• No results found

A comparison of different homogenization models and experimental results

N/A
N/A
Protected

Academic year: 2021

Share "A comparison of different homogenization models and experimental results"

Copied!
3
0
0

Loading.... (view fulltext now)

Full text

(1)

ICCE/6

Edited by

David Hui

June 27-July 3, 1999

Orlando, Florida

SIXTH ANNUAL INTERNATIONAL CONFERENCE ON COMPOSITES ENGINEERING

Sponsored and Organized by

International Community for Composites Engineering and College of Engineering, University of New Orleans

(2)

D FRPSDULVRQ RI GLIIHUHQW

KRPRJHQL]DWLRQ PRGHOV DQG H[SHULPHQWDO UHVXOWV

Mrkdq E|vwuùp/Qrupxqgv Mhndevrqv2 dqg Oduv0Huln Shuvvrq

Ghsw1 ri Pdwk1/ Oxohè Xqlyhuvlw| ri Whfkqrorj|/ V0<:4;: Oxohè/ Vzhghq

2Gly1 ri Sro|phu Hqjlqhhulqj/ Oxohè Xqlyhuvlw| ri Whfkqrorj|/ V0<:4;: Oxohè/ Vzhghq

4 Lqwurgxfwlrq

Lq wklv sdshu zh frqvlghu wkh sureohp ri krz wr prgho wkh hodvwlf surshuwlhv ri zryhq frpsrvlwhv1 Pruh vshflf/ zh zloo xvh pdwkhpdwlfdo krprjh0 ql}dwlrq wkhru| dv d uhihuhqfh wr hydoxdwh glhuhqw vhpl0dqdo|wlfdo krprjhql}dwlrq phwkrgv wkdw duh xvhg iru frpsxwdwlrq ri wkh hodvwlf surshuwlhv1

H{lvwlqj krprjhql}dwlrq prghov fdq eh glylghg lqwr wkuhh glhuhqw fdwhjrulhv  vhpl0dqdo|wlf hqjl0 qhhulqj prghov/ prghov edvhg rq IHP fdofxodwlrqv dqg wkh uhodwlyho| qhz pdwkhpdwlfdo krprjhql}d0 wlrq phwkrg1 Zh zloo lq sduwlfxodu hydoxdwh wkh Ndud|dnd0Nxudwk Prgho ^8` +NNP, dqg wkh prgl0

hg prvdlf sdudooho prgho +PPSP, +vhh Lvklndzd dqg Fkrx ^6`/ ^7`, e| xvlqj uhlwhudwhg krprjhql}d0 wlrq1 Wkh vxemhfw ri pdwkhpdwlfdo krprjhql}dwlrq fdq eh irxqg lq wkh errnv e| Ehqvrxvvdq hw do1 ^4`

dqg Shuvvrq hw do1 ^9`1

5 Uhlwhudwhg krprjhql}dwlrq

D wkrurxjk ghvfulswlrq ri wkh xvh ri uhlwhudwhg kr0 prjhql}dwlrq iru zryhq frpsrvlwhv fdq eh irxqg lq wkh xsfrplqj duwlfoh ^5`1 Zh dvvxph wkh frp0 srvlwh wr h{whqg ryhu d grpdlq  U dqg dv0 vxph wkdw wkh uhsuhvhqwdwlyh xqlw fhoov ri wkh zr0 yhq frpsrvlwh kdyh d shulrglflw| ri \= Pruhryhu/

zh dvvxph wkh ehuv lq hyhu| ehu wrz kdyh d sh0 ulrglflw| ri ]= Zh ohw % eh d vpdoo sdudphwhu/ sxw

| @ {@% dqg } @ {@%2> dqg h{sdqg wkh glvsodfh0

phqw hog x lq wkh dv|pswrwlf vhulhv x +{> |> }, @ xf+{> |> },.%x+{> |> },.%2x2+{> |> },.= = = > zkhuh x duh \ shulrglf z1u1w1 | dqg ]shulrglf z1u1w1 }= E| wkh fkdlq uxoh/ lw wkhq iroorzv wkdw wkh vwudlq h +xqghuolqlqj lqglfdwhv d vhfrqg rughu whqvru, lv jlyhq e|

h @ 4 5



u%x. +u%x,A .4

%

u+x. +u+x,A

.4

%2

u5x. +u5x,A=

Ohw xv ghqrwh hk+x, @ 4 5

kukx. +ukx,Al>  @

{> |> }= Wkhq zh fdq zulwh h @ 4

%2hf.4

%h. h2 .

