' 4, ./1 7")j reeo rh rk) ,'6~ft } Ir,à ":?" 1tJu:-V1 1:'''' ~r et
it1~-=[»1 v, ...ul \'1. ..,(.Al vJJi:
N'p~1U I.ü r"c.honA rJ, "'pla (lhVP) Aut'..lt:ïP~~-&NI:u~
(bn ~M--Y "Jp = 01, -+ clz ~ ~~
111 -= dl. ... ds")t 01, ~~&M) _IDf'/rI.! /hQh/e"e/("~ "',.,~}
l '1WA..c
~I - [G] 10lf (3' -~)-•,
[G] ~ [~"'X .~ 0 0 ;Jltû'tLo ,0 ..-1 )t
• ~.
~1d f .-: {d, cl oI~" 0/ 4 ri '01',JéL' S
.,
3.2. 2. l~/rif-'(&i!"~ _~ ...:cl1j1'~'
. a ) i-u~ UJ. cp"),'"",, rf..t;~ b ~~'&v.' e'e4'I-
.P~ 10n cl,. 0 ri /lP!t4~
,/') ~ rbp/a UII'U"J.J ~ ~f v A;,,;' ~ilI~~
il -ô .,(pnj J" c.,Rq~. eo,L, /~ ~n c..' VJnJ."r'WJ;, ~ r:6"IQ "hItll~
dt da ~n '~91'/'Ih ~ ~on)/e-u.j. ch /i'hlrun).· ~,,} rÛ'IlI',
mliuJ pa f' la J.ev~ f!-!:)nntMjJe1n cA. .~ """'Jc filp IQ~m~/)J.J
4~~x aMx ~.ô,;~ /.1PhtnuJ, du @1)?t:Un..c;' en~"'/ la (pt)
j..,'fU,u'j,' r/.(A d.t~/QuhUJ'lh ~j. auu"'-f~ pail ~'etn),~'~ ),'on
rit4 rbf la cJ 'hl n )J rn»d.au )C i,'.
e) .r.,. c!OM tt ~h1,b / o r» pOJ-l Â,/c.~'~1r'uu'I/- ,- _ J,'=' P ~u/~./ a!P,M...,(,I:' c..J')MJ.4nlt~ V-=o: Ira~
}(J J/Or) ~q~t,' (lIr ~
_ d,' "=- P ~I 01" i CI/O;lf,lj v:' CfJ~I-t6nA.! ...p =l' J' k tu td
k J./"n ~tf/tJ'6 Q"c1
tlff ":~ -:. o/'l.
~'I·fAI rh /rU) 6
_ 0/,''':. 0 ~/ riS ::: - 0/3 = w;' a/4M ..A/ =_~ ,e,1-
J ) ,. ,V ': W~ .. )It;1J. Q ' ,·on Q,vlo~r ~ D./UF'"Iv ..-(pCO/.
eu·~' -6.3 'h.P ltÎ.d /U"" r1u PD~'Hu th ul- ~~hl- ti.q 1&4
A-"/ f> !(Jn p>" j, (gn).Il.IWJ cf.p,.q -& et(Jht~ rA itje>/tl unv")J
cl) ~ rûle> l'", CI JÙ)'W AP ft;' .jrJll kA . (~uVl J.tI" k .'
19 ~ ~ :- cl, Ir~: ~ ..~ "- oJ~ .. "IJ / -G
.I(ptr\P#"" 81) cio n Co .AUPf c..k :
~i1
11
1
..,.....-.- --- -- - -------.?«-u.
~f1
. 1ch
,
JI - - - - - - - '>~
(6J L1Lc..( r"~ ,r1tJn cJt#1VJ ~ plo/) 'a'fJ' ~ col
"F-iB~: é/~;,dleJft rU ~,.kaJn.,l,./ rLt/Jla '"nPnh mo ~)C
G.J é.~~~J. 'ul &"c.'~ tf!P~ rbp/aUhH'h; IUtr d r!tshj'/tV'
() ~ ~lA}~J' &., .e KiP/'~ 6. CJ)n~eP''' CI ~ la IJglul,~n ~~oo~
.j2.3, 1701",.u _fle.Jù!J~~'/.l..',
~6 ( -:: [el/tif(~?' IZ) ~. •.4 0 0 0 0 0
[c] r :'0 ~ e 0 ...... 0 0
=-"-.A 0 !Jj2. 0 0 e
<.&" A Z-&4)0 0 0 .4 0 MJ'~
. .", ~Ji ~iJ o '0 0."#J\o 0 ~
.,.,~J~
••
?1tJ~' eJ YJ,' .ek-a'()}' &,-J (Dpl' 6"1lI (" .dM rwe» rI~ Jt';Le] PA- Jo m;1,/u rit-/ra·""'-Tprntah'(),. <k cb/,/Qu'N"~.;
Co lev/" D,., a,'
• o ·0 0 C!) 0 (!)
0 -1 C!> O, O, Vt ,1' ;
t8aeJ [E] LBiJ =3- ,,0 0 .A-v 0; .A-~ 0Z --r-.
.,...A_v'!. 0 0 .o e ~ 0
0 O'4-~ 0 .A.-~ 0Z. 7-
e V e o 0 .A
in: l~;!' "
. ,;
or: ·.~lnlf9"" a/D~pur D'H'!ir !k~/J!ifl-l~~..1J 4"'''''''"'''' glf"i'l tI~ '!Y" ).lu al-, rb"N' .lm, ~p.p.e.n tI/u. i . 0 n Q "
.....----- '
0" fl4p/U"tIf .l(" 7H·)
~/,*1 du .,.,",..p.!J t'rA
.~ .
3. 2.4 _c}~~!1~ _~"tI!!. /l~.j,!
~" (!..II".H' cû~ CD'!'h'r e~a1'/JIl,J:
. _ k c-RaJ'Ip5 ~ w'",t'~fJ 1,-e/:. [/V«, R,~1 t: LI ~"J. ~
u>~p(}.dQ,../u et~ .p.D/cI~ vo lvfN~c 9'"" tAS/'1""). ,nu'lbll J f1 -u-!I. _ 'k c;.,fa,hlM rIA .ÀU'fa cA Ilî1-: ( 6~1 ivJ 1:: t.c ~"J- ciJ
c..-/«JIjl;\ ftepahJ./~ ([i"!/~]) '/'"". a,,'u"J. .iwr -4 ~,4-.i rb 1~1"
IN,./- j}w"JelnJ..f!? eJJI./ ~r~4 h'o" (2 o } . r/;"M
...6' œ., J" Id G!,q,'f" Itllf~t;/.f ~J.."..~ l''~~ ~"'pli)cc/ c.tt~~·1
(aPf IfNM "bN .,1." ~,.,~J;'/)" ÎU' /0 &'''!J..P-IU~ ck q,.),'e~
9-' (,' on ~l'fJ>i't t;u rD'" c:a """'I.lcRJ,."p ...(!,-N.'(j&/~ 6« fvl.. '!,tA.(
'{
'..... ,
•
~~-----~~
. .'", :',
-:c.,", , el'
. .",
.A i.Jz. 1 J~. - - 1,'- 1 -,'
2.' 1 ; l'J,1- ~ -
2> "1 J1'. h' ',
ma,,} p"on
(J)'If ~Çi~,.h
~ 7; '0--,+' l>;)C
1;' DI" ,--ho/ir; ~.' !.tA ~/~j I~A r ~r n,uM.l~() .J:n';' u~· ~
~~ 'djP~OI-l;' ~/J!n' .~ ~-A "A .Jt.o &~ -4 ~t14 ~ ~,~~ ~ (,~
2. M.fAl. e: ~r4 -,,',û/~ e; ,.fA fD#'3 ~ 4 hJJeur4 fI.·.u-rJ~~'
0'" fûrl'''~ ~," k ~~ ck hCf!p lA; rb" t- /.;-,. (/''u .vI- -8~ ~J _7<r'')~/~ NX.tA rih; C!.J:)f7 ,,·6.,oM ~et.n ~K~m,,'4 ..& ~ /-4' 2 ~j I~).:
. .'pJ.tnoM .la ~~Jt/~ON~~ en C tN'!J'ev du CD1, 1
fj>H /;~./,.u-. 6)1}/. 0 ~ lle/tl,wd a"ul' ,,&eu di .lix/~A\I4o'("t (.p.,t,;.
~ /014 ~ ()f~ -= ~J~, 1- ~~. .: flQ~' fU»-" (A.) ./;= j, .J ~; -:. /;0, . 2.. ~
lA ': ~'ff:~ T lé ~" ".' 1., a~Ç }('::- X+~t, ~rJI:: Y~JIc.
P?': L la !.Pn~~.-: :l'~ )a ~/4,., pn .J',.,/-fjH...,,,, l =~l- ~',
~()f~'f. ,dM e.tJ./.I' ··w),/A't· y -' p >< ~'>. p''''.; )!,j - 'V',,. i r' &i- x~.. "
..R,,1LP."p/t:.u(t~ ~(uJ",~J.tIlnlPJ:',~ fJ()/l -~ ~ ~~I b" L4U-c..~
V'lfw.M b" Qj,:"~6;)' ",'~"~/ftJAat~""",~"tcfJJ"lUraJ';-4. .' , ',',', " ., .· '. va u,..,.\ 0, -: tl/~-':ru'<. ftVIpi "'lù,/R'A1AoJo"~ Û"/''''
,,,~= ' ài~' 6~ ~ 'I·~~.h·/;~: 4!Y'/U4~o~ dc.-\
'P" J. '.., ,", ~'. .." i
"E~JJ .' eiaJ,1J!. b~ r~ /~ '~thJ}t lA ul/ 2 ,,/, '/,ln,,.;.
" .'
y~) q r;: . i,• Ii '
6,-= (b-./~/,_ brr,i)1~/ "(J, = '(~'L+ 6"iJt/~) /2. J"
rki,;NÂ ~ "l" r
, ". \. ; l'·
~ cNJ bvt1 tI.u .;~'n. J"g r-~ û/' ..b''li~'~ ',ù" J. tIPI' IVU .e" a,.ru« e
j(/Jc.~~~r~~ f6.7~:,.l611tJ ,J~f:, 0" #t/w.!,k ~/al6 ~~
vu1h,.'J a' ./tJNt'p ':~ ?Jtu,j' d4M lG} fJ~ ~ .f.»O~rlJ-,qM
.Rf", .ID" er/o,",tb. X e,J. '1,1y"J :y l'lM iJ,ttlftc./'t-(M.<Jn JZn /0,., e,
',-I-,o~ J.J. X,I' :c.a/o pM~ cA.'tfcaktf.e". ,,k _';"A)~q'" ,ÀlPi/~".J.
)Je ,tIN fJ,.,., fi ~ tD1' Jt: rix. /. ~ f!t ~ af'A-'d ./>w4 ~ . Ca leu /s
je; ~~ .IwJi:,,·.te ..
. i
. '~.
r
j
!
'-f.tt rn1trvumpA, rd
\ :
co 1CAl 1 fÂ( -I~' J
·Ira/J cd,~ .
49
3.3 ELEI1E/Yr TIJIAIY(JviAIIlE EN ,c'I./:.)(J()/V
~3',3. A·' ~h P /JI,"- «. kA'",.! 1/0"_ ~ !,I;la~~/Jt. ... . .
IJ ;;p"~Jl' l..e4 ./Utld f/()n~ ~/J.a /Il/t/J cIct"J 70 tHtl//)". . .
2. 3)O~ fJeP/- riI"'~ tlP t · ...
_ 'la I/,(ej,~ ur rYjf"iv:J. .e,..f/eLl~,,1- J~'j.tlJ. rh )a
p1a f-fAfi ~ \ ~:"." -1~" 1, 'evr .~ cil> /YI Q.,I ',tu.
,_ 74l(!"!)f?rJ,,'f/()n~ ~': eonl-,'I1/-U'I.' erdr« .Jl'h'",pn;~ ~,.
50
. ~. .
i .:
~SI ~r &, g f')CI1fWcIJ rU / ~ thUn J. J D n e::t..v nr neo/ ~N~
dt ~b tJ)J,' ~ -/4vl: '1~/ f ': [LV,' ~', ~'J t ~I-
. id~":. [W , 'at, ~, W 1 ~lfl ~. WJ ~J ~.] ~&r t:.t,n'J.tfUln) , ..,,"/ ./aN cl".,/ I~ palu,; 1rV I~J .D&A eP.D.lI ~/)n~~
r 'ru r Q,f"H'tA rk fl,-J ) t4 ID n e J/()n rb rII; 1~ u nu /1;". 1t:H~ ,4;P'i.n fù!yn$1tU CN,,~ U:H'~,0 ILl- UJ" J./~,,). '<'< !q.hliJ .e.-+
-lovA Jupp~~n d~" IfIl"", ~ ,DPfj'NWII. M pevl· .rj,~'fM ·tJ1lI)J'lrtJ.Ik~· (;a I/~, her (/~' 2.) t:')."'pI' 0P()U 1 )a /l'nt-h',," .,hu\/o"le".·
. .W :.- J. T Jz~ ... ,J~J .-+ J~)1 Z., Jslt~ -t J,~ \oi)l"l-t ~")I~ 2-+~~3
...~. f~~·~,'Q~ Y\J' fU'~'dl pa,.j.;UN. ••/~hUW~ JAPwuk/~ ~
f.?nl~ " ~. IQt~'èJ.t:r .QJJ ~ 6J,1nJ .
.:.....~ c;cr}1~ ....... n,pa1r~" CD,..,.t;J~" d(;,,~t4 ~' i~'( ~V'"J.
.tIH :","n-krfJÂJ~é4. '(t)/1I~ • CDtrtp~H~1 ri.NN ?ru. __ p a4
.' dwx '~hUnh.· . i6"j·:[FIAb" F~. ts;p,.J1: ".~. :,'~ ~t:rA.f,."'(:JI)()fv, --,~..d .~ ~~t!fnl'r.ur.-k '>'" /itiu'rc.&'
;'~J t:b,~n; 1),.e . mdùn.Jtnt:l"I-'~4f~ tif -I4/A ',46/>1,
r-'C ~f· ~. pr,! âM;j.' ,A-<~/a.,'rp. . A ;;rJ,nÎl'l. ~ fraA/~//".In
," ..-I~~,../. e(U';ie>:"'tfUIJ,' ~n o'P/tJ'l..t"Q' dt /~ 4If~'#)~ho,,)
Îacb1"N :1-//),., .A'z..v '(/(1" ft. ..
\ .
~l<<' CJ)n-l'41.,,-IU"'~ C!.JJ"~tAfUJ" rl~nk jJ;,.r, ql') leu'J; ~ e,,~
'~t.4 """~m'flh riA jlt "'//)f" e) ~ -I9/?hOr, p~ ~",/j, 1 olt.~"~eu'" . d.tJ,.., -4 'rPAJcJ/~NJ .~ ~ / ~ tt' 1eN 1 r6 I;N!'I
. ,;, rb b' dt? r m 0 1/')1"'/ .~;, "" n,,!-, 1 .1J ,., 41'p4t» di Ct .
v
o4!) ..A_v
l. 2.f~~
~/e-:t . .dh !ru17)J . r6. lu 'rte.-l-"DrI /1:> n} IYlPn IHJ a'/a ??H N, .
W ":. rJJ-tr}~:J T ~~!1 2-t c4 Ji j
~ "::' 01'l -+ rJS ~ -t ~ ~ t'. .~, .'~w;:(' a.cA'~ ~J- jn CD"rW~.c/t· V-~,., rb'.l~J-I if. Ar,'K ..,~"
)-,'OM: kJ'x ~(JrrU~ N ~ le ,aAJ>< ~hf:;Wrh A M 2 .' 'W, ~ ~,
~) Wz) ~:NLI ~l.)., -4 rUpu'Jcb ~;~,4 '.'n.I Jh,,#',c~)PQ4 Q ~
}" rb'l·"./J./'),.. (.J)"'~ ,L, if /:« enA J' dû U1--. 6" l dlJ fDlt A'
h.W Ù J ~/6 rtufl J. ' ~'u~ fJcv.J c.o"!I.D,.m~i. (IhPn U).6?;,ru~~).
.~ c ) } ~'IthVrt J. un j../#,,). 4. l'fVJ du /U?'~.,
~ : ·,01: __.... -IteM la JI'~" ..& iPr'3 ~ ) ~~~. $
'w,-" ~l'" "". ,/\.plo. h'1J",:~/'<lr rit. / ~ ~~ JI~. -_ oIl~ -~ Jt.ph,I-/D~· autOIlr' fÛ. ):'''t. X
. .5. ~.2y'f/·rlf_f.a..!.,'o.!' -:-d.JJ' p-/le',.tJ_ .
. . 0) J~ c,I,(}tr',D tt-J-J. un J,ru. ath'YI â rbl'n~'"", : e. '",,1-
~ (L( ~ /.1)" ~/() n fJ-Pifn.$l'n.f' .',' 6). l{' c-,h()rn~ "TV ..j.#),j!a/) pa4 ~ (f)n ~'}/~M
rh t!Jtr'f:JQ ;.,./;n';"j,' k~ . ritp!(J uwr.t,,)../ ' e::tMÀ. /ron-!J'eu,I.: .en -7r" CPrt t.' '" f..D rvj 'Lt '0/1' A - 2~.9~ . Ii1p.1 / » ~ 0;' ..i 1 .erI--~ahQ /
~'6 arl, 1 !:JXtjJ' ..J/ tW rcvi /~/I.v '1~ . w .u. Je ,P"~./J 1VJf'",,,4.~ -;:. "dw. ~'e(lf' (L)"J,'n.ve .: ~~n ~'K
52.
'l'r
J) / ',jRftv"} v;n A~n} cûa rn» rIu ),J:'h',~At~ fJDU"
d~ = J,": cI~ ~ D ••
~ ~ Ut,'" eoI~ 'tt
f~ = 201, of 201{rt..,.· '01~ ~
f)ll1 '" clS -+ 2~
5.3.3. ntJlJu'CJ rh Jù' "'cV·/f 1- -- - .- :.9- - -.(y. 12 ) -=- it.\/ = (e] ~al(
-" .A e 0 0 0 0 e () 0
.' .. le] "; "
~ 0 e  0 0 0 e 0 e"'
0 .~ 0 0 0 0 0 0 e., '. ~t'l
3, . Â 0 ~1 0 0 0 0 ~t
.A 2~t~ 3 l · ~1Al.~) ,0 0 0 0 0 0 ~r...
-1 0 0,
00 0 0 -~1- -~.,
-4 ~'1.~ ')Ct 1. 1
')C~ ~~ ')C3~~ 1c1) ~~~ ~'~ '.; . 5
0 0 Â 0 ~ ~s 0 2.~u, i)~1- 1-
0 -1 0 -~j-~'
0 .3ëJf& -~~ 0... ..
