.1 ( 9\? 9\ (h/a) = D>0? Q] 9\? 9: C? 1?Y Q]? = 1? <? 4a.? 9V :27

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1 -37!"# ( / 3 3 *.,-. / FGC HCIJ F K L M - 7 ) D C /B- = 7 9: ; <. I- HCIJ F K L M - = L> HP>.- -. O 9: C F7 T < / -. I- GM. O B HP> 8. Q- G HP> R (.5) 6,- 7).** 389) :-.*4-,/ *) * 3-.-/, )-.*% &'(!) Y U V: LB HW X - HCIJ F K L M - 7 9: C ST-.- GM F7 C. - Z B HP;. - X ; - C :7 / G:B.,GQ V () Q] /B :7 9\ () D> /B,GQ :7 V V 83 X.- FJ7 8:[ \ HJ 9\ < 9\ 9: C ` D> /B :7 < <_:V. 9: C ^ Y 9\ 9\ (/) = D> Q] 9\ 9: C Y Q] = < 4. 9V 8 I. 9V :7. F K L > 7 9: =:3' 3>=-, Tel Buklig Alysis of -Dietiol FGM Ciul Plte Usig Fist-Ode Se Defotio Teoy S. Yousefzde Deptet of Meil gieeig, Isli Azd Uivesity Aligudz B, Aligudz, I Astt I tis ese, te itil uklig tepetues of -Dietiol FGM iul plte ude te two types of tepetue ise e lulted sed o fist ode se defotio plte teoy (FSDT) i te ses of lped suppot edge. Te equiliiu d stility equtios fo -Dietiol FGM iul plte e deived odig to FSDT d usig te eegy etod d ule equtios d te te stility equtios e solved y seies etod d opute pogig d te itil uklig tepetues e deived. At te ed, te esults e illustted y tles d gps d te effet of vious petes su s te volue ftio idexes o te itil uklig tepetues e studied d oped wit esults of soe ote tiles. Te esults sow tt fo diffeet vlues of volue ftio idexes i -dietio (), te volue ftio idex i z-dietio () s little effet o te itil uklig tepetues. Also we is positive, te itil uklig tepetues e deesed y iesig ut we is egtive, vie ves. Also, fo FGM tikess ostt, itil uklig tepetue is iesed y iesig te spet tio (/), wile deesed y iesig volue ftio expoet. Keywods: Ciul Plte, Tel Buklig, Futiolly Gded Mteils, Fist-Ode Se Defotio Teoy. kj < V. V WC p V< V V.- 3 o -/,GQ. \ / /Z 8:3 O-. H>g i /- V.- /Z.- q,gq. O ) /Z. I :/ 9; >J V i F /Z. >.- HI / V F3 D. \ d /Z <_:V. <5:V = / kj /Z.. F3 5:V p <5:V p p 8.Q i- kj.-3.-:v.-i d. B F : V > 984 L- R 8:3 O- < K 5 fg- fg g i.[] 9 5- F3 j JWi <. \. 5. i 9 k. l [ P d -. V F; / P ; P:>. 7 T- 8 <. / db i- \G 6 - F` HI SB. V B. 7 i 8\:V Futiolly Gded Mteils Hoogeeous * sy@iu-ligudz..i : 94// :! 94/7/6 :( )!

