8/2/2019 SSG 516 Mechanics of Continua 3

1/20

@saf{ Ldefobsdnbh ]{`}f{sdf~Hfnsv{f Sa{ff

Ldefobsdn~7 ^svct `j Cd~}hbnfofes~ * O`sd`e

Saf cfj`{obsd`e i{bcdfes bs b }`des n`o}hfsfht cfsf{odef~

saf {`sbsd`e bec saf nabeif de hfeisa `j bet jdk{f `j obsf{dbh

fobebsdei j{`o sabs }`des%

FA CdhhAfh}jvh [fbcdei7 K`yf{ }} 2>/>1( Jbldehfcf 23:/299

8/2/2019 SSG 516 Mechanics of Continua 3

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De sad~ ~fnsd`e yf ~abhh h``l bs ~fzf{bh `saf{

ldefobsdnbh }{`}f{sdf~

Ldefobsdnbh ]{`}f{sdf~

8/2/2019 SSG 516 Mechanics of Continua 3

3/20

Saf ~nbhb{ rvbesdst(

d~ saf {bsd` `j saf hfeisa `j be

fhfofes de saf cfj`{ofc ~sbsf s` saf hfeisa `j saf ~bof

fhfofes de saf `{didebh ~sbsf( d~ nbhhfc saf ~s{fsna {bsd`%

Afenf

^s{fsna [bsd`

8/2/2019 SSG 516 Mechanics of Continua 3

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Kfideedei ydsa saf dezf{~f `j saf ~bof frvbsd`e(

Yf `ksbde( ( ~` sabs(

2

8/2/2019 SSG 516 Mechanics of Continua 3

5/20

S` jdec saf beihf kfsyffe sy` jdkf{~ de saf dedsdbh ~sbsf( hfs( kfsaf veds zfns`{~ bh`ei saf jdkf{~

n`~

!$ !$!$!$

^afb{ Beihf

8/2/2019 SSG 516 Mechanics of Continua 3

6/20

Hfs( kf saf veds zfns`{~ bh`ei saf ~bof jdkf{~ de saf cfj`{ofc ~sbsf%Saft b{f e`y denhdefc s` fbna `saf{ bs beihf % bec

n`~ !$ S ! $

!$ S ! $ !$ S ! $

!$!$ !$!$

^afb{ Beihf

8/2/2019 SSG 516 Mechanics of Continua 3

7/20

N`e~dcf{ e`y sy` jdkf{~ sabs yf{f dedsdbhhtbs {dias beihf~%

Bjsf{ cfj`{obsd`e( hfs saf {dias beihf kfcfn{fb~fc kt

~` sabs saf beihf denhvcfc

de saf jdkf{~( % J{`o saf bk`zf( dsd~ nhfb{ sabs(

n`~ ~de

Sad~ d~ saf ~sbecb{c cfjdedsd`e `j ~afb{ ~s{bde%Ds d~ b jvensd`e `j saf [dias Nbvnat/I{ffesfe~`{ bec saf ~s{fsnaf~ b~ ~a`ye%

^afb{ ^s{bde

8/2/2019 SSG 516 Mechanics of Continua 3

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Saf i{fbs do}`{sbenf `j saf [dias Nbvnat/I{ffesfe~`{ de cfsf{odedei saf do}`{sbes ldefobsdnbhrvbesdsdf~ d~ nhfb{ j{`o saf j`{fi`dei% De saf efqs jfy

~hdcf~ yf ydhh sblf b nh`~f{ h``l bs ~`of `saf{ `j ds~}{`}f{sdf~%

]`hb{ cfn`o}`~dsd`e saf`{fo nbe kf besdnd}bsfc ktsaf j`hh`ydei }at~dnbh `k~f{zbsd`e7 Saf jdebh ~sbsf `jsaf cfj`{ofc nvkf ~a`ye kfh`y nbe kf bnadfzfc desy` cdjjf{fes ybt~7 B cfj`{obsd`e j`hh`yfc kt b{`sbsd`e( `{ b {`sbsd`e j`hh`yfc kt b cfj`{obsd`e b~saf cdbi{bo !Ydld}fcdb$ ~a`y~7

Saf ]`hb{ Cfn`o}`~dsd`e

8/2/2019 SSG 516 Mechanics of Continua 3

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]`hb{ Cfn`o}`~dsd`e

8/2/2019 SSG 516 Mechanics of Continua 3

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Yf ~sbsf( ydsa`vs }{``j( saf j`hh`ydei do}`{sbes {f~vhs7

J`{ b idzfe cfj`{obsd`e i{bcdfes( saf{f d~ b vedrvf{`sbsd`e sfe~`{( bec vedrvf( }`~dsdzf cfjdedsf ~toofs{dnsfe~`{~ bec j`{ yadna( bec bk`zf b{f nbhhfc saf {dias bec hfjs ~s{fsna

sfe~`{~ {f~}fnsdzfht% Nhfb{ht(

bec

]`hb{ Cfn`o}`~dsd`e Saf`{fo

8/2/2019 SSG 516 Mechanics of Continua 3

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[fnbhh sabs saf ~s{fsna {bsd` d~ cfjdefc b~7

Yadna bhh`y~ v~ s` y{dsf sabs( saf ~s{fsna bh`ei b veds zfns`{

( d~ Vo

Saf ^s{fsna Sfe~`{~

8/2/2019 SSG 516 Mechanics of Continua 3

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[fnbhh sabs saf ~s{fsna sfe~`{~ becb{f ~toofs{dn bec}`~dsdzf cfjdedsf% Ds j`hh`y~ sabs saf {dias Nbvnat/I{ffe

Sfe~`{ d~ bh~` ~toofs{dn bec }`~dsdzf cfjdedsf%Saf ^}fns{bh Cfn`o}`~dsd`e Saf`{fo7

J`{ bet ~toofs{dn Sfe~`{ ( saf{f d~ be `{sa`e`{obh kb~d~ ( 2 > `j saf fdifezfns`{~ `j ~vna sabs

?