~ . .Jo) ~ ftl" LBJ fit,' .AU', tu. a..~a 1f1.. lB..J~~1" o oe2 00'')\ 0 0"
--.:.'> L~1=- 0 0 0 0 0 2 0 2')\ 'V (-4 . .,10-')
1e 0 0 0 - 2.0 0 -"~ 0 J
~9' 13) ~~ id( -; le-1 ~, => 1fl-= l8clJ Le -1 i~ i
(&" /Id) -." /.Ill -:: Le-1 Ltlk1 iF!L8.JJrIv fc. ·1
Jet /le /"I,·ru\. m»W'#n;'.. œ "f'èvYf. .;,;n; \li ".,JO J< rb. 1';"-/~!J ~fZ f/Dn
~r 1~ptU·J.J(.AJ~ A q{l )Q fJ /"tp,( e ~ {E7 al- Alh'~ /~u'~
lD2' .cv/tlh. 1 0'" a.".' UI)" Le. -1ZI#.] i:LJ>7 1.8«1dALe-Ji:
-oe 0 CI
I! , .
e o 0 0 0
!>l' J. LK.tJ-jLBJ LM L&]~ /
tLBd1 iD] /!3ci)::..
e 0 e ~ 0 000 o
o 0 0·0 0 00 o•
o
e . 0 e 4· 0 '-t~. 12>\ 4v)\ )2Y~
00 .0 0 . 2. (.-i-~) 0 0;. 4]ttA-v') 0
o 0 0 ~\I 0 • 4 12~, ~')\ l7.~
o 0 0 12.x e l2.v)\ 'U;xt 12.v)t t ~~? 4)('".... ~
·~o 0 t.v.ac· .4u. f J~',) 4'\4 I~\ht ,. 1')a V' " ... R~ &lA-v). c.~~
_ 0 0 0 J2Y~ 0 I~~ ""y~ ..A2:i\~ ~'~ 7. ~
o .., ..in ~ "jrl tA. tif ~~p~ /ho" Ab r- / a Jz.t'>fu.( e jpMU) h:u'rf~".AN Î 1> n
C6/QJI4. .. //lJ .
. .., .:-. .
. 3.3.·~ _Ch~"~~ _1l.~~/'n!!.J_
t)r1 conh' rIJA., toM m" JahPM:
~I
[c.-"] ~LGJ t{FJJv -:. ~.PtJ.l c.-/
_ /&1 c.tiN'pJ t/>f~/I'I6'J,i9,.,ut ~j:: P~." a D))~ (#Wt~J6,.,
-1-'1 '-tM''''''';;$ dv. p'irfJ ~WIW~
_ I~ (,t~f â.t ÂWl~ Co( IItI ':: ,t:'JeJ .: e W ~M
.ff) CJ ri." tJf'~~~':p,...' r: et#,,'Jo ~ la ,.dz..ch~ C.( rit. / q6AU"~,IU/Jti"} cr ~) .J 'A~/V'~ er» b/hJ t. .
J'.tfra ;,'/Jf't (2 o) rb,.,M l'~ .€t..,iN·"D 1,,.). rU U4 cjJ~p:'
1(lf:/j")
1 ("À~!J")
t ()f~~")
1 ()(~~")
J (t, ~ .. )l ~·t ~t.)
r hl.~O)
1 \·l,~l.)
r\lt,~S)
//t:Jur Id c~a!'c'Jt. rU ~jtJ V, On Jv~pOI-l r ~/& INA/U'# -titi'
aiM ':'" ta).- ,du r: 1(J .4z.c.hr CA .en I~""Û/o n c4. )1 VJ' · ~
9 f3J' ,:. ~+ b.~ t gf~q,.J. '!?JS1 1 fJ31. .u p~J 4 ~1<4 Jl/f.1"f~ rIA 1s ~
'tU~dU riA". n otAJ~ rh l J; 1 J~. /UAp< "J. ,'oHmln J.,
: au. npwC! j" P.J~: a -=-'> (2:' Es.,
p..,. n~C!J; ,/J5z: ~ + c;,z ~> C'-:; (1?J31 - a)/ !/'I.()No ~J d" • ~J~ -: a -+ b>fJ'"~~ 1> ': 0Js - a .. cgJ JI1I(JJ~ f/:,,,ru~ ~ As,. ~lc" flpevrlJ j.' rbnrw. /~~/:Jrtl'h'~" r4
PJj l,t'l" 1,.;,,.., r P'" peul e'o/~ It.,. Lc' AJ1IG]Ir{I,IJJ /. U'I
fai', Or" ",;,,-If:J'" huit )(JAwt/ou A fi, /'.l!JV'fl.I~;/ on CI c1P"t.. :
55
•
~. r~",~") 1" b.ll)t~ ~ .. ).. c J (.)t~1;r)
a. ] (~~ ~p) ~ 6.} ()t ~ ~p ) "t c..] ~)IA1~i)
(]A. l (~P/~") ;. b.l(~l, ~.A) -t e. J()tj).~t)
a . r ()t~ ~ p) + ~. J l~l,~p) -+ C.) ll'\&,~)
~ . r (~A}~A) ,1"" b· l l~~ ~ ..) .,. C' J (11.-II~t)
(,\.. l ()(p)' ~ 2J... b.} ~~AJ~ 1. ) -t. c- l ~P, ~s)
a"}(}{~/1jP)-t b. jlltt,/~P)+ c- l~')~J~")
. a. !\,.\4,~Z) 1'. b..ll~~~t) i' c..l,~')lA,.~~)
'. a.Il~~J~\)-t b?l~A) ~~) ~ t,ll~,tJ ~c.)
.3,4 LE VOILE DINt€.;
Xh .W1·/fJ M/,.,c:e-l pnj... ~. ~'bm..,")J ~l Ibn Av. '
pu-po·u. pl' l///YlJ/1'j. rh (Dnl,.-ain1t.J f> /af')a/re4 .a f~" .e·b~" J.
fi,. f' I~ 1pJ .~~ 16 y/()t') i. c. t~.t"fU'.( .n.fEI.,l ri a rb" Co (]A 'nt .~rtl
de~'h~r-le' ..,/n (bp,,.,rLqf7JJ:~~)( -U' l.Pnl':'a..t~h, /J/~n(/U'rG1
e I-IrQJ €,rl pVlq'J ;"./'/V y -Tai''''' )0. Âu/,llr,ep~'I/~~,J .a» c./q" Jo(
~ 1 ~.
Jt.: ."d:'~ l'eJ . dA :I,'6 e r ~ J .. c/r; tYJ ..N'" .0» rk-t I~'r: ! t:f rrlf:IJ I~/{.,f
a1'I "/9 i'rb'it 1 lb,'/- e:::v.u~ 0..1 ~J./IIj...eJ')~ ·i'!~rtJ.. riD,,/V' ~~n
rbl/ra .j;Jt!J4.IJ.U· du1!JJ1.fW\.f /f)'.eI/ rh. 1 e~~,.f . au lIJ 1~Îh..c·l . . . . •
~~/ tiJ. J~ "J kA,l(.k~o.I.pn a ,A,')( ~.J rit '/"6~/~~J
.9~ "",""-kac4..u·J.~1 .m('A./,,-I~n(;nl- c16n.1. -& J;jJI.iwu. iPce;IJ "..<.4 "
~)(;Il,·I'l'Ù-d.J?' lA )/1> eh/.l' ~'. ~. .u4- !~ ,/lpf4j./~,n ,1 .en
. ÂI~ ·f/h' /'CI,.... ) a.u 1"v" rIJ./a xe ..& ,;/,$' :'!t-..,. '
, ~, .
3.4. A -fltd.Ju~u ~3P-t~rLt:Jt'j(1;,'_eJ_c{aI1~ _~~/~/~
5G
S97'V J. ll<p]: mil1,,"VI cf, Njt/rb'f.t· er» (pro IrtJV·,. #J ~ I",,~~
r,p~: ~/tl/ljtA ~~(1 ;'"Ief -e» (gnlra"n~ ;olilncv~
L"17; /ruIIlu 'u rb /ù~' t6'ob' .er» .u.,,;, r6. .fit ~/o r»
1111/1 ~ JtAft~ ~r~~hnlf4 V» l.JtlJ. tb j&tf/D"Ûj Ih ~ tIu 'etA .,e,? IN.cleur1 d4h'p"..o" 1- rhJ;" C i.tt. t. D 1~/a:) .
j»'u-J- ~,1 -= c/.e.,.û a.. .,&'kJ,p 1 .e'" c.P" kttu'nk 1" levna.t:.u"
~/J -: rhJ/&l; tif /;6el' If' -U"t e,)}QJ. r6j-dtcip ",
{~.tf ~ riJ.r j rb ~'~p rk "",,'b:'fV"U, <1t1NJ ..e 1#'J~
1t'\A' 1,,,e b UJ /
Or> p- idJ ~ ;'#1= [f4o1)ft.11. SlJo. SiS i , 'bJJ ] ~d fpNl J dtIin.j Gt4 ~n cV'f,o'IQl
{d'I -: dtr' cL, It-t~/I' dA/fIJ ~ lIJ ! U 'lU tff~ "-/ rit /q
A k-,H cJ.N/ui '
(€If, JJ')
1
kp :--- ...... -!.-.r
•
..' /(./'11/-- ~ ... _.-, : 0
a,AI~'- L~J =:. f'n(/J IA/u riA .Iù,?·rt·.p' w&'C!t:J 1~ cl. 1~ cltc ..Al x /1
6. "'" hrA -& iNJ ~r c.. Jlaj)cP -f.F',,~ !4n.p ~ r.4)~ f.t. fblf1
.AA. 4yJ 1, itv .(p CiJ / al-
Jp~f -;; [ P~fl' j ,il&,;/. o, ()•or3.1... 2 .A.IJ~~().J!:... ~ -iI~~,!!J_
1~*", t1a:J e CDnnj le ca \ ,CD / t# k,. -4 1h fi ~/'C44
IR}, i~1f tA' {pl -e'5PNN~ rk;M) ~~t:Jllo" (22) ~n ~ fÛf
Sr
~/cvl rb E p~ la AUo~f./on . rif e.e-IA 1nf1l'Ll
C1· /1) - jPJ:; .;[lk:JJ
L~] el J la ff'6IJu'o r!Jt /Ujh'rJ.,'" ' e.h~f) ,t~A..t ckJlVJ ~ ~J/I~
cl ~ let 9 {Pfn,/ rit 10 .,I!rA"l cI-...u..ui .•,ll ~"th'ln;' cb"t.. ri." -l''f7M~1
nul' III .(!,rI ll<gJ )4/'n .rlr.~~ClI/O;" /tUÀJe /4 ~ Inhtt:i h~"o
(~(" f~ 3-h) .
S:h'~" I-~"c~l j ~) b 'JyJlùrv ri ox~ J.p(.a/ l'kJpN q~ /~~~,,)
,gj (X, YJ r) li. JyJ -lit.~. ri QI<t. 9 !P,~ / rb Iq ~ J,.,u cJ'pl-(
'J>,0J l~J. la ma 1.Jî/~ ~. ~h"H"IJ dt» lfe»r-J ~ a,.u 6P
eau~ pM ÀtI,jW2f ~J< ax~ fjLo6Ct.fJ/<,
,.. à}t;~ ~ilJ 'y ~~,è . ,. ~II ~.A 1-
LÀ]": ltyl)( '>-h'Y ~IJ'? - ~l' ~lt
l ~\/I '>.l'Y . >-$'~ .. J~ ~'H
rf:JtJ' Alf,x·-= À" :: ' CDh'fUA J, ciI:.u cJtw r: rU )~:t lL pah Àd,RP.Ilhf. t'A r X
:/("'':fJ'-If.~ ri ~)<.' & co 1 e4- ·Ie./~ r b . CO';'l hrj ; ul
fJdla:/t~ t:/ /;')c~J' 1 el /., na» clef e4'). )b~;r~ (fj)· /, eJ./i~
S<h 1- (Xi, J Yt') ~;) .~ cr)f~" ~"N~ g !p~/e4 du n.œP a ..(ptrAtf)
..& Cf) # r ;, ..~jl U J. rh!,'v' fJa/7 li ~,i·.ev'" ~2.' p~". ~ r
Xz... -)(, . Xli
.,"tt~ =Y2.- Y, ,,-: Yi' ....... t.t - z ,: ~ll
; l ,
s, /ony eu" t!.Il- -i:tl :: V"Xl.2..,. Y14'1-.,. èzt i
/RJ e,;;",,'fWJ d,/l·.,G/eurJ rh /IA~( ,~c.al f}) ~nJ.
fNAA ~ COlM rbnNi4 ~ .HcJ-eur ....h",,·I4U~ ~ 1 .::
o,.
58
~n .o J."//J(;p} /~~. pr()prÙl 'I,~ du prodw'J. /l"tw-o./V'.el e-I- d~
~ c.J-w,. pn/lœ·n..1 .or» -I~UAI(. AjaJ~~n). lu 1/4leu rI J.u .. i '
e>b"fW.J rUh c.Jev~J du (;W h~ ca k~ I.P ~)( . /éI r6 nvNJ t-~ JI;'''; 1
tJJ f/JnfN~ en (7;," dlu el" n ca.'
'\u,: Xl I/lA7. ~2Z.~ Yu / ...f,I. · t\zs:. ?:lA/~t
~~ = (Yl1 lz.. - Yt, tl1) / .f$ 1
>. Jl ~ l~l1 'CL. - ~e.X~-)III 1
,\ 'U : PC\1 y24 - Xl-f Yf1) / -lE '
~II ': ~H ~u - ~3Z. ~l.J" .\'2."= Al.)'\i1 - ~3~'\2.-I
~3 -= ~l' ~3l - >'il .-\l~
.{J 'a! /(A /l'''~IZU'' ~ ",thN,. ~ ~ ~J X 'ttl.~ . cg,.;fW J ditV d-w,J VJ"AUJ.,I on pep;' (.D / eu 6". lu CIJ",n rit, l'Ullt,
i1u hJ12N ri4 dt I~.'~ hun). l'~ j)c;/~oA j ~ ~J -I~~ fp (!~ ~. U4
(Do cIo",,,,, 'eA ~ .on ~a.Neu·} ad~·). ÂV/PP",,:e,., CDI)/UlJ 1 c::P/Pi4
r '~:/'p/LI"h/J .~~ ~ ~tVH:hf)I'lI~ X", ~';vl-~' -& AD";' i J4fIf'
~~nd),,~ J..',,, rb .C,feo/~ / ~r ac.e~' ~,.'V; ~" c:I'p,P'''et/tA .
cl. ~i) cl Y,', d. i-/ /JP" r ~ d.If; la " ,""p)J ,n,Utlt:lf?) X 'y, f 2
2)(/, /).y,', R~,· 1 JDnf lM /lsJ}o JimJ a,u/~1J'" dA Je, Ye; ?
(3J) 1
)a mo -/A/u dl!' 'v~ f' tNt .'
~.t( ~ L~] ItJ f .: ~. 31)
f79J (uJ. la ~c:11Â.1è:.t rh.. -/"Q'nJ?YIf't~ /-/fJI') :/-' Dwu 'j."I?~./
l>e 1(~(.IO I,'~ ri ~ n lu:k/ Jo J ~,,/M:._if> '-:J" tIJ LïiJ ] o'
5~
(;) (;) Ci) 0 o
o..
o
o
oo
& 0o 0
oG
o
o 0 0 0 0'
ft'( l~f "''( 0
ft~ ~If n" 0
o
o Q o
Q 0
o 0
Go : 0
() 0 0
o o
o o G o Ci) , o o o
o
o
o
o
Ci)
o
o
G'
G
o 0,0
G) 0 Q
o .. Q 0(;) Q
Q'i", Q
l7. ~ 0
Q ',:;-0 Q
Cl rl~ ll\,
,0 Q.o
\1~ 0 Q Q G> 0 0 Cl
h\, ' ,Q Q Q (JI" 0 G Q
o Hr1f~, l-t~O 0 0 Ci)
Q o 0 0 n'f'l~, l1y o
Q 0 G ,0 "~I~ "ZI~ II~ 0
-0 li) (;) . G.' '() (;) 0 ~f~.
o 0
o 0
o o CA)
o h", ll~ ~,<, 0' Cl
Q Çl~ ~'~' "~ @' 0
Q G OG> ·',0 0
o
o
.. Q
-(;)
a
o
(jj)
Q
o
o
o
Ci' 0 .0
G Ci) G
,0
o ',' (j) (;) -, 0 Q o
QI 0 'i:1~ 11~
G Q t,~ ~I~
Q
Q
o 0
(j), {l" ll~ "\" Q 0 0 Qo
"o
Q(il. Ci)
Q
o
- ,, '
~·J.I'!I /é)tp~~,. ,'~ L.p/la.4 dOM &'YJ/~nv. fJb.ft,/
IFf e ;-1t./, J'ï?, if} {J1: ~t. {iil : [1;,. ,cy,' fi, /hi ny,- n,,·J~/fU'- p'.; b AJlJ';~~ 1 k:s l'L'A Ud #U-.AJ~"). /1 ~nu
IreuI(li~ cpm~/c. #nurLu cI.t;"/6 UlVl.lph &1we<Jpp" dDnj.J,'
1:: ' é
IF1 J6( -: If;1 /tJ(1(3B)--,> '1~/-:. /7j] 1411 e)- J'il ~ lïj7 1Ft
6kJ /F/~l '" â7jJlf f/'(L7jjht) -: IFIPil[TsJi4j. " :. '
'\
Ifl ~ LlI)l #/1~ ,'7j}1F/~ /Kfl[~]{/JI .!! '~L'J·J L7jJ1'( ~ LIj-1[I'I/[7jJ{1J1~ :" IFl -= Lli-1 1kl] /1jl/~1
CPmwu iFI:; LII] 'l!JI, _ a!p~ .. .
1 ~,. t,on (3J) . fY\!m I~ r: .[ktl tI~ .4>·"f'<'hê.v,"/"..J>· i
J'e~'.j:/) o,,·.Jtp;rt/dQU /4 /lP"J molNu' IIW/& /..oJ rb r/"iN"
, . h~o" '3)( 3,.,.odAJt /t:f -1n~t',Nu .4u·cJQftJt,X{,.I'N~ p~"
1). . '.A -O,S ' 9s..~JJ
t~ ~ ri EtlJ
rS/ J
. .
"
, '
~ 'll,'c/PfI J- 7~' ~ 1; a \ rb 'le r Mln.uj" , U tU' d'J."u IV JI' tv1-/0 ,.,
p,.optJJ.'~ ~(;Vl . O" o'enû"'.f.w/c:J/ uAP /ltV'tfA,r ÂV/jf1{,hvn
-IcuitR. ~'n/trv>e(') Jo, .J!..~ /a,;/-~ le4 /t.UVll-fJ h.; (!A/1 ~/6 ~ck,
le" , h!Jt»riJ . =n.t~ ~ . ~ 6.wvflh 1v' ~nJr'a4 cz>;u1tPna.lAu~' a~,..
Co( rL, l 'IJ rbn'V.?..M-t, rk /lIÂV /fd("J' . O/~N> c ~J.)' ' ./'/ ~ro/,t'~
rh pJt.ui Ju d ~ftt,' M"',,: r:/0,.,/«" rh, ~ "" (!,;1,A.t IOl)Nt M4Fn
~' .r: ri ~ 0,03".
3.5' J<ES,Ot.UT/OIV '~ES, EGV4TIOIII.J ~"T CAI.(.~1. /)éJ
, " tON71<A INTl.é.5' "
~'& ".a.;,ï-" ,ch. ./~:)v.x.r. ~ ,4&>lvll~n> III r6 / ~~tI ;';Drt ll'\elA-/
4/'elft. (22)," Ja..':,,~w;'(·Ort ~/t:UI;C~ ·fk fJrD t!e'r/"i IWhUIl,' "
5JI )u.p,t:t~#n-lv. ,'1e:J'1 rk/J lau~(')JI 01~~, --6, NJeV/.J 'rk (q
Ak.,(JJb~e. ')a' thJ'j/,p,r6 p f ,:-t;"'( u J 64'~( A/7AÀ );'-tN;'t::IhQ~. .J .. ' '" "
• i.·
I rb. ,Ci.4 Js S" . , ,
Jtd r6'p /o ti'irtJ,,,I-J :" ~,.n;vJ,P n' ~I- ,t:l/~ eolevu'~ leI .
