ميكانيك المواد المركبة

830

description

Mechanics of Composite Materials Robert M. Jones

Transcript of ميكانيك المواد المركبة

?=QAzy ?+Av ?zTzSG

v9

D

v h

G

Z K?I9 b @P V I FU

wV I FU

wP

w V I FUwP

wV I FUwP

!

P V I FU P P V I FU P V I FU P QXPEHU VTXDUHG P P

P P P P V I FU V I FU

9 I (P(I

9 I

K

9 IK F

V I FU

V F PD[ 9 I V I FU

9 I

9 I (P(I

9 I

[ [

H I FU

9I 9 I

(P

(I

( V P

( P H I FU

V F PD[ 9 I V I FU 9 P V P

V F PD[

(P 9 I 9 V I ( I FU

V F PD[

( 9 I (P(I

9 I 9 I P ( I 9 I

(I (P

[ \ J [\

wY wX

w[ w\

[ X\ Y

GYG[

GXG[

\

wXw\

>X F X F @ F

X F

K GYF G[

wXw\

K GYF G[

J [\

K GY F G[

W [\

* P J [\

'8 P

W [\ J [\ G9 9

'8 P

K S* P F F /

Q DQ

Q

V I FU

*PS ( I PK

9 I 9 I /

/P K / V I FU

*P9 I 9 I

V I FU

*P

9 I

H FU

* P

9 I 9 I ( I

03D NVL 03D NVL 03D NVL >@ 5RVHQ 'RZ

'RZ >@5RVHQ

(I*P (I*P

'RZ > @5RVHQ

6FKXHUFK >@ 6 *UHV]F]XN>@ -XQH /DJHU

>@

V F PD[

9 I

V F PD[

9 I ( P ( I

9 I

* P

9 I

> @5RVHQ'RZ

/DJHU > @-XQH

>@ /DWRXU =KDQJ

9I 9I 9I

6WHSKHQ : 7VDL 6WUXFWXUDO %HKDYLRU RI &RPSRVLWH 0DWHULDOV1$6$&5-XO\ - & (NYDOO 6WUXFWXUDO %HKDYLRU RI 0RQRILODPHQW&RPSRVLWHV 3DSHUSUHVHQWHG DW 3URFHHGLQJVRIWKH$,$$ WK6WUXFWXUHVDQG0DWHULDOV&RQIHUHQFH3DOP6SULQJV&DOOIRPLD$SULO$,$$1HZ@

V [ V \ W

44

44

H H 4 J

4LM

V [ V \ W [\

4 44 44 4

4 H [ 4 H \ 4 J [\

4LM 4LM

N ^V `N

>4 @N ^H `N

] J []

J \]

J [] J \]

H ]

Z YX ][ ] \[ % [ XR R $%&'

& X F XD ] F E

$%&'[ E

[]

E

w:D

w[

X

X XD ]

w:D

w[

\Y

Y YD ]

w:D

w\

J [\ H \ H [ H ]

J []

J \]

H[

H \J [\

wXw[wY

w\wX wY

w\ w[

YX

H[

H \J [\

w :DwX D]w[w[ w :DwYD]w\w\

w :DwX D wYD ]

w[w\w\ w[

H [D N [ D H \ ] N \ J [\D N [\

H [ H \ J [\

H HJ

D[D\D[\

wXD w[ wYD w\ wX wY D D w\ w[

N[ N \ N [\

w :D w[ w :D

w\ w :D w[w\

N [\ N \ N [ \ P[E H \ U :RU

N V [ V \ W [\ N

444

444

N [ 4 H [D 4 H \D ] N \ N [\ 4 N J [\D

4LM

1 [

W

W

V [ G] 0 [

W

W

V [ ]G]

1[

0[ 0[ 1[ 1

1[ 1 \ 1 [\

V [ V \ G]W W [\ W

V [ V \ G] N = N W [\ N1

=N

0[ 0 \ 0 [\

V [ V \ ]G]W W [\

V [ V \ ]G] N = N W [\ N

W

1

=N

]N]N]]L ]N N ]N ]D

W N

] 1

W ]

W W 1 ] 1

W W

\ [ ]

1

> @

4LM N

1[ 1 \ 1 [\

44N 4

N[ 4 = N H [D =N 4 H \D G] N \ ]G] = N 4 N =N J [\D N [\

444

1

0[ 0 \ 0 [\

44N 41

444

N[ 4 = N H [D =N D4 H \ ]G] N \ ] G] = N 4 N = N J [\D N [\

> @

4LM N

> @

4LM N ] ] N [\ N \ N [ J [\D H [D H [D

1[ 1 \ 1 [\

$$ $

1[ 1 \ 1 [\

%% %

$$$%%%

$ H [D % $ H \D %$ J [\D %% H [D ' % H \D '% J [\D '

%%%'''

% N [ % N \ % N [\ ' N [ ' N \ ' N [\

$LM %LM

'LM

1

4 =N

LM N

N

= N

14 LM N = N = N N

1 4 LM N = N = N N

$LM 'LM %LM @ %LM > %LM 1[ D 1[ 1[\ 0[ 0[\ [ D1[ 1 [

D [

D \

$ H $ H %N [\

N [\ 1[ H \D H [D

>@

$'LM%LM$LM $ %LM ' ' VSDQZLVH

>@

>@

'LM %LM $LM

> @

*[\ Q [\ (\ ([ x x x

Q ( W $

$

(W ' Q

'

(W

Q

' % 'LM

W N 4LM N W N = N %LM N 1

1

4N

W = N $LM

LM N N

1

4N

W

LM N N

= N WN 4LM N N

( Q D ( Q D D D 1 [

D [

D\

$ H $H %N [\

4LM D % $ $ W0[

W ( $

(W Q

$ '

$ $ $ $ $

(W Q

(W Q

'

Q$ ' Q'

$ %LM

'

'

'

'

Q$ '

(W Q

Q'

1[ 1 \ 1 [\ 0[ 0 \ 0 [\

H [D $ Q$ Q$ $ H \D Q D $ J [\

N [ ' Q' Q' ' N \ Q ' N [\

'

$W

W $ $ $

4W '

4W

4W '

4 W

4W %LM

$

'

4W

$

'

$

'

4 W '

4

LM

4W

1[ 1 \ 1 [\ 0[ 0 \ 0 [\

$$

$$

''

''

D H [ H D \ $ J [\D

N [ N \ ' N [\

W 4LM $LM

4LM W %LM

'LM

4LM W

1[ 1 \ 1 [\ 0[ 0 \ 0 [\

$$ $ '' '

$$$'''

$ H [D $ H \D $ J [\D

' N [ ' N \ ' N [\

J [\D H \D H [D 1[\

N \ N [ N [\

4LM 4LM $LM

4LM W %LM

'LM

4LM W

4LM N VWUDGGOH

WN 4LM N %LM

1[ 1 \ 1 [\

$$ $

$$$

$ H [D $ H \D $ J [\D

0[ 0 \ 0 [\

'' '

'''

' N [ ' N \ ' N [\

'LM$LM

W

W

W

( Q

( Q

W

( Q

W

( Q

W

( Q

W

( Q

N 4 N

4 N

4 N

(N 4 N Q

Q N (N 4 N Q N

4 N

(N

Q N

1[ 1 \ 1 [\

$$

$$

0[ 0 \ 0 [\

''

''

H [D H \D $ J [\D

N [ N \ ' N [\

' '$ $$LM 'LM

' $ $ ' >4LM @N >4LM @N N 4 N

(N

N Q N Q

4 N

4 N

4 N

Q N (N 4 NN Q N Q

4 N

(N

N Q N Q

*N

'$ $ 4 N 4 N %LM ' ''$$

4

4

4

4

W

)

)

)

)

W

*

*

*

*

W

+

+

+

+

W

*

*

*

*

W

)

)

)

)

>ttt@ t

$LM

1

4 ]N

LM N

N

]N

4 LM $LM 4 LM $LM 4 LM 4 LM 4 4 4 4 $ $ $ $ 7ULJRQRPHWLF 4 4 $ $ $LM

14 LM N ]N ]N N

%LM $LM

4 LM N ]N ]N N 1

= N = N 4 LM 'LM ' ' ' 4 4 4 4 4 4 ' ' '

%LM 'LM $LM ''$$ ;$ IRUZDUGVZHSW 0\ GLYHUJHQFH ' '

' ' >@ :HLVVKDDU 6KLQN+HUW]

>@

W

4 )

W

*

*

*

*

W

+

+

+

+

W

*

*

*

*

W

)

)

)

)

4 )

4 )

4 )

''$$ 1 1 1 1'$ $

1

4 ]N

N

N

]N

'

1 4 N ]N ]N N

'$ 4 D

4 D

'LM$LM''$$ %LM ' ' $ $ ' ' $ $'$ ''$$

%LM ' ' $ $ $ 4LM

>@ DQWLV\PPHWULF

> @

4 LM N

> @

4 LM N [

> @

4 LM

N

$ $

1

4 ] N

N

N

]N

4 D

4 D

$ 4 N ' '

14 N ]N ]N N

4 N ' %LM

1[ 1 \ 1 [\

$$

$$

H [D % H \D %$ J [\D %

%%%

% N [ % N \ % N [\

0[ 0 \ 0 [\

%% %

%%%

% H [D ' % H \D '% J [\D

''

N [ N \ ' N [\

$ $ ' '

W WWWWW

1[ 1 \ 1 [\

$$

0[ 0\ 0 [\

%

444 ) ) ) * * * + + + + + +***)))

$$

%

H [D % H \D $ J [\D H [D ' H D\ ' J [\D

''

%

4 ) * + +*)

N [ N \ N [\

N [ N \ ' N [\

%

444 4W ) ) ) )

W * * * *

W + + + +

W + + + +

W ****

W ))))

1[ 1 \ 1 [\ 0[ 0 \ 0 [\

$$ %

$$

%

H H$ J

D[D\D[\

%

% H [D ' % H \D ' J [\D

%''

% N [ % N \ N [\ N [ N \ ' N [\

% %

XQV\PPHWULF WN N (N 4 N

4 N

4 N

(N 4 N Q N

4 N

Q N (N 4 N Q N

(N

Q N

WN 1[ 1 \ 1 [\

$$

$$

D H [ % H D % \ $ J [\D

%%

N [ N \ % N [\

0[ 0 \ 0 [\

%%

%%

H [D ' H \D '% J [\D

''

N [ N \ ' N [\

% $ ' % $ '