2 83 Q-. 8 K ( }[ ~ 5.[7] q 8; HW 5i x = 9: i- = 6 7 9: >g 8:V B. O 6 \ C VP FQGQ. I- H K (. L> HP> <>.i C FQGQ 8\ G:B.,GQ V Y{ /..[8] Z - 9: 6. I- Gg = 6 9: H> i V. X Z - GGC / C >[ / 83 X. - ( \.[9] 9\ Q] L[ 9\ 9: uq] d - V - 7 9: FGC 8:V : (. };C <.i C 8; 7 C - V- 7 9: C 8: GGC - VM. -V Q- S -C.- I- 83 };C < X.- I M. P 3 - M 7 9: C.[] FGM = 9: FGC 8.I L M. I- `i - 6 \ VP };C < X.i. O HCIJ F K = Q] 6 \ P Q] 9\ \.[] 9\ 9: C ; 8G:V FJ. I- P i = HP> <. - (> >[ / <> 9: FGC. O - ] ( 8_:V V Y 9V.[] Z - >[ / 9: C - 6 9: FGC 8:V - 5 L- C [ V ; > FGM SB. - H/B - i x.i B x V q- M }[ L> HP> /.- K Q] [.i DQM ( HP> F7 <> F K < 9:,GQ V Y{ -. S / C 9: \ Y{ ; V -. i- = 7 9: FGC ; <.[3] q HCIJ F K L M. I- Q- G HP>. I- L> HP>.- - 9: 9 V L> HP> 3p F7 ST- -C 9: C HP> F7.- D> - :7 G:B.,GQ V LB dz X Z - 9: C (Q] /B O; i K) i 7 U V:.- Z ; Y 5 HP; VM X db /Z u/ V.. I- <i- :V 8:3 ).- = 9: /.I. i ; < F; V > ) C = 9: FGC 4- L> HP> H K 8. I- i V 9: 9 V HP> <. I- - O,/ M HP>. -C 9: C 3 []..- gi p B 9 C = 9: FGC 7.I P d F K M. I- i > ) k HW H K - L> HP> U\B F I HP> H K (. I- - x z. 3 C = 9: FGC - - U \B HW X - Z - i > M - = 9: V X.-.[3] - ; F K L 4 = 9: 8; 9:i FGC y X < O.i F K q- M. I- q- M. I- = 9:. GJ7 = 9: 8; 9:i F K M 6 \ = > HW i q VFGC H :7 i 8Z. \ - K Q] F i H Y.- x L M HCIJ 9: 9:i = 9: X < ; \ - Z - q- F K q- M. I- - - V= 6-4 M V= L M VF7 F K Y{ 8 83 L M 83 I CIJ 9: 8; 9:i.[4] \,GQ VM d P d = 9: 8; 9:i FGC 8:V B / q- F K Z 8 M. I- C V8: V VF K U F7 i.i.[5] 6-4 M. I- 9:i 9: / C Q] /B = 9: FGC 7 d F K M. I- i 7,GQ V V X - L> HP> P 6-4 L F K M HP7 9: C.[6] : ; FGM uq] = 6 7 9: 8:V 8-Z L> HP>. Z >g 7 ) D C. Q- F K L M - s/b- = s7 9: FGC... M - 5 Bifutio 6 Reddy 7 Kizevsky Buklig Kioff 3 Sdes 4 Wg 38

$HJ CIJ 9 VI u w v u w ε =, ε = u v v w w ε = w w ε z = φ, ε z = φ () :, >. HJ \ VC <_:V k = φ,, k = φ, φ, k = φ, φ, φ () 8 () g. U\B }3 5 "," 8 : 8 K 9 G F ) /-8D-8. F'% G-,- 6 -. / VP V V.$ $T > @ - 6 - \G.. VP < F3 i \G 5 fg- fg- 6. - u4 g / i :[], >. HW > i. K P( z) = PV PV () 6 - \G :7 d V V 8 :[]. HW q V V z = ( ), V = V ( ) :u () g () g )5B z P ( z ) = P P ( ) (3) S. 6 - \G i d 8.$

