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(7 Estr ijkijk ( + + + + + + + + + + + + + + + + + + + + + + + + + + + + (7 (6(8 * * * 0 0 0 0 0 0 0 0 0 * 44 * * 0 0 55 0 66 (8 (7(9 Estr + + + + + 44 55 66 + + + (9
ij ordr paramtr E str E g( + α ( + α ( + α ( str 0 0 0 + + + + + + 44 55 66 + + + ( g ( ij α ii α ii δ ij ij εδ ( ij ij Estr g( + α ( 0 ε + α ( 0 ε + α ( 0 ε + ε + ε + ε + ε ε + ε ε + ε ε ( ij εδ ij ij E str E str str E 0 E str 0,, 0 ε ε ε E ε E ε E ε str str str ε + ε + ε α( 0 + ( ε + ε + ε 0, α 0 ε + ε + ε α ( 0 + ( ε + ε + ε 0, α ( 0 ε + ε + ε α( 0 + ( ε + ε + ε 0, α 0 ε ij η ij ε ij ηij ( 0 Vgard α α ( η + η + η α ( η + η + η (4 α ( η + η + η α ii ε ij ηij ( 0 (
Estr g( ( η + η + η η( 0 ( η + η + η η ( ( η + η + η η ( L NM + η + η + η + ηη + ηη + ηη ( 0 QP g ( + R S RS 0 0 ( η + η + η η ( η + η + η η ( η + η + η η ( L NM + η + η + η + η η + η η + η η g ( η + η + η + ηη + ηη + ηη ( 0 O U V O QP W UVW 0 (5 g ( RS g ( η + η + η + ηη + ηη + ηη ( 0 (6 (4,(6( m m Estr η + η + η + ηη + ηη + ηη ( 0 (7 ( η + η + η + ( η + η + η + ( η + η + η ( 0 + + + + + + (7 ijk r UVW 44 55 66 + + + Estr ijkηη ij k ( 0 ijkijηk ( 0 + ijkij k (8 ijkijη k ( 0 dr ijkijkdr (8 (9 r
L NM Estr ijkηη ij k ( 0 ijkijηk ( 0 + ijkijk dr ijkηη ij k ( 0 ijkijηk ( 0 dr ijkηη ij k ( 0 dr ijkηk ij ( 0 dr O QP (9 (0 ( r 0 Q( xp( ir (0 ij ( r pqmn{ ninqω ( n + njnqωpi( n} η mnq( xp( ir Ω p ( n pqk n q n k ( ( G ( r n n Ω ( nxp{ i( r } p j G ( r { ( } d nnω ( nxp{ i( r } Q( ' xp( i' d ' p j nnω ( n Q( ' xp( i r xp{( i' } d ' p j nnω ( n Q( xp( ir p j 0 ( (4 ( Pur diatation ( r η n n Ω ( n Q( xp( ir jj ppmm mm p j η n n Ω ( n Q( xp( ir ppmm mm p j (5(6 jj ( r ppmmη mm G ( r { ( 0} d (5 (6
P M 0 M (6{ ( 0 } { ( M } r r ( ( M, { ( M } 0 (6 (6 (6(7 mm ( r η ( G ( r d G ( r (7 jj d mm P M ppmm mm mm η mm( P M (7( ppmm G ( r d ppmm npnjω ( nxp{ i( r } dd ( π L NM L NM ppmm ppmm npnjω ( n xp{ i( r } d ds( n d ( π S ( n 0 ppmm n pn jω ( n r xp{ i( r } d ds( n d ( π S ( n ppmm npnjω ( n r δ{ nr ( } qds( n d ( π S ( n ppmm p j S ( n r n n Ω ( n δ{ n( r } d ds( n ( π (8 O QP O QP (8 x a x x + + (9 a a x / a y, x / a y, x / a y x '/ a y ', x '/ a y ', x '/ a y ',, / m, / m, / m + + + + (0 x y n mxx y y n m (8 (0 (
δ{ n ( r } δ{ n ( x x ' + n ( x x ' + n ( x x '} δ{ ( y y' + ( y y ' + ( y y' } δ{ ( y y ' + ( y y ' + ( y y '} δ{ m ( y y ' + m ( y y ' + m ( y y '} δ{ m ( y y' } ( n r r m y y y y (8 0 y m y y y m ign 0 R ( y m R ( y m ( y ( r, θ, r y (y' m y y θ y R (8
δ{ nr ( } d x' x ' x ' y ' y ' y ' θ r π R 0 0 δ{ nr ( } dx ' dx ' dx ' a a a δ{ m ( y y' } dy ' dy ' dy ' δ( m y rddθ dr a a a δ( m y d dθr r dr π δ( m y R d π ( δ( m y d π ( δ( m y d π m y d ( ' / δ( ' ' π { ( m y / }/ π { ( m y }/ ( ' ( m y my + my + my x x + + a a x a ( nx + nx + nx ( n r ( n r + + δ{ nr ( } d π { ( m y }/ R S ( n r π U V W (4