VWDFNLQJVHTXHQFH >ttt@ >@

> D # W D # W D # W @ > WD DW D W @ >tttttt@ >ttt@ >ttt@ >ttt@

>

D D

@

>ttttt@

>ttt@ >tttttt@

>

@

q q 6 >ttt@ 7 >ttttt @7

TXDVLLVRWURSLF H[WHQVLRQDO VWLIIQHVVHV $ $$ $ $

Q$ $ $

$LM

$LM

4LM 3RLVVRQ 4 LM @ t@ >ttt >ttt t t t1 'LM %LM $LM 1

EDODQFHGODPLQDWHV t u

u

K\EULGODPLQDWHV r

>

@

D% r D* *D 6

' %$ &DUG -RQHV

%LM 4 D

4 D

u

>@ % % %%'HYHORS $ $ ' ' 1[ 1[ 4LM>@ W 1[ 0[ [ [ [

10

D $ % H

% ' N

1

$H %N

%H D 'N

0

D

H D H D

$ 1 $ %N

0

%$ 1 %$ % 'N

H D 0

$ %$

$ % 1 ' %$ % N

H D 0

$ 1 % N

+ 1 'N

N + % N

'0 ' + 1

H D % ' 0 $ % ' + 1

H D N

$ % ' +

' +

% ' 1 ' 0

H D N

$c %c 1 + c ' c 0

' % $ % + c

' % $ 'c %c $c % c 7 + c 'c %c $c '%$

FURVVSO\ODPLQDWH 1 [ \ VSHFLDOFURVVSO\ODPLQDWHV > D # W D # W D # W D # W @

01

WW

0

N RGG

N HYHQ

N

N

> WD DW DW DW DW @

W W WW W

0

0 0 W 0 $LM

%LM %LM

1

4N

= N = N

LM N

1 4LM N = N = N N

1 4LM N = N = N N

1 0)

)

44

(

(

>@ 7VDL (( ) W1

0 ) 4W $ 0 $ $

0) 4W 0 $

$

$ %LM '

4W 0)$ 0 )

4 W

> ) 3 @4W > ) 3 @ 0

$W

0 )

'

'

'

4W

3

0 1 >0 1 1 @

1 0 0

1 $

0 ) 4W 0 $

$

$

$0 ) 4W

1 0 % % '

%

4 W0 ) $W1 0 0 )

% %

%

> ) 5 @4W > ) 5 ) @ 0

$W

0 )

'

'

0)$ 0 )

0) 4W 0 $

%

4W

4W

> ) 5 ) @4W > ) 5 ) @ 0

$W

0 )

'

'

'

4W

5

0 0

0 1 0

1 $LM 1 1 W)0 $ $ $ ) $ 0 4W 4W0$$0$$ $ $ ) %LM

1 0 % % \ 1% 1 %

1 1% % 71\ [

@ 7VDL 0 $>

@7VDL0$>

0 % >@7VDL

1 'LM ' ) 0 ' ' 0 1 ) '$W ' 1 1 1

$W ) 1 0 '

>@7VDL0'

0 ' >@7VDL

([WUVVD >@ 7VDL 863RO\PHULF&R(18)

0 0

H N

$c % c7

%c 1

'c 0

'c %c $c $ $ z $c 'c %c $c ' % PP PP LQ 6SDQ PP

W

W H LD N L

L

H LD N L

H LXSSHUH LORZHU

W %c %c $cc 'c %

$c $c

%c %c 1

c 0 'c 'c '

c %c %c'

c $c%c $

'c

c $

' '

3/

:F

$ :F

>@7VDL

>@7VDL6,

1

[

>

D # W D # W D # W D # W

@

6

1 W 4LM 1

4

$LM

N

= N = N

LM N

%LM

1 4LM N = N = N N

'LM

14LM N = N = N N

W 4LM 1 4LM

4D

4D

4D

4D

4D

4D

4D

4D

4D

4D

4D

4D

>@ 7VDL

4W

$ $ $ $$ $

4

4

' '

4

1

%LM' ' ' '

4 4 4 W

4

4 4 4

4

W

W 1 1

1

$ $ $ $$ $

4

% %

' ' ' '' '

% % % %

4 4 4 W

4 4

W1

W444

4

$LM $ $ 1 $ $ $ $

1111 $ $ 1

>@7VDL

%LM 1 % % W $ 1 %0 [\%

W$ W1 [ H [D

% >@7VDL

1 T

%W$

0 [\

W1 \

D

' ' 1 '

'

1

1 1 ' ' D ' ' ' ' 1

' >@7VDL

% % ' ' $ $ u D $ $ J [\

J [\XSSHU

XSSHUH H [XSSHU H \XSSHU D

J [\ORZHU

ORZHUH H [ORZHU H \ORZHU D

\ [ D H D

>@7VDL

>@7VDL6,

' %LM $ $ '

W RGG

W HYHQ

W1

W RGG

W HYHQ

W1

0 W RGG

W HYHQ

W1

0 W RGG

W HYHQ

W 1

0 W RGG

W HYHQ

W1

IDLOXUH GXFWLOH EULWWOH GHIOHFWLRQ

K\JURWKHUPHFKDQLFDO

0\ 0[1\ 1[

( 7VDL+LOO 7VDL+LOO (

WKHUPRHODVWLF LM

,QYHUVLRQ LM

GLVWRUWLRQ 3ULQFLSDO0DWHULDO&RRUROLQDOHV30&

V V W

44

H D '7 H D '7 4 J

44

NWK

V [ V \ W [\ N

444

44 4

4 H [ D [ '7 4 H \ D \ '7 4 J [\ D [\ '7

D [\

1[ 1 \ 1 [\

$$ $

$$$

$ H [D % $ H \D %$ J [\D %

%%%

% N [ 1 [7 % N \ 1 7\ % N [\ 1 [\7

%LM $LM 1[ 1 \ 1 [\

4 44

4 4 4

4 4 4

D [ D \ '7G] D [\ NN

17 0[ 0 \ 0 [\

%% %

%%%

% H [D ' % H \D '% J [\D '

'''

' N [ 0 [7 ' N \ 0 7\ 7 ' N [\ 0 [\

'LM 0 [7 0 7\ 0 [\7

4 44

44 4

4 4 4

D [ D \ '7]G] D [\ NN

07 17

1[ 1\ 1 [\

1 [ 1 [7 7 1\ 1\ 1 [\ 1 [\7

$$ $

$$$

$ H [D % $ H \D %$ J [\D %

%%%

% N [ % N \ % N [\

0 [ 0 \ 0 [\

0 [ 0 [7 7 0\ 0\ 0 [\ 0 [\7

%% %

%%%

% H [D ' % H \D '% J [\D '

'''

' N [ ' N \ ' N [\

07 17 0101 0 1 1 0

$ % H D % ' N

H D N

$c % c 1 + c ' c 0

+\JURVFRSLF E E D D D L > @ PP LQ 7 & ) > @

' W ' 'W >@ ' [ >@ LQKU 7 >@6 >@

>@

>@ >@ 1[ 1 [ \ 0 LQ PPLQPP

0

(( [SVL*3D

( [ SVL*3D

;W ;F NVL03D

@

@

[ OE LQ [ 1 P

>OE LQ> [

@ 1 P @

c $

[ OE LQ [ 1 P

c $

[

1 7; 1

'703D q& < '7 SVL q )

@

@

q& q) q& '7 q ) q& q)1 ; SVL03D W

'7

1;W

SVL03D

1;# '7SVL q) SVL'703D q& 03D W

q) q& q)

q&

1;W

SVL03D

q& q)

1;W

SVL03D

q& q) V ; \ [ W03D @

[ WSVL > [ W03D @ c $

[ WSVL > [ W03D @

c $

V ; V '7 )& 1[W SVL03D

GHJUDGHG [ \ 4

4

[ SVL *3D

$c

[ WSVL > W*3D @

$cc $

[ WSVL > W*3D @

V ;

1;

W

[

1; W

H

D;

$c W

[ SVL *3D

1[ V ;

SVL 03D

NVL V ; NVL 03D 03D

'V ;

'1 ;W

SVL SVL 03D

1;W

SVL SVL SVL03D

> @0

URXWLQJ

>@

D >@ >@ (

PP LQ PP LQ 4

4

[ SVL *3D

4

4

[ SVL *3D

4

4

[ SVL *3D

4

4

4

4

4

[ SVL*3D [ SVL*3D

4

[ SVL*3D

D [ D \ D [\

[ q ) [ q&

D \ D [ D [\

[ q) [ q& [ q ) [ q&

$c

[ OE LQ V\PPHWULF

[ 1 P V\PPHWULF

$c

1 7; 1 @

x

x

x

x

x

>@

RIIVHW

SODQH VWUHVV @ >

T D D D [\ D \ D [ D [\ D [\ 1 c[\ 1 c\ 1 [c 0

V [ 0 0

FODVVLFDOODPLQDWLRQWKHRU\&/7 W ]\ W ][ V ] 1 [ LQWHUODPLQDUVWUHVVHV &/7 W [\ V \ V [ \ [

3LSHV > @3DJDQR

W [\ V \

W ]\ W ][ V ]

1[]\[

V V V N

H D H D 4 J D

4 44 4

V [ V \ W [\ N

4 44 44 4

4 H [D 4 H \D 4 J [\D

$LM

1

4N

LM

N = N = N

1 [

$$

$$

H [D H \D $ J [\D

H \D

$ 1 [ H [D

$ $ $

$ 1 [

$ $ $

J [\D

H H J N

$ FRV T VLQ T $$$ 1 [

FRV T VLQ T

$$$$

$ FRV T VLQ T $ N

V [ D D W [\ &/7

&/7

W [\ [] W [\ $%&' $%&'&' $% W [\ [ W [] $%&' W [\ W [] W []

>@

V V V W W W

&& &

&& &

&& &

&

&

H H H J J & J

V [ V \V ] W \] W ][ W [\

&&& &

&& &

&&&

&

&

&

&

&

&

& H [ & H \ & H ] J \] J ][ & J [\

H [ J \]

9C] :C\

8 C[

H \

J ][

:C[ 8 C]

9C\

H ]

:C]

J [\

8 C\ 9C[

[ [ ] \ X

.[ 8 \ ] Y 9 \ ]

Z : \ ]

W [\ \ W ][ ]

V \ \ W \] ] W \] \ V ] ]

&8 \\ &8 ]] & 9 \\ &9 ]] & & : \]

&8 \\ &8 ]] &9 \\ &9 ]] & & : \]

& & 8 \] & & 9 \] &: \\ &: ]]

\] [ W \]

V ]

W []

W [\

V \

W \]

:98]