3 . /,-. 3-, 6/) KJ/ /B- > SB. o = ; < -3.- Z 7 ) C =. Q] D> HWQ VC ;- C = 6 7 [ F 3-.-/, > KLMN-(.- 9: L < o F K L M. I- (,, z ) V/B d (U,V,W) / K 8 :[7 6]. HW U (,, z ) = u (, ) z φ (, ) V (,, z ) = v (, ) z φ (, ) W (,, z ) = w (, ). VC L7 9i ^ d U V φ, (8) = φ = z z - HWQ 5- VB V9 < g φ φ (7) :[7]. U W V U W ε =, ε = U V V W W ε = U W W W εz = z z V W W W ε z =, ε zz z z (9) F B-9 O (9) O (7) O )5B :[7] () HP> ε = ε zk, ε = ε zk, ε = ε zk, ε = ε () z z C CIJ 9 I F H V :, >. HJ CIJ 9 VI u w v u w ε =, ε = u v v w w ε = w w ε z = φ, ε z = φ () :, >. HJ \ VC <_:V k = φ,, k = φ, φ, k = φ, φ, φ () 8 () g. U\B }3 5 "," 8 : 8 K 9 G F ) /-8D-8. F'% G-, / VP V V.T \G.. VP < F3 i \G 5 fg- fg u4 g / i :[], >. HW > i. K P( z) = PV PV () 6 - \G :7 d V V 8 :[]. HW q V V z = ( ), V = V ( ) :u () g () g )5B z P ( z ) = P P ( ) (3) S. 6 - \G i d 8. HW (3) g }[ 5^ P P d ] -P L ( ) = ( ), α ( ) = α α ( ) ( z) V ( V ) z V V z V V : - ρ = ρ ρ (4) : o Y \ 8- d ] ν ( z ) - = ν (5) d ] -P L i, > 4] u I-. O. /B D. z = (, z ) = ( ) e z α = α(, z ) = α ( α α ) e :[5 z K = K (, z ) = K ( K K ) e ( 6) Qs] s- d :7 8 }s[ i 7 6 (6) g }g -P L. D> H,/ / 4I4J- 6, K-.5) &-( : F : 39 Reddy Volue Ftio Idex

4 Q = σ dz = ε dz = ε dz ( ν ) ( ν ) z z z ( ) [ ] A e = ε z = e Q ν ( ν ) ( ν ) ' Q = σ dz = ε dz = ε dz z z z ( ) [ ] A ' = e εz = e Q ν (7) <. <> uv 3 } [ :, >. HJ A, B, C, T, O k T z A = ( ) dz = ( ) z B = ( ) Z dz 3 3( ) = ( ) ( )( )( 3) (8) z C = ( ) zdz = ( )( ) ( ) ( ) ( ) ( ) = (, ) α (, ) (, ) T, z α, z T, z zdz T z z T z dz k =. i- = F F R > G 7 :[8 7]. HW 7 V C > V = U Ω R Ω 3 R U = F F R 3 = 3 R Bi ( 9) V = g V. F :[9], >. F U π / = ε / ijσ ij dd dz () π / U = ( z z ε σ εσ ε σ ε σ / ε σ αt σ σ dd dz () ( )) z z :. - H Ω R.- π ( ) Ω = p u p v p w dd d = H z i, j =, 8 () F R 9-9 O )5B.- z V/B u w ε = z ( φ, ) v u w ε = z φ, φ u v v w w ε = z φ, φ, φ w w εz = φ, ε z = φ ( 3) :u. F 9 9 O V 8Z. I- σ = ε νε ( ν ) αt ν σ = ε νε ( ν ) αt ν σ = ε, σ z = εz, σ z = ε z (4) ( ν ) ( ν ) ( ν ) :-. F L g (, z ) G (, z ) = (5) ( ν ) :- H V G F = N σ (, z ) dz, ij = ij M ij = σ (, z ) zdz Qi σ iz (, z ) zdz ( 6) (6) O (4) () O )5B.- i, j =, : -. HW V N = σ dz = ε νε ( ν ) αt dz ν = ε ( ) zk ν ε zk ( ν ) αt dz ν A C T = e k k = e N ν ν ν ' [ ε νε ] [ ν ] M = σ zdz = ε νε ( ν ) αt zdz ν = ε ( ) zk ν ε zk ( ν ) αt zdz ν C B T = e k k = e M ν ν ν k ' [ ε νε ] [ ν ] ij s/b- = s7 9: FGC... M - Potetil egy Sti egy 3 xtel Foes 3