~'rryn)J iR)u~clprUcb' .~~~ il:'~"~ k,~nr/~'/l.f -) e:z,v)( -JN)ii;~ c6.1' ' , (Wll§>/l(k~. :7V' C:O" kaj'n.Jt~ ~"J,,fpn -
rv~ dP,.... f6 '!!~""': .-6 ce / · "'..<-/q~ ";t. ',,:,~j? <,,.ft
u/a, or- ~ cJ!"I-i.~'Le,J., dutlC' ca-J "rb.'r:.Dnkt:t."'n~ :/(e:lndiAeJ
~'J d~ ;t~:lo".~;" rpppn J~R1m.1'~); , '
,in' .~(Z ~ p10 n ~~h f.i.~~.j, J )~ }ll./c h~" (pn /rev'n~ rt;'ltli Cof .
:~it~ io"r~. LE] 1rt)· j ~fu0 fIOf)' -kt3) . rhnNf)j. I~~C.
:J. '~e; .h'f);' flo ) .. , ." !' ,. ~
. . :,,' ~~f ~ :l e]L&~1~~? ~ LF]1801J~ [c -A]111 fOl,A' ~o-~ ~~ th'f'rtA' ~'paJ, ~crit',~[\J~ ~~. :"~J:'l'n~nr'onl- 1t7'1 pNl I~PatiJeû,. c,~ Ja,o/a~J';' DI? ot .. ,
~ J. "
S2.
-,...
r
! ~, iJ" u~;;F ~ \'. .'. '".,
".. :
..
dt:lM o/I-t" *1111/(1 ~~d'~lYtf~)' r/p" ....
,~ , .
. .'~
, "\ ~ l'
, :,' ~
jn1Cf't :~,,/ .cç,hl'll et:-"" 1~..h D.,(1ttJQ (rk 1'N' tiu~6 pa/! ~'W'~/,,' 6 -IJ"P-"
/?'vr It:i~, Ye$.pwJ./~nJ 0" /./,".1-, ~IY'I'J-k et'td o'p}U""j rit,)o ~IrM,
~;t:Jn~"~·c/.t,u .~~,IH,J . il~n..rLt .N'r'r6'~,).,/~ ,1iJ. . l' . ' ..'
't!JWd.t .~',:,~ (~ff;)W/~nj,~:tiu. IU~-tau , rk Q~fUUj~' /lA . rJ.,,;,kt.A.
fnJ,nk eo U4 p!'1'I1.),~ .~,,) . ,,<f'/)'WJ ,claHtI" (.t" u- ~"J. IW!.J/ .&:Jn, '
'pt!AJJ. f:bne- 'cbŒt.uM'}a : C/'a!.w,., ~ .A.f:a,,tI'6'~J' '.JU't CU "'~ft), ."
-en ~/J.,:'p.[,'t,,.; j'o~p;'1 rk,J ~jJ/a uhllfJfJ ',o,'e.n )d A~"'Y,'
~I-Ik/ ,\.o~ ~ ~~'~;'a ~nc ~&:.t: ~rA :/UAke//))J,','{,
,.
"
j~
" "
1...'0 ;;
.",. ,
. !....- ..
. ,
· (}-'APIT'RE Nv '
-. ,
DU/LOGICiEL ..
.'.
, .... , .
, lovr "IQ?"tU. ;jrD '64hf.,t,a \ -1rCù:;~ ~ ,;;/ / a.u 1- c/Ut,- -u"
;fbliu- ,da,,~' ~FI .on' n;v/l,q -Io~/e,j lu cb",.,4-..s?",'
~. ~;f. 'r:e/(JI-/~~/ (J. &rI- tJ 1 è~i: ~, ciPl')NéJ ~ if
pr~"'o'';'~ ...t'ra 'tAt. C.D1I~ d~ J.Dn Il>''~ ~f'!J~' .,.,' / 01- -:$4,I.,ftt~,.i YllU~~'M c4' ,do,,~,.....un no'ln 'au ~~~.",. rI~ ./llN/1,1:J
r: ~,fJl'~ran."v er'~t'"d' éUJ J..o",(ZJ./~gl'YiUJj." d rLtrUW l.t.'f'Uel
..,/1 in.t lira' '--& A.Uu/f,l r4 Cd I~!J/' 1'ÏfJU" f2 /!tJ~ ~rfH""r tudt#'~n/'". l'/,,,,Hl .~ 1~'x.:<:.u f,'r~ dv r~5rtJ//MV.
. .:
"
, "
•~
4,1 L.ECTt/J2,E ')E~I)(jNN~E.5
·1..~.4, 'j)on'll~ 9e.'n.Jh:;/~, " "
!' , ~'prti"':'~V;l'7:'~',/v "', /ttprb, -,,(./û·oc.l'f LtJ' n1J~J 411
f'et'trt; ~.ck/'';'b,,' ..~f~ rlt~ r'lV/~etl:J-, '/.f?~r(J1lhhLJ ):J~~'cU al
}" ,(,,,f..u'l du iPn~~", tJ'(~~o/e-J ~ ~"f~'~M. IfMdu r4.... , .
.L~ d-..urt .' .'''.,.~;" , • ,',', 'f ;,: ' ,
_'_ ne/:, ,n.Dfrlb~ 'ri D'!.t,."tnh" dJ. la ~k.ucj;.t;,,1... 6;wh'J/;
_ n» J' : , '~j" lin' '..j 'Jf~ 1 rh 1Ul!MJ.s cU Id Ji/y"u' d'JA,.e" ' ,,~": ", '.- . .
_ n til: fI1)m~rl'c!.R cI~:J~~ 6. l'/;.f' Il' fJ~ •n..œu,rI ,
• _.tin.' .A rro rk I..t • ri 't'IIAA/-J 'c/A 1 ~ Intf/;~/'au gn.-G",,/1Y:t ~ ',' :';. '.' '..' . ....:_pc.: b:' c.P#'o,~,.,J ,rh, ~.D;-Jun V, .",,' ,','.
,_ ",,: : l.t nom ~r,~' 'rb n~r!J,'fi.et,lrf/~ JJ ;' , '
~ "",;: 4 '/~. rh' r" .f1l"r\)f~ 'du ",~ lu/w .~", iN/hi Sj' ',",', , ,~'. .
, :~" / ~Jle , ".,q,[è&J,.,t i!, 'dM, ',.JyJ-HN d(P~ 1 u J. ci/A.t?' r.Hd /., ~, ...,1 ':',' .::,. " ' , , '
, 'Aertlt, 'Ju;ik 1 D,D',,'j,'cN/'NIlJ. c/t:iM:t(' cae UJnlra.l~ '~"IU""~1iA• - r .; ,- . l ,.. • .', Il •.
• '.ô v~f.tVt, ~~al-I~:/,~ ~~.'4 .~ tUl)u~~, , ," . _ora,~ "CP#'C'~II) ,tff'I-/~tJf tPtyt~.J.t ~ ~X,t ~ ~, '
Le. .e.~~ 1/ ~ ~ N~' -4t.c4.f,: ...i ! JaJU~ e» L 0"03 e-r 0,
, " .. ,
. .. ..
, ,
" ., ; '\
., ',.
f>Q Il r .or: Rra Id.;in.t rh ~ /(1 '1.MA ~ t:1;r '..e,4 f N;" ~.1.
~, fJ~ff;'a"'nv Co / euA ' o/PMI '.'
_ ,y, P. -:. YI0""~ rt rLtJiN; ri." .& 'J.fII ft ' ,P t:A/1 .&I.t /'lIA" ~
_ 'nn -= f;\pm ~w ,/01-" l 'rit. r/fl:JAJ; rJ" .,e"~;"
,1
.'
"
" ~ ;...4. 2: D» "",é>. rIu' fl.fXWib, '~J, conN e./''J>'~ •~ .e--6"."t>).J'.' \. ~----------~--------
:,. «:': )q -4 vI"A,I"'" . ~ J'!!) (,.H·'U.;;", ~l t,t /6 dA •
(,':','~ ,'~, }wnv~ rJ~,. n.r;ev~, 4P'~~~ ., ~~ (t r:'0 /'w'tJJ W'~d 1< rkJM lA Jzj~ -I~hv. . r1 b/ui /
,11/ (~) '=<, ,:1.rfo~nfl ~ ',~ .~ tl ~' " , fi l'
1 • tJ·{~ J'":.'" "'CD /l!. 0{, f,llWrL' ~ , , (. ' '1
,r.:.tu" A.t-:! "e;'~ t~ ,:ckA .~ (IJ ,1.:1" J "4~J.e-f rk c,4.iJ ' c:(r;ikJ• ~t ~ .
.s.i:«t:W J'~.:\' ',.
, \. 'J'/U1 (,.,tl ':J) ~ nvfh.I. ro. ,,~ ...." (, /ri 1 l'?IJ#» ri' fie.J J" t;" J.:.. , , , . '. . . .,'
'_~//Le-J, C;>J) :- /ÛA k~/,,/.t ",:AJ:Jt:1~} ri' ~ '.;I".t~u naw fi A.ed t.~n):
~ ~'•.~ -A o.' ·~V='" .~'6' "'~j cf, 1,6U1~'" '.•,'"/VA ~ (.'<i/.=0 ~~,:.;& .~~ ,,AU'''' fi j. ,fA j. r l'tV j ,
~M .. ("/'v") = -1'~' '·4 ~«A!fl'~~P; '.u).. JZ",pAcA '.
/?;t.Ah ~ !Q "'~"~'c.I-/J'> ~p.' ,LvI' .e-b "uf) J) 'iJn o.'• ',' " , ,1 " ~
~. (()lt.) .. :(J~ d J' ~'Ji. ) ~ IJ.fn.t,,) '~ ) d' rHJcJv~" i- .. rA ,A0'3, ' ,:mt:' ~·f~.,., mi(flJ oh ';'j;~ '.) ~~~;- t (~J ~ )~ '6»up j
lrlsHI
. . '
.JZv 11,/P ~ ; ~ .e r> • m. ,. ~•
,t1; 2.. ~ ;
on, ~c:;lloofe ,b ve,c.t~rmo,)(al CPIYf!4p;ftd..l!JflA ~x drJ"fJHJ' tiu dt~ , ..
~ "~!b.J.j,.l1-fW'/Yl.tI- çI #V-~~~, /~M'\f1o~:;~ )a -fA.,;,,6 rh 'epmph' .
6S
..,, ,
~ . ~
J '." .. -1'
1 • ':'{!' '·t;; \ ' • ~ 1
\ f/~n / 4/1- rI/U""~iv JG,ftlCR ./U.~'; -1.9"./1 /a. ~ h-/ë.c dA.. ~eP,.tz!,"k'/'_ 1 (
a/k _th9/Mt dt I~~~(J~, mw &/ P"'~ U rD O/DA.li Q
1;n;!/o.,ejaf/tJn:, rL. /0' rn~;;','u' ..tf,Jv?:',[/-b' . <9.# J,,; , 'J t •
t.F, 3 !3 oo eLE /)E CAl. CV/.. J)fJ J)ONIVEE.l ~é.! EIE/1éAlT~sl' . ,
ce/ft 'pa';,~ ,Itiv." QI',P el (/, t1t11/'eAA~1 ' .l'ov.1 ro"J.,,.,/ ~cUJ
,;.,im'/J}, (JH /aJJ.' ()ppe/:~.",' "
~ eDtJ"J/o(.: edit' ~~.s ro~}:"t &;lIeu/" Lu eoh'
..~. diA.o~~~" w~)C~;b._~ at;?t;/) ~ >v;/-.e: lMe.DO? don~~ '~ : h.Deurh· du -l""", t :: ef.plllj lA. , ~,J..wu. .4(tI{
t:U~,,.; 'ltl (III~ &) .fk~ 1~ ttlU~ JIU. fi IJ fIl,' l'lœ:u ~ ~' ,J., /; '/, ~,. J. ,4-
: .~,(:ile.) ~' oh rbn:.u~ du "'cv,~'rJ., 1i/~WU"} t... .3"{,,,",~ 1) -:. CO ft ~ ',1!itP ri j J., . 1 1. ~;"".,,,} .~
; 1 ~inJfJ", : . !'
tAt pori,';- ~ '~P/1 r/r;,,~i?, /;~ /~ ~\,g U J, or» c!~/~/~ 4 .
,/,,1,1""61 "a... ~ L"~i) -:: l 6/-')J?-:J =fi:'}J~j tf,.'!J 't:.D'/0:J .~ " ' ~ .. '
",/1,/6 ,~~14AI4 /" ma Vue.,' riA ~'r1//I' ~ 11~·'It.'mtn; Rn'~"Ir~""./-c) fJ~nllJ dtJM IÙ>n . p/Jlu~u --ID(~I/:-.,~IA :,Ir>U4
ÀP"J./i/~· t iqp,P' l, do t> fi ::w IAJJ.~I.IJ. ~(ll'/~ ~ .. ~'AP·" ~ .:
. , :""'~ '~-Iro."c!.tm: ~'cP/wlt I~ Intl/Nü: .rb· ..jr~fVJlorNÏ•.
,h?" ~\J,p1(;u1'N"h ~,,\ lf~J. l'tU", jy(J lU, (fi e~ ,fP;,.,J~~~
, tJ "d(;;\!~. 4P~J """~;,,.. g~~" j . 1;"n<lf/ll-l \ fd- '~Jt>'~ '''Illrc,.:I ',' \"" : . fi,. 7'l ,'~ .~'. \ :.
. "
';'~~,H 'pro~,·~: F' /PJ'J. la '-/Ju'p1.t. ",",/h~~I-'bf'O)Le-A] IslkJjla-''Y,-: ,... .
d'\ /~ b"j.,', .tk ~I'I~I )~: 1ntll.Ju·u
,, ,! "
..... -
.,
- col-t~ ". ~/~It la /V~·et',L,' /lt/c6/~),,",,,J.~,,
j6xif7n./ i!,/(" lev"f euo«, e'J~~~ ~t tr~~rf7~r:J~ Lt ~/wJ
dl /(,1 'mr:; t,v rt. -1~(J;wIDr m.i/",:, rk .rit;, III Uhl,glllt ifSM &
CJ%,J rit lt:/6;/0'" ;/""'.J. a' 1!-r;g~:.J .~ -IrO")lo.. .-
ee:/!< Ib~J rov/-;'IV. _cD/4V/t 'la mt) /At'u' rU Ir~,,.,,t'i}/~"~.
~'(f'JF :[~J dt . / ~,'4:.ruIl; ~." '. ' ,_~j"eJ·.· ....
_~/,. "ca(~~' la }ù~·d;/t./.4/'.e~~,.·J. ..fL~' #n*"t lJ'ht~A tb4') • il .".
ef~JJ li~'n( )1C.-pJ. ,~~ :.cb./~>c;'o,~· (/1 c/l~/j '. /r tl n4rr-'": ~/I< :U~'(j,,'.f.p' .t:;r:~.(J6;·. J1-/ ~1P'/~~ ~~/e:w AJI' ' -/-.~\mJl. :J!P~·;'e~.:' '~~,'~~f je, }U?'rb'/t 1 d""~1- . '.
-a d".~·~ ~ ',~. .-. - .'.
~/&" ('A(w/~. -& 0t.~f''' '. cl b etr(JJ.fJ,' ..~':; ri ett; .!l el (J" éJ' .e..f(!RIon"; ~ Id Ju~;"'./I" rh '/J'/"MI"} ·-Ir~'-J.,.~ ,c/tlM ,JfA' ;l.,.~'6
i • . '. (7'
ft. , fJ('klt.. J/!!4 ", '..,.. ','. . •.... ,_ aJJ.(~b . ,-. .., ~.. : .
t ~/k. fJ"'Ou:..~: 'a~ (;;JJP""~t. ..diJ' 'Jl.{j/~-;Jj ", Qlr'!ol- d';,w'
.:& gli. ; e. r ~ f / Q' .~ 'pAin d ~>'. j", 6,,~:4 .dq ,14:"n il ·. .. ..'.' . '.. .
. .
.• _- '_..: '~". fÎ ' • if - , , . ; ,
J.lt .'Tli.AIT€nE/tI·r· /Ji}; i<EsrPE'INTE S. ET 'DECOMPO~/'TION:_'
~. .~ /;cu'.h'mtnJ.... ~':t:'J~ l~ . a/ C-'&'1t";" Q'o~ ..&~I/
-4 /ùj-t"c6'-k'; ~" ~r"'~ponilLn J- ".éMAX'~.i~~ ',"'rb -&6-t/)/~"
/lt4 f1c.fi ~fJ .tU-- (/;; ro» /1lu ' .--v" i ~ Ilr a~ ~~'."LA..,/o~ .b'/114
.4r la. .Jù:r'o!t.~ '_./~·;",e . . ;otpro.J Y'o~htt. ·Ia/J.· a~;.,J··~"" la ~f)UJ ~~J//U. -IJù',P/d ..
~' p".DU rh. o( la, .dJi'cbml',p~";,·(')i") _~'.6'Çt(AJ~J u.J/4.lticJ>'e,./-o
•• _.t
, 1 Il. ~ \ '
i ,
, "
..
V4 aor/!I'&'~~}J rI... #/1 ~ , ~:n ..,uN ~~ -JA,~ -INdl?~/N/u
HvfJdvétH" ~-" ~i';ft cl:",.., WLI" J; :ttv: fi'( c.J.eAn" tir J CJ7~~ / ~ n
lai~ ,f.Np{.d . ~~~PDH ?~/{,.en~,. P"J)tkv:J. 6. -J"~'J1n4 1)u '(,f;j ,' ~_N rn.(J.7/U'U -I/v"t,"r11JU;v.;,/,,;.lA/.uvf, pN m4
-IN'u rit~9n(J1.c ~N'/~~ ~.N"j m.1,A"~:' j,';'';Jk'/t!U~ ÂV'p,u/ttu'"t
IA4~fJP#~ . dl. , 10' ~.IN'u 1;Ua~ /tVP ,,"/WWI'ï C '*~ (1 1
~ dafJ'~ J:',., <10;; (Jl,llll erl: ~NY.D#>-j,"":JLI tlIJ".· elb ~v/l4if. J,f rJ.r •..
1. '. 0 '
','
1 . ,.
~~U" :'., . ".
-'" P!J (i,l:)~· ul,'d. jJ>c~""~ ;'p~'J.Ù. en JcJ>~u .~Of ' • '" '
J t.rt~,;J. -P../ ,,~~I!U~~dN ~~". n~jld'" <~. • "
. _ :"~Ic,.~, .." !"Dmb,ed '~!fq"m t."-;J, ifilt.t.· :cfi(;"'9~.) rejJ~, .~.Vd .~.~. .
+,.~~ ;4r7r: le C;91~'. ., '
-:-... ~'l!L. ~ .'ëlf"/lcJ"'!l.RfXÂJ.Ie;.:.~ 4 ""j,j, Û "",?':J4... J
~~".t:J,~ J.' ~ cLMr.i-,'() ~ ~~ ',Aup.ie.I-,~~nl-
_~ e-A~ "/"-/'0 d.u..t~ 1 D" .C# revIt kw-. #~ '~"'~ f.,,,~
·,4-,5 S(JIIl,LE' lJéS CA.s '/)E CHA/l~tnENr
0,., .f.y.u" a' 1" 1,,,1-...,.. fi." .)7"",? tI,,~ Lt !eJC., ,u,. ~ . ~, .
".. ciP;;iv.'''':' ,o..' '
'~ nn el., , 0np';'Jn.,. rh nteVr/.>' :'~'#aP~~ '//&J~h~nJ;,' ",'/ al-, "'., .4<. • 1 .
r- ,)U'(;"''(YI;'" rI./ rit ~I(N"un l1JS!,Q'd: .4Nx ,~~ du l'J''''''~J DW'
rk •~~~ u'nuf~~~ 0 ~n J.', 6',P,.P &p"~~ '" ~ , ,. _ v~:' "'<.Je:- y t!M. c ttN>? ;on cf -,J. ~. uev..pe-J :
o (J)",.Ü~IN~,. ~I-, ) Vf-I- €'MI',)t:;~"~ ·rlu av~ ~aJt~ -:.•
Ù4 Ji". ~f1J.J.' \...,' • . .