9 ] \

8 ] \

: \

: 9 8 \

9 ]

8 ] : \ ]

>@

EKR QXPHULFDO

W [] V ] W \] :98

( [SVL*3D* * * [SVL *3D

( ( [SVL*3D Q Q Q

E K ] K W [] W [\ V [ W [\ V [ \ E W [] K

* * * Q Q

W [] W []

W []

> @

>@

>@ 0RLUp 0RLUp )ULQJHV >@

0RLUp 6 0RLUp 0RLUp u D GLDJRQDO W [] 6

>@0RLU

] K >@

V \ >@6 $%&' \ $%&' V \ W \] \ W \] W \] V \ [ V ] V ] ] V ] >@ V ]

V ] W \]

> @

>@6 >@6 > @ V ] >@ >@6 0SD SVL

[ V ] V \ V \ V ] >@ V ] V \ V ] V ]

@ >@6 >@6 > >@6 > @6 V ]

>@

] >@

> r T @ W [] >@ W [] W []

> r T r T @ V ] W \] W []

> T T >@6 @6 >@6 >@6 'LM$LM

>@

V[H[

[ SVL *3D

W [\H[

[ SVL *3D

V \ W [\

X

& ] & \ & \ & ] & [ 8 \ ]

& [ 9 \ ]

& [ Z & [\ & [ : \ ]

Y & ] & [

] \ >@

.63LVWHUDQG6%'RQJ(ODVWLF%HQGLQJRI/D\HUHG3ODWHV-RXUQDORIWKH(QJLQHHULQJ0HFKDQLFV'LYLVLRQ$6&(2FWREHUSS (5HLVVQHUDQG@5HGG\>@9DVLOLHY

1[ 1 \ 1[\

$ $

$

$

$

H R [ R H \ J R [\

0[ 0 \0 [\

'

'

'

'

'

N [ N \ N [\

' ' ' ' ' '

%LM

UHVWULFWLRQV DVVXPSWLRQV

DE DVSHFW UDWLR 1[ 0[0\0[\1\1[\ .LUFKKRII .[ .\ S[\

x x x

[\ x ][]\] [\ [\[] [] xVWDWHPHQW ] ]

XYZ x [ \ [\ x LQHUWLD x

x x[ \ [\ ] X Y ] x ] [] \]

S[\ 1 1 0

[ [[

[ [

1

1

[\ [ 0

S

[\ \

\ \

[\ [\

0

\ \\

$ X $ X $ X $ Y $ $ Y $ Y [[ [\ \\ [[ [\ \\

% Z% Z % % Z % Z

[[[ [[\ [\\ \\\

$ X $ $ X $ X $ Y $ Y $ Y [[

[\ \\ [[ [\ \\ % Z % % Z % Z % Z

[[[

[[\ [\\ \\\

' Z ' Z ' ' Z ' Z [[[[ [[[\

[[\\ [\\\ ' Z % X% X % % X % X \\\\ [[[ [[\ [\\ \\\ % Y % % Y% Y % YS [[[ [[\ [\\ \\\

%LM %LM %LM 'LM $LMW Z ZXY

FODPSHG VLPSO\ VXSSRUWHG IUHH HGJHV XYZ Z

X

XQQX XWWZZQQZ Z

1

1

Q

1

Q

1QWQW

00QQ40.QW WQQ

WQWQ .Q 4Q 7LPRVKHQNR >@ :RLQRZVN\.ULHJHU [ X

1[

>@&6>@$OPURWK

6

Z

0

6

Z

0

6

Z

0

6

Z

0

&

Z

&

Z

Z Q

&

Z

&

Z

QQQQ

Z Q

Z Q

Z Q

X

Q

X

Q11QQXXQQ11QQXXQQ11QQXXQQ11QQ

XX11

WW

QW

XX

W

W1

1

QW

QWQWX XWWX XWW 11QWQW11QWQW

URWDWLRQDO UHVWUDLQW 6 0[ \ \ WUDQVODWLRQZ \

6Y X \[ 1[\1[ 6 [ \ 1[Y X\ 1[\ 6 \ [ 1[X Y[1[\ 6 Y[\1[\1[ X Z[ Z

EXFNOLQJ ORDG ELIXUFDWLRQ +HQQHPDQQ -RQHV >@ HLJHQYDOXH

G0

[ [[

G0

G 1 [ [ G 1 [\ \

G 1 [\ [ G 1 \ \

[\ [\

G0

\ \\

1 GZ 1 GZ 1 GZ[ [[[\ [\\ \\

1[ 0[ Z X Y Z Z 1 [ 1 \ 1 [\ 1 [

G 1[ G 1 \ G 1 [\

R $$$ GH[ %%% GN

[ R $ $ $ GH \ % % % GN\ $ R %$$%%GN GJ [\ [\

R % % % GH [ ' ' ' G N [ G GH R %%%'''N

\ \ % % % GJ R ' ' ' G N [\ [\

G 0 [ G 0 \G 0 [\

GH GN

R

[

[

G X [ GH

R

GZ

GN

[[

G Y \ GJ

\

\

GZ

R

[\

G X \ G Y [

GN

\\

[\

GZ

[\

6

6 6 6

GZGZGZGZ

G0QG0QG0QG0Q

GX

QG1

QGX

QG1

Q

GX WGX W

G1

QWG1

QW

GZGZGZGZ

& & & &

G Z QG Z QG Z QG Z Q

G XQG 1QG XQG 1Q

G XW G XW

G 1 QW G 1 QW

G0

[ [[

G0

[\ [\

G 1 [ [ G 1 [\ \

G 1 [\ [ G 1 \ \

G0

\ \\

1 GZ 1 GZ 1 GZ[ [[[\ [\\\\

UGZ WW

1 [ 1 \ 1 [\

5RWDU\ ,QHUWLD

*DOHUNLQ 5D\OHLJK5LW]

\ [ >@ :DQJ $VKWRQ >@

S[\ [ [ \ \ E 'RXEOH)RXULHUVLQH6HULHVf fPS[QS\ VLQ U PQ VLQDEP Q

3 [ \

S S [ \

ff SR PS[QS\

VLQVLQ

PQDESP Q

>@

S[\

' ' %LM

VSHFLDOO\ RWKRWURSLF ODPLQDWH $ $ $ $ ' ' ' ' ' Z [[[[ ' ' Z [[\\ ' Z \\\\

S [ \

[ D

Z

\ E

Z

0 ' Z ' Z [ [[ \\ 0 ' Z ' Z \ [[ \\

XY

Z

ffPS[QS\

VLQVLQ DDEP Q PQ

D

PQ

S PQS

>@

> @> @

>@

P Q P Q

''' ' D D E E

Z

SRS

ffP Q

PS[QS\

VLQVLQ

PQDE

PQ P Q ' ' '' D D E E

>@

> @> @

>@

' ' ' '

V\PPHWULFDQJOHSO\ODPLQDWHV

'' Z $ $

[

D

Z

\

E

Z

0 ' Z ' Z ' Z

[ [[ \\ [\

0 ' Z ' Z ' Z

\ [[ \\ [\

Y X ' ' Z H[SDQVLRQ ' ' '' @ZVWDWLRQDU\ > 9

Y > ' Z [[ 'Z [[ Z \\ ' Z \\ ' Z [\ ' Z Z ' Z Z SZ@ G[G\ [[ [\ \\ [\

SZ S >@ :KLWQH\ >@ /DQJKDDU H[DFW HQHUJ\ Z[ Z 0 Q

0 Q1 Q

1Q

VWDWLRQDU\ Z 0Q FRQYHUJHQFH Q P Q P

'' '''

>@ '' ''

D S

'

' '

ZPD[

' ' '' ''' D3

ZPD['

VNHZ

S ;@ *HUH> @

1RGDO

1

PDJQLWXGHV

$ $ $ $ '''' 'GZ [[[[ ' ' GZ [[\\ 'GZ \\\\ 1 [GZ [[

[ D G0 [\ E G0 \

'GZ [[ 'GZ \\

'GZ [[ 'GZ \\

Y X Z Y X Z G Z

$PQ VLQ

P S[QS\VLQ

DE

\ [ Q P

PQQ D 1 [ S ' ' ' ' DE E P Q 1 [

1 [

P D ' ' ' DE E P

S '

P 1 [ DE$VSHFW5DWLR ''' '' 1

[

P D S ' E P E D

[ DE 1

[

S '

E

DE 1 [ [ 1 [

S '

E

1;

''' '

$ '' $

'G Z [[[[ ' G Z [[[\ ' ' G Z [[\\ ' G Z [\\\ ' G Z \\\\ 1 [ G Z [[

[ D GZ G0 [

'GZ [[ 'GZ \\ 'GZ [\

E GZ G0 [ 'GZ [[ 'GZ \\ 'GZ [\ \ ' ' \[Z >@ :DGGRXSV $VKWRQ>@&KDPLV GZ

f

f

$P Q

PQ

VLQ

PS[QS\

VLQDE

$PQ Z 0Q (( *( u P Q >@ 0DQGHOO

> @:KLWQH\1;

$ $ $ $$ ''% % % % '' ' % $GX [[ $GX \\ $ $ GY [\ %GZ [[[

$ $ GX [\ $G9 [[ $GY \\ %GZ \\\

' GZ [[[[ GZ \\\\ ' ' GZ [[\\ % GX [[[ GY \\\\ 1 [GZ [[

6 -RQHV>@[ D GZ GY

G1 [

\ E GZ GX

G0 [ G0 \

G1 \

%GX [ 'GZ [[ 'GZ \\

$GX [ $GY \ %GZ [[

%GY \ 'GZ [[ 'GZ \\$GX [ $GY \ %GZ \\

P S[Q S\VLQ

GX X FRVDEPS[QS\

GY Y VLQFRVDEPS[QS\

GZ Z VLQVLQDE 1 [

>

D 7 7 7 7 7 7 7 @ 7 PS 77 7

7 7

PS QS $ $ D E $ $ PS QS D E

7

PS %

D

7

QS PS $ $

E D

7

QS 7 % E

PS QS PS QS

'

'

'

D E D E

77% Q P 7 7 7 ' ' Q Q QP >@ Q P QP 1 [ Q P P(O

S P S /P Q P DE Q P 1 [ QP Q PP Q P

QP Q P VWDWLRQDU\ Q P

Q P LQIOHFWLRQ Q P QRQLQWHJHU

QP Q P Q PQ @ PPQ> ' & Q ' &

(( *( ' E

>@-RQHV1;