5 . /,-. 3 w w w w N N N N ( Q ) ( Q ) Q M ( M ) ( M ) Q M ( M ) ( M ) ( 6) N N 7 S. = HP>. 9: 9 V N )-.% &'(!)-4 x s> sc 8s; s7 = 9s: s- s L7 Is- N, N 9: 9 V.u. 7 ) s. HsW 9s:. FsZ sv8 l)s7 (3) L> HP>. : FJ7 d u du d φ d φ A u C φ d d d d du u d φ φ A ν C ν d = d d u du du u u ν d d = d d u du u (7) d d 6 = HP> qp. (34) g }[ u = (8) C :u-. - zb 8 F7 > :, >. HW =. O u = fiite (9) u = > F7 L > (7) g q- q HP> )5B HP>. I-. - u 3 φ A ; - : -. HW 9: 9 V (9) (7) T N = N =, N (3) ν / H-8 &-P- H!), &'.-5 V = T = u x s.u- = /,. <. T 9s s 7 sv9s ( T = T T ) s C s l4si < s 9s: s C s l4si.s, >. O,9: :, >. HW i 9\ 7 T ( z ) = T = T = T T (3) :-. HW. O u() = φ () = Fiite, dw () w () = (3) d [7] G HP> L: Q] /B L 5 (9) F : -. L> > X R k N N N e e N ( N ) p N N e e N ( N ) p w w w w N N N N ( Q ) ( Q ) pz Q M ( M ) ( M ) Q ( ) ( ) (3) M M M = O. - K ( G- /Z HP> :[ 7]. - H F F R G 3 V = δv δ V δ V (4)! 3! < δ V V H K < kz δ V g <. 7 δ V q/i <. V H K V8 K G =. δ V > J (,). δ V < J (z). L> 7.. L> 7. V8 K G = = HP> u u 5 o δ V J 8i uv j - ; kz C.u - < : C 5 H. : 6 L> Z IJ <. δ V > 8. - < C 8 δ V 8. = 6. FJ7 Bi 6 FJ7 B 8 -.[ 7] - HY \ O- FJ < :u ] B VI 6^ ; 6 5:V L> u u u, v v v, w w w φ φ φ, φ φ φ (5) kz ( φ, φ, w, v, u) VB (5) g > ) C L> 7 B ; 8:V φ φ 8 K 6^ ; (,, w, v, u) VB )5B. L> 7. 6^ : = HP> G HP>. I- (5) () (5) O : -. HW N N N e e N ( N ) N N e e N ( N ) Vitiol Metod Tefftz

6 zb.- - = q > F7. γ = 8. FJ7 9: C / - / / Q.R &-P- H!), &'. -6 HMS H = D>s Qs]. >s,k = s -,7 < s>.ss s o () g HW -. :, >. HW 9- d dt ( K (, z ) ) dz dz = (4 ) :u (4) () O. I- K s d T dt ds K K s ds.- (4) s s- zsb.-- = > F7 z s = s sgi p 9\s s7 9: C g /.u- Q] /B >-/8, 6,- q. /B-FGM SB. = ; < -7 GZ HP; zb zb u - I- < u I- LB }g VY ; 8:V. u: ; -., P D-8-6, \G i 6 - i = 7 GP 6 α 3 = /C K 4 ( W / K ) ν.3 = 78 GP 6 α = 7.8 /C :[ 8] K.4 ( W / K ) ν.3 - s = 9s: C 3 /B = s = i 7 ) C /B s s / D>s s Q],GQ ; = LsB <s. s gs:v.s- s U D> - :7 s; < s so s 9s: s C / 9\ - };C <. FJ7 X LB < <_:V. 9\,GQ < i }g - ; kb - i 7.i u3^ X < - s = 9s: C 5 4 /B s = Q] /B K ) C /B s / D>s s Qs],GQ ; = = LB <. g:v.