%h .= = = > zkhuh hf @ h5+xf, > h @ h++xf,.h5+x, >

dqg h @ h%+x32, .h++x3, .h5+x, > l @ 5 = = = 4=

Xvlqj F+|> }, dv wkh irxuwk0udqn frqvwlwxwlyh whq0 vru/ wkh vwuhvv fdq eh zulwwhq dv  @ F +|> }, h @

4

%2f.4

%. 2. % .= = = = Wkh htxloleulxp htxd0 wlrqv wkhq jlyh u @ u%.4

%u+.4

%2u5 @ 3>

ru zulwwhq rxw lq ixoo 4

%eu5 f. 4

% ^u+ f. u5 ` .4

%2^u% f. u+ . u5 2`

.["'%32^u% . u+ n. u5 n2` @ 3=

Vlqfh wklv htxdwlrq pxvw krog iru hyhu| %> zh jhw d v|vwhp ri htxdwlrqv wr vroyh1 Vroxwlrq ri wkh yh

uvw htxdwlrqv wkhq |lhogv wkh krprjhql}hg whqvru

<:

(3)

D e| wkh irupxod D @ 4

m\ m ]

t

F +|, he ++ . Z#, g|>

zkhuh Z# lv wkh \ shulrglf vroxwlrq ri wkh \ fhoo sureohp u+  F +|, he ++ . Z#, @ 3> erxqgdu|

frqglwlrqv or @ o|r> dqg F+|, lv wkh ] fhoo kr0e prjhql}hg whqvru1 KhuhF+|, lv jlyhq e|e

F+|, @e 4 m]m

]

~F +|> }, h5+ . Yl, g}>

zkhuh Yl lv wkh ]shulrglf vroxwlrq ri wkh ] fhoo sureohp u5  +F +|> }, h5+ . Yl,, @ 3 zlwk wkh erxqgdu| frqglwlrqv or @ o}r=

6 Qxphulfdo uhvxowv

Zh lqyhvwljdwhg sodlq zhdyh jodvv0ehu2hsr{| dqg fduerq0ehu2hsr{| frpsrvlwhv zlwk wkh iroorzlqj frqvwlwxhqw surshuwlhv=

Surshuw| JI2HS FI2HS

Ilehu yro1 iudf12wrz 3=<4 3=99 Ryhudoo yro1 iudf1 3=93 3=74 D{ldo prg1 e1 +JSd, :5 56;

Wudqvy1 p1 e1 +JSd, :5 73 Wudqvy1 Srlvvrq*v e1 3=5 3=55 Pdmru Srlvvrq*v e1 3=58 3=55 Lq so1 vkhdu e1 +JSd, 55 5<=;

\rxqj*v prg1 pdwul{ 6 6=7 Srlvvrq*v udwlr pdwul{ 3=6; 3=69

Wkh frpsrvlwhv kdg wkh iroorzlqj phdvxuhg lq0 sodqh surshuwlhv=

Surshuw| JI2HS FI2HS

\rxqj*v p1 +JSd, 59=6 5 79=8 5 Srlvvrq*v udwlr 3=47 3=4 3=38 3=33<

Vkhdu prg1 +JSd, 7=8 3=6 7=3 3=6 Wkh glhuhqw vhpl0dqdo|wlfdo prghov +NNP dqg PPSP, frpsduhg zlwk uhlwhudwhg krprjhql}d0 wlrq +UK, jdyh wkh iroorzlqj uhvxowv iru wkh jodvv0

ehu2hsr{| frpsrvlwh=

Surshuw| UK NNP PPSP

\rxqj*v p1 +JSd, 5:=6 5:=7 5;=3 Srlvvrq*v udwlr 3=48 3=45 3=44 Vkhdu prg1 +JSd, 6=< 7=4 6=9

dqg wkh iroorzlqj uhvxowv iru wkh fduerq0ehu2hsr{|

frpsrvlwh=

Surshuw| UK NNP PPSP

\rxqj*v p1 +JSd, 76=4 77=6 86=:

Srlvvrq*v udwlr 3=377 3=37: 3=36<

Vkhdu prg1 +JSd, 6=3 6=4 5=8

Dovr wkh rxw0ri0sodqh surshuwlhv zhuh phdvxuhg dqg lqyhvwljdwhg wrjhwkhu zlwk pruh prghov lq wkh sdshu

^5` e| wkh dxwkruv1

Uhihuhqfhv

^4` D1 Ehqvrxvvdq/ M1 O1 Olrqv/ J1 Sdsdqlfrodx1 Dv|pswrwlf Dqdo|vlv iru Shulrglf Vwuxfwxuhv/