((

*( % ((

> @-RQHV

$$$$ '''' %% $GX [[ $GX \\ $ $ GY [\ %GZ [[\ %GZ \\\ $ $ GX [\ $GY [[ $GY \\ %GZ [[[ %GZ [\\

'Z [[[[ ' ' G: [[\\ 'GZ \\\\

% GX [[\ GY [[[ % GX \\\ GY [\\ 1 [GZ [[

6 6 > @

[

D GZ G0 [

GX \

G1 [\

E GZ G0 \

GY

G1 [\

% GY [ GX \ 'GZ [[ 'GZ \\$ GY [ GX \ %GZ [[ %GZ \\% GY [ GX \ 'GZ [[ 'GZ \\$ GY [ GX \ %GZ [[ %GZ \\

PS[QS\

GX X VLQFRVDEPS[QS\ GY Y FRVVLQ

DEPS[QS\

GZ Z VLQVLQDE

JRYHUQLQJ 1 [

D PS

777 77 77 7

77

7

7

PS QS $ $ D E

7

$ $ PS QS

7

D E

PS QS QS % % E E D

7 7

QS PS $ $

E D

PS QS PS % % E D D

7

PS PS QS QS ' ' ' ' D D E E

7 7 % %

(( *( 8QFRQVHUYDWLYH

0RUJDQ -RQHV 1; >@:KLWQH\

1[ W ,QHTXDOLWLHV 8QLGLUFWLRQDH 8' '8'!'8'&URVVSOD\ &3 '8'!'&3 '&3!'8' (W ' ' P DE '

P P DEDE6HW 'HWHUPLQDQW

[ [ D \ \ E 1RW )RUFHG >@

' $ $ $ $ ' ' ' 'GZ[[[[ ' ' GZ[[\\ 'GZ \\\\ UGZWW

D GZ

[ \

E GZ

G0 [ G0 \

'GZ[[ 'GZ \\ 'GZ[[ 'GZ \\

+DULQRQLF GZ [ \ W

$ FRV ZW % VLQ ZW GZ[ \

>@ QS \PS[

GZ [ \ VLQVLQDE Z

S PP QQ ' ' ' 'U D D E E

ZQP

Q P '' '' N Z

NS E

'

U

NQP

NQP

' ' QRGDO OLQHV P Q P Q P Q P Q

$ ' ' $ 'GZ[[[[ 'GZ[[[\ ' ' GZ[[\\ 'GZ[\\\ 'GZ \\\\ UGZWW

[

D GZ

\

G0 [

E GZ

'GZ[[ 'GZ \\ 'GZ[\

G0 \

'GZ [[ 'GZ \\ 'GZ [\

' ' \ [ Z GZ

f

f

$P Q

PQ

VLQ

PS[QS\

VLQDE

Z 0Q

$ $ $ $ $ ' % % % 7HUPV ' ' ' '%% $GX[[ $GX \\ $ $ GY[\ %GZ[[[

$ $ GX[\ $GY[[ $GY \\ %GZ \\\

' Z[[[[ GZ \\\\ ' ' GZ[[\\ % GX[[[ GY \\\ UGZWW

GX [ \W X FRV

PS[QS\ LZWVLQH DE

GY [ \W Y VLQ GZ [ \W

Z VLQ

PS[QS\ LZWFRVH DE

PS[QS\ LZWVLQH DE

6

[ D

GZ G0 [ %GX[ 'GZ[[ 'GZ \\ GY G1 [

$GX[ $GY \ %GZ[[

\ E

GZ G0 \ %GY \ 'GZ[[ 'GZ \\ GX G1 \

$GX[ $GY \ %GZ \\

Z

S

7 S

777 77 77 77 7

% > @ 7LM 7 7 7 7 7 ' ' 'HQRPLQDWRU Q P Q PQ P

Q P (( *(

>@-RQHV

> @-RQHV

$QOLV\PPHWULF$QJOH3O\ /DPLQDWHG3ODWHV%%$$$$

' ' ' ' $GX [[ $GX \\ $ $ GY [\ %GZ [[\ %GZ \\\

$ $ GX [\ $GY [[ $GY \\ %GZ [[[ %GZ [\\

'G: [[[[ ' ' GZ [[\\ 'GZ \\\\

% GX [[\ GY [[[ % GX \\\ GY [\\ UGZWW GX [ \W GY [ \W GZ [ \W

[ D

PS[QS\ LZWX VLQFRVH DEPS[QS\ LZW

Y FRVVLQH DEPS[QS\ LZWZ VLQVLQH DE 6

GZ G0 [ % GY [ GX \ 'GZ [[ 'GZ \\ GX G1 [\ $ GY [ GX \ %GZ [[ %GZ \\

\ E

GZ G0 \ GY G1 [\

% GY [ GX \ 'GZ [[ 'GZ \\$ GY [ GX \ %GZ [[ %GZ \\

Z

SU

777 77 77 7

77 7

% % > @ 7LM 7 7

% (( *( %%

:KLWQH\ 0RUJDQ -RQHV >@

>@ >@ 0RUJDQ -RQHV [

>@-RQHV

EDVHOLQHD E [ %LM

\ [

>@0RUJDQ-RQHV

H[WUDSRODWLQJ [ $ ' \ $ '

%4W

1

( 1 (

1 ' $ 1 %4W ' PDJQLWXLWHV %

>@-RQHV

EDVHOLQH %LM %LM \ [

' ' ' %LM P Q '

1 [ / S ' ' '

>@-RQHV

'

XQFRQVHUYDWLYH

>@-RQHV

>@ (( 44 1 [

1 \

>@$VKWRQ

(( >@

>@:KLWQH\ 1E 4 W

P Q

44 44 44

t

6WDYVN\ 5HLVVQHU DSSUR[LPDWH DSSURDFK >@ >@5HGXFHG6WLIIQHVV0DWUL[UHGXFHGEHQGLQJ VWLIIQHVV 5%6 '

' %$ %

' ' ' ' ' %$$ ' ' '

'

%

$

'' >@ 5%6 5%6 (ZLQJ >@ /HLVVD +LQJHU >@ 6

6 u

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

>@3LQFNQH\

>@6DONLQG

6DYLQ >@ > @ /HNKQLWVNL >@ t t

VT >@*UHV]F]XNV

T >@ *UHVKFKXN V D D t t D T

q

>@ 1T W W 1T

D >@*UHV]F]XN

>@*UHV]F]XN

$LU)RUFH

(OHFWUD &$ ) PDWUL[ >:X @

> $$*ULIILWK @8 6

w6

wD

w8wD D

w8wD

>@ ,UZLQ 3 D

>@:X

3H

8

/H

P

3H

GD

wHwD

w8wD

w3 wH 3H wD wD

w8wD

w3H wD

w3wD

wHw H P wDwD P

3 wPP wD

w8wD

3 wPP wD

*>@

*

3 wPP wD

* P3 ,UZLQ 6NHZ V f W f V\PPHWULF

f 6XSHUVFULSW

V [

Vf D

TTT FRV VLQ VLQ

U

W

f

TTT DVLQ FRV FRV

U

W [\ V \ W f D V f D U

N N

Vf DWf D

N N

*

SN

(

FRPSOH[YDULDEOH

>@:X W[\V\V[ W f D V f D >@:X &ROOLQHDU

N V f D N

V

N F N F

fF

D

F

>@:XDF V Ff N ORJDF ORJ V Ff

ORJ NF

ORJ V Ff ORJ D F

>@:X

>@ &RUWHQ >@ 7HWHOPDQ &KHQ 6LK >@(LVHQPDQ :DGGRXSV 1RQFROOLQHDU> 6ZHGORZ .RQLVK .DPLQVN\ @ &UXVH+DQVRQ &KDPLV >@ 6HUDILQL

PDWUL[

([ *\] *[] \] []

>@ \ 3 3[

X

X[

Y

\

Z Z [

[]

$X [[ % Z [[[ ' Z [[[[ %X [[[ S

X [[[

%Z [[[[$

Z [[[[

$S'

' $ ' %

S

SR VLQ

QS[/

Z

$ SR / QS[

VLQ' QS /

X

% SR'

QS& / QS FRV /

H [

X [ ]Z [[

QS[ $ ] % / SR VLQ'/ QS

SR 4N $ ] % / QS[VLQ'/ QS

V[

N

SR 4N $ ] % / QS[VLQ QS '/

V \

N

[] ]

W [] ]

V [ [

V ]]

W [] [

W []N

V ]N

N

SR 4 / $ QS[] % ] + N FRV' QS /

N

SR 4 $ % QS[] ] + N ] /N VLQ'

/

/N +N

( [SVL*3D

( [SVL*3D

* [SVL*3D

* [SVL*3D

9 Y

@S SRVLQ[/ Z > 6 /W 6

>@3DJDQR

[ 6 6 W[] 6 6 X 6 6 6 V] W[]]

6 6 > @ >@ > @>@

>@3DJDQR6 V

> @3DJDQR6 V

>@3DJDQRW[]

>@3DJDQRX

@ >@ > >@ >@ >@ >@

H ]

V ] FH [ FH \ F

WK

. H] V [ V \ W \] W [] W [\ N

4 44 4

4

H[

H \

J \] 4 J [] 4 N J [\ N

W

W

N[]

N\]

FL F M FLM LI L M 4LM

FFLLM

I

LM

>4 I ] D @ ) [ \ >4 I ] D @ ) [ \ N

N

N

[

N

\

@

N

J []N

J \[

N I ] D )[N 4 N I ] D )\N 4

] ]Z

>

@

XN

]Z [ - ] J N ] ) ;

.