Yaf{f d~ saf fdifezbhvf n`{{f~}`ecdei s` ( 2 >

Saf ^}fns{bh Cfn`o}`~dsd`e

8/2/2019 SSG 516 Mechanics of Continua 3

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Saf ~}fns{bh cfn`o}`~dsd`e ~a`ye fb{hdf{ d~ vedrvf`eht yafe saf fdifezbhvf~ b{f cd~sdens% Sy` `saf{nb~f~7

7 [fnbhh sabs saf dcfesdst sfe~`{

~` sabs De sad~ nb~fsaf{fj`{f(

? Bec j`{ (

Frvbh {``s~

8/2/2019 SSG 516 Mechanics of Continua 3

14/20

Hfs ( kf saf fdifezbhvf~ `j saf {dias ~s{fsna sfe~`{ !saf~f b{f bh~` nbhhfc saf }{dend}bh ~s{fsnaf~$ bec hfs( kf saf n`{{f~}`ecdei fdifezfns`{~( Saf ~}fns{bhsaf`{fo do}hdf~ sabs(

B cd{fns }{`cvns `j sad~ ydsa ds~fhj hfbc~ doofcdbsfht s`

^` sabs saf fdifezbhvf~ `j saf [dias Nbvnat/I{ffe Sfe~`{ b{fsaf ~rvb{f~ `j sa`~f `j saf [dias ^s{fsna sfe~`{%

Saf [dias ^s{fsna Sfe~`{

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B Sfe~`{ d~ ~bdc s` kf {`sbsfc yafe ds d~ }{fovhsd}hdfc kt b {`sbsd`e bec }`~sovhsd}hdfc kt ds~ s{be~}`~f% Yf ~a`y de saf j`hh`ydei saf do}`{sbes jbns sabssad~ `}f{bsd`e c`f~ e`s bjjfns saf ~nbhb{ dezb{dbes~ `j b sfe~`{7

S s{ S s{ S s{ !$

S 2; s{

S s{ SS 2; D!$s{ S

2

;D!$ s{ S

2

;D!$ s{ !$

S cfs S cfs S cfs Be doofcdbsf n`e~frvfenf `j sad~ d~ sabs b {`sbsd`e }{f~f{zf~ saf fdifezbhvf~ `j

saf sfe~`{% Yf vsdhdwf sad~ {f~vhs de saf j`hh`ydei cfcvnsd`e~%

]{dend}bh Dezb{dbes~ de [`sbsd`e

8/2/2019 SSG 516 Mechanics of Continua 3

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@k~f{zdei sabs ds d~ fb~dht~ffe sabs saf fdifezbhvf~ b{f }{f~f{zfc kt saf{`sbsd`e `j b sfe~`{% Afenf ( b{f bh~`fdifezbhvf~ `j % A`yfzf{ fdifezfns`{~ b{f cdjjf{feskfnbv~f `j saf {`sbsd`e~% De jbns( S S S

Yaf{f 2(;(>%Bec saf Hfjs Nbvnat/I{ffe Sfe~`{ ~ab{f~ saf~ffdifezfns`{~ ydsa ~rvb{f fdifezbhvf~ b~ fq}fnsfc7

Saf Hfjs ^s{fsna Sfe~`{

8/2/2019 SSG 516 Mechanics of Continua 3

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J`{ be fhfofes `j b{fb de saf cfj`{ofc k`ct ydsa bzfns`{ }{`gfnsdei `vs `j ds~ }hbef !c`f~ e`s abzf s` kfe`{obh s` ds$ yf abzf saf j`hh`ydei {fhbsd`e~ad}7 yaf{f

d~ saf fhfofes `j b{fb sabs s{be~j`{ofc s`

bec

d~ saf dobif `j de saf vecfj`{ofc obsf{dbh% E`sdei sabs( yf abzf(

Cdhbsbsd`e bec B{fb Nabeif~

8/2/2019 SSG 516 Mechanics of Continua 3

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~` sabs( Sad~ d~ Ebe~`e~ j`{ovhb j`{ `ksbdedei saf s{be~j`{ofc

b{fb kb~fc `e b idzfe b{fb fhfofes de saf vecfj`{ofck`ct%

Yf abzf ~ffe fb{hdf{ sabs saf z`hvof {bsd`( cfs

Ebe~`e~ J`{ovhb

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>% V~f saf Nbthft/Abodhs`e saf`{fo s` ~a`y sabs(

b$ s{ ; k$ ; n$ cfs cfs cfs

c$ ,

f$