_ 1ie/~'1 : . ~,..:.I".. èJ/, '1,;"",,6, tb/. e, ~~~')IR~;~:" e "
: .~!~ -
.' .
'.. .
.. .
. .'
••
. ... .. . .
'..
. ..... .
••:. ~ 1 .•
.'
.. "
:....,.' .
~. ...,
. ... " .~ . e .
'~, r
.{
. .~..
.. .
" .
.....• t .'..
..
.. ... \li _.
• .'\J. ..... - ..
. J:IN .,,' ;..•.
. S'lit/UE b~.s CHAÀ~ENT~ ••• ET ·I<É.5œl;·tl.riiJ,v,)-: .'
•.:. : .~. ..•. ,.. .• f
9' • . '.' .' . ~
ALr:oR/.THI7E· J)V R~l)6.RAn(lE. P!<-INClPAI.. •. ,:.,:' .- .... . ... . ' .. .... .. ~ .
e •• • ". # 1.' •
1 bE8u;:-f~: .' ...., '. .; -; , '.' •t, ;-. .. . .' ".,: ~ ":' ,:: ., ..' .1." • .. • ~.. • . i, . ..' ~.; ..------'-'~Ih_--'--~J,IL.-.- _---.,.:.:::.~. ..
; .L~:c;rJJ:R.E··DE.~ '.f::> ~i:Ne-E~ ., Il .. ·• • • • • •. . " .. 1'·.' ..', .Qf t ••
'.. . ' '1 .• •••• ••.• •,...,.:. -.:.----:"..............;..,;...~-.....-_-...:;...,...---,.---:. ':..t •• e ••.• e . ..~'. '
,CAL «o: /)E.~ 'A~J<E.S.$E ~.G'" . .t ~. f . r. ., ..DIA.6()/'(A'lE,~ .... .,,~. ..'. ." '.
• •. ·•.. t·· !t'.: • ,"f •.•.~.» ' .• :.. f' ~ • ,~ ..
• o. • •
B" '. . .,... .. . .' .. ' "
. ' •. O.Uc..LE: DE~.iLEJ\1fNT.5 ..... tw.·.~· .:~.,. .' . . .
:'" 11-......-.,;..---~-..::..-.,;. ......--,~---:........,;.--:'--... .....
..
.' " '.~ ..
. "
•. .
• .• •
1 .'. .•••
•
••
•• •
...
•....lI!'"
••
.\.,. .
,., .. .
·:.;:t·
.. '
1
'0' •• •.'
• ~ • O.
•
'.....
.'• ·0...
.. e·
.,.' .
..;'0···
1
l'i,
l'l ."
- 1
i1
,. i" ,~
• ' , -'1
" 11,./:: r.:' i, -j. ,
J. .~'"
'1'
li .'II ' ' .ta '"" /,""il. ' <1 '''''-P''"''J r»m~~ cl '01'1//"" f ev"", "R. ;uu i
i,1~re' _~n~E, r- ItJpAt(: Qf/f)/"" #c.l:.u; ~ e--JJa,,',1'
III.L "J' -../_ J' .J 1.: I,J..~ \~' ~ p()/J', W.II~"J .' fUI" rpn tp""t'J'" U4 -"""
h]p rllL 1L~ Lfflj " }~ t:"~r r ~ ,., ci, 8.: c': ciD r» tU riI4 oR 'le~m~~
.M~Lv.u .~t rtD~. el /1(Jn~ -Ird,"-Itr~ 4/,'n ~(/)lf'\fJort,.
Jipi~ rf!fvll-o fJ ' .. 1 - .
. 11 ,Lof ~r'tlm'/t/ ~. e6'j,·,ut.,/ ci A.,~ ,sla~~ 0::1,..-
.... f Au~·~O";' du IpJt uA'c!.,M: i.D" p c: / -&J v"fu.u"
clJ poJ\a~4 ru" ~~ Jo : :"
, E::: A' 'j \! =- 0 4 :3 ".' ' lzp,t:A.! 1UiJ"., h -; fJ.4 ~. L ':. .."f
.; 3
•
..' ,,"
2. ' . . • . ....----..,.....;.,.~ 0.5 .__-,.;.......-...,...-41
,.1
\ ,
t,e"""
..' •
"
,-
~o.)
,. .',1
i: .fi 1tA>
1 !
: ;
(b)!
1 ~ ...
....
70
.\i
. ,L'··...;
.... :".
. liin oP 1,.1//-1 h '"-'"" M""'/I...!( r- u t.u. -" t;;"H' rI"M .
)", ~ ;".etnc.a 6 J d.f wUhv ~~ ti..4' ~ï.#~lIh .jc!R"J../~fJ,,'
~/# la (tMN~I,'..h·/f' r!..u J/,lt,MAnt, I)? 'ut-/Jad la l'rI.1wu,· Û'Il'
/Ü6v / ft;1J Db)., II\..UJ A-.b n ). ./'cf."" l,'~ J' re fY'IAA1'~~"d ~
1 J~. ,"1""'" WI 9" .. ';"e. C<IU rû <-IfaI'.!JR MA" J. a noif'''~·~ li
liA. l'AA ), ~ dA. Ît; Irt (J f.IV 'c.t 6."A.,j /d./-k' .,e!) c.I'" /!e.J-~ j /1q 1')
J' tfJ/? ~'rt-A~;. f>/u~ 1U'~W'~./I/ ...i1 A-I 1'rou.cM.. ~ /; /rt\Il"" ritllI4, (.( ~ ~ un .l'D"~',' 'p~ t:U/~"J ./i>Jv1 du
1
. y - J /
1yaJ1f.m.Q";- ,~ ~ J.,u/')-ed ~ o·~ Jt:,,. J. J2'nplt. c.1'." )~ I-Ol-iA
IIi" ~/~v,.. rb. //:;)t;.~$Ip.rp"dt'cP/tWu t:UJ/J!t:3 n ll,..'
1: . J. • i' /1: ' .r AIl-~ ~ 'a" "~I oP" (il l''ÂI,J. -U . nœu a ./;l; CL{(J J&W'1t'Lt
.d '~,/u' ,/~ A'''/r'é'aA/#,' fh 'la. lU;'; rf",4;...l tf' ~ 4CJ~',
rJ. .: piUj ~d c- 0.>."J. ~"r~1.NU VtP~' ~"~nJ ~ ~ï
~fal'~ In'~rt .dA. ,/~~' , rL~ Irt~ -IM).~.!W' ri« ecu ;W!.l,
tt:lr:. Jpn~,... CÙ"". 4.' rt:> l';e /""':J~ ~. ÀUI~,,~..~Jrnp;UIn·()f" iJ.. "I.P~ NfLI/lal-J.·
". !
..
7~ ..
'. ..
.'
C'ONCLU SIO'N
... ."
~ .
•
" .
'.
•
!
••
Donnees generales*********************
nombre d.elements _nombre de noeudsnombre de de~res de libeIte'_~odule d elasticite ~_
~c'oeff icient de. Poisson· _nombre de noeuds restreints
.p c i ds 901 umi que..~4. -------
AJ fa
**********************. '. ..'ponnees des noeuds
**~**t****************
456
1 . D.3000
2.0000
1.000000
noeud coordx coordy1 .aoo 1 .000
2 1 .000 1 : 000
3 .OOP. . '000
4 1·.00 0 .000.
'! :50 n .500
****************.***~***~
(estre~ntes aux noeuds Q
******~****~*****•• ***~*.noeud dxdy dz
1 1 1 ·13 1 0 1
***********~*********.**~****
con~ecti9ite des e~ements
*************.*. ****.* ********
coordz.000.QOO.000.000.000
rota.x rota.y rota.z001D 0 0
elmt • n oeud• 0
1i <5. ••t· 2 S
3 , 54 5
. noeud 2. noeud 3·1 22 44 .• J3 .,
epaisseu~
.1'000..1000; 1000.1000
•.nombPe ..d e qu at t on s = 30
espace requis - 429
...********************~*****
• CAS DE. CHARGEMENT NO*************************
•
..
.'
.f •
... "
.....- '':-''-._._,....,~....;...---~--;,-.-_.......----~----------------- .•• charges aUB noeuds.·••••••••••••••••••••••
-.:"
11
..,
nombre de noeuds charges = 2
noeud fa fy f" HB Ky Mz2 .500 .000 .000 .000 .000 .000
4 .500 .000 .000 .000 .000 .000
~........~......, ',
Deplacements••••••••••••••••
noeud dB dy dz rota.B rota.y rota.z1 0.0000 0.0000 .0000 .0000 .0000 .0000
2 10.0000 0,0000 .0000 .0000 .0000 .0000
3 0.0000 3.0000 .0000 .0000 .0000 .0000
4 10.0000 3 ..0000 .00'00 .0000 .0000 .0000
5 5.0000 1.5000 .0000 .0000 .0000 .0000
••••••••••••••••••••••••• ~\..(!~..elements de' r e du c t ion ,.
'1
.~ ..................~....ele)il. noeuds ·NB . :. Ny NBY MB My MBY
1 .. 1 '. SOOi)·· :5000' . -.'5000 .0000 .0000 .000
1 2 .SOOO .SOQO -.5000 .0000 .0000 .000
1 3 .5000 .5-000 '- . 5000 .0000 .0000 .000
2 l' .5000 .. 5000 ..5000 .0000 .0000 .000
2 1 .5000 .5000 '.5000 .0000 .0000 .000
2 3 ... 5000 .5'000 .5000' '-0000 .0000 .000
3 1 .5000 " . SO~Q -.5000 .000'0 .0000 .000
3 2 .5000 .5000 -.5000 .0000 .0000 .000
3 . 3 .5000 .. 5000 ... 5000' .0000 .0000 .000
4 1 .5000 .5000" .5000 :0000 .0000 ..000
4 2 . 5000' .50'0.0 .5000 ·.. liooo .0000 .0004 • 3 .5000 .. SOtO .5000 .0000 .0000 .000
",..........~ ............. ,
reactions aUB appuis••••••••••••••••••••••••n eeud rB ry ri KB My Mz
.' .'.l , -.500 0.000 . 000 .000' .000 .0003 -.500 .000 .000 .000 .000 :000
.\
r.,11
,
. (1)
...~ .CÂS ,DE CHARGEMENT NO 2
•••••••••••••••••••••••••··chargeslat~rale~ ••
"73
1
f·
i'1
1
.1
, 1
" ..' ;.,.... ,
nombre d elements charges
• , ' .. l .,11.-_ ••.•"
'~I el em. cote bal ba2 byl by2.: 2 1 ·1 .0 eue 1 .00-60 .1.0000 1.0000:i
*********.~*****.t. .,Deptacements
.1 ****t*******.**~
noeud da Idy dl tota.a • rota.y rota.11
~~1 0.09 00 0.0000. .0000 .0000 .0'000 .0000
:~ 2 10.0.000 0.0000 .0000 .0800 .0g·00 . '0000.~: 3 0 ..0000· .. 3.~OtO .0000 .0000 .0.000 .'0000
4 '0.0000.. 3.00.00 ·.0000 .0000 .0000 .0000
$ !.~OOO 1.5 Dt 0 .0000 .0000 .0000 .0000
. •*************************elements de redud'ion
********f****************
•elem. noeuds Na Ny Nay Ma My Mayl' 1 .5000 .5000 -.5000 .0000 .0000 .000lt
~. î 2· .5000 .5900 -.5000 .0000 .0000 .00001
3 .5000 -.5000 .0000 '.000'01 .5000 .00002 .. 1 .5000 .5000 . 5 O~aO .0000 .OOQO .00002 2 .5000 '. SOOO .5000 . .0000 .0000 ,DODO2 .~ '.•000 .5000 .50(10 .0000 .0000 .GOOO~ 1 ."5000 .5000 - .. 5000 ·,0000 .0000 . DO'lrO
·3 2 , .5000 .5000 -.5.000 .0000 .0000 .0000. 3 .- ··r· .sooi! .5000 -.5000 .0000 .0000 .00004 .'5000 .5000 .5000 .00017 ;'0000 .0000
•• ·21 ..
. li0(f0 .5000 .5000 . ' .0000 .0000 .00004 ; :"3"·· .5000 .5000 . 5~00 .0000 .0000 • .0000
'.; •• ~ ,
,*****.****~*****.******. ....reaction!; ap~uis •. :". aua
.... a
******~*****************
noeud '; "r a ty rz th iMy Mz
1 .... 500 0.000 .000 .. 000 . .ood" .000 ..3 -.SOO .000 .000 .. 0ft 0 .ooe ...
.000". " . 1 ••
i1,
*****~********.*********** .. ..•
.**charges raterale.'~*
******************.'.*.' .
.', .' .'
.'.
CAS DE CHARGEMENT NO 3*********************i***
nombre'd 'lements ch~rges
'.
1
".
7~
' ..~.
~ .•.;
. ...
.' .l
.. .'
• •
..•
•
.~. ~;
,j
elem. cote bBl bB2 byt by2
2 1 3.0000 .0000 3.0000 .0000
****************Deplacements
****************
noeud dB dy dz rota.B rota.y rota.z1 0.0000 0.0000 .0000 .0000 .0000 .00002 23.7750 -8.7750 .0000 .0000 .0000 .00003 0.0000 4.5000 .0000 .0000 .0000 .00004 6.2250 -4.2750 .0000 ': .0000 .0000 .00005 7.5000 -.0250 .0000 , .0000 .0000 .0000
....************************~
elements de reduct ion ' ~:
*.**********************~:..elem. noeuds NB Ny NBY MB My MIY
1 1 1.0750 1.0750 ;-1.2500 .0000 .0000 .0000.. 1 2 1.0750 1.0750 -1.2500 ,DODO .0000 .0000
1 3 1.0750 1.0750 -1.2500 .0000 .0000 .00002 1 .5750 .9250 .7500 .0000 .0000 .00002 2 .5750 .9250 .7500 .0000 .0000 .0000
'2 3 .5750 .9250 .7500 .0000 .0000 .00003 1 .4250 .4250 -.2500 .0000 .0000 .00003 2 .4250 .4250 -.2500 .0000 .0000 .00003 3 .4250 .4250 -.2500 .0000 .0000 .00004 1 .9250 .5750 .7500, .0000 .0000 .0000
v4 2 .9250 .~750 .7500 .0000 .0000 .00004 3
ê ,
.9250 .5750 .7500 .0000 .0000 .0000
************************reactions aUB appuis
*********************a**
noeud rB ry rz MB My Mz
1 -1.000 0.000 .000 .000 .000 .0003 -.500 .000 .000 .000 .000 .000
******.*******************CAS DE CHARCEMENT NO 4
*************************
**charges laterales **'******a***************
nombre d elements charges
,elem.
tcote
1blll
.0000bB2
3.0000byt
.0000
75
by23:0000
. 1
• : r., ".... .," .. -:" " . ' "
****************Deplacements
****************
noeud dB dy ds rota,a ' rota.y rota.s1 0.0000 0.0000 ,DODO .0000 .0000 .0000
2 -17.5500 61.1000 .0000 ,DODO .0000 .0000
3 0.0000 1'.5500 .0000 ,DODO .0·000 .0000
4 17.5500 4S.5500 .0000 .0000 .0000 .0000
5 4.2250 26.3250 .0000, ,DODO .0000 .0000
, **.**.****~.*************elelllents da reduction
.~***i*****l*************
, ;el em. noeuds • Nlt Ny, NBY Ma M~ MIlY1 1 .7000 -2,QOI1O 1.0000 .OOQO . 0000 .00·00 .1 2 .7000 -2,0000 1.0090 .0000 .0000 ' . 00001 3 .7000 -2,0000 1.0000 .0000 .0000 .OOÔO2 1 0.0000 1,3000 -1.0000 .OOU .0000 .OQOO2 2 ' 0.0000 1.3000 -l,DODO .0000 .0000 .0000
" 2 ~' 0.0000 1.3000 -1.0000 .0000 .0000 .00003 1 1.3GOO 0.0000 -1.0000 ,DODO ,DODO ,0000
, 3 2 1.300,0' D,DODO -1.0000 ,00,00 .0000 ,0000! 3 3 1.3000 0.0000 -1.0000 ,0000 .0000 ,DODO
i 4 1 -2.0000 .7000 1.0000 .0000 .0000 ,DODO4 ,2 -2.0000 .7000 1.0000 .0000 .0000 .OODO
• 4 '3 -2.0000 ,7000 '1.0000 .0000 .00:00 .00000
•j************************
°t rea,'ctions, aUB ~'puU
I****i**~~******l********l '.noeud '" rR',' ry
;~..·..·.000
.000
MI
. . ."
" ..,, .
.000.000 '
My
.000
100::;
1
, Ma
, ,." '.
1l'
•• .,
,. ·• ~1• • .
~ ,-·î"
l,! .
• ..,..
""
" :
'.0'
76
.000·.pOG . .•. . . .
rz,
•
\."1"
-1.500.000
t"·· .
, , .
, 1.000-1 .000
,.
..."
• 1
• 3,."
• . '
•,..... ~
"t••,1A'1
t 1 "
J•t,,:.
~
"
Lo. /'rII'/ /'0~ ,~' ~rtth:3t:~.s~'" ~_':' d On clwf. /CU'r, (,Inmo.i/la9~ n 'eJ 1- fJO-J, ~\h'd,,.,.J~J' a'aru " l'r~Wl''er ~ ~
~LI~ '-'frt!JnJ d» -l''aJ~jr.,,. I~ .VVtelU'//OJ-t N~.J 1//--41'). tÛ>nN'.
Fn, !#.tk1 on a (ra/l,' Ji €.ad d~np ~ !a9.AJA. eo ,.,.,!t-Iravo..iJ(Qn f ....v n f&1(~ ~f), ,~t.c ~ c.RGlhc:9.c4 ~.e"P en d"ft.-,.,
kv~u, ~' .JOrt ' ~ 10 ,,'.., c.D~'~' L, Yn./) n-l~ Jo r';Vr-f 19;)a
r0~f.f')fJ. ',Jo'. frcu'/t', u .~hu, C4Â aNfc..,AJn L4~flJ.
f~J:J. ,CA"r~; ·on ,J'. ~tU·JciDnL. d #c.J.P~~rt
rnOJ'I/oj ll ~ et ,ik ~'r' 'c.D,"'m.l~). la ~kpc.l--urt ~~,
l'oJ1~,,: "":' .,/0"_ ~, iap#u' ~,,Â.I.tN/I-e;)J ~ d'y'.)(/~n.s dv Î>1>1'~ J-J. AI' 13, C " .hw·Jdft" ~ 1 P n UJAdl-cr..f.t..
1-»- t ~~, .~Ju e/J/~n " ,rb ."-D,J ./ù~/}Qh·,!~'( 'av-tc. b hlt!U'/IQ9~
'l~ -fy~. ' ,J k '1i/n;f'i.J ; J!a/~ .. " ' /.p l).9'it, IJH 0'; ~~"j.J -en,'.
~~~JJ:','i ". ,
lJiJu,o· 'ticl1M " RjJc::f~' rb.j ~ Jil ' ,,~</i~~ ,1Y~'k/~~ J
• .. ... J .. ~ , ".
p~J ~-t (c.::f?~'() • ik ' ~~h,.n,h . :.:fZ.'(anClJ, PU!j kpl.l..l
( Irt~n"b .JJ-/JtI\/e )'j tl!J~ ,., avoM.jQ':.It:?,j.~J pu ,orfp~,."," . ." ';. .
~ fJf';' ~ m~/I~ -a( ~#cJ-~~r" aln'~'d ô~~Il1,. Ja ,btu
f,'on }(J pk j)~GI~, ~jJ,a..,~16.. .' . ~_.
i' t'~ Ira .u·· 'la ,f.!)U~~. r!~.!.' tJ4/1IG ,L/~M ;~~, rA/dX/eM4
~~ Jn'"h . AI' B il :,C, .~:nr'" J-/:'O r,,; iu. ,m ~l/I~~ 1 9 r»
(!:,,'W fci ( f( ~ t. '.' ' . , , ..
. .<~ /~J clf&K/~OM /~~fjr~~~~ rk ./6~p~J
.1k"u J,( tri /~~tfP'.J );' ,?n p&J.;'J-ra//- I9"nl-tÂ.~ ~ -IaIJ .tU J..:'
h:>rtr'ei/ &;JV7. .s. ..e...~b" J~ .'.~" J. . d.o nA ~., Ct'M ~~/'tu
" --:. .~'. ch,l& )(1'I)M·,~n.,j. ~~hl·i,;,.tPtAl' ~dJA .IJ,'ltItvIl~
~Wlt1 ') .f.~6,~nl:j .~- ÂJ?t(k, (MtUIIQ}A s. 32. ~1J/'I\J,.ti)
71••
, " . "': 1;in 1(:: 0,2 jn
E =j.,(104~/.in 1. Y =0."3 ~o/~"'&.
, .
""
, 1
•
•
..
l ", , •
/J'
, .... l ':t' •
,Zt..----*---~-~'-''"",,'15
",,~ iii
•
' .. '.
, '
,,\b)
(a)
.,' ,.'
~ ..
• .•••• t • J
"
:', 1~~', .. .
, ,
.. ,
. '
•
..:
..
.1 •• ' • t .
• ~" '~ ...! . • ,-.,',', J' ,", ,', '~ ~ . , 'r' . ~' , , •" )t' ~t1.,;I!~'(I,f. ,Vt'~ -it ',-. " ";";///0Sk" ~ ':.. ,;.. :', ':'
, ' " , , ..A ' 2. ' , ' ,,' ••,." ' /' "li' ' ( 14 !."A .' '4 ~ , ~, 1 I·;~.•, " ~ ,
A rf (-."'--,,'7~,"",r--1'~";-;-..!....1j-L-~-,> J , • J.
,..';
f
8 ,
~, l'n~/~~ ,n! .3 . t: ~
" '
. ' ..
.. ', ~
. '
, ,~, ',"
..
" ., "
. ,.:". ""
.". . . .' .... "' ',' r,· .': ..;..',....
,Sj I.~:' .(pLf'~'cF-'~ ~.t'1,(, ?fÂ~'~,~::~fi cl ~f ~~f~1,~,.tJ;
".' ...~ ':~'i.~~~ JI ; (Id; ."rb~N:~ 'Ina! flop. :'/iJi/;Jo'· .
"" 78
.i .
/1. pn m/u ,."ev"!I~.s~ 9' ~Jr.U rbr»1U. rûA dJj& X/OM
j.luJ .p!IJ U~(l~R CA /IJJ dAIS th (I..i//tI~ dJ J ~16 Îh.#ttl-.J/ -Jou J..c~'I)
on iw,'ffl" ~ l« p/IAU;"'f)n eure-: ..A.J" Wlcv'I/~tf' c:i.A /' IfI~.1
&J. ~.f,!F p,,.h. ru n=lM' ~rNlI~rJJ-,A:U rb'Y0b4
flQ/f)J)"g..'~.?· Jrb,' ?ag>n. c.ftuh ~ JVI'~ GI :p 1 ~ ;a r 0 -
gr,:: -.,."'~ J • .; tiaN1- .4-1. r",,/,P' Lv~ . / 'du.,~,,;t k /<7".1""
la.I~ da M'~'" .kA CCM t:p. C-Jfan.~.fWll"J /1? el j,~ cM
CPrfP'trU} ~ ~: ~i-- d,(y ...~ J~ t!D"V'-lh~1? U dl/.J ÀD
..eu hOf\1 . ~. 'ut p~ (.Dit u ~"t.;, f'n..O'lb;'~'U./
A!~cM ('ri ~olW fJCl/J -eo b -l'(lnfVJ rh (f)'n ;";ar ~(J)n'lJ'Y>/! ! Jt~J, ", rIM (2..u -1J.(A lIr:W~ ~ / mai" ))inpÀl Gli,: 1) ,.,
il • 1
<J, ,cu ~/f~.h ai.vJta/r ~~ ,#.PWlf1a H.t ' ,,;/ul- *" L, , , . .', l '
~ .fa.,'</-t:A /(â d.J. ./)A ~,., ~1i.r ./2.ri co~ ÂW'" -8 ~1"0t!JrtSm'
<>: Ja~'!JàH-r Â'lA!"l'. u :;D/~'>},-t./Y)tPl/()gf «n ;«:~'1 ~ cbnVJI rlu. JU-hAfla~ tlA/.I. ~ l.l>/~ ,. cl ~~'tv~ (f/oh", O"'fU~f.,)
.._ --' t:Jltu,.., .r/.fJ fiJ,I8~/·.,"'II\ o YrfJW(J
_ JolvJ.,·o"'J ~ R~a c.i-f.' .
"
. .'.: ,
'.
"
Q .•
, A.:-'-- -' II - - - - '- -- ." '1 :0;'
" :, , ..
.~
"st ~
.4 8 .,
·~C 24> ~ a If.,u Ho d11 'd:t'ft'l;~fV3.
79
..
..
.. . ;
•
••
.'.
.;..
•
••
•
.C\
•.
•
...'.
.,..' ,
•R E'F'E~ R·E)'~ ~ E.~.. .
' .
:
..•<,:j
..•. .
•
· .~ .
•
. ,
.-
d .. '
". '..'
.'"
•. f·
•
•
•
".~,. \
,..'
•
• • Il
li.
•
"
•
•,
•
• •
..
"
.•
o"
... 1
'. .. 0;
l' . .'
.'~.. ;. :
(r~lf;!'i?lf;;I!Ft· .>.: );li.:.j.~:~{~~~~;,: j
1;"l" l'
r' ~!' it .
APPENDlcé
. .1'
. " .
'·It
A.~ [NERGlf D['DffotnA7/0N PIlOJ:)fJ'TE fA~ LA FLExION
D '~!:'é PlA (j. UE .1 .1
A-,A. Â ( j: LC!lo;orl ,1n';",~ 6!' ::• '.: " ~ • • 1 ; • • . '. ~ .. : ' • . •.: . f~r~~ :.u·ru /)/a.~·:, MI- l!Jck'(:~ rk WlDIN~Js
16~·YJ~~JJ'1 n~ .. u-':! ~~r~~j.,.tA,,;.cbj~·~4· (fj.tP)JDI\
&;/eu~ .: ' l'Qn,';9/1l. 'cP r/'r"1:t:J/a/'o", accutrt~/Jl~ ~4m~'"
~;, ~~,"J..' ~ Ie.:t 1~ f el /W· "~nt~~' ~ \IQ !');v~ '10 ./ln rI.;~,IN'ha,,!- !A.·lr~;".I.· .yrd--~.l' ·~.~·.kt hU)fI1~"IJ ~ rf! ~I- ~ ~
\ avl- J~ '/, J,.,., "Ir:, p.ln â4f? 1- la r6 lC/D ;' rit.· le; ,,-D Itlf-""t. ,
h,,)~ l-tA U21~j JuJli,.;· ~/Q"J" b "';""l/tSI/ / #' c.J-û4' •
(JO"~. ~#..;".~ ~1t ~ 'D6.)/~n) V'. p~"a;'; la /IV,'h,' ,du
/"" dw~J. ": ....~~~"/. .~I-.'!.it 1~"c94 ..~. ~,.). JYt f,f ~1t .
1,t,J' CP PJ Cf)"e'JfJD" rfp,.,J..J" rJ,' / ~!t'fI/\I"J. a~ IIJ)(/'.)" ~~ (f)".N,
- .~ 'vv .' JurAef'n.J.<· o/!Aro)c/mcl-/t/'I~,. J. ; {~ C1JU"bH rit./4~)t 1.. l ' . • '.
1>Ia.~: do.'m·· lA l'/an.: dbJ "l1J ~: / ~nJ'&., CDr''''J~ da,,).:.'
aw t'fvJtr'fl "jJ!J.r,r/u . ~'J. ~ (:"~~) d'hi.~r b.J;cWaJ'!f(hch.. ".' . C? ~~,.1..·· . 1Y-pd1 ai /W)1'Yt./J"j. > eJ 1-. . .~ ..
,. Tf d2! -. ~ 1t ~ 1)4rjy.
~ .. ,: .
...... ... \'. 1 1 Il II .,~~.., aN\fiHo. j~1U' .A.~Q lOr". ~."Q/~JP"'''. a. ,7rewtV" ~~
.~1. I.:~ ~ ~f'M"J.J. '}(h.!~··. . \&it 1t'e:WOA'/ /-D id;. R~<J/ o:~/~ru"!J/~··p;H"I,~/6. .J., I~/,~,,~
U~.· d V ': -1. (1))t d ?~ .... nI! cl L.) d)1 JI.! . (C2~. ~"ll:l )
. 2.. '?~ t cI".<;Y'Z.,' tf;' , 1 •
'.
Q/t 1~r4ll~'" :1 .(J"tt~ .Ue'~1 VD ri. IlV '.
. , . .;oj•
Cil ..l'·
.'1.' .1~()J"a.ro (c) riP~1I.l Oo )' .o r ' : Cft c4u.)
, , '" U.: i i jll ~'fJfrlb .d.t u,'
"
. ,,'
, .,
pDurtW~n)- ~ .u;ie.u.~ ~, 0o".~.Ic:,IQ1~,~.d~ /l~:;O{"' '.;11;,,/10 CA, k,'. MOhlI~j.J ,j)o/" l~, .Jly~DM ("'. 34-4~
/. 'Vv~'~'f' .clRlorma I-/on .)J. r-a ~~':~(/,PaJ:> . ,
, i. ~ , ': .du=. J)f{ lli )'~ (;)'~) 2"1" eV ~ t," ~,] d..'rr J,~', , .' ',". 1. LJ. ~~ 1. ,,~/f t: , . ~)t 1.. ~ Z ' . C? .
. '.. . .
).~'r~': -/a)-tS/~f -, ;4 'othi"rtra,Lf' -,'n1~r.t7n Jo œ.lp .A.lc;~I\.CA~o~
.'
,'J:A-.~FLI(}tif11"l dpl1.J.l'..Ia~.~~ I~c.ho,n ,d;.fV~l~r<
1;'l.e~~ k , ... .
,.s.,' ~~ Njjt3~",' cI4,.,J .. :..AJ r1 • Jel ea-4 . J~hc';!/t r;k' rlyo,~Ç; ......
~On .. :.ck~ .. a-u)(.~g/lh t.~" c~,.11 .~'. U !;y ~ ~" 1~'u0 .. 'î": .' j ~hL~~'~: cb.; 'o/t:Jr,!,(3h~,,'· ~ ./~'6~ttj. ".p~ ~!J((J/.( '~ ,
-I"tÙ/~Y: :,f;/f,!~11 ,,~,r J.t~hv~) ~'.: lM . lwJm.t,"~J, -/6.,,~j .,Jd"h 1)~ ~":ri! .!j.°c/À .'~ ~~ -';e'~~, thD~pjJ rb ftJA.h'.on t>,.jfA- ':J~ rI~ /': ~tn1hA.·q0' 'Uj 19 (!~ ) W·,·J- ~. #M!J .kQI"t'
J,,,n)J t/fl1f./e.~~",kV'" /a.'c3vr ~':'f.. rit. le:; ~r ce. ~~'., .,' ',', .' .,,' .' . ' .
t'Fel !~''n)~j//e'' cb ·~:'r{ila'r~.~}/o~ "Ck.t. av~ ~nv"~J/4· ..'cJuJJ(}")J' ,krti,yeprtù,.,/el. "~. l~':P~i!':on • r..J\JJj1'c/,,. ../1
./n.k?,~ pO!lAu. ,UL1 · rit: I~ '/&~)'an i-;'mr> ~" ' , ", ..' . ... "
.,' f;.vr~)C.r>"/Nler'··~RIu';f/~ .. cb., c!0r'''''Q~O/),~; .~~~;'j.J ".: fi<:VO;"h~~/7.t;y~), ôn /lP~a,r~,,.a ,9pA: );;ry {t
rk,'.f !)~rh(;~ 'eorrlJpD n~nl- ~j (~EvIcl)o~) ri}L,,' uJ,4 ~·ru'7"va j .<b" c. ' ...,:. '; . ' ' ~ .
~, " -, ~n~~)<~i~.&= {MÂ:.;)~)l" .. ,, ~
• , 4, .
}(A mi'i.-w 'rq,,!/.-k' d~~~/( A-ertl l''''D~'A pot' k (.pv~
'/!In. rJ~ 1. r6 ~u/t /, 9~ / ~N:? ( dM..t a.u" ~vp~ fb -/(J)'t}.'rJ,..
eYJ..
,~; e)
I::'U/JF }r; -/DM,.·q" .' h '# c/-, pal ~ Ira~tV'/'p~rk,,~ ~M
~ /"rvJ'Vi" h /&~·J-Io.jt~i.l 1L.1U';1' ~ jDhrl.( dt c/Y(;)~""'tI j,;'n
rilu,. .e,6 Mt" f ~,Iiid~ ~ 't,')./u-) 4" a c!.ri" 'I,~ " "tI,. ;. )~fUIt1"( clJ. JIu" (m.. u'" œl&. "rb. IO"d7~n.· .
dv= ~ J)r~).~~): lY~~l cl~tt~ T• ,l..' (t~~.~.. \. ~t. . c~l't L W~ èJ
" .: -r.~ b(À_~)('è~)tâ~~:.. \~~.' .
"
on (J)Nf-O ~ r~ 1~~q J./rJ " (c)~;'.4 ~~.:.u !J:'w4 -?,./Mrn~ h,./ 'CIbI(, pDh .:0 "". ""
. ". .. du -: 4.{ f.l [b7 lei ~fJ" ' ..
• . ~J. . u.= J~o1dtLJ)] ft! '~1t .{.~.c1). ,. •• t . , . .•••..•• . r • _ •• • • : o. •
~: -r-": MJ." <:Ar,ldhpw ." ~ >/'ifP. r::"h~" (6) ~J~'"~,. j. Fie.. lIA/"1''''''' t,a" Jf'''' r... /ij,'" 'sm; . ~ , bw>"-t .
.(~.::
. '" .
-,
... . ~:. 2 JNTEG.R.AL.!,j DE, :Bv/l..FACé Fï LI/lIE/t1IlE5
! .' .
• '. ,,' ' .. . . .
A~ 2: .AIn/~ord!L" rh .4v~CA·. . . '. . .. ' .
. .' .~"/ .;J "og /1. d .,'D 'vo IvL.~ ~ ,..;e )c'p.AW- '4,. dt". ...'n-,<'tf) ;t?~ :CL c!P-"~ ..#, '. '. . .
., , ' . ](lt'\y"! .,JJ~".cr" d» '!Y (..,.'0.)0" . ~,h' /,~: œ". CP ~/I"rb"'N tA 11"/0,:#1/ !t:V~ ,.;. f e-J,1 ~
,. . ~ = ):.[.-A:....~ J·it l'· . ':' ".
- ..... ~ =. 
<... "J' . , ., \\.". :.":.;'
1· ' •l '
'. '.
. .. ',1
-,'. '.
"
~/PJQ"? T6n 'bl'-=:{ r.A-?J"k-7Z);'3T~J~fJ'l r~. d)
Of1tJ J:l r~"'l) -: :~:~:'lt ; J (l\-,,,) ... ,
', ~
.,
. ,
, .-'
. , .
.' . ".' . .'
.' ~
-, . ,.• '., '. .'.,.' " • ~ 1·
~ r '-"JtfhnvJ,J" q rr e:t,' "'"h.A fi·.1 ...c;", ln 'fh ;,"l.', J. , , __.rvf,. . . . .'.' . . ..... 1"
'S (0 j f) ~: ' d'fl .", e , Ir (. 0 J .~ _.-1 ) : • ,'. . . iIo...:--I .- '"'1 '1 . . .•. , " .•. •
, .• f~ ...• ~ •.. ~ .••
CP~ '.i7'1 :. • J
. ..
'.:,.. ~.'
' ...
' ... ,
..." .
, :. ','
. .
. '.1 .' •. :. : .
",' .. '...
. .: ....• • o'. "•• •~... ',; .. ,. . "
'....
•
•
." ..,• •
....
.'
. ' .., .
. i .
.' .
. ' ," .
" ..
.~ ." :.' .:
•
~ ,-.
...'. , ...
;'; ····f···: .', ~·..Jto-r €" 'rv- .. : l' ',: ': '.
"" .., 1
•..
.. .
. . .
..
"
•j"
.. ' .
:as",·' ,: '.:O. ",.:.". " .
"i • ' .. ,'
' .....• .
. ,~. . '.'
'.
-", ." '
j ~i'
, 1.. ': ,0
.~.
L~li
on a .,: ~ /()~1 .:
"!"f~'L ·lt"t~l:J jI ~J:(~ ~ ~l \).f- =l " '1.,', '4! e'.
p3,!}.;o, .Jt~iiL.=n 4..1~4)~ =-t:-' .
" LI;'.~' '1
onp,-~nd lbJu$/N. dJ~,p"",,J- C (fj.4-Z),~,," "'''SD/r,:~ t ia'6J4IP tk l't.JifWd..J
's ~'J. ·Sz. ;(~ b~~ ;tIu/,~'f) ~.'''~1~ 6.Ju'n.r rit c U-/-.Fe z 0 '
. 1'· . ,~"a }, l' tt '::' 0 ,Jt.' C KI- Lt '"""''tu du ~~tlJ. lA· 2.]
'. . ..JI>.' J.L !fJo, fp"",9f.1lvro ' tk ~gii"f) J. i a /~~ S2 - !, = L
!' , ';'l ' ~.,
. ! .< ~. " ,:..~ .
. ':1..; •
c•~~'.';;o':~ \
,,,..t:J ~I/~r/~,
'-.. '. .." .
: '
. ,
: .
, , 1
'7.~
..' ..'. \~ .;
'-!
~:,
,~' .' ", '." -:1 .... .. ". .(s\ '~.A'" ~.A 1, ~,
,~I ~21 • .r ·~zi ~ZJ
l' À~ ~~)' ~i)
, \'
, 1
$:>i ~ ~ ~3: .,urt ~ 1,1'lV. J ~kU ri/f. jp Coo/
I>;J.)r YI-' ·pn fA,v -/~ 1f<J/~~' cl ::')Q>J rJ/;' f}/D/,e; /
p; 1- L), 7, )() ft? t$ 1lU u. ',rLM. (.D Jo,ï\.CM it).."c). tw,oS duc:l )ç.e-I b (Ar,1l
, PAY'/l(Jt>poJlI- '@JI: 'O)((,) fJ/&>iQp~
Àlt:~ ,Xl(g , i,~~, ~.-q '.~Ai~)j;Y:)./J~ -;: }2) .i.!2. ,,)z.~
).~ ''1 ,).$ i ,?~ .).~1. ,~~3
."J "
,.