]Z \ - ] J ] )

N

@

- ]

I ] G]

N

J ] D4N

J ] D4N

N

] E

N

N

N

N

] E

Y X

Y X ]YX )< ) ;

'LM )LM + LML

W

W

4 LMN ]- ] G]

W

W

4 ]J ] G]NLM

NL

L M

L

4\ 4;

W

W

W

W

W []N G]

W G]N\]

. ) ;

N ) \

N

LL

W

>4 I ] D @G]N

W

L

NLL

LL

0 [ [ 0 [\ \ 4[

0 [\ [ 0 \ \ 4\

4[ [ 4\ \ S 1 [ Z [[ 1 [\ Z [\ 1 \ Z \\

'Z [[[ ' ' Z [\\ ) + ) [ [[ ) + ) [ \\

) ) + + ) \ [\ . )

' ' Z [[\ ' Z \\\ ) ) + + ) [ [\ ) + ) \ [[ ) + ) \ \\ . ) \

. ) [ [ . ) \ \ S 1 [ Z [[ 1 [\ Z [\ 1 \ Z \\

4Q

Z

0Q

ZQ 0QW

XW ] ]

WQ

S

Z ) [ ) \

SR VLQ

PS[QS\VLQDE

PS[QS\VLQDEPS[QS\VLQ% FRVDEPS[QS\FRV& VLQDE

$ VLQ

0 [ 0 \

X ]

]

Y ]

]

Z

Z

[

\

E

D

>@

] I ] W

&%$

PS ' P ' ' Q 5 $ D

>

@

. 56 ) + P ) + Q 5 %S ) ) + + PQ5&

QS5 ' ' P ' Q 5 $ ) ) + + PQ5% D

>

@

. 56 ) + P ) + Q 5 &S

SR D

. P% . Q5&

S

6 DW5 DE

>RRRR@>@ SRVLQS[DVLQS\D

((

*(

*(

Y

SR VLQ SS[D VLQSS\D :KLWQH\ >@ >@ W[\ V\ V[

>@:KLWQH\SRVLQSS[D

DW SR VLQ SS[D >@:KLWQH\$VKWRQ >@ >@ W[\ V\ V[ >@ YDULDWLRQDO>@>@

+\HU>@

[ \[ \ \ [ \[

>@+\HU >@

Z [ \

D[ E\

X R [ \ F[ Y [ \ R

D [DE[\

E \ DE[ \G\

7

( [ SVL*3D

( [ SVL*3D * [SVL*3D

9

[R)[R& [R)[R&

t& t) t&t) >@7

D E\ E[ D6 67 77ULIXUFDWH

\ [ [ \ PP>@7

>@+\HU 7 7 7 7

67 7 7 / / \ [

[ 7 7 \ [ \ / 7 7 [ 0[ 77 PP PP >@7 PP >@7PP>@ +\HU

)ULHG >@

6SULQJHU>@

@ > 7J $6 >@

JDOYDQLF FRUURVLRQ )

>@ >@>@>@ >@

>@ >@

>@ >@ >@ >@ 9LVFRHODVWLF0DWUL[ >@ >@ >@

0 - 6DONLQG 972/ $LUFUDIW LQ $SSOLFDWLRQV RI &RPSRVLWH0DWHULDOV 0LFKDHO - 6DONLQG DQG *HRIIU\ 6 +ROOLVWHU HGV$670673$PHULFDQ6RFLHW\IRU7HVWLQJDQG0DWHULDOVSSUHSULQWHGZLWKSHUPLVVLRQ

./5HLIVQLGHU(*+HQQHNH::6WLQFKFRPEDQG-&'XNH 'DPDJH 0HFKDQLFV DQG 1'( RI &RPSRVLWH/DPLQDWHV 3DSHU SUHVHQWHG DW 0HFKDQLFV RI &RPSRVLWH0DWHULDOV 5HFHQW $GYDQFHV 3URFHHGLQJ RI WKH ,87$06\PSRVLXPRQ0HFKDQLFVRI&RPSRVLWH0DWHULDOV=YL+DVKLQDQG &DUL 7 +HUDNRYLFK HGV %ODFNVEXUJ 9LUJLQLD $XJXVW3HUJDPRQ3UHVV1HZ8

8 FRV T 8 FRV T @ ]] G]

888

$ % '

W 8 W 8 FRV T ]] G]

8 FRV T ]] G] 9L$%' 9 $% '

W W

9 $% '

FRV T ]] G]

9 $% ' 9 $ % ' 9 $ % '

VLQ T ]] G]

FRV T ]] G]

VLQ T ]] G]

1

: ]

9L$ 9L% 9L'

N

N 1

N

] N

:N ] N ] NN 1:N ] N ] NN

>@3DJDQR7VDL9$%' 9$%' 9$%' 9$%' 9$%'

88

8888

88

88

8888

$%'$%'$%'$%'$%'$%'

1]L

FRV T N LVLQ TLNFRV T N LVLQ T N L

:N [ N N 1 N [

$

8 W 8 FRV T I G] 8 FRV T I G]

7ULJRQRPHWULF FRVD E FRV D FRV E VLQ D VLQ E

] 7ULJRQRPHWULF $

8W 8 9 $ FRV I 8 9 $ VLQ I 8 9 $ FRV I 8 9 $ VLQ I

$ LM 9L$ % LM ' LM $LM 9L' 9L% 9L$ 4LM 'LM %LM

3DJDQR7VDL$LM>@VLQ

FRV

VLQ

FRV

89$89$

89$89$

89$ 89$89$ 89$

89$89$

89$

89$

89$

89$

89$

89$

89$

89$ 89$ 89$

89$

89$ 89$ 89$

$ $ $ $

$ $

9]

RGG IXQFWLRQ G]]

]

HYHQ IXQFWLRQ G]

L $ % '

ILQLWH

]

] ] ] ] 1

S

1

]N u 9 FRV ST ]

L $ % '

,QWHJUDQGV

VLQ ST ]

FRV ST ]

VLQ ST ]

S 9 $

9 $

9%

9 %

9 '

9 '

@ 3DJDQR 7VDL > $

$

%

%

%

%

'

'

%% ] N

9 FRV ST ]

L $ % '

VLQ ST ]

FRV ST ]

VLQ ST ]

9%

9 %

9 %

9 %

%LM 'LM$LM ]

9L$%'9 L

9 L

S

S

S

S

FRV ST

W VLQ ST ] ] G] GT W

S S

9L GT

S 9 L

W

S

S S

W

FRV ST

VLQ ST GT ] ] G]

9L$%' $ %LM

$

8 W

$

8 W

'LM

$

$LM W

8 W

$

$

$$ $ 1! 1

9 $

S

19$

SS WFRV 1 FRV 1 " FRV S 1

FRV [ FRV [ " FRV Q[

VLQ Q [

[

VLQ

[ 9 $

S SVLQ 1 VLQ 1 " VLQ S

S1W

1

VLQ [ VLQ [ " VLQ Q[

VLQ

QQ[ VLQ [

[VLQ

9$ [

S1

S1 $LM

9$ [

%LM >@ %LM > @'LM

S

$LM GI

S FRV SI GI

VLQ SI

S $LM 8 8 888 $LM 8 88 $ LM 88 $ LM % LM ' LM

8 8 8 4 8 4 8 8 > @

8 8 8 ( 88 $LM 4LMW $LM t $ LM $ $ 0 $ $ *(

7VDL

>@3DJDQR

>@ 8

(

8

*

( (

* # ( (

( #

( (

$ $ $ $ $ $

$ $ $ ]

4 4 4

$ $

] $ $

$ $

4 4

% % % % %

' ' ' ' '

@ >>@6FKPLW

$$ '' 0 1 ' $$' 0 1

$ $ % & ' % &

&

1[

1[\ 1[ 1\ QQQ

>@6

[ \ >@ 7VDL [ \

u u

-DPHV ( $VKWRQ >@$,$$$60(6$(

0XUSK\

>@6>@6>@6t t $ $

$ $ ' ' u u

DXWRFODYH

*UXPPDQ %LM >@ $VKWRQ '

' %$ %

%$%

DQWLV\PPHWULF DV\PPHWULF >@>@

* (

3DJDQR 3LSHV6LQJXODU >@

QRUPDOV

>@ 3DJDQR :KLWQH\

RSWLPL]DWLRQ

SUHSUHJJHU

+HQU\ )RUG

*HRUJH /XELQ HG +DQGERRN RI &RPSRVLWHV 1HZ

9+"t @

?+@ Q+j A|

9+"t @

&*

( | ?+"t @

bS } KaT y

9 S (t @

9} +T @

Iteration

9 = + = A 9 < ? * (t @

Qw@

Design-Analysis Iterations

~ + }Z Ay { + z ;

Isotropy

9f

Qw@

,I 9 "C { C9 E

Expansionl

OE

Symmetry

Qc9 "@

Frequencies

JG GG YRqG YRqGh YRqGHGGG FG GG,F

Q@ (@

O

Stress Distribution

9%F

gqd

Strain Distribution

( WA y

Weibul Distribution

(= *

Tape Laying

(@

(@

(@

? a * QW y h \ ( @

G F G

Holes in Laminates

? +t= a y K 9 qZy ,p

Orthotropic

(t C

,I 9 "C ,C ; C

Orthotropy

,I 9 "C ,C ; C

fh

Bimetals

O gC , 9 "C

Elastic Constants

? ! Q C B< ( C

Engineering Constants

? + S O " $ B< ( C

Y

Beam||z

9gV

R 9F

Stiffness

IA

?+ y (a y ( WA y

Longitudinal Stiffness

G )g

G J

9| 9t|h

( IA

? s9 s Q y (W A y ?| 9 t|

Lamina Stiffness

G )g

q

G

? y RA M C

h

n

Reduced Bending Stiffness

G a

9 T@9 T@

( IA

G g

G

G

9 TF

9 a g ! : 9 TFG IA

r + zy 9 : ] ? = T " y 9 < ? + ! 9 \ Q g y 9 T@

Stiffness Transverse to Fiber Direction

G

E

G IA

G

[ ty 9 TF

Shear Stiffness

q

G IA

Reduced Stiffness

?y R A M C 9 T@

Specific Stiffness

? + f( " y 9 T@

G IA

G IA

Stiffness in Arbitrary Coordinates

)

?+ _ 9 = A f ?+ q + v 9 + C O I , p 9 T@G(

J

G

E

IA

G

G

Stiffness in Fiber Direction

r + zy 9 : up

Special Cases For

{ F # | ?Y 9L :9I

q

G g

G

h IA

C

Plane Stress State

9 T@

G

G

J

j

( AT | 9% F ?y9IO

E

, }AI

Deterministic

~+} ZAy ?y( > OIq

Design Load Limit

G

Buckling-Critical

L

9 g =!: OIq qG j

9 T @ OI

Stiffness-Critical

IA

Strength-Critical

? | 9 tC OI

Padding Up

_a = @ ( WI

qG j

qG j

h

,

?! Q C {I

Elasticity Solution

h

G

, }d f } { }A

Ultimate Load

G

G

First-Ply Failure Load

] } ? s9 sQ z y 9 + 8 : { >

Design Ultimate Load

, }d f } ~+ }ZA y { >

h

G

Q

G

G

? 8p 9 w }Ay ?+w +! 9 w +C

Equivalent Mechanical Loads

G

G

G J

:( }A

G

Transverse Load

?+ !9\Q f ? y( >

Plywood

, t 9 s > WLF

Nodal Line

j

||{

Q

O tf bL

? aL

Linear

+

Properties of

qUG (

? w 9w

Mechanical Properties

+

+!