r δ{ n( r } d R S R S ( n r rπ U V W ( nx + nx + nx rπ π ( n + n + n π (5(8 G ( r d ppmm ppmm npnjω( n r δ{ n( r } d ds( n ( π S ( n ( π n n Ω ppmm S ( n p j ppmm n p n j ( Ω n ds ( n S ( n U V W L π ( n ds( n NM O QP (5 (6 a n + a n + a n (6r ign ndn δ n n ds ( n n n n dn dn dn δ n δ n δ n (7 m m m / / / ds( m dm dm dm adn / adn / adn / δ m δ m δ m aδ n / a δ n / a δ n / ds( n (8 (8(6
G ( r d ppmm n n ppmm p jω ( n ds ( n S ( n ppmm npnjω ( n ds( m S ( m (9 m n m m m + + + + + + (0 (6 S jjmm ppmmg d ppmm n p n j ( r Ω ( n ds ( n pm A ( S ( n A p j nn ds nn p j ds Ω ( n ( n Ω S ( n ( m ( ( n S ( m (7 η ( G ( r d jj mm P M ppmm mm ppmm jjmm mm G ( r d S A pm mm ( rr (( * ( ( ij ijk k k ijk k * k (4 * * ign k ijk ijk * * ((4 (4 k k ijk ijk k k
* * ( + ( + ( ( + ( + ( * * * ( + ( + ( ( + ( + ( * * * ( + ( + ( ( + ( + ( S + S + S S + S + S S + S + S * (5,,,, (5 (5 ( + ( + ( * * * * * * * * * ( + ( + ( * * * * * * * * * * * * * * * * * * ( + ( + ( S S S 0 S S S S S S 0 (6 0 S ijk p Ap S A A + A + A p p S A A + A + A p p S A A + A + A p p S A A + A + A p p S A A + A + A p p S A A + A + A p p S A A + A + A p p S A A + A + A p p S A A + A + A p p (7
A A A A A A nn Ω( n ds( n nn Ω( n ds( m S( n S( m nn Ω( n ds( n nn Ω( n ds( m S( n S( m nn Ω( n ds( n nn Ω( n ds( m S( n S( m nn Ω( n ds( n n n Ω ( n ds( m A S( n S( m nn Ω( n ds( n nnω ( n ds( m A S( n S( m nn Ω( n ds( n nn Ω( n ds( m A S( n S( m (8 ( n n n ω p ( pqk q k Ω Ω Ω Ω Ω Ω ( n n n n n + n n + n n n + n + n qi q i qi q i 66 66 55 ( n n n n n + n n + n n n + n + n ( n n n n n + n n + n n n + n + n qi q i 55 44 ( n n n n n + n n ( + n n Ω ( n qi q i 66 ( n n n n n + n n ( + n n Ω ( n qi q i 44 ( n n n n n + n n ( + n n Ω ( n qi q i 55 44 (9 Ω ( n (6(6 ( + ( + ( * * * {( S + ( S + ( S } + {( S + ( S + ( S } + {( S + ( S + ( S } * * * * * * ( + ( + ( * * * {( S + ( S + ( S } + {( S + ( S + ( S } + {( S + ( S + ( S } * * * * * * (40
* * * ( + ( + ( {( S + ( S + ( S } + {( S + ( S + ( S } + {( S + ( S + ( S } * * * * * * (5 (9 Estr ijkηη ij k ( 0 dr ijkηk ij ( 0 dr * * [ ijkηk ( 0 ij ijkηijηk ( 0 ] dr * * * * * [ ijkk ij ijkk ij ] dr * * * k ijk ( ij ij dr Vp * ijk * k * ij ( ij Vp ijk * k ij ( ij S jjmm V p (4 E str Vp V * * * p ijk k ij ij * ijk * ij * k * ijk ij * ( [ k ] (4 * * * ijk ij k + + * * * * * * * * * * * * ijk ij k + + + * * * * * * * * * + + + * * * * * * * * * (4 + + * * * * * * * * ijk ij k + + + * * * * * * + + + * * * * * * (44
m + +, m, + + m + + α + + m m m α m α m α m n, n, n a a a m,m,m, a,a,a n + n + n α m m m n + n + n α + + a a a α m a m m + + a a n α m α m α m, n, n (46 a a a (45