- U D> - :7 s; < s so s 9s: s C / 9\ - }s;c <. FJ7 X LB < <_:V. 9\,GQ \s 7 < - ; kb - i 7. B X < < i }g v. uss s = s sc 8; 7 B s s u o l J H;3 G <_:V φ 5s- sb 8s s- HP> < uvi s VB d7 > d u du u du u A ν d d d (6) > X : Vi F d φ dφ dφ φ C φ ν d d d dw d φ d w dw A φ φ e d d d d d dw N d d d φ dφ dφ B d d d φ ν φ. HJ d u du u du u C d d ν d dw A φ d (33) 8 A = A, B = B, C C = ν ν ν A = A, B = B, C = C ( ν ) ( ν ) ( ν ) (34) :u (33) g q- > L > )5B d φ d φ d φ φ ν φ d d d dw β φ d (35) C β = A 8 B A :u. F (33) g q > dw dφ d w φ e d d d dw d dw φ e α d = d d (36) :. V K K. I-. N α = A dw ' d w Y =, Y = d d q = φe e α Y (37) : F. q (36) > q q ' (38) > )5B (37) >. I- (38) > F7. S d φ dφ α d γ γν β φ = d α e :u (36) s/b- = s7 9: FGC... M - (39) 3

7 . /,-. =, -/.V V) 7T, 3-. H-8 )-.% 3-UV H!) 4-,/ ) 3-.-/, &' -.! 3/-6, [8] [] [6] CPT FSDT HSDT (FSDT) ]7 ; = / 5 = = - / 5 = - / /76 / 7 / 78 3 / 4 6 / 39 / 73 5 / / 77 / 5 /866 5 / / 769 / 55 4 / 93 5 / 8 / 9 / 7 / 4 /449 4 / 9 3 / 99 7 / / / 3 / / 657 / 3 3 /465 3 / 333 / 6 48 / / 97 / / / 989 / 4 37 /94 35 / 6 34 / / / / / 55 3 / 993 / 5 =, -/.V) 7T, 3-. H-8 )-.% 3-UV H!) 4-,/ ) 3-.-/, &' -.! 3/-36, [8] [] [6] CPT FSDT HSDT (FSDT) ]7 ; = / 5 = = - / 5 = - / 5/97 5/ 96 5/ 94 / 43 / 898 5/ 96 / 966 4/ 484 / 3/63 3/ 63 3/ 59 5/ 648 / 585 3/ 65 47/ 85 97/ 9 / 53/69 53/ 9 5/ 989 / 689 6/ 7 53/ 35 7/ 447 / 6 / 3 94/5 94/ 8 93/ 97 / 58 46/ 7 94/ 9 9/ 63 39/ 877 / 4 47/694 46/ 85 46/ / 69 7/ / 63 97/ 6 69/ 98 / 5 =, -/.V V) 7T, )-.% 3-UV H!) 4-,/ ) 3-.-/, &' -.! 3/-46, [8] [] [6] CPT FSDT HSDT (FSDT) ]7 ; = / 5 = - / 5 = - / 5 /433 5 / 49 5 / 46 6 / 84 / 479 5/ 47 5/ 54 5/ 45 / /455 / 59 / / 3 49 / 86 / 6 5/ 84 4/ 4 / 8 /898 8 / 8 7 / / 598 / 99 8/ 5 46/ / 35 / 3 45 /8 44/ / 3 96 / / / 7 89/ 96 68/ 979 / /88 63/ 3 69 / 85 5 / / 39 63/ / 63/ 986 / 5 =, -/.V V) 7T, )-.% 3-UV H!) 4-,/ ) 3-.-/, &' -.! 3/-56, [8] [] [6] CPT FSDT HSDT (FSDT) ]7 ; = / 5 = - / 5 = - / 5 /378 5 / / 37 3 / / / / / 748 / 6 /5 6 / 44 6 / 48 4 / 75 3 / 59 6 / / / 87 / 38 / / / / / / / / 7 / 3 64/5 44/ / / 596 / 44/ / 54 7/ 58 / 4 384/453 38/ / 43 9/ 96 87/ 38 38/ / / 839 / 5,sZ =. 9V < 9V 9\ 9: C s = T us- 9s: s C s : /G.,sGQ s; s i 7 ) 7 d7 s 9s: s C s V 83 V: < g:v.- o74 FZ g =. 9V < 9V 9\ s = T 9s: s C s s: 4 3/Gs.,sGQ ; d i 7 ) 7 d7 s sv 83 V: < g:v.- u- / s : 6 5 /G. 9V 9\ 9: C s 7 )s s7 ds7 s = T 9s: C.s- s us- /,sgq s; s ds s i p 9\s s 9s: C V 83 V: < g:v. 9V ds7 = T u- 9: C : 4 3 /G,GQ ; i 7 ) 7 / 9\ 9: C V 83 V: < g:v.- s;. s3 I ; 9\ < 9\ /. (<5:V 7) IJ ` ds7 = T 9: C : 6 5 /G u-,gq ; i p 7 ) 7 / 9: C V 83 V: < g:v.-. 9V 9\ 9\ < 9\ / 9\ ds7 = T us- 9: C : 8 7 /G,GQ ; i p 7 ) 7 / s 9s: s C V 83 V: < g:v.-. s3 si ; 9\ < 9\ / 9\. (<5:V 7) IJ ` ; d7 = T 9: C : 9/G s; i p i d 7 ) 7 V 83 V: < g:v.- u- /,GQ 33