qUG (

L

Q jA| :

qUG (

L

Q jA| :

qUG (

L

Q ? F O < ? a = @ Q|

qUG (

L

OG(

q q

*

Invariant Properties

I

Invariant Properties of

I

IQG

+ CG U G (B G

}z y ? OI

Extrema Of Material Properties

Temperature-Dependent Properties of

AG

q

+q

+

Q

Mohr's Circle

Q(

? S9T

Sensitivity Studies

+

Glass-Transition Temperature

,

F9 F R y

q

G d(

JAy

| QI

AG J

G IQG

9S

J

hat ? tz j | 9|9fCG

J

O AGRE

FG O

G QO

QI ?F

StiffenersOpen-Versus Closed-Section Stiffeners

L

QO

9|9f

h at ?I A q| 9|9f

Dummy Index

CG

(

J

) , G h( Q

q

+ O

?z 9| 9s 9s

Cross-Ply

?=y9 ZA| 9s 9s

J

J

Q JG P

Q JG P

?s 9s

LaminaOrthotropic Lamina

,

I9 ? C; C ?s 9 s"CG

+

Specially Orthotropic Lamina

?Y 9 L I9 ? C; C ?s 9 s

Generally Orthotropic Lamina

? |9 f I9 ? C; C ?s 9 s

q

,

"CG

,

Anisotropic Lamina

,

+

"CG

+

I9 ? z C 9 }A | Q i ?s 9 s"CG

+

?w ?s 9s

Woven Lamina

+I

9

Unidirectionally Reinforced Lamina

k

Laminated Glass

J

Saint-Venant, Barre De

jO Q

O

QwA | { y

Angle-Ply

F

O

q

* Q (I I G(

t| ?s 9s

9t= ay O g A| 9FG O

L

Q

Q

Q

Q

Q

Q

Q

R

9< B 9 p B 9Sv vvv

! !(

!

v vv v

>JS

PultrusionStrain-Energy-Release Rate

qg(

|||

WA y ?s 9 _ QG

Q

q

Og | ?fQ Sq

; )d

(

Fiber-Matrix Interface

? a < GQ I O 9 | v vv v r+ y ) ," + = y G( {Y 9 qy G K a Ty G

Load-Deflection Behavior

{ }A G A 9 " J ! :G c (z S

Mechanical Behavior of

,w + ! 9 w + CG c( z Ty G

Mechanical Behavior of Composite

q

? = v Q C G O G (} zy ,w + ! 9 w + CG c( z Ty G

MaterialsNonlinear Stress-Strain Behavior

q

,a L Q + i O 9 % FE vvv v g ( W@ c (z Sq

Linear Stress-Strain Behavior

q

,a L O 9 % FE vvv v g ( W@ c (z S

Orthotropic Behavior

, I9 " CG ,C ; C c (z S

Nonlinear Behavior

,a L Q + i c (z S

Anisotropic Behavior

,I 9 " C G { C 9 } A | Q + i c (z S

Isotropic Behavior

, I9 " CG {C 9 } A | c (z S

Viscoelastic Behavior

LR y f Q | c (z S

Micromechanical Behavior

u + s O ,w + ! 9 w + | c (z S

Macromechanical Behavior

P 9 + f ,w + ! 9 w + | c (z S

Orthogrid

I O | 9 gA | ? w = V

Isogrid

?z C9 }A | ?w =V

Staggered Square Array

qq) >+ @ Q A y G ? = s9 gA | ( ? J ! Q A | ? g< Q | ? w = V

Kirchoff Free-Edge Condition

a ( VQ + w y IQ A G ?p 9 A G W Q V

Boundary Conditions

?* O hO A G W h Q Wy G

Beam Boundary Conditions

R F 9 G z y ?* O hO A G W h Q Wy G

Plate Boundary Conditions

q

?J + q Zz y ?* O hO A G W h Q Wy G

Boundary Conditions

q

? * O h OI W hQ V

Bimetallic Strip

f O g CG ?+ F 9 " C ? a * Q V

Microcrack

j Q % H uV

Initial Form

[ h} G { w Wy G

Flaws

? *Q% H Yh O Y

||}

Plastic-Based Laminates

? w A S; < ? t = _ K 9 q Y?Y9L I 9 ? C ;C ? t =_ K 9q Y? = y 9 ZA | 9 s9 sQc9 A| : ? t =_ K 9q Y? z 9 | 9 s9 sQc9 A | ? t =_ K 9q Y?z 9| 9s 9s Qc9 Ay ?T v 9g | ? t =_ K 9q YQc9 Ay ? qy9MA | K 9q Y9 t= a y Og A | K 9 q YR v Q } A | : { w W< t | 9 Q Ws K 9 q Y?J qY? t= _ ? J q Y? z 9 | 9 s9 s ? t= _ ? J q Y? = y 9 Z A | 9 s9 s ? t= _ ? J q YI9 ? zC 9 }A | = V ? t = _ ? J q YQc 9 A | Q i ? t = _ ? J q YQc9 A| : ? t= _ ? J q YQ c 9 A y ?Tv 9 g | ? t= _ ? J q Y? }d A | ? t= _ ? J q Y?z 9| 9s 9sQ c 9 A | ? }d A | ? t= _ ? J q Y?= y9ZA| 9s 9sQ c 9 A | ? }d A | ? t= _ ? J q Y9 s 9 s Q c 9 A y ? T v9 g | ? } d A | ? t = _ ? J q Y? z 9|I9 ? zC 9 }A | ? J q Yb= \? t =ay ? J q Zy b= \?=v Qb= \W Ay ?s 9_9 Oy ? | 9 w y ?s 9 a y+

Special Orthotropic Laminates

q

Unsymmetric Cross-Ply Laminates

J

Symmetric Angle-Ply Laminates

F

Antisymmetric Angle-Ply Laminates

F

Skew Plates

,

"CG

+

"

Q J GP I

J

J

+

"

Q J GP I

"

Q JG P

G

"

Laminated Plates

+

F

+

F

+

F

+

F

F

G IO

q

IG (

Plate

F

G

J

Eccentrically Stiffened Plates And Shells

+

F

J *

h

F

+

LaminateAngle-Ply Laminate

F

Cross-Ply LaminateQuasi-Isotropic Laminate

,

Nonsymmetric Laminate

Q J GP

+

+

J

Q J GP

+

+

&

+

+

+

+

+

+

+

+

"

+

+

"C G

"

"

Regular LaminateRegular Symmetric Angle-Ply Laminate

F

Regular Symmetric Cross-Ply LaminateRegular Antisymmetric Angle-Ply Laminate

J v

+

"

I

Antisymmetric Laminate

+

J

I

Asymmetric Laminate

+

G

J

Q JG P I

"

"

+

+

J

Q JG P I

"

"

+

+

v Q JGP

v

v"v v G

v

v

v v

v v

v v"v

v+v v v

v+v v

v

F

Isotropic PlateTailoring ofLaminate TailoringTailoring of Composite MaterialsStrain EnergyMinimum Potential Energy

,

"C G

+

+

+

G

G

q

C G O G (C Gqg(

+!

||~

G

"

G

G

G

Total Potential Energy

? + zw y G ? " | 9 w y G ? s 9 a y G

Minimum Complementary Energy

x9 +! OyG ?z }w C G ?s 9 a yG

Potential Energy

?" |9v ?s 9_

Stationary Potential Energy

)?A< 9C( I QtAT | ?" |9v ?s 9_

Semi-Inverse Method

,qZ "yG H ( z tC G ?t *Q _

Rayleigh-Ritz Method

R A *Q vv vv \ *GQ ?t *Q _

Galerkin Method

_v Q +y 9 i ?t *Q _

Newton's Method

# @( +! ?t *Q_

Apparent

jQ$ 9c

Apparent for a Lamina

?s 9 sQ y j Q $ 9 c

Apparent for Orthotropic Lamina

,I 9 " C G ? + C ; C ? s 9 s Q zy j Q $ 9 c

Materials Utilization Factor

O G ( C G d 9 } gA SG {| 9 f

Contiguity Factor

Q h 9 G A y G {| 9 fp

Stress Concentration Factor

O9%F

Fiber Misalignment Factor

G R + v Q@ { | 9 f

r+ z y G a 9 qa YG e Of {| 9 f

Complex Variable Mapping

qqj O tf ) d (J A | ( Q + j A | j P h < 9 A < ? t< 9 a C G Q = f

Heterogeneity

U!9 : e Of

Inhomogeneity

U!9 : e Of

Anisotropy

, I9 "C G { C9 E e Of

Transverse to Fiber Direction

r+ z y G g9 : G ] E ? = T" y 9 < P 9 \Q f

Benign Failure

~ + z S >a f

Damage

QQ \ , >a f

Stress-Strain Relations

qg ( W@ v vv v O 9 % F E J 9 s; f

Constitutive Relations

? + S9 S }G J 9 s; g y G

Strain-Displacement Relations

qM9 * R ! :G vvv v g ( WA y G J 9 s; f

Linear Strain-Displacement Relations

q

q

?+ a L )H 9 J T ! G , d 9 t A ! G ( M9 * R ! G v vvv g( W @ J 9 s; f

|}u

O9%FE v v g(q W@ J9s;f? + Tw f J 9 s; f? + w + ! 9 w + | J 9 s; f, I 9 " C G ? + C ; C O G ( C G , p ? f h 9 a C G J; | 9 g } < ? s ; f

Strain-Stress RelationsReciprocal RelationsMechanistic RelationshipsRelation to Compliances for OrthotropicMaterials

G

O G G I A9 T F J ; | 9 g | ? s; f

,I 9 "C ?+ C; C ( C

Relation to Stiffnesses for OrthotropicMaterials

I9 + I , Q }fh+"ZA yG J 9 +z }fQ Tw y G ?+ z }f

LifeManufacturing ProcessesFracture Process

? + %A " | Q Y 9 " f

Finite Elementsx

{ DF ,}G I Q Z"f

Representative Volume Element

Gr+ z y G Q 9 + A LG {| G (fO9%F G R+vQ@ IOq V {|G(fI O ( @ G ? = s G Q| { | G ( fQ9 + A L : G ? p ( q Z | { | G ( f? + F G OA < G H (+ f{| (f

FactorsFiber Selection FactorsStress-Intensity FactorsQuality Control FactorsMatrix Selection FactorsInitial Imperfections

,} AI Q +i

Nondeterministic

,H( zs Q+ib j ]y Gh O Wy G ,p h9 T A | Q + imq, = T" y G g (W A y G J 9 + \Q pc ( zT y G O (+ s h J 9 + \ Q pa ( VQ + v ? + \Q p? + %A " | J 9 sh Q pJ 9t =ayG { ZpJGQ+q jACG {Zp, |9d! Q+i

