Comparisons of the Solutions of Common FFS Standard Procedures to Benchmark Problems

Comparisons of the Solutions of Common FFS Standard Procedures to Benchmark Problems

Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 130 (2015) 1327 – 1342 WK,QWHUQDWLRQDO&RQIHUHQFHRQ3UHVVXUH9HVVHO...

1MB Sizes 0 Downloads 15 Views

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 130 (2015) 1327 – 1342

WK,QWHUQDWLRQDO&RQIHUHQFHRQ3UHVVXUH9HVVHO7HFKQRORJ\

&RPSDULVRQVRIWKH6ROXWLRQVRI&RPPRQ))66WDQGDUG3URFHGXUHV WR%HQFKPDUN3UREOHPV 12/DUURVDD 5$$LQVZRUWKE b

a School of Materials, The University of Manchester, Manchester M13 9PL, UK School of Mechanical, Aerospace & Civil Engineering, The University of Manchester, Manchester M13 9PL, UK

$EVWUDFW 7KHFRPPRQSUDFWLFHLQLQGXVWU\WRDVVHVVWKHVHYHULW\RIFUDFNOLNHGHIHFWVLQVWUXFWXUDOFRPSRQHQWVLVWRIROORZPHWKRGRORJLHV XVXDOO\FRPSLOHGZLWKLQVWDQGDUGLVHGSURFHGXUHVRUFRGHV7KHPRVWSRSXODU)LWQHVV)RU6HUYLFH ))6 SURFHGXUHVDUH  WKH8. QXFOHDULQGXVWU\VWDQGDUGIRUIUDFWXUHDVVHVVPHQW5  WKH$PHULFDQ3HWUROHXP,QVWLWXWH))6SURFHGXUHV$3,DQG  WKH %ULWLVK6WDQGDUGV,QVWLWXWLRQDVVHVVPHQWSURFHGXUH%67KHVHFRGHVXVXDOO\DVVHVVVWUXFWXUDOLQWHJULW\E\PHDQVRIWKH)DLOXUH $VVHVVPHQW'LDJUDPV )$' LQZKLFKHODVWLFIUDFWXUHDQGSODVWLFFROODSVHDUHDVVHVVHGLQGHSHQGHQWO\DQGFRPELQHGLQDJUDSKLFDO ZD\'XHWRWKHIRUPXODWLRQVZLWKLQWKHFRGHVEHLQJGLIIHUHQWVRPHGLYHUJHQFHLVH[SHFWHGLQWKHUHVXOWVSURYLGHG7KHDLPRIWKLV SDSHULVWRVKRZWKHGLIIHUHQFHVLQWKHUHVXOWVLQWKHDVVHVVPHQWRIWZRFDQGLGDWHSUREOHPVDVVHVVHGE\WKH$3,5DQG%6 SURFHGXUHVDQGWRKLJKOLJKWDQGGLVFXVVWKHSRVVLEOHUHDVRQVEHKLQGWKHVHGLIIHUHQFHV ‹7KH$XWKRUV3XEOLVKHGE\(OVHYLHU/WG © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 3HHUUHYLHZXQGHUUHVSRQVLELOLW\RIWKHRUJDQL]LQJFRPPLWWHHRI,&397 Peer-review under responsibility of the organizing committee of ICPVT-14 Keywords:)LWQHVVIRUVHUYLFH)$'VROXWLRQV5%6$3,

,QWURGXFWLRQ 'LIIHUHQWFDXVHVPD\OHDGWRWKHIDLOXUHRISUHVVXUHYHVVHOVDQGSLSLQJLQVHUYLFH)UDFWXUHFRUURVLRQFUHHSIDWLJXH SODVWLFFROODSVHDQGWKHLULQWHUDFWLRQDUHH[DPSOHVRIIDLOXUHPHFKDQLVPVWKDWDUHOLNHO\WRFRQWULEXWHWRFRPSRQHQW GHJUDGDWLRQDQGSRWHQWLDOIDLOXUH7KHUHIRUHDVVHVVLQJWKHVHYHULW\RIGHIHFWVDWJLYHQORDGLQJFRQGLWLRQVLVHVVHQWLDO  

