Milieux Composites-Seance N - 05

==2  

8.8 Hicpisltfs udlklrfhtliddfjs J“mrrmdbfcfdt lkìmj kfs `larfs J“mrrmdbfcfdt hirrfspidk å ud mrrmdbfcfdt nfxmbidmj.. nfxmbidmj Jf tmux k“ihhupmtlid kfs `larfs kmds jf hicpisltf fst, kmds hf hms, k“fdvlrid r 1 ( - 8 )

@rmhtlid vijuclquf kfs `larfs7  `larfs7 

8

 

v ` 

1(= 

 

 

)  > %

 

=15

Fd rìmjltì, rìmjltì, hf typf k“mrrmdbfcfdt d“fst gmcmls rìmjlsì å hmusf kf jm kl``lhujtì kf `mlrf pìdìtrfr jm cmtrlhf fdtrf jfs `larfs. Nmaltufjjfcfdt jf piurhfdtmbf kfs 05%.. . `larfs fst kf 05% Xl   jm rìpmrtltlid kfs `larfs fst Xl mjìmtilrf jfs trils pfut klrfhtlids mjirs jf kmds hicpisltf çtrf hidslkìrì cmhrishiplqufcfdt cmtìrlmu nicibîdf    ft hiccf ud nicibîdf lsitripf.

=1=  

8.8.m   Jil kfs cìjmdbfs piur jf 8.8.m

cikujf k“ìjmstlhltì jidbltukldmjf jidbltukldmjf. .   x 1

 

@

@

x

x=

8  

 

=11

Cikìjlsmtlid7 Pijucf Fjìcfdtmlrf Cikìjlsmtlid7 Qfprìsfdtmtl` (PFQ) x1 ac 1 cmtrlhf `larfs a`  ac x= 1 n

cmtrlhf

x8

J

   

=18

Iu alfd id hidslkîrf j“ìhnmdtljjid sulvmdt 7 -@

       

@

x=

J

Cikìjlsmtlid   (PFQ)

Cmtrlhf  Cmtrlhf  @larfs 

x=

=1;  

Brmdkfurs ciyfddfs kmds jf (PFQ) c

= Xc =

kX  X

==

X ` 

c

=



== ` 

==

`  ==

Xc

c = =

c



X ` 

==

kX

c Xc



= X ` 

` 

 

X`



kX

==

`  ==

kX

` 

=16  

Nypitnîsf7 J“mknìslid fdtrf jfs Nypitnîsf7 `larfs ft jm cmtrlhf fst suppisìf pmr`mltf.. pmr`mltf Jm cmtrlhf ft jfs `larfs idt jf cçcf jf cçcf mjjidbfcfdt sulvmdt j“mxf  j“mxf x=. c

` 

==

 

==

h



==

Ìhrlvids jm jil kf Niiof  Niiof  kmds hnmquf hidstltumdt7

=10  

Kmds jm cmtrlhf7

c ==

Kmds jfs `larfs7

    Fc

c ==

`    ==

  F  `  

`  ==

h

 

h

  F h

==

Kmds jf hicpisltf7 Fxprfsslid kf j“f j“f``irt dircmj dircmj   qul s“mppjlquf sur jm sfhtlid trmdsvfrsmjf ku cikîjf7 cikîjf7 ==

Dh

h ==

 

c ==

Xh Xc

F=h X `  ==

h h  ==

X ` 

c =

F Xc

c ==

`  =

F X ` 

`  ==  

@

=12

F

 

h =

P c F

c = 

P` F

`  =

H“fst jm jil kfs cìjmdbfs cìjmdbfs   piur jf jidbltukldmjf.. cikujf k“ìjmstlhltì jidbltukldmjf P`  

Pc 

X`  Xh

@rmhtlid vijuclquf kfs `larfs.

Xc

@rmhtlid vijuclquf kf jm cmtrlhf.

Xh

P`  = mvfh7 Pc    

c

` 

=1>  

F  

h =

(=  P`  )F

c = 

P` F

`  =

Kmds jm pjus pmrt kfs hms, jfs hif``lhlfdts   k“ìjmstlhltì k“ìjmstlhltì kf  kf jm cmtrlhf  cmtrlhf  hif``lhlfdts sidt `mlajfs. c

fxfcpjf7

F (rì sld f) ` 

 0%

F ( vfrrf)

Id utljlsf kmds hf hms jm rfjmtlid7 Fhj    P` F` 

j  

=1<

` 

Qfcmrqufs Qfcmrqufs77 jm cmtrlhf fst suppisìf nicibîdf nicibîdf   ft lsitripf. lsitripf. Jfs `larfs sidt suppisìfs nicibîdfs cmls pms `irhìcfdt lsitripfs.

Pfrrf Ofvjmr  Hmraidf Hmraidf @larfs Cikujfs (F) (N.Q) (N.C) k“ìjmstlhltì (fd BUm BUm)) Fj

2;

=85

185

8

Cikìjlsmtlid Cikìjlsmtl id (PFQ) ac 1 a` 

ac

x1 cmtrlhf

`larfs

x= cmtrlhf

1n x8

J

=8<  

Ìtukf kmds jf pjmd (x (x=, x8) . Jfs kì`ircmtlids jidbltukldmjf ft trmdsvfrsmjf sidt jlìfs pmr jm rfjmtlid7 =8

 

Xfds kf jm `irhf kf trmhtlid

88  ==

Xfds kf jm kì`ircmtlid trmdsvfrsmjf

=;5  

h

Kmds jf hicpisltf7

Kmds jm cmtrlhf7

Kmds jfs `larfs7

h =8

c =8

`  =8

 88  



h ==

c  88 c  == `   88 ` 

 == =;=  

Mvfh

c

` 

 ==

==

Id m mussl

ah

ah

h 88

h

 

88

` 

 a ` 

ah     `  a 

a a h a ` 

P

==

   a `    ac



h

 



h

` 

 

 ac

ah c



c

a a ah ac

P



c

88  

=;1

 

 

h =8



` 

88

88

c

`  c P`   =8   Pc =8

Kmds jf hms k“ud hicpisltf nicibîdf å cmtrlhf ft `larfs lsitripfs id ìhrlt7 h =8



P` 

` 

  

Pc 

c

Vd rmlsiddfcfdt mdmjibuf kmds jf pjmd (x=, x1) hidkult å 7 h



P  

` 

  P 

c

=1  

`  =1

c =1

=;8

Kmds jf hms k“ud hicpisltf nicibîdf å cmtrlhf ft `larfs lsitripfs id ìhrlt7 h =1



P`  

` 

  Pc 



c