Qruwk0Kroodqg/ 4<:;1

^5` M1 E|vwuùp/ Q1 Mhndevrqv dqg M1 Yduqd1 Dq hydo0 xdwlrq ri glhuhqw prghov iru suhglfwlrq ri hodv0 wlf surshuwlhv ri zryhq frpsrvlwhv +wr dsshdu lq Frpsrvlwhv= Sduw E,/ 4<<<1

^6` W1 Lvklndzd/ Dqwl0v|pphwulf hodvwlf surshuwlhv ri frpsrvlwh sodwhv ri vdwlq zhdyh forwk/ Ilehu Vfl1 Whfk1/ y1 48/ 4<;4/ ss1 45:04781

^7` W1 Lvklndzd dqg W1 Z1 Fkrx/ Hodvwlf ehkdylru ri zryhq k|eulg pdwhuldov/ M1 Frpsrvlwh Pdwhuldov/

y1 49/ 4<;5/ ss1 504<1

^8` P1 Ndud|dnd dqg S1 Nxudwk/ Ghirupdwlrq dqg idloxuh ehkdylru ri zryhq frpsrvlwh odplqdwhv/

M1 Hqjlqhhulqj Pdwhuldov dqg Whfkqrorj|/ y1 4493/ 4<<7/ ss1 46904751

^9` O1 H1 Shuvvrq/ O1 Shuvvrq/ Q1 Vydqvwhgw/ M1 Z|oohu1 Wkh Krprjhql}dwlrq Phwkrg= Dq Lqwur0 gxfwlrq1 Vwxghqwolwwhudwxu/ Oxqg/ 4<<61

<;

References

Related documents

Zh kdyh hydoxdwhg wzr glhuhqw zryhq frpsrvlwh uhlqirufhphqwv wkdw duh xvhg lq wkh frqvwuxfwlrq ri hqjlqh krrgv dqg wdlojdwhv rq YROYR fduv1 Wkh wdlojdwh phqwlrqhg lv fxuuhqwo|

ri krprjhql}dwlrq ri sduwldo glhuhqwldo rshudwruv1 Wkh wkhvlv frqvlvwv ri dq hohphqwdu| lqwurgxfwlrq dqg yh glhuhqw sduwv/ D0H1 Lq wkh lqwurgxfwlrq zh jlyh dq hohphqwdu|

Wklv uhlwhudwhg krprjhql}dwlrq frxog ri frxuvh eh jhqhudol}hg wr q vfdohv/ dqg zh frqfoxgh wkdw lw frxog eh d xvhixo wrro iru ghwhuplqdwlrq ri wkh vwlqhvv whqvruv ri shulrglf

Dv fdq eh vhhq iurp Iljxuh  dqg Iljxuh 2 wkh htxdwlrq E  jlyhv d eldvhg uhvxow iru qlwh vdpsoh vl}hv1 Orrnlqj edfn dw wkh ghulydwlyhv ri htxdwlrq E  lw fdq eh vhhq wkdw

Li zh kdyh rqo| sxuh zdwhu lq wkh v|vwhp/ htxdwlrq 7155 jlyhv xv d yhu| dffxudwh hvwlpdwlrq ri wkh sursdjdwlrq wlph1 Wkhq zh dvvxph wkdw rxu vxvshqvlrq frqvlvwv ri erwk sxuh zdwhu

Iurp wkh vlpxodwlrqv zh frqfoxgh wkdw wklv prgho fdq eh xvhg wr txdolwdwlyho| ghvfuleh wkh hhfw ri vfdwwhu0 lqj ri xowudvrxqg iru wklv h{shulphqwdo vhwxs1 Lw lv fohdu wkdw wkh

VRIWZDUH DQG WHFKQLTXHV WKH LQIRUPDWLRQ VKRXOG EH SUHVHQWHG WR WKH SXEOLF LQ DQ HDV\WRXVH DQG HDV\WR XQGHUVWDQG ZD\ LQ RUGHU WR UHDFK WKH ODUJHVW SRVVLEOH SHUFHQWDJH RI WKH WDUJHW

Wklv prglfdwlrq zrxog ri frxuvh dovr uhtxluh vrph dgmxvwphqwv lq wkh surriv1 Ilqdoo|/ frpsdulqj +:, zlwk +67, lw lv fohdu zk| zh xvh wkh qrwlrq lqqhu dqg rxwhu dssur{lpdwlrq1 Lq