8 s/b- = s7 9: FGC H!) 4-,/ ) 3-.-/, &' -.! 3/-6( =, -/.V) 7T, 3-. H-8.R )-.% 3-UV H!) 4-,/ ) 3-.-/, &' -.! 3/-3( =, -/.V V) 7T, 3-. H-8 )-.% 3-UV - M... H!) 4-,/ ) 3-.-/, &' -.! 3/ -7( =, -/.V) 7T, 3-. H-8.R )-.% 3-UV H!) 4-,/ ) 3-.-/, &' -.! 3/-4( =, -/.V) 7T, 3-. H-8 )-.% 3-UV H!) 4-,/ ) 3-.-/, &' -.! 3/-8( =, -/.V) 7T, 3-. H-8.R )-.% 3-UV H!) 4-,/ ) 3-.-/, &' -.! 3/ -5( =-, -/.V) 7T, 3-. H-8.R )-.% 3-UV 34

9 .,-. / H!) 4-,/ ) 3-.-/, &' -.! 3/-( /=.5, -/.V) 7T, 3-. H-8 )-.% 3-UV H!) 4-,/ ) 3-.-/, &' -.! 3/-9( =, -/.V V) 7T, 3-. H-8 )-.% 3-UV H!) 4-,/ ) 3-.-/, &' -.! 3/-3( =5, -/.V V) 7T, 3-. H-8 )-.% 3-UV H!) 4-,/ ) 3-.-/, &' -.! 3/ -( =.5, -/.V) 7T, 3-. H-8.R )-.% 3-UV -4( 3-UV H!) 4-,/ ) 3-.-/, &' -.! 3/ /=.5, -/.V) 7T, 3-.H-8 )-.% H!) 4-,/ ) 3-.-/, &' -.! 3/-( /=.5, -/.V V) 7T, 3-. H-8 )-.% 3-UV 35

10 [3] Njfizde M. M., Heydi H.R., Tel uklig of futiolly gded iul pltes sed o ige ode se defotio plte teoy, uope Joul of Meis A/Solid 3(6): pp. 85-, 4. [4] M L. S., Wg T.J., Nolie edig d post uklig of futiolly gded iul plte ude eil d tel lodig. Itetiol Joul of Solid d Stutues;4:33 3, 3. [5] Sjedi A., Byt M., Mustp F. Spu S.M., Zi, R. Fee Vitio Alysis of Futiolly Gded Qudgle Pltes Usig Seod Ode Se Defotio Teoy. Austli Joul of Bsi d Applied Siees. 4(5): pp ,. [6] Njfizde M. M., Heydi H.R., A ext solutio fo uklig of futiolly gded iul pltes sed o ige ode se defotio plte teoy ude uifo dil opessio. Itetiol Joul of Meil Siees. 5(3): pp. 63-6, 8. [7] Gisi S.., Kii Y., Sdigi M., sli M. R., Tel uklig of se defole tepetue depedet iul/ul FGM pltes. Itetiol Joul of Meil Siees. 8, pp , 4. [8] Ji M., Joue,. F., Mojedi A. Tel uklig lysis of poous iul plte wit piezoeleti tutos sed o fist ode se defotio teoy. Itetiol Joul of Meil Siees. 