•
'. .~~x. ~ ÀAA ut -f,. f!Jh'fWI cbÂfthvr âJ. J~,," ~I~),?~~j. a'l " " ' '.,
? (J 'U, x)· ,' "'" . • ' . 1
'e'fIP'" J~ fjyJu 3.r"//"'/{Y"K -"3,' ~ .Jy:/~;';;' rlo~.!p cal~ ', -k-!tfAM'~ , '.PH' 'fÎ1-j~ du l'''~n~ ~ , .e-Uhv"/~;U
~I- p~~/h'Û ~\./~){~ JlI ," . 5'~"I-\'(t,;1f'/'~;) 4) (PP/tf'''l~.t.J .rfoM' ~ .1fI'/tAv~!iJ'-/.tI~". '.. " ," . , ".'~'''J. /,-0),., ,-!!J 'C;~,,"l' J/ 'J~ r: rb" \ . r6?,N' pect' 6 ~~r~!
.e;' rr. J/"n ",~. tJ)O/) rfp"~J e:Y-6~;~ .'~g,."h rJ/ -c J. j1.' J:'~ .'-,• 1.
, .: .' ,x.~ _x~ X~I
"~ t ~ 'Yi,-Y, 0:: Yz. ;'.,2'2'-r l ' ,12,';
J",f1pr~o" lo';1PM si" -42. "jXz.;' .. Y2< '.. 22<L'
, , 1
4 CPn'tWi d;Â;JJw~J,rLtJ.()~~ j' /•. /<J.P" ~ dP~ ~j ~4" )f14 e#-'/~ '.
Jp"/I't-i, rk, ~c)-~r pru'Jài~ Yf~~ , .. ~
, ,.' '; . ,! •Ali ',x .. '.À 2; , .'d' • ' '.
11/1 ':: À/J'Y -:: )2l" '~ ~ . ".~i\ , , -t~ · .".rtl/ l " J 2s ') <.
'~
81
\ l' ,
, .1
,<t., •
l) .J.
..
"
..
'p;J~ ~J....-'-''' ~creu~ ,~a/" 6 ,aN C-D I!-' J;"J;,()/p-w' .. ' VJ ,'=' '~3 X \~u: ;1ÂJ. ,,,,u,. ~r.J.w,. M"Hf"1
rU <~ ~"": ," ~ ':'1 x~ )(~ - >C" '1
',F ,.'~ 2 :;.' Y", ~ YS:7 Y", t!J leM '~ (J ,
~ .' .. ' , '.... 2.,' ." ,l~ .- ~, " <
., .
)(~ ',Yl1 èl-t.. rt,. t,~ .' . .·"'s'Vs '=' .Y'A·: X ~2r' -. ,~I!~>C~·.~~x~ :: ~~
b.. ." 't-. ,... , . i '~. "
. ;~ ..' ... ~. ',')(\1 !LI :-.~. Y';. ~s',. .. . .
• • • ft"
" ....
"... ,. ':J.~ ".. t . , .,. •. ;. . • •• . 0 •• •
",' .:. ~~f.i,~ ,.(.iJ CJJ,~'~J (b~~'O ri /~~ 'lt,;' ~ :..{~ï~~j rL:;V'v~.
, rft!''&. '~":"'" cpi>/1 rb-~,~.~~ <~ ·w~J.&,t: ·.~~~·ht.J.~;»~~~/~~, »rÔ, • '. • •• • • • ,
~' .·~'k'~·t~~~/~.·.N:h\JJ~. ~.~ .~J- lIf ;" ~ ·~Jp.n L', v'
.: "c .' • ••.• . • .' ", <:~ ~~~ , ~Z1 )~
:. U:: •• 1i"~ ,X'~',,:, ~~y' -.A . '~' ,\ ." ~ u.!', " .:.\ )1 . ..,. ; fi" 1 ., - • ,- Il..-' Ir. ," ,jl ,~,-.;..
. '. , '' ,.,' .~.."~i .', ~" '. 1 J" \, . .,0' 1.. :- '.' '. . , • /4$ • t1'ts 1",5)'· ','
~: '.. )tl.À~~ '~~~i~'i~ , ~,.". · .
~ IJ~.·~··::';- ~1~À~' '- rl3'~:À~,' '. • ~ ••. .:. ~t1 ~3t - ~~;.~i·~' '.~'" ..;
... !j ••• '. . ••.
"
~J. ~ 'pi'~~ .11' :j;, ~(J,,:rbf»:~J' (x, Yi ~ ?t!:. ~?I·~V·:3") ~4 '.. }U~ 1 (.an 1ù,',~ l '. (() , 1, -S ,F)" ~t .(0;;;/j/I ') ,~~#l.1.~~,.;:
88
:. .•
'.' ....
--"f1ri 1 ...:..\.N. -
•
"..., • III
, ~. ~ .
',...'
~ . '...
.,1 ~ •••
. .
..
..dt
1 .~.& )A'f
.~., ~li •AH,_.
,- . :t' ''\ili' 5'1..
.~ "• -e .
. .:.
.,
"
" .
.'..'.
" .'
'.
#
• 0
•, .
• 1 ..
"
, .., '
. ". .~.
, "
.•
•
,....
.. . '... .. '.. .....
.. "
.' "...~
•
• •
•
"
.'.
.'
, '..'
'< •· '
·,"
·,
"
.."".
.' "
" .. ...
... ..~,, :
.'~..'
•
..'
. .
•
. q
•
,.. «
, .•
, .
••......
•
. '
.. .... .
..
.,'
....~ .:
, .'
. ',.'
._ f'!.
o '.
.....
",
" '•
'or:'..'''..' . ~
•ï' ..
. ~'
,,; ... ......•. '.....
.... 'a
'.,II..
.~ .
"d'1 .....o,
•.. ....."
. ' -.' ,
-.~
. ,
. '
.' •...
'1
:.' .-'
~..
" .." .
.......~ ..~ {
'f
~.. ... '.
'.'
..,1
...'
•
•'..
..
6 Jun 15:44 1986 princip.fPage 1
CALCUL DE ~OaUES
(analyse
ECOLE PO~YTECHNIQUE DE THIE5DEPARTEMENT ~U GENIE CIVIL
Yve"s 'hàb~~ f r a n e i s KONATE:Mouham~dou Moustapha NDtAYE
FINI5PAR ELEMENT5elastique)
DE,' FIN D ETUDES
,,.. ' .
PRO.JET
iluteurdirecteur
li
lt'
lt'
lt
*.*.**.
***
cccc
ccccc
cc
cc
cc'Pou't e a e c u t a r ,creer un ficpier'de dorm e'e s d abordc • Si 1e f i ch i er des r e su l ta t s e Bis t e de j a 1 ç as sur e r. .c q'IJ i 1 es t' v ide ' ..
"ci mp l I-c Lt real*,B(~'-h"o-z"
character*6 stdon,stratdi me n Il. 0 n' r c f ( 9 , 9) , cc f ( 9. 9 ) , _ in t ( 5 , 5 ) , ccp ( & , '6 ) , r cp ( 6 , 6 ) ,
1 al ( 3 , 3 ) , ire; ( 50 , 7 ) " tx' ( 50 ) , t y'( 50 ) • t ~ ~ 5 0) , fi ( 3 , 50) l' i h ( 300) , ,2 ~ t ( 5 0 ) , t g ( 1Il ,-18 ) , gr,'1e ( 6 0 0 0 ) , ma tr 8 '( 6 0 0e). 1 • b c P ( 3 , 6 ) , e b cf, ( 3 19 ), dimension ·p52:(3,59)',vc(~O~0)~.flJ(18)'B(3150l,y(~:50), '
. " l' .a~ù t ( 18 , 18 ) 1 b a (2 .3 1 50 ), b y ( 2 1 3" 5 () t f i ( lI!) 1 lIY ( 3 ) 1
Z' , i ad ( 1 8 )~, z (~ , 50 ) ; r e a ct ( 6 ) l 'i1 ( 6 ), .'
c
500
'1 .
.50.5
c .c
c
print 500t o r e e t t t s , 'fichier de. tlonneesreadl ,stdon'f o r ma tta é )
print SOS'f o r a a t t t a , 'fich·ier.de: resu1tat'n!a.d 1,5 tr a topen(unit=5,fi1e=5tdo~}
,open(unit=6,fi1e=strat)tewind(5)
.r ew i n d t é )
DONNEE5 GE~ERALES
•
'1 ' , $ )
1 1 " $ )
• '.
.'
p t,i nt 100r e a d* 1 ne l,no d, nd 1 , em', pc, nn r , Qama 1 al fa, necp r in t :t OS, n e'l ln 0 d, n dl, em , p Co 1 ~nr , g'ama 1ai i a
nle=3*nd1nn e nd 1*nodn a e nn s I
,c
2
do' 2 i=1,nnrdO,2 ;=1,7ire5~i,jh:O
c
c c 0 0 r d Cln n e e 5 des n 0 e-u d 5p r i n t 110do 3 i=1,nod
90
6' Jun 15:44 1986 . princip.f Page 2'
3
r ead fl , le, t 11 (k) , t Y(Ir) , t z (Ir)
p r i n t 115,k,tx(k),ty<t),tz(k),.-
c·o
'14
restreintes au. noeudsprint 120do 14 i e I s nn rr e a d .• ,Ie,(iresO,j),j=l,ndl)1ires(i,7)=kprin t 125, le , <i r es ( i ,'j ) , j = 1 , tI d J) ....
.,.
. "
·· .•
••
... .
• 1; ,cslcul d~ 1 'adre~se des diagon~les..
,do 5 i=1;nnih(i)=O
cc ~onnectivjte de. elements
prlnt 130do 4 i=l,nel ~
t e a d 11 , le , t. ( le ) , ( j if j 1 k ) 1 j =1- , 3 )
ptint 135,k,(ji(j,k);'=1,3),t(lr)4c,c
e-Ô,
5c
do' 6 lr=l,nelcali ad r es (.j i , n dl" n k , i ad; fi el, le )mi e r a d Ll ) ~
c
•.. . , do 7 i=l,nleif (iad(i)·.lt.mi) mi e i a d t f )
·d 0 8 f =-1 , n ki ie i a d.t i)
ihid i.miih i b·.i h Ci L')
'if Cihl.gt:iltii) ih(ii)=ihtconf}nueco-'t i nu e%llaxa(l)=i..lBaBa( 2 )=2.do .. 9 i=2,nnmaB~(i+t)=maK~(i)+ih(i)+l
••Jtl.~=maBa(nn+l )-1print .20S,nnprimi 200,nwk
.'
.' ,
•
•
,
.. ., .. ,
•
• •
· .
•
DONNEES nss ELEI1F.ltrS :RIGtnlTE;ASSr.MBr.AG'~.'
" .
• i
,."
"
"... " .ri . " •
.,
~',
., .-: . j' i '1 .
-...i' ..
. "'.'
. .
•
..., ....'
e a l c u I: d.s Ln t e q r a l e s ~
cd} ,K'i n Ü·~ r (a in t 1 Bk 3 , y le 3 , Yk2'
do lOi = t , nwkgrk(i)=p.dO.
dot t ,« = l , n \ 1 •.h =.t ~ t ) ',~.., . . .. ; " .cali c C7\tr ,lt1o.c ( B, Y r 1'.. a 1 , Ir , t 11 , t Y , t z , j j , no d , ne 1 ) ".llk~=B(3,1e.· ,;yt3=y(3,1e)yk2=y(2.'1e)
"
. '.
6 Jun 15:44 1986 princip.f Page 3
c rigidite des elements et assemblage~all co~lag(rc~,6,em,pc,h,Rk3,ylc3,ykZ)
ca II co fie 9 ( r cf, 9 , em, pc , h , ai nt, Rk:3 , Yle 3 , Yle 2 )cali transfo(tg,al)cail rigel(amat,18,6,9,r~p,rcf;tg,alfa,em,h,Rk:3,yk2)
call'adres(ji,ndl,tllc;iad;nel,k)cali assemb(iad,nk,amit,grk,~wk,~a~a,nR,nn)
c11 continuecc 'introduction des restreintes
do 21 i::::l,nnrlc::::ires<i,7)do 21 j::::l,ndl
·ii.(jies(i,j).eq.l) thenlek~maxa(ndlt(k-l)+j)
grk(klc)::::grlc(lck)+1.d60
endif •21 continuec
ca'll tripld(grk,maR~,nn,nwk,nR'
a. DONNEES DES CHARGES,
do 12 ncck::::l,nccprint 165,ncckdo 13 i e l v n e Id'io 13i c == l , 3Jp\sz( i c • i ) =0 . dO
. • do l!'i i :::: 1 , 2bx(j~,ic,i)::::O.dO
13 by(ii,ic,i)::::O.dOdo 20 i::::l,nn
,20 vc(i)::::O.dOdo 50 i::::l,18fl(i)::::O,dO
50 fg(j)::::O.dOc
re.d* ,nnchif(n~ch,.eq.O)goto 23pr in t ,140print 145,nnchprint 160do 15 i=l,nnchr e a d 11 , k J (v c ( n· -,1 ) *n d 1 + j ) , j :::: 1 , ndl)
il 5 .p r in t 175 , le , ,( v c ( ( k-1 ) *n d 1 + j ) , j:::: 1 J n dl)c23
16c
lre a d s , ne 1cr sif ( ne Ic r s , e q . 0 )g 0 t 0 24print170print 180,nelcrsprint 185do 16.i=1,T)elcrsread*,k,·(psz(j,Ie),j=1,3)print 190,lc,(psz(j,k),j=1,3) ,1
calcul des ch3rges equivalentes aux noeuds
6 Jun 15:44 1996 princip.f Page 4
24 read*,nelcrcif(nelcrc.eq.O)goto 25print 195print 180,nelcrcprint Z10do 19 i=l,nelcrcread*,k,nccekdo 19 j=l,nccekread'll,ic,(bx(ii,ic,k) ,ii=l ,Z)read*,(by(ii,ic,k),ii=1,2) .
19 print Z35,k,ic,(bx(ii,ic,!t),ii=1,Z),(by(ii,ic,k),ii=1,Z)cccZ5 do 26 k=l,nel
calI coordloc(x,y,z,al,k,tx,ty,tz,ji,nod,nel)h=t<k)X3=1(3,k)y3=y(3,k)yZ=y(Z,k)calI xintegr(aint,x3,y3,yZ)cali trandem(ccp,a3,y3,yZ,6)calI trandef(ccf,x3,y3,yZ,9)calI tran~[o(tg,al)
dit 55 i=l,355 pv(i)=gama*al(i,3)c
c a l I cheqpla(fl,pv,aint,h,bx,by,ll,y,nel,k,ccp)c a l I cheflex(fl,pv,aint,h,pst,x,y,nel,k,ccf)
cdo.35 id, 18fg(i)=O.dOdo 35 j=l., 18
35 fg(i)=tg(j,i)'Ilfl(j)+fg(i)c e Ll adres(ji,ndl,nk,iad,nel,k)do 17 j=1,18
17 vc(iad(i»=vc(iad(j»+fg(j)c26 continuec
calcul des deplacements par resolution des equationscc
2Zccc
calI resolv(grk,vc,maxa,nn,nwk,na)pr i n t :150do Z2 i=l,nod .p r in t 155, i ,<vc (n dl 'Il ( i - i )+ j') , ; =1 , n dl)continue
c3lcul des contraintes
print Z30do 30 k=l,nelcalI coordIoc(x,y,z,al,k,ts,ty,tz,jj ,nod,nel)hd <k)
a3=a'<3,k)y1=yCZ,k)
•
•..
..~ ~ ."j :.).; ~. \',
6 Jun 15:~4 1986 princip,~ Page 5
.,;
1.
40/
45
7065
6030ccc
y3=y(3,k)calI trandem(ccp,x3,y3,y2,6)cali t r a n d e f t c c f ,x3,y3,yZ,9)calI transfo(tg,al)
, cal l' ad r es' ( ; i , n dl, n k , i ad, n'e l,y)'do 40 i e L, 18, 'fl(i)=O.dOdo 40 ;=1,1-.8f 1 ( i ) = f I~ ( i )'+tg(i , ; ) '/1 V c ri 'a d ( j , )
cali sigmap(ebcp,em,pc,ccp),do 45 i=1,3s(i)=O.dOdo 45 ;=1,6s( i )=s( i )+ebcp( i,; )1If 1 (; ) 1Ih
do 60 i=1,3, ,x i =x ( i , l' )
yt'=y(i,k)c a II sigma f ( e b cf, em, pc, h , xi, yi, cc f )do 65 ii=l,3s(ii+3)=0.dOdo 70 ;=1,95 ( i i +3 ) =5 ( i i +3 ) +e bcf ( i i , ; ) *f 1 ( ; +6 )continue,irint 235,t,i,(s(;),;~1,6)
"c'oJ:ltinue .'
continue
calcul d~s reactiods
print 240do 85 i=l,nnrk=ires(i,7)do '90 ; =1 , n dlreact (; )=0. dOif(ires(i,;) .eq:l) thenr e ac t ( ; ) =- v c ( ( k - 1 ) '/1 n d 1+ ; ) 11 1 . d 60endifcon ti nue , ,
p r in t 175 , k , Cr e ac t ( ; ) , ; = 1 , n dl)continuecontinuet o r aa t t 'format('
',tl0, 'D6nnees generales' l' 'tB,21(:'/I'» ,',tl0,'nombre d elements.:',t40,i5"l", , t 1 0 , , nom br e den 0 e u d s • .,:', ~ 40 , i 5 "'',tIO', 'nombre de degres deUber,tes',:' ,t40,i51
. -., . . ~. "
, , t 1 0 , 'mo d u 1e dei as t ici te. : ' , t 40 , f 12 . 1'1',tl0, 'coefficient de Poisson, :' ,t40,f12.41',tl0,'nombre 'de noeuds re'streirÙs'_:',t40,i51.'
, ' , t 1 0 , ' po i d s vol um i Il u e , :', t 4 0 , f 12 , 4 1, , t 1 0 , 'AI fa '.. :', t 4 0 ,f 1 a 6 1.)
format(II' ',tB,Z2('1I'l,/' ',tl0,'Oonnees d e sv nc e u d s " r ' ',t8,22(''/I')/j~ ·,t8. 'noeud' ,t17, 'coordx';t27, '~oo~dy' ,t3B.'coordz')format(' ',Sll,i5,3(x,fl0.3», ' ','
, format (III' "':,t8, 2S (','/l') 1 tl0,' restreintes aux noeuds,'/'tB,25(''/I')ltl0,'noeud',211',' dx',3x,' dy',4x,' dz ',lx,~rota.x' ,lx, 'rota.y· ,lx, 'rota.z')
90
851'2
,100105
12345'
67
110
115120
12
", 'l
6 Jun lS:44 1986 princip.f Page 6
•
.,.,b1l2' ,
Ns' , t 32,
bll1',t32,'
de reduction ''noeuds',t20,'My , , t B:3 , 1 Mxy --)
for ma t (' " t 7 , 7 ( 1 S , i 6 ) ) ,format<III' ',t8,29('*')/t10,'connectlvite des elements'(.'.