SingularUnequal In Tension and CompressionStrain AssumptionsBehavioral Restrictions and AssumptionsKirchoff HypothesisFinite DifferencesDelaminationSeparation of Variables

|}v

q

Simplified Design Space

b T= CG ~ + }Z A y G A 9 ]p

Debonding

b 9ZAy :G x p

Design-Analysis Philosophy

~ + } Z A y G {+ z; ? q Tz p

Rule Of Mixtures

H F G R CG I O f9 s

Cramer's Rule

Q |G Q v I O f9s

Law Of Mixtures

HF GR C G f( !9sv

Generalized Betti's Law

~}g C G , A+< f( !9 s

Hook's Law

c ( $ f( !9sq

Hat

?g =s

Shells

J 9 * Q Ws

Laminated Shells

J 9 t= a y G I O Og A | J 9 * Q Ws

Shells, Laminated

J 9 t = _ O Og A | , J 9 * Q Ws

Brittle

rZs

q

Shear-Shear

q

[s v v [s

Sandwich Core

) X * hO ! 9 T y G ( IQ + a Wy G >z s

Honeycomb Core

{T g y G U Q s >z s

q

Kirchoff Shear Force

[ tz y a (V Q + v I (s

Molding of

?= y (s

Sheet Molding

?J + q Zy G ) { + w W@ ( ?= y (s

Resin-Transfer Molding

d 9 tA ! :9 < H " @ GQ y G ?= y (s

Laminate Forces And Moments

? + t = a y G ?J + qZ y G e h R fh i (s

Measurement of

S9+s

Measurement of Strength

?| h9 t CG S 9 + s

Measurements of Stiffness

I A9T @G J9S 9+s

Restriction on

^f

Constraints

O+ s

O( +s

|}w

Artificial Constraint

? +f9" a YG

Restrictions on Micromechanical Behavior

u + sO y G

, w + ! 9 w + CG

c( z Ty G

^f

O( +s

? *Qd"yG

^f

O( +s

) "=yG

? qz v

Restrictions on TheoryComposite Structures Cost

?=v QC G

O( +s

) JG A 9 W ! G (

Life-Cycle Cost

I9 + A G I Q hO ? qz v

Anisotropic

,I 9 "C G

Eccentricity

{C 9 }A | :? * R vQ | :

qa9+y}G )a9qA yG( r y

Filament WindingInterlaminar

J9 t = a y G

Orthotropic MaterialSpecially Orthotropic Material

q

?Y9L

Matrix (Material)

#+ agyG J9qzq j|,i Q =y9 < J ;Yh J GQ 9 +8Gb9ZAy:9< Jm;Yh JGQ9+8G

Failure EnvelopesFailures in Bolted JointsFailures in Bonded JointsFatigue

>g@

Fiber Buckling

r+z y

G L9 g =!G

G a 9 qa YG e Of {| 9 fr+ z y G Q 9 + A LG {| G (fq? + F 9 FR a 9 + y z < i (t | ,T v (= * E? a < GQ I O 9 | v v r+ y ) ," + = y G( {Y 9 qy G K a Ty Ga9+y}9< IG(q t| J9t=ayG IOOgA| ?=vQ| OG(|

Fiber Misalignment Factor

r+z y

Fiber Selection FactorsFiberglass-EpoxyFiber-Matrix InterfaceFiber-Reinforced Laminated CompositeMaterials

a9+y Ca 9 + y ~ y ? + }G A G ?= T" y Gq?+q +y ?=v Q | O G( |a9+y}G )a9qAyG( rq y? + % A " C G J9 s h Q q y G ? < Q 9 t |? + %A " | J 9 sh Q p? + %A " CG Q Y 9 " g y G ? < Q 9 t |

FibersFiber-Volume FractionFibrous Composite MaterialsFilament WindingFinite Difference ApproachFinite DifferencesFinite Element ApproachFinite Elements

? + %A " | Q Y 9 " f

]h }G ? s9 sQ z y Q 9 + 8 : G { >

First-Ply Failure LoadFlaws

? *Q%H

Yh O Y

& + * Q ( p J; T z T A |

Fourrier Series

G

Fracture Mechanics

QT wy x+!9w+ |

Fracture Process

G

Q Tw y ?+ z }f

Frequencies

q jQGQI g(q W@J GQ@ G( @

Galerkin Method

_v Q +y 9 i ?t *Q _

Free Thermal Strain

QI

|~z

Galvanic CorrosionGeneralized Betti's LawGenerally Orthotropic LaminaGlass-EpoxyGlass-Transition TemperatureGoverning EquationsGraphite FibersGraphite-EpoxyGrowthHalpin-Tsai EquationsHatHeterogeneityHoffman CriterionHoffman Failure CriterionHoles in LaminatesHomogeneityHoneycomb CoreHook's LawHybridHygroscopicImpact ResistanceImplicationsIndex NotationInhomogeneityInitial FormInitial Imperfections

P

9q y9i {v5@

v CG , + f(!

~}g

? |9f

F9 F R y

9s

, "CG +I9

,,

A z s

Sandwich-Blade

) X * hO ! 9 T y G( IQ + a W y G ) IQ q V( {Z !kq9 + zL G O u T A | LP ( } !

Self-Consistent ModelSemi-Inverse Method

, " G H( CG *qZ y

}ux

zt

?t Q_

? + S 9 TA G J 9 SG Q O

Sensitivity StudiesSeparation of Variables

JG

Q+q jACG {Zp

[q tyG g(q W@ ?*Qd!

Shear Deformation Theory

[q s b}!

Shear Mode

[q tyG J;|9g|

Shear ModuliShear Stiffness

[q tyG IA9TF

Shear Strength

[q tyG ?|h9t|

Shear-Extension

[q s v v ?y9aASG[q tyG v v ?y9aAS:G LhGR@

Shear-Extension Coupling

[q s v v [q s

Shear-Shear

[q s v v [q s LhGR@

Shear-Shear Coupling

?J + q Zy G ) { + w W@ ( ?= y (s

Sheet Molding

q

? J + qZ y G ?= y (s > v Q |

Sheet Molding CompoundShells

J

Shells, Laminated

J

9 * Q Ws

9 t = _ O Og A | , J 9 * Q Ws

o

? 8 z } C G ? g a t y G e G O M A S 9 < ( b = ] y 9 < ) J; Y h (

Shimmed

) p

bTq =CG ~+}ZAyG A9]p

Simplified Design SpaceSingular

, |9d! Q+i ,H( zs Q+i

Skew Plates

Qc9" AyG ? qy9MA | KF9q Yq

?a * Q W y G f O z @ e (% q |

Softening Strip Concept

q

{ AG J9+"t @

Solution Techniques

{ FC # | ?Y 9 L J :9 I

Special Cases for

?Y9 L ,I 9 "C G ?+C ; C ?+t =_ KF9 q Yq

Special Orthotropic LaminatesSpecially Orthotropic Lamina

?Yq 9L ,I9"CG ?+C;C ?s9sQ

Specially Orthotropic Material

?Yq 9L ,I9"CG ?+C;C IO9|? + f( " y G IA 9 T@ G

Specific Stiffness

}uy

Specific Strength

? + f( ! ?| h9 t |

Stacking Sequence

O +]"A yG h+ @ Q A y G ? = s9 gA | ( ? J ! Q A | ? g< Q | ? w = V

Staggered Square ArrayStationary Potential Energy

)?A< 9C( I QtAT | ?" |9v ?s 9_

Statistical Approaches

? +F9ZI Ev

Stiffened Structures

o

?} fO|

Stiffener Design

J9 +@QAy 9T @ ?+ QF

Tsai's Laminate Ranking Procedure

G

F

G

j

{+$

Tsai-Hill CriterionTsai-Hill Failure Criterion

Q

}u|

9+8;y { +$

v vv v j

v vv v j

FG

E

9 T@ 9 + g |Q

9 T@ 9 + g |Q

Tsai-Wu Criterion

h h v v j 9 T@ Q 9 + g |q

Tsai-Wu Tensor Failure Criterion

Q 9 + 8 ; y j Q @ ( C G h h v v j 9 T@ Q 9 + g |

Tsai-Wu Tensor Failure Criterion

qQ 9 + 8 ; y h h v v j 9 T@ Q 9 + g | )Q ( T" @ ( Q @ ( |

Ultimate Load

, }d f }

Underdesign

G { }AG

H ( z a CG #| { s C ~ + } Z@ , r + g \ ~ + }Z @

Unequal in Tension and Compression

b j ]y Gh O Wy G

,p

h9 T A | Q + im

qj Q ( J C G O Wy G Q 9 = A LG

Uniaxial Tension Test

k

Unidirectionally Reinforced

q

9 * Q (I i (t |

k

Unidirectionally Reinforced Lamina

q

9 * Q (I I G( t| ?s 9 s Q

Unsymmetric Cross-Ply Laminates

? = y 9 Z A | J9 s 9 s Q J G P I Q c 9 " A | : ? + t = _ K F 9 q Y

Unsymmetric Laminate

I Qc9"A| : ? +t= _ ? J+q Y

Variational Techniques

?+@G Q+j A| J9+"t @

Variations in Displacements

q

q,J:9v v v v vtv v v v vAv v v v v!:G( J9v v v v vI9v v v v v*Rv v v v v!:G ,v v v v vp JGQv v v v v+v v v v vjv v v v v@) J 9vvzvvZvvAvvy G JGP JGQvv}vv vvy

Tv =

,107

y G ?= y9 ZA}y G v v v v v

G JGQvvvvvvvv}vvvvvvvv vvvvvvvvy

, (*

,108

q36 :?f QqA}y G vvvvv

)

G

,183

,112

+

(

vvvvvvvv=vvvvvvvv

,115

36 :? aMy G vvvvv

36 : J;Y

( *

741 ,704 ,640 ,611

$@ >$@7

$ #

" $ "

## " $PQ 6FDODU 8QLW0DWUL[,GHQWLW\0DWUL[ " "

>, @ # ## " 'HWHUPLQDQW $

$$ $ $ $

'$

$

'

$

$

$

$$

$$

$$

$

$

$

$

$

$

$$

$$ $ $$

$$

0L Q 'LWKQ

'

$ $ " $Q$ $ " $Q###$Q $Q " $ QQ

$0 $0 " $Q0Q Q

0LQ QL0L$L0LQRU

$L&RIDFWRU

L M 0 LM

D LM

'