83, pp , 4. [9] Reddy J. N., Kdei A. A., Buklig d vitio of lited oposite plte usig vious plte teoies. AIAA Joul; 7(): pp.88 7, 989. [] Dvize M., Dvize A., Tel uklig lysis of odetely tik oposite ylidil sells ude xisyeti tel lodig. Ii Joul of Meil gieeig; 6(): pp. 99 7, 7 [] Njfizde M. M. Ov, A. Meil uklig lysis of FGM iul plte wit tuto-tuto piezoeleti lyes, sed o eutl-axis positio d usig fist-fde se defotio plte teoy. Ii Joul of Meil gieeig; 6(): pp , [] Kizevsky G., Stvsky Y., Refied teoy fo vitios d uklig of lited isotopi ul pltes. Itetiol Joul of Meil Siees.38(5): pp , 996. [3] Stoui S., Kgovi M. H., Allki F., Asji A., Applitio of tid ode se defotio teoy i uklig lysis of D-futiolly gded ylidil sell eifoed y xil stiffees. Coposites Pt B: gieeig. 79, pp , 5. [4] Se H. S., Futiolly Gded Mteils: Nolie Alysis of Pltes d Sells, CRC Pess, Tylo d Fis Goup, Bo Rto, 9. [5] Alipou M. M., Siyt M., Stess Alysis of Two-dietiol FGM Modetely Tik Costied Ciul Pltes wit Nouifo Lod d Sustte Stiffess Distiutios. Joul of Solid Meis Vol., No. 4, pp ,. [6] Reddy J. N., Ceg Z.Q., Tee diesiol tet defotios of futiolly gded etgul pltes. uope Joul of Meis A/Solids;: pp ,. [7] Bus D.O., Alot B.O., Buklig of s, pltes d sells. New Yok: MGw Hill; 975. [8] Njfizde M. M., sli M.R., Buklig lysis of iul pltes of futiolly gded teils ude uifo dil opessio. Itetiol Joul of Meil Siees 44(): pp ,. [9] Sues S., Motese A., Fudetls of futiolly gded teils, Bes d Nole Pulitios; 998. [] Fuiy T., Nod N., Tsuji T., Ot Y., Alysis of tel stess d stess itesity fto of futiolly gdiet teils. Cei Tstios Futiolly Gdiet Mteils. 34: pp.45 3, 993. [] Njfizde M. M., sli M. R., Fist-ode teoy- sed teoelsti stility of futiolly gded teil iul pltes. AIAA Joul 4(7): pp ,. [] Njfizde M. M., Hedyti B., Meil stility lysis of FGM iul pltes usig fist ode se defotio teoy. ISM Ii Joul of Meil gieeig 5(): pp. 8-34, 4. H!) 4-,/ ) 3-.-/, &' -.! 3/-5( =, -/.V) 7T, 3-. H-8.R )-.% 3-UV H!) 4-,/ ) 3-.-/, &' -.! 3/-6( /=.5, -/.V) 7T, 3-. H-8.R )-.% 3-UV 3.V 4-8 SB. = 6 7 9: C ; < i p i 7 ) D C /B- > 7 HCIJ F K L M - FZ 9Q V: LB X.- Z >g : - FZ F Q] L[ 9\ = 9: C - :7 I ; 9\ < 9\ /. IJ ` ;. 3 d7 = 9: C 9V - D> /B :7 9\ Q] /B :7. 9: C ; Y 6. 3 o F F K L M. FJ7 X -3 M. FJ7 X i 7 /3i ^ < V 83 D] <.- 6\ F K P.V i Z. FJ7 /B W-. - s/b- = s7 9: FGC... M - [] Youi M., Koizui M., Futiolly gdiet teils. Poeedig Of Te Fist Itetiol Syposiu O Futiolly Gded Mteils, 99. [] Njfizde, M. M., sli M.R., Teoelsti Stility of ototopi iul pltes. Joul of Tel Stesses 5(): pp ,. 36

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