1 t8,29('*')II' ',t8,'elmt',t18,'noeud l',t28,'noeud 2',t38,'2 'noeud 3' ,t4B,'epaisseur')
for ma t (' " t 8 " i S , 3 ( SR, i 5 ) , t 4 8 , f 9 . 4 )format(/' ',t20,22( '*' ),' ',t22, 'charges aux noeuds' ,l't 20 , 2 2 (:' 1r ' ) 1 )
t e r aa t t r ' ',t8,'nombre de noeuds c h a r q e s s» ',iS/)'format(/' ',t20,16('*' )/' ',t22, 'Deplacements'I' ',t20,16('1r')1
l' ',tB, 'noeud' ,tlB, 'dx' ,t2B, 'dy' ,t3B,idz' ,t46, 'rota.x' ,tS6,'rota.y' ,t66, 'rota,z')forma t (' " t 8, i:3, t 12,6 (f 10,4) )for mat (' ',t B, 'n 0 e u d' , t 1 B, • f II ' , t 2 9 , ' f Y , , t 4 0 , , f z ' , t S 1', 'M x ' , t 6 2 ,, My , , t 73 , 'Mz ' )
format(IIII' ',t8,26('1I')/tlO,'CAS DE CHARr,r.t1F.Nr NO',t31,t31,i2/t9,2S('1r'»format(/' ',t20,24('.'),' ',t22, 'charges de ~urface ',1'
t20,24('*')/)format(' ',5ll,iS,60s,fl0.3»t o r ma t t ' ',t8,'nombre d elements c h a r q e s v i i â r )format(' ',tB, 'element' ,t'lB, 'pszl' ,t48, 'psz2' ,t68, 'psz3')format(' ',Sll,i7,'(10B,dl0.3» •format(/" ,t20,22( '*'),' • ,t2Z, 'cbarges lateralesl' ',t20,22('lI')f)
f o r n a t t r,' ',tB,'es.pace requis =',i/j)t o r ma t t r ' ',t8,'nombr~ d equations =',i4)format(' ',t7, 'elem.' ,t13,' cote' ,t20,'t ,4 4 , ',' b Yl ' , t 5 6 , , b Y'2 ' )forma t (' " SB, i 7 , 10 II , 4 ( 10 X , d 1 0 . 3) )f o'ima t (l' " t 2'0, '2 S ( , 11 ' ) 1 t 2 2, , el emen t sl' " t 20 , 2 S ( , 11 ' ) 1 l' " t 7 , , e 1em .• , t 1 3 ,
Ny , , t 44 , , Nx y , , t S8 " Mx', t 7 1 , 1
format(' ';6u,i4,ls,i6,6(fll.4»format(/' ',tB,24( '11' )/' ',tl0, 'reactions aun ap~uis 'l'
tB,24('*')II' ',tB, 'noeud' ,t20, 'rll' ,t30, 'ry' ,t40, 'rz' ,t48,Mll',tS7,' My',t69,' Mz'/),
1
2
12
i'2
12S130
165
14 S
150
135
140
170
20020S210
1 S S
160
215230
17518018S190195
235, UO
ce l o s e t un i t e â j
.,cl o s e t un I t=6)stopend
"C
•."
95
5 Jun' 17:05 '1'86 coordloc.f Page 1
su b r 0 u tin e '. co 0 rd 10 c (B , Yi Z', ~ 1 , k , t.a , t Y , t z , ; i , no d, ne 1 )
ccc
ccccccc
'c
c
1
1'2
ccc
*******************,~**********.******************
* la sous-r~utine calcule: , *'. ! . .• ~
* les cosinus d i r e c t ë'ur s des axes .locaux :al*'. .
* les c o c r d on n ë ë s du systeme local'x,y,.z ** de element le .,conn~i5sant ** 'les coordonnees dans' le systeme -q l ob a L: tH,** ty,tz ** ;i: v e ct eu r connectivite. ** nod :nombre de noeuds **. riel :nombre d elements ~ ********************************~~~***~************implicit real*S(a-h,o-z.dimension x;(3),y;(3),z;(3)~tx(nod)ity(nod)itz(~od)
, ; i ( 3 ,ne! ) • x ( 3 , ne 1 ) ,y ( 3 ,'riel ~ , z ( 3 , ne 1 i, a l( 3., 3 ) .do 12 i=1,3
.. x;(i)=tB(;i(i,k», yj(i)=ty(;i<i,k»z;(i)=tz(;i(i,k»i21=x;(2)-x;(1)
'. . y 21 =y; ( t> -y; ( 1>z21=z;(2)-z;(1)d12=(x21**2.dO+y21**2.dO+z21**2.dO)**.5dOal (2,l)=x21/d12â 1 ( 2,1. ) =y 21 1d' 2al(2,3)::z21/d12&31=x; (3)-x; (1)y31=y;(3)-yj( 1)z31=zj (3)-z; (1)xVz=y31*z21-y21*z31yVz=z31*H21~z21*R31
zVz=x31*y21-x21*y31dVz=(xVz**2.dO+yVa**2.dO+zVz**2.dO)**.5dOa 1 ( 3 , 1 ) =x V z 1d V~~ .•
al(3,2)=yVz/dVza!(3,3.)::zVz/dYzal ( 1 , 1 ) =al ( 2 , 2) *al ( 3 , 3 ) - al ( 3 , 2 ) *al ( 2 , 3 )al(l,2)::al(2~3)*al(3/1)-al(3,3)*al(2,l)
al(l,3)=al(2,l)*al(3,2)-al(3,1)*al(2,2)
coordonnees locales
x(l,k)=O.dOy<1,k>=O.dOx(2,k)::x21*al(1,1)+y21*al(1,2)+z21*a!(l,3)x(3,k)=x31*al(1,1)+y31*al(l,2)+z31*aJ(1,3)y(2,k)=x21*al(2,1)+y1.1*al(2,2)+z21*al~Z,3)
y(3,k)=n31*al(2,l)+y31*al(2,2)+z31*a'!(2,3)z ( 2 , k ) =~ 21" al (3 , 1 ) +y21 *al ( 3 , 2) +,z:il *al ( 3 , 3 )
,;'t.( 3. k ) = 'B3 l'lia l- (3, 1 ) ~ y31 *a 1 (3, 2 ) +Z 3 1*a 1 ( 3~, 3>
returnend
..,;( .
5 Jun 17:09 19S6 cofleg.f Page 1
subroutine cofleg(rkalfa,n,em,pc,t,aint,R3,y3,yZ)cct
cccc
************************************************** la sous-routine calcule la matrice de rigite ** elementaire dans le syst. locAl pour la plaque** en flexion. ************************************************.*
implicit real*S(~-h,o-z)
d imens i on r ka 1 f a (9,9) , cc (9,9) •ai n t (5,5).t emp <'9.9)
c calcul de cc et de cinvcalI trandef(cc,K3,y3,yZ,n)
.f
•
e·
•
calcul de rkalfaconst=em*(t**3)/(1Z.dO*(1.dO-pc**Z»t!oZOi=1,n·do ZO j:::1,nrlralfa(i,j)=O.dOrkalfa(4,4):::4.dO*aint(1,1)rlralfa(4,6)=rkalfa(4,4)*pcrkalfa(4,7)=lZ.!O*aint(2,1)rkalfa(4,S)=t!.dO*aint(Z,1)*pcrkalfa(4.9)=12.dO~aint(1,Z)*pc
rlralfa(5,5)=2..dO*aint(1,1)*(1.dO-pc)rkalfa(5,S)=4.dO*aint(1,2.)*(1.dO-pc)rkalfa(6,6)=rkalfa(4,4)rkalfa(6,7)=rkalfa(4,7)*pcrlralfa(6,S)=4.dO*aint(Z,l)rkalfa(6,9)=12..dO*aint(1,2.)rkalfa<7,7)=36.dO*aint(3,l)rka1fa(7,S)=12..dO*aint(3,1)*pcrkalf~(7,9)=36.dO*aint(Z~Z)*pc
rk~lfa(S,S)=4.dO*aint(3,1)+S.dO*aint(l,3)*(1.dO-pc)
riralfa(S,9)=lZ.dO*aint(Z,Z)rkalfa(9,9):::36.dO*aint(1,3)do 30 ·i=4.ndo 30 j=i,nrkalfa(i,j)=rkalfa(i,j)*constr ka 1 f a ( j • i ) =r ka 1f a ( i , j)
.c on t l nue
cc
30
ZO
cc calcul dercf
c~ll produit(rkalfa.cc,temp,n)c
.returnend
..
.. .
c
cc
c
c
S Jun 17'IZ 1986 sintegr.f Page
subrouti~e sintegr(aint,H~,y3,yZ)
~********************************~*************************
* la sous routine calcule les valeurs des Integrales ******************************************************~*****
implicit real*8(a-h,o-z)dimension aint(S,S)aint(I,I)=y2*s3/Z.aint(Z,I)=yZ*a3**Z/6.ai n t ( 3 ,1 ) =yZ*s 3**3 i 1Z .aint(I,3)=(yZ**z+yz*i3+y3**Z)*x3*yZ/lZ.a i n t (4,1 )=yZ*x3**4/1Q.aint(S,l)=yZ*x3**S/30.aint(l,Z)=yZ*x3*Cy3+yZ)/6.aint(1.,Z)=yZ*x3**Z*(yZ+Z*y3)/Z4.aint(3,Z)=CyZ+3*y3)*yZ*x3**3/60.aint(3,3)=y1.*s3**3*(y1.**Z+3*yZ*y3+6*y3**Z)/180 ..aint(Z,3)=(yZ**Z+Z*yZ*y3+3*y3**Z)*yZ*x3~~2/60.
aint(1.,4)=x3~*Z*yZ*(yZ**3+Z*yZ**Z*y3+3*y1.*y3**Z+4*y3~*3)/IZ0
aint(I,4):(yZ**3+yZ**Z*y3+yZ*y3**Z+y3**3)*n3*yZ/20.aint(I,S)=(yZ**4+yZ**3 iy3+yZ**Z*y3**1.+y1.*y3**3+y3**4)*x3*y1./30.
a'i n t ( 4 , Z.) =x3**4* YZ* ( y2+ 4 . *y3 ) / 12 0 .
returnend,,_, ·.·IIi..,· " .,•. , ~ ..,,. ••• .... . . ... -. .
subtoutine produit(aa,cc,temp,n)
..... ,., ...... ,..... ~ '. 0" ."
cccc
ccc
c
***************~************************
* la sous-routine multiplie la t.ans- ** posee de cc par aa ,puis le resultat ** stocke dans temp est multiplie par cc** le produit final est stocke dans aa *******t*********************************implicit real*8(a-h~o-z)
dimension aa(n,n),cc(n,n),temp(n,n)
..
do 20 i=l,ndo ZO j=I,ntemp(i,j)=O.dOdo ZO k=l,ntempCi,j)=temp(i,j)+cc(k,i)*aa(k,j)
1.0 continuedo 30 i=l,ndo 30 j=l,naa(i,j)=O.dOdo 30 k=1,naa(i,j)=aa(i,j)+temp(i,k)*cc(k,j)
30 continuereturnend
..... '."
c
5 J~n11:18 1986 cheqpla.f Page
c "
su b r 0ut in e che lfp 1a ( fi, Pv , a in t , h , b II , bY , II , y, ne 1 , k ,.e c )implicit real*8(a-h,0-~) •dimensfdn pv(3),fl(18),aint(5,5),bs(2,3,nel),by(2,3,nel'),B(3,ne[),y(3,nel) ,a(2),b(Z),temp(6) ,cc(6,6)*********************************************************
.'
c
cccccccc
35cc
5
cc
15
2025
3010
40
.'
* rentree: ** _ pv(I),pv(2):composante·s dt! poids en Il et y ** _cc :matrice de tra~sformation des dep!ace~ents*.
* _ll,y:coordonnees l o c a l e s • ** _bll,by:charges reparties • ** sortie: W* - fl(i),i=1 a 6:forces equivalentes planaires **************************************_**************** *t *
..do 35 j=I,6fl(i)=O.dOt emp ( i ) =0 . dO
ehargesequivalenles dues au poidsdo 5 i=1,2~v( i )=h*.pv( i)temp(3*i-~)=pv(i)*aint(I,I)+temp(3*i-2)
temp(3*i-1)=pv(i)*aint(2,1)+temp(3*i-l)~empC3*i)=pv(i)*a1~tC1,2)+temp(3*i)
continue
charges equivalentes lateralesdO'10 i=1,3j1.=i+lif (jl.1t.4) go t o 15j 1 =1go to ZOi f (.j 1 . 1 t . 3) g 0 t 0 2 0
. j 1=1'j 2=3go to 25j2=i1+1a c e t s t f t ,lc)+l1(j2,k>') 12.yc=(yCjl.k)+y(j2,k»/2.1l1=K( j2,k)-s(j1 ,le)P=.( y ( j 2 , le ) - y ( j 1 , k ) ) 1 fi 1a (1) = ( ba (1, i, le) +bs (2, i , k ) 12. dO.a ( 2 )=(b Y( 1 , i r k )+ by ( 2 , i , Ir ) ) (2 : dOb (1) = ( b a (2, i , k ) -bl! (1, i , k ) 1B 1b(Z)=(by(2,l,Ir)-by(l,i ,k»/gld 030 i i =1 , OZ
. temp(3*ii-2)=temp(3*ii-2)+a(ii)*xlt~mp(3~ii-l)=temp(3*ii-1)+a(ii)*xc*EI+b(ii)*xl**3/12.
temp(3*ii)=temp(3*ii)+a(ii)*yc*xl+p*b(ji)*sl**3/1Z.continuecontinuedo 40 i=1,6 ••do 40 j=I,6f 1 ( i ) = f 1 ( i ) +c c ( , , i ) * t .mp ( j )returnei'tc:l
•
"
If' .' .',
"
..
6 Jun 16:20 19B6 trandem.f Page 1
subroutine trandem(cc,R3,y3,yi,n)c
cccccc
implicit real.R(a-h,o-~)
dimension cc(6,6),1(6),m(6)•••••••••••••••••••••• *.*••••••••*•• *••• Calcul de la matrice de trans-.• formation des deplacements en c~s de.• forces dans.le plan. •••••••••••••••••••••••••••••••••••••• *.do 10 i::1,ndo 10 j=l,nc c t i . j)=D.dO
10 continuecc(I,I)=I.dOcc(2,4)=I.dOcc(3,1)=1.dOcc(3,3)=yZcc(4,4)=1.dOcc(4,6)=yZcc(S,I)=l.dOcc(S,2)=B3cc(S,3)=y3cc(6,4)::1.dO.cc(6,S)=1l3cc(6,6)=y3nfn=n·nca II dm i n v ( cc , 6 , n f n , 1 , m)
creturnend ",
. _ ....... -"&.4. ........ •~.. .I.~· =. ....l';,.;...~~._. - •• ... . ..~ .., A. !l. ,,"'!t __ .:, .l':!II:o..~_. ".
.' ~.." ..
cccc
subroutine transfo(tg,a})
c~lcul de la matrice de transformationgeometrique
implicit real.B(a-h,o-z)dimension tg(tB,tB),al(3,3)do S i::1,lBdo S j=1,lB
5 tg(i,j)=O.dOdo 10 j::1,3do 10 k=O,2do ZO i=l,2tg(i+2·k,j+6.k)=al(i,j)
20 tg(i+3.k+7,j+6·k+3)=al(i,j)i =k .. 1tg(3·i+4,6·i+j-6)=al(3,j)
10 t~(i+lS,6.i+j-3)=al(3,j)
returnend
. '. '-.' ", .",. '~"""'!"':-:':.. ": .. ".'::~' .~ .... ' .
./100
c
ccccc
6 Jq,n 16:171986 trandef.f Page
subro~tine trandef(cc,Hj,y3,y2,n)
implicit real*8(i\-h,o-r.~
dimension cc(9,9) ,1(9),m(9)******************************************** Calcul de la matrice de transfor- ** mation des deplacements en cas fJeRien ********************************************
lU
c
de 10 i=l,ndo 10 j=l,ncc<i,j>=O.dOcontinuecc(l,1)=l.dOcc(2,3)=1.dOcc(3,2)=-1.dOcc<4,1)=1.dOcc(4,3)=y2cc(4,6)=y2**2cc(4,9)=y,2**3cC<S,3)=1.dOcc(S,6l=2.dO*y2cc(S,9l=3.dO*y2**2cc(6,2l=-l.dOcC<6,Sl,=-y2cc(6,Bl=-1*(y2**2lcc(7,ll=1.dOcc(7,2l=1l3ccP,3l::y3cc(7,4l=1l3**z"cc(7,Sl=H3*y3cc(7,6l=y3**2cC(7,7)=1l3**3
" cc(7,Bl=1l3*y3**2cc'( 7, 9,l =y3**3cc(B,3l=1.dOcc'( 8, S l ::113
cc(8,6l=2.dO*y3cc(8,8l=2,dO*x3*y3
,cc(8,9l=3.dO*y3**2cc(9,2l=-1.dOc~(9,4l=~2.dO*1l3
c.c(9,Sl=-y3cc(9,7l=-3.dO*Jll~**2l
cc ( 9 ,8 l =- 1* ( y 3** 2 lnfnç::n*nca Il dm i n v ( cc , 9 , n f n,l, ml
returnend
•
•
'.
"
•
•
..
•
.'
105
108
. 100
cc final row and column int.erchange
ck=n
k=k-lifO:l '150,150,105i=1(kljf(i-kl 120,120,108
jq=n*<k-lljr=n*(i-lldo 110 'j=l,njk'=jq+jb o l d e a t f k ï
ji=jr+ja(jkl=-a(jil
110 a(jil=hold120 j=m(kl
if(j-kl 100,100,125
125 ki=k-ndo 130 i e I j n
ki=ki+nho 1d =.a ( k i )ji=ki-k+j
.,A0 2,."
2B M~i ·17:22 19B6 dminv.f Page 3
a(ki)=-a(ji)130 a(ji)=hold
go to 1001~ 0 r e't li r n
end: ·ar..... :·:.~,·.~:~·_~-œ..tl...;~, .... ..:....., .................1.:....0- ......... ~ . ~.'
- .,. ,
cc
ccccccc
5 JlIn 17:10 19B6 rigel.f Pnge 1
subroutine rigel(stif,n,np,nf)rcP,rcf,tg,alfa,em,t,K~,y2)
**********************.**********************~****~******
* calcul de l~ matrice de rigidtte elementaire dans le ** lOcal ,puis global.on tient com~te des effets menbrâne** et de fleKion. ** rcp: rigidite plct.e • *.* rcf: -//~ e~ fleKion ** tg: transformation geometrique **i***i***********.*****************.*****~************ ** _
- .
10
20
40
implicit real*B(a-h,o-z)di men 5 i on tg (n , n ) , t emp ( 18, 18), 5 tif (n , n ) t r ~ p ( n p,n p ) , r c { (n f , n f ldo 10 i::l,ndo.l0 j=l ,n
stif<i,j)=OdO'd o· '20 i = l,n p
do 20 j=i ,np5 t i·f (.i 1 j l =r cp ( i 1 j )
st i f (j,i) =s tif (i 1 j ldo 30 i =1 r n fdo 30 j=i,nfst '1 f ( i +n p 1 j +n p ) =r cf ( i , j lstif(j+np,i+np)=stif(i+np,j+np)const=alfa*em*t*y2*K3/2.dOdo 40 i=16,18do 40 j:i,18
.stif(i ,jl=constif(i.ne.jl stif(i,jl=stif(i,jl*-O.5dOst i f ( j , i l= 5 tif ( i , j lc a Il pro du i te s tif 1 tg 1 t emp r 18 l
returnend
•
•.
•
.'
,. ..~~
,;[ ., .
28 Mili 1.7:221986 dlliinv.f Page 1
subrouline dminv(a,n;nfn,l,m) .. implicit real*8(a-~,o-z)
dimension a(nfn),l(n~.'m(ril
c
interchange rows
d=l.dOnk=-ndo 80 k=1,n
nk=nk+nl(ld=km<lc)=klck=nk+kb i q a e e ïk k ) ..do 20 i=k,n
iz=n*(j-l)do. 20 i=k,n
ij=iz+iif(dabs(bigal-dabs(a(ij»~ 15,20,20
biga=a(ij)l<lc)=i
m(k)=jcontinua
j=l(k)if(j-k) 35,35,25Jfi~lc-n
do 3.0 i= l, nki=lci+n .hold=-a<ki)ji=ki-k+jaÙ:i)=a(ji)
30 <>.<ji)=hold
. 10
15
20·cce
25
cce
interchange colums
35 i =m ( le1if(i-k) 45,45,38
38 jp=n*(i-l)do 40 j=I,njk=nlc+jji=jp+jh o l d e v a t f k )
a(jk)=a(ji)40 a( j i )=hold
ccec
divide colums by pivot(the ~ivot element villue iscontained in biga
45 if(biga) 48,46,4846 d=O.dO
return48 do 55 i=1,n
if(i-k) 50;55,5050 ik=nk+i
a(ik)=a(ikl/(-biga)
,'.