&RUUHVSRQGLQJDXWKRU7HO   E-mail address:QLFRODVODUURVD#PDQFKHVWHUDFXN

1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICPVT-14

doi:10.1016/j.proeng.2015.12.303

1328

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

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

 )LJ)DLOXUHDVVHVVPHQWGLDJUDPLOOXVWUDWLQJVDIHUHJLRQERXQGHGE\WKH)$'FXUYHDQGFXWRII

7KHIDLOXUHDVVHVVPHQWGLDJUDP )$' SURYLGHVDJUDSKLFDOUHSUHVHQWDWLRQRIWKHOLPLWLQJYDOXHRIWKHQRUPDOLVHG GULYLQJIRUFHDVDIXQFWLRQRIWKHQRUPDOLVHGDSSOLHGORDG,QJHQHUDOWKHVKDSHRIWKHFXUYHGHSHQGVRQWKHPDWHULDO SURSHUWLHVDQGJHRPHWU\RIWKHFRPSRQHQWXQGHUDQDO\VLV+RZHYHUVLPSOLILHG)$'FXUYHVLQGHSHQGHQWRIJHRPHWU\ DQG PDWHULDO GDWD KDYH EHHQ GHULYHG E\ DSSO\LQJ FRQVHUYDWLYH DVVXPSWLRQV >±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

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

1329

1RPHQFODWXUH 2a B 2c E F L KI P

KI S KI Kmat

Kr P

Kr S Kr

Lr LPD[ r P PL  Qm Qb ri rm ro 7 9 V Vref Vf Vys Vr

FUDFNGHSWK VSHFLPHQWKLFNQHVV FUDFNOHQJWK HODVWLFPRGXOXV UHVHUYHIDFWRURQORDG PRGH,VWUHVVLQWHQVLW\IDFWRU VWUHVVLQWHQVLW\IDFWRUGXHWRSULPDU\ORDGV VWUHVVLQWHQVLW\IDFWRUGXHWRVHFRQGDU\ORDGV IUDFWXUHWRXJKQHVV IUDFWXUHUDWLR IUDFWXUHUDWLRGXHWRSULPDU\ORDGV IUDFWXUHUDWLRGXHWRVHFRQGDU\ORDGV QRQGLPHQVLRQDOSODVWLFFROODSVHSDUDPHWHU QRQGLPHQVLRQDOSODVWLFFROODSVHSDUDPHWHUFXWRIIYDOXH LQWHUQDOSUHVVXUH FROODSVHSUHVVXUH VHFRQGDU\PHPEUDQHVWUHVV VHFRQGDU\EHQGLQJVWUHVV LQWHUQDOUDGLXV PHDQUDGLXV RXWHUUDGLXV RSHUDWLQJWHPSHUDWXUH SODVWLFLW\LQWHUDFWLRQIDFWRU VWUHVVHVGXHWRDSSOLHGORDGV UHIHUHQFHVWUHVV IORZVWUHVV \LHOGVWUHVV UHVLGXDOVWUHVVSURILOH