Q

L

$ LM D

Q

LM

M

$ LM D

LM

,QGH[

NN

D

D D " DQD D " D Q

###D Q D Q " D QQ

>%@ >$@ >&@ >%@>$@

& LM

$ LM % LM

F F $ $ % % $ % $ % F F $ $ % % $ % $ %

&RPPXWDWLYH > $@ >% @

>%@ >$@

$PRLRWLYH >> $@ >% @@ >& @

>$@ >>%@ >& @@

>$@ >%@ & LM

$ LM % LM

>%@ >$@

V >$@ V>$@ V > $ @

$V $

$ $

V$ V$

V$ V$

>%@ >%@>$@ >$@>%@>$@ >%@>$@>%@ >$@>%@ MWK >$@ LWK

>& @ >$@>%@ >$ % @ LN

NM

>$@N

$ $ $

$$$

$ % $ % $ %

$% $ % $ % $ % $ % $ % $% $ % $ %

& & &

P>$@Q>%@ S >%@ S >$@ Q P >&@ >%@ >%@>$@ >$@>%@>$@ >$@ >%@>$@>%@>$@>%@>%@ >%@>$@ >%@>$@ >$@>%@ &RPPXWDWLYH>$@>%@

,QYHUVH > $@

>D@7$

$GMRLQW > $@> $@

>$@ >$@ >@

>$@ 6LQJXODU 0DWUL[ >$@

^< `

>$@^; `

^;`^ $@ ^< `

>$@ >$@^; ` ^; `

&UDPHU ^ $@^; `

>$@ +RPRJHQHRXV >$@

>$@^` ^`

^; `

^;` >$@ $

> @ >>$@ @

>$@

7

7

> $@>% @>& @

7

> $@>% @>& @

>& @7 >%@7 >$@7

>& @ >%@ >$@

YHFWRUV YHFWRUV

YHFWRUV 7HQVRUV >$@ [LL[[[[L[LM L ,QGLFHV FLMNO ELMN DLM DLM D FLMNO DLM DLNQ 1 QN

UDQJH VXPPDWLRQ 'XPP\,QGH[

[ \ ] ]

] c ] [c \ c ] c

>D @ >7 @LM

FRV T VLQ T

VLQ T

FRV T

[\

MWK [c \ c ] c LWK D LM [\] D LM

FRV[cM [ M

[Lc D LM [ M

[c D [ D [[c D [ D [ [c D [ D [

D [ D [ D [

[c [c [c

D D D [ D D D [ D D D [

[c

LM !NL

D LPD MQ "D NRD S [PQ"RS

6FDODU YHFWRUV $Lc D LM $M

$ M DLM $Lc YHFWRUV $LMc

D LND ML $NL

c $LMNO

D LP D MQD NRD LSD PQRS

V LM

&LMNO H NO

H LM

6LMNOV NO

&RQWUDFWHG ,QGLFHV

HHHHHHHHH JJHHH JJHHH JJHHH JJHHH JJHHH JJ

VVVVVVVV WW

V

V WW

V

V WW

V

V WW

V

V WW

V

V WW

V L

&LMH M

H L

6 LMV M

V LM

V ML

H LM

H ML

6LM&LM 6LM &LM & LM

& ML

6 ML

6 LM

6LM &LM

& LM

>& @

&& &&&&

&

&

&

&

&

&

&

&

& & &

&

&

&

& &

& &

& &

&

&

&

&

& & & & & &

&LMNO&LM

$ $ $

>$@

D L

D L

>$@ >$

$

$ @

$ $ $

D LM > $@ $ $ $ $ $ $

D L

>$@

$ $ $ $ $ $ $ $ $

[ [$UUD\ ]

^ `

V

>7 @^V `

V

V V

V V

V

FRV TVLQ T

FRV T VLQ T

TTTFRVVLQFRVVLQT

FRVT VLQT VLQT FRVT

FRVT VLQT V FRVT VLQT V V

V

V FRV T VLQ T V

V V W

FRV T

VLQ T FRV T VLQ T

VLQ T

FRV TFRV T VLQ T

FRV T VLQ T V FRV T VLQ T V FRV T VLQ T W

0RKUV >$@

$ 6WHSKHQ : 7VDL 0HFKDQLFV RI &RPSRVLWH 0DWHULDOV 3DUW ,,7KHRUHWLFDO$VSHFWV $LU)RUFH0DWHULDOV /DERUDWRU\ 7HFKQLFDO5HSRUW$)0/751RYHPEHU

[ [9[[9G9

G[ [ [ 9

,QIOHFWLRQ9[ 1HXWUDO 9[ 9[

9[

9[ 6WDWLRQDU\ [ [ 9 [ K 9 [ K

G9G[

[ [

K G 9 G[

[ [

K G 9 G[

[ [

"

[([SDQVLRQSDUDPHWHUK

[ [9[

9 '9 '9

K

G9G[

K G 9 G[

[ [

[ [

K G 9 G[

[ [

"

K '9 '9

K G 9 G[

[ [

K G 9 G[

[ [

K G 9 G[

[ [

"

[ [ '9 '9 '9 '9 K

K G 9

G[

[ [

KK

G 9G[

[ [

[ [9[

G 9G[

[ [

[ [9[

G 9G[

[ [

K G 9 G[

[ [

K[

[9[K '9 9[

K G 9

G[

[ [

9[

[ [ [ [ 9[ [ [ 9[9[ [ [ 9[

9 [ 9 [[ 9 9 cc

[

9?

9 [

9 [ 9 [[ 9 9 cc

[

[

[

9 ccc

[

9?

9 [ 9 [ 9 [[ 9 9 cc

[

[

9 ccc

[

[

[ [

9 cccc

[

9?

9 [

9 [ 9 [[ 9

9 cc

[

9 ,;

[

9;

[

9?

9 [ 9 9>%@

% +HQU\ / /DQJKDDU (QHUJ\ 0HWKRGV LQ $SSOLHG 0HFKDQLFV1HZ&@ 0 ;36 Q

Q

>&@ Q

1DUPFR >&@

0 ;36 V HH >&@

0;36 VHH >&@

0 ;36 V HH >&@

0 ;36 V HH >&@

0;36 >&@

>&@VHH

>&@VHH

>&@VHH

>&@VHH

>&@

>&@

>&@VHH

>&@VHH

>&@VHH

>&@VHH

>&@

>&@

& 3ODVWLFV IRU $HURVSDFH 9HKLFOHV 3DUW 5HLQIRUFHG 3ODVWLFV0LOLWDU\+DQGERRN0,/+'%.$-DQXDU\& -($VKWRQ-&+DOSLQDQG3+3HWLW3ULPHURQ&RPSRVLWH0DWHULDOV$QDO\VLV:HVWSRUW&77HFKQRPLF

[G1 1 1 G[

G1

G[

]G9 9 SG[ 9 G[ G[

G9

G[

S

E 0 SG[

G[ G9 G0 9 G[ G[ 0 G[ G[ G[

G[

G0 9G[ G[ G[

9

G0

G[

1

1

09

09

8:

:

8: :

] [ Z X [

S

G9G[

0

G G0 G 0

G[ G[ G[

(OZ

S

(OZ

X

1\ 0[\ 0\ 0[ 1[\ 1[S[\ 4\ 4[

[w1 [\ w1 [ 1 [ G\ 1 [\ G[ 1 [\ G\ G[ 1 [ G[ G\w\w[

G[G\

ww1[

[

w1 [\w\

\w1 \ w1 [\ 1 [\ G\ 1 \ G[ 1 \ G\ G[ 1 [\ G[ G\w\[w

G[G\

w1 [\w[

w1 \w\

]w4 \ w4[ 4[ G\ 4 \ G[ 4 \ G\ G[ 4[ G[ G\ S G[ G\w[w\

G[G\

w4 [ w4 \

Sw[w\

[ [

0

[\

w0 \ w0 [\ G\ 0 \ G[ 0 \ G\ G[ 0 [\ G[ G\w\[w

4 G\ G\ 4[

\

G\w4G\ S G[ G\G\ G[G\ 4[ [ G[ G\

w\w[

w4 \

G[G\

G[G\

4 \

w0 [\w[

w0 \w\

\ 4 [

w0 [ w0 [\

w[w\

4\ 4[ ]

w w0 [ w0 [\

w[ w[w\

w w0 [\ w0 \

w\ w\ w[

S

w 0 [\ w 0 \w0 [

w[w\w[ w\

S

[1[

1[

1 [\

1 [\

0[

0[

0 [\

4[

XYwZw[

0 [\4[

XY wZw[

Z [\

Z [\

Z

Z

\

1\ 1 [\

1\1 [\

0\

0\

0 [\

4\

0 [\4\

YXwZw\

YX wZw\

Z [\Z

Z [\Z

0 [

(W N [ YN \ Y

0 \

(W N \ YN [ Y

(W N [\ Y

0 [\

N [

wZ w[

N \

wZ

w\

wZ

w[w\

N [\

wZw[

wZwZ w\ w[ w\

3

'

.[

4;

0[

w0 [\w\

.[

Z

Z

0[

Z [

Z [

.\

4\

w0 [\w[

.\

Z

Z

0\

0\

Z \

Z \

N\N[

(WX [ YY \ Y

1 [

1 \ 1 [\

(WY \ YX [ Y

(WX \ Y [ Y

X [[ YY [\ Y X \\ Y [\

Y X

\[

Y [[ Y \\ YX [\

] [ Z 0[ 6

6 Y X [ 6Y R1[ X\\ 6 X R 1[\ Y [ \ [1[\ Y1[ X

wZ w[ Z YX &Z wZ w[ wZ w[ Z[\ & Y X Y 1[ [

& \X 1[\ [ \\[1[\ 1[

4\4[]S 4[

W

[]

G]

4\

W

\]

G]

\] [\

9[][]G0

G[ []

9

W [] ]

V [ [

W []

9O

W ]

>'@> '@>'@ Z Y XZ X Y 1[\ 1\ 1[0[\0\ 0[ 1[\ 1\ 1[0[\0\0[ [

G1 [ G0 [

G. [ G1 [\

GX wGZ w[

GZ GY

' 5REHUW 0 -RQHV %XFNOLQJ RI %DUV 3ODWHV DQG 6KHOOV WREH3XEOLVKHG' 6WHSKHQ 3 7LPRVKHQNR DQG -DPHV 0 *HUH 7KHRU\ RI(ODVWLF6WDELOLW\QGHG1HZ GyAt"+9J G:SAQG@+G+? hGCAtOq |?

G9QuGO G9Qd8?Z

,

.