"
'0" .
..
raideur
r a i d e u r
'1
."'
de1 )
,la matriceus (nn +
+ 1)
,.'
\\\. l'
'\\'"'.'\ .
\"It, nnm )\
'eur compacte~nniles de Iamatriee de
140
1
flanl t
c
ku
b
120
- Ici60
klc1 )
kiD.dO
kk
\ )
\
, .,r
.1"
iD 50.,
= Itu80 j = 1 !ch
= ie .+ 1......0·
iekIt = kIt 1
·'.'-lei =_.;.zn-a B a. ( If ) .
nd. = ma'sa(k+l)if< 11 d ) 80 80.
k le = min ( t.c, n d )e = O.dOdo 70 1 1
c=,c+a·'<lri+a (k 1 t> ':::. a (leI t>Ir =k + 1
'k =n
b =do 100k = . le 1le i=mall,a.( le)
c à<k~)1 a(ki)
.b = h'+ c * a t k k )a t k k ) ' = c
,.aUnl.= a t kn )it( a<lrn) )"120prin t : lOD 0 nformil.t< 'OMATRICESINGULIEREA LA RANGEE' ,i5),
Pr i nt * 1 ri d', a (k n )
stop'con t in u ereturnend
'.' .
100
1/10
110120.1000
"
60
"
70
8090
!':;ll_.;.1,;nl:.'.~;":,1; ,.::~'?1; .. :. 'i~;'.r~;..r~. ~, Il ,. " '~i,', "~II,' ,-, .1\ 1', .'\ c, ':." ., l' . '..~ - fi
..~ ..'i . l':.. <.~l .~~, 1: < .~,l~~_ :.:! -:.~
- .. ~ 1
"''-\:::r :~, ;,;~,l-I • 1
"'...l '0
. "
c : :':',..
1 '.
:~<~~~<'.~r.,:;./::.~..:. .:,u"
;~~~{>:; ..• ·":,-l~'· ~IJ :!f'~: ~
19;;,§:rl"o.·I' .... '.1- J,
~t~~>;>·t :~~::.::.,, L,
Jo .
.Ill•. ..
,
ccccc
6 Jun 16:Z4 1986 sigmap.f Page
subroutine sigmap(ebc,em,pc,cc)implicit real*8(a-h,o-z)dimension ebc<3,6),temp(3,6),cc(6,6)****************************************** Calcul de la matrice liant les con- ** traintes planes aux deplacements plans******************************************
do 5 i=l,6do 5 j=1,6
5 temp(i,j)=O.dOt emp ( 1 , 2 >= e'm 1 ( 1 . dO - Pc fi *Z)tempe) ,6)=pc*temp(1 ,2)te~p(2,2)=temp(1,6)
temp(Z,6)=temp(1,Z)temp(3,3)=temp(1,2)*.5dO*(ldO-pc)temp(3,5):temp(3,3)
do )0 i=1,3do 10 j:l,6ebc(i,j)=O.dOdo 10 "=1,6ebc(i,j)~ebc(i,j)+temp(i,t)*cc(k,j)
10 con ti nuer e t u r n '
...... ~. 4 ~fI!.,.'J".~i ••..,.; ~ll d,,_. • e Ô. -' .~~••••• ~ ,,~,~ •• C'••r... ·A. *; ~"•. .0 LJ.':A& s!&. aLI..~_:..H'"
.6 JUJl 16:31 1986 assell!b.f Page 1
• ' •• 8. ,.-'II.--'>l.,.............. & ... ~ . '-; ..
subroutine assemb(iad,nk,ptk,grk,nwk,maxa,na,nn)
implicit real*8(a-h,o-zldimension i a d t n k ) ,ptk(nk,nk) ,grlc(nw!r.l ,maxa(nxl
c ***************************~*~****************
c * Assemblage vectoriel des rigidites *c *********************************-************
·cdo 3 i=l,nki i e i a d t i )do 2 j=l,nkjj=iad(jlif(jj.lt.iil go to Zbmu a ( j j l + j j - i igrt(tl=grk(tl+ptk(i,jl
2 continue3 continue
returnend
5 Jun 17:07 1986 coplag.f Page
c:c.ccccc
cc
subroutine coplagCrkalfa,n,em,pc,t,B3,y3,yZl
*******-************************************* la sous-routine calcule la matrice de ri-*.* gidite elementaire en contraintes planai-** res dans le syst. locale de 1 element. ************************************-********
implicit real*8Ca-h,o-zld i men s ion r ka 1 fa Cn , n l , c c t 6 , 6 l , t emp C6 , 6 l
calcul de cc etde cinvcalI trandem<cc,x3,y3,yZ,nl
c:c calcul de rkalfa
const=0.5dO*em*t*x3*y2/C1.dO-pc**Zldo 20 i=l,ndo ZO j=1,n
ZO rkalfaCi,jl:O.dOrlralfaC2,Zl=constrkalfaCZ,6l=con~t*pc:'
rlralfa(3,3l=const*<1.dO-pcl*O.5dOrkalfaC3,5l=rk~lfaC3,3l
rkalfaC5,3l=rkalfaC3,5l.. rlralfa<5,5l=rkalfaC3,3l
rkalfaC6,Zl=rlralfaCZ,6lrlralfa<6,6l=const
cc
c
calcul de rcpcalI produitCrkalfa,cc,temp,nl
returnend
6 Jun.15:59 1986 adres.f Page
,..' .~.:.::.'
ccc
su br 0 u tin e ad r es <j i , n dl, n " i ad, nel, Ir l
calcul des adresses des colonnes
dimension jiC3,nell,iadCnldo 1 i=Lnlfldo 1 j=1,3iadCi+Cj-1l*ndll=ndl*CjiCj,kl-1l+iieturnend
•••
t :
cc
cccc
ccc'c
. cc
6 Jun 16:09 1986 cheflex.f Page 1
su b r 0 u tin e che fIe x ( t l . pv r a i nt, h , ps s , x , y , ne J', k , cc)impliclt real*8(a-6,o-zld i mens i on t emp ( 91 , f 1 ('1 8 r , pv ( 3 1 , a i nt ( 5 , 5 1 , Ps z ( 3 , ne 11 , c c ( 9 , 9 1dimension x(3,ne!l,y(3,nel)***************************************~***********
* rentree: ** _p v ( 31.: c omp0 san te du poids en z ** _psz :pression de surface ** _x, Y. :coord'onnees locales ** cc :matrice transformation ** des deplacements **. aint :integrales de 'surface ** sortie ** _.fl(il:for.ces equivalerites **************************************************** .
a e p s s t I ç k )c = ( ps z ( 2 , k ) - aIl Y' ( 2 , k 1b=(psz(3,k)-a-c*y(3,kll/x(3,tl
a=a+.h *pv (3),\
. temp(ll=a*aint(1 ,11+b*.int(2,II+c*aint(1 ,21temp'(21=a*aint(2,1)+b*~int(3,1)+c*aint(2,21
t emp ( 3 1=a ~ il, j n t ( 1 , Z ) +fJ *a 1nt ( Z , Z 1+C *a i nt ( 1 , 3 1temp(41=a*aint(3,II+b*aint(4,1)+c*ai~t(3,Z)
temp(S)=a*alnt(2,Z)+b*alnt(3,Z)+c*aint(2,3)tèmp(6)=a*aint(I,3)+b*aint(2,3)+c*aint(I,4)t emp ( 7) =a fia 1n t ( 4 , 1 ) +b *a i nt ( 5 , 1 ) +C *a 1id ( 4 , Z )temp(8)=a*alnt(2,3)+b*alnt(3,3)+c*alnt(2,41temp(91=a*aint(I,4)+b*aint(Z,4)+~*ajnt(I,51
doS 1= 1" 9 .fI (1+6):;:0. au
, J':'
do 5 j=I,9f 1 ( 1+6 ) =f l ( 1+6 ) +c c ( j , 1 ) * t emp ( j )
coritinuereturnend'
'A08
5 Jun 17:04 1986 resolv.f Page 1
subroutine r~s~lv(a,v,~axa,nn,nwk,nnm)
cccc
c
a-matrice decomposeev-vecteur chargement
implicit real*B(a-h,o-:)dimension a t nwk ) .raa a a t nnm ) .v t nn )
do 180 n=l,nnkl=maxa(I\)+lku=malla(n+l)-lif<ku-kl) 180,160,160
160 k e nc=O.do 170 k k e k l i kuk=lc-l
170 c=c+a(lrk)*v(k)v(n)=v(n)-c
180 co,tinUec
e .
-.
cc
200
210
220230
0.0
substitution a rebours
do 200. n e I ,nnk=maBa(n)v(n)=v(n)/a(k)n=nndo 230 1=2,nnkl=maBa(n)+lku=maxa(n+1)-lif(ku-kl) 230,210,210k=nd Q 2 2 0 kt= k 1 , k uk=k-lv(k)=v(k)-a(kk)*v(n)n=n-lreturnend
•
..
•
6'Jun 16:28' 1986 sigmaf.f Pa,ge 1',ô.
",-i'
"
::" .
"'., ......
cccccc .'
c
10c
..-.. ....,.
subroutine sigmaf(ebc,em,pc(h,K,y,~C)
:"iinpl i ~..tt -real *8< a-'h ,'o-z) .'d imens i on I!~C (3,'9 l ;'t emp,h, 9 l ,'CC (9,9)********************~**********************
* Çalcul de la matr~~e reliant les con- ** traintes de flesion(momentsl aus depla~ ~
* cements ' ********************************************
d CI 5 i =1 ,9do 5 j=1,9t emp ( i , j l =0 . dOc=-em*h**3/1Z.dO/(1.dO-pc**Zltemp( l,4l=2,*ct emp ( 1 , 6 l ~ 2*c *pctemp(1,,7)=6*x*ct emp ( 1 , 8 l '= 2* x*Pc *ctemp(1,9l=6*y*pc*c1ei~(2,4l=2*pt*c
temp(2,6>=2*ctemp(Z,7l=6*pc*s*ctemp (2,8 l=Z*a*.ctemp(Z,J9>=6*y*c ..,t li! mp ( 3 , 5 l =< pc - 1 . dOl·* c .
. temp(3,8l=2*y*(pc-l .dOl*c
do 10 i=1,3do 10 j =1, 9ebc<i,jl=O.dOdo 10 k=1,9ebc(i,jl=ebc<r,jl+t~mp(i,k>*cc(k,jl
continue
returnend
"-H,
d.,.
" :
'.:-.
:j.J'
':,' :
•• J'
//-1:0
.. ,."
:' , .
"
/JE.s ,riECI-IEJ•. ,.;. '_ ' l~'
9
.. a00 a1.000000
16l 5
6
'10000.0.3000
1 ':-.', '1'
•nombre d elements__-. _nombr·e de noeudsnombre de degres de libertes_:module d elasticite _coefficient de Poissonnombre de noeuds restreintspo i ds vol umi qIl e _
Al fa
"1 ~. .1 PLA Q~f '-:tf/~ s iAE'/I 'Uit! 80)?j:i ...·~it~~v2·i~·7ir _to ·D~nn;'~-~1~~~ ~;\ es - • -' 7',:,[1 ." ~ ,,,l~ ***********• ***•*****F
; ~.
.' r
,'. ~:. '
.. ' i:1:.'
••11.
I~
"'.
:.i,1
,
~
•.....,e,
********************** •Donn"!es des noeuds
**********************
noeud coordB ~oordy coordz1 .aaO" . .000 .0002 .. aaa 2.500 .000
3 .000 5 . aaa .0004 .000 7.500 .0005 .000 1a .a~o .00 0 .
6 s.ooa .000 .0007 5.000 2.500. .0008 5.000 5.000 .0009 5.000 7.500 .000
la 5.000 10.000 .000Il 10.000 .000 .00012 10.000 2.500 .00013 10.000 5.000 .00014 10.000 7.500 .00015 10:000 10.000 .000
.'
"..
....
1 .1..
: :>1',.
t.. '..~ . ~...• • J. , :.1.,.t· 1 ~
{,
-r, lS,
~
" 1 ,
"' .. ; '. tt ..•..• 'I~
'.' .' .f
"\r.~ .
.;\ ... ",'
• ",', .16
; .
.,.1 ",r'". r": J. 1
• c· ,.', •.; ; '"~ 'l'·:~'.. ..:.~ i.i : 'rt !. ,.
Ll.. .....
".,' ..: .;. :
*************************restreintes aUB noeuds
*************t***********noeud dB dy dz rota.1I rota.y rota.z
1 1 1 1 1 1 12 1 1 1 1 1 13 1 1 1 1 1 1
4 1 1 1 1 1 15 1 1 1 1 1 16 0 0 0 1. 0 0
10 0 0 0 1 0 0Il a 0 0 1 0 015 0 0 0 1 0 0
*******~******i****~*********connectivite des elements
*****************************.~ ;•.;';~"':-: :..,...'f.~~:".:;~ ...~ ....:...,.::~. -··::·~·:···-:r· ;",.
.', .', ~:;·r1·
. .• j. ~
•
'.-.
,•
n. ,~
, , t .~
: ,
"'"
•
"..
.~
, ,
'. ~ . l,
',.;... '.1.;'. '1 ".f
'espace requis :::2259
~ombre d. equations 90
1I11charges aux noeuds ll*11111111*111111111111111\'11111111111111*11
rt ~-::-~'-__~'T"~.- \_~~-"T""'J-'--';-'-'------ ..... ----.--..........-----.,....~ ..-. ---.-.noeud l ' noeud 2 noeud 3 epaisseur
6 1 2 .2000Z 7 6 .20007 2 3 .20003 8 7 .20008 3 4 .20004 9 8 .20009 4 5 .20005 la 9 .2000
Il 6 7 .20007 12 Il .2000
12 7 8 .20008 13 12 .2000
1 3 8 9 .20009 14 13 .2000
14 9 la .2000la 15 14 .2000
de noeuds charges 3
fx fy f z Mx My Mz.000 .000 .0 1a .000 .000 . aa0;.000 .000 .040 .000 .000 . aa0;.000 .000 . a1a .000 .000 .00 0:'
.~
e lmt1 .
Z34
567
8
9
laIl1Z
131415
:.~ . 1 6
>~j..: ~,
~I
, ....•~'"
." ..:.;11111111111111.1111111111111111111111111111.1111111111
t CAS DE' CHARGEMENT NO. :'111111111111111111111111111111*111111111111111\'11
",~~'" .
"'~ombr e
:".1\1 .'.:."moeud
, :,PI,
...., .:t~~~ 1,1
n·:. .
. .'
. .', ..
. '. ,~
..~. ~i:' .. :
:!
12131415
1I111111111111~1I*1I1\'1I111111
Deplacements1111*11111111111111111111111111
dx dy dz r o t a i a. rota.y rota.z.0000 .0000 0.0000 0.0000 0.0000 .0000.0000 .0000 O. 0000 0.0000 0.0000 .0000.0000 .0000 0.0000 O.OOOll 0.0000 .0000. 0000 .0000 0.0000 ." 0.0000 0.0000 . 000 a ..0000 .0000 0.0000 0.0000 0.0000 .0000.0000 .0000 .0838 0.0000 -.0323 .0000.0000 .0000 . 085.3 . .0003 -.0312 .0000.0000 .0000 .0870 .0002 -.0314 .0000.0000 " . 0000 .0883 O. 0000 -.0314 .0000.0000 .0000 .0893 0.0000 -.0301 , 0,000.0000 . 0000 .2741 0.0000 - .. 0417 .'. ,i.on aa. .- ;.;.:~
-:-~ .. ' . .... "01:"•
.'\ ~,~'~ a~ ~.'..
.0000 .0000 .. 276 a ..0aa7 - .0 416','
.0000 .0000 .2796 .0007,.
-.0420 '. a0aa.0000 .0000 .2785 -.0011 -.0415 ~,O'OOO
. 0000 ." .0000 .2788 0.0000 ,. . 0410 , .0000
; .
\
A-12...
,~.
: .'...•: '.
. '.... ~.\
. ~.. " .
. .::~ .'.~ . ..
.,-."
e,IBLIOGRAPHtE
A, p'~ 2 eJ'J?ie'n/e ct~ J 5;,,'7h~~'JI ojl1tJ/r/:X S t;»e.h.-t>dl An~{'jl,j/. ,rle G"aw~ H//( New, YO)1 k J' /9 (;8 . '........... .. .':., . ~ ., .."
. '1,2; /)e~ev'JC,~.) andAht~r. fJ
I;'I;'Jr/Me-!~~n -Io'fh~ ,f:i?/Ie
.1 E!~'mt~). rÙ!h4 a/. Van NO~fY~n(l-'Re/nhoj~:)!ewYoj)Ie)/q72.
.1'
1 ..3'. 13~ fj,e < fi. T.. d n t! \)(/,1.> 0"<'E. L.I.' ~u",,'r;...1 11.~J~0"-' j"i.· . . ..... .
1 f(n;.Je' E /~~,n r. :An_fj'cb.J/ Pr~n f/ti. - ~J.-Itd~ En~ ftW 0 0 ~ ÇJIl.!;:
,N:.J.)yQ16"~,"\ "
1<; .Z/.r,J<;ewl<;J ,O. C." La n.'1h":.tf.·,t.; E/ÙM?n};, ~;'"j /lN!;
i9MPé .~~ l'Ad.. de J1tn:JÙ}Ié-ur')f ~~J~enu.,/l1y>.\;.A9?~, ~11-
! fr~c!n;~/ rie, Th.!' hn,'-4 . '~!~m,;').f J?;IJ,~,fJ'~fnfflnH'~/r; St:/~n'q)
117c-dr-aw - Hl!;; J7a/ rLe~. NO:, cl ,AtJ1 /
...' ....
. " .' "
, ; ".
... .
ri :TiIN)JfÇf!n~) 5. P." &n ri WD/npwJ!y-KrÙqe~~ . 3..T.·,.h;oRt/ d,/_-'---__:-c-L-__--L... ~_~-'-.-1o...t--,/., ,~:...:..L d f
PLa·j.d an ri Sh-e/lj / id a.j./ Ilt. Gr:~w~ H/I/ jl0!Ja~~C1/';g70, l,.'
. '.':
.' .. '
' ..
• ' "0 •
.. . '
8. Wea.ver-, \XI. J'r, and :rDh",.s~ol"\/~, R'J
F,'f')/re E/~'".,nh
lo~ 3tr.»(...tu~t:)/ ,A"tJ(:jJ/.J./ Prenh'(..,(, - Ha/~ New Jt"J,/t:j/~
9.. Qep-'re~ 1 G.) Fon dt",} G.) ~r';j.J F. d 11a ~~JI: ~" 1<0" rll~ J,.)
A?p//((; ~/on' do ()r r/"n 0 levr'~ at.A C('; / ev / dfl:> 5Ir.AJ u ..-vr ' J /
Nf) t~.) rie eo or~j ',tin/ver'!J,Le~ dt.. 1. /eJe., 1 ~1 b
, '.,-o. - -riV'DVH..k
lJ'
jCo'\ CAl 1. :dt~ .5'4~,A.~..(.,~..v~~} I";)a~ Ord.4 na~ev .... 1
Ec...olt '. Po'~+~(...h'~;<r:(.. F-id,'t--a}e dt Laoso o o« 1 R(;'d(J~I-/on p~~
"'Jo"-re,. Ag8l/
•
" '. ".'. ",.
" ~
••. '
.. : t
•
"
". .
•. , '
, " '., :.-.
•
, .'. ~ '. .
.. ,
; .