)$'EDVHGFRPSDULVRQ 7KHREMHFWLYHRIWKLVZRUNLVWRKLJKOLJKWGLIIHUHQFHVLQ))6DVVHVVPHQWSURFHGXUHVLQDVVHVVLQJWKHVLJQLILFDQFH RI FUDFNOLNH GHIHFWV E\ IRFXVLQJ RQ VWUHVV LQWHQVLW\ IDFWRU 6,)  DQG SODVWLF FROODSVH VROXWLRQV DV ZHOO DV WKH VLJQLILFDQFH LQ WKH DVVHVVPHQW RI FRQVLGHULQJ UHVLGXDO VWUHVVHV DQG KRZ WKH SURFHGXUHV DFFRXQW IRU WKH HIIHFWV RI UHVLGXDO VWUHVVHV RQ WKH FUDFNGULYLQJIRUFH 7KH )$' )LJ LV WKH PRVWZLGHO\XVHG DSSURDFK IRU DVVHVVLQJ WKH LQWHJULW\RIVWUXFWXUHVFRQWDLQLQJFUDFNOLNHGHIHFWVVRFRPSDULVRQVZLOOEHPDGHEDVHGRQWKH)$'IUDPHZRUNZKHUH DVVHVVPHQWUHVXOWVDUHSORWWHGLQWKH)$'SURYLGLQJDVLPSOHDQGVWUDLJKWIRUZDUGZD\RIVKRZLQJWKHGULYLQJIRUFH IRU ERWK SODVWLF FROODSVH DQG HODVWLFSODVWLF IUDFWXUH PHFKDQLVPV DQG WR FRPSDUH VROXWLRQV DPRQJ WKH FRGHV )RU FRPSDULVRQSXUSRVHWKHHIIHFWVRIRWKHUIHDWXUHV HJSDUWLDOVDIHW\IDFWRUVPDWHULDOSURSHUW\HVWLPDWLRQHWF WKDW PD\DOVRDIIHFWUHVXOWVDUHH[FOXGHGLQWKHDQDO\VHV 7KHVROXWLRQVXVHGLQWKLVZRUNZHUHWKHEHVWDYDLODEOHLQHDFKSURFHGXUHIRUWKH6,)DQGSODVWLFFROODSVHVROXWLRQV 7KDWLVLIVD\D6,)VROXWLRQVZDVQRWDYDLODEOHIRUDF\OLQGHUXQGHUDQDO\VLVEXWDSODVWLFFROODSVHVROXWLRQZDVWKHQ D IODW SODWH VROXWLRQ ZDV XVHG IRU WKH 6,) FDOFXODWLRQ ZLWK D F\OLQGHU VROXWLRQ IRU SODVWLF FROODSVH WR REWDLQ WKH DVVHVVPHQWSRLQW Kr, Lr 

1330

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

%HQFKPDUNSUREOHPV ,QWKLVZRUNµ([DPSOH3UREOHP¶DQGµ([DPSOH3UREOHP¶IURP>@KDYHEHHQFRQVLGHUHG7KHVHDGGUHVVWKH DVVHVVPHQWRIDQLQWHUQDOVXUIDFHIODZLQWKHD[LDOZHOGRIDSLSHF\OLQGHUDQGDIXOO\FLUFXPIHUHQWLDOFUDFNOLNHIODZ LQWKHJLUWKZHOGRQWKHRXWVLGHVXUIDFHRIDSLSHF\OLQGHUUHVSHFWLYHO\7KHVHH[DPSOHVDUHODEHOOHGKHUHDIWHUµ&DVH VWXG\¶DQGµ&DVHVWXG\¶)LJ 

D 

E 



 )LJ*HRPHWULHVFRQVLGHUHGIRUWKHFRPSDULVRQRIWKH))6DVVHVVPHQWSURFHGXUHV D  µ&DVHVWXG\¶ E µ&DVHVWXG\¶)LJXUHVREWDLQHGIURPCrackwise®>@OLEUDU\

3.1. Case study 1 7KHILUVWH[DPSOHLVWKDWRIDFUDFNOLNHGHIHFWORFDWHGLQWKHKHDWDIIHFWHG]RQH +$= SDUDOOHOWRDORQJLWXGLQDO GRXEOH9JURRYHVHDPRQWKHLQVLGHVXUIDFHRIDF\OLQGULFDOSUHVVXUHYHVVHO7KHSUHVVXUHYHVVHOLVPDGHRI6$ *UDGH VWHHO DQGGHVLJQHGDV SHU WKH $60( % 39 FRGH 6HFWLRQ9,,,'LYLVLRQ  7KH F\OLQGHU LV IXOO\ SUHVVXULVHGZKHQWHPSHUDWXUH7•o)WRDQLQWHUQDOSUHVVXUHP psig7KHYHVVHOLVQRWVXEMHFWWRSRVWZHOGKHDW WUHDWPHQW 3:+7 DWWKHWLPHRIIDEULFDWLRQ>1RWHWKHEHQFKPDUNSUREOHPVLQ>@DUHSURYLGHGLQ,PSHULDOXQLWVEXW DVVHVVPHQWVDUHJHQHUDOO\UHSRUWHGKHUHLQQRQGLPHQVLRQDOIRUPRUFRQYHUWHGWR6,XQLWVZKHUHQHFHVVDU\@ 7KH GHWHFWHG IODZ GHSWK a  PP LV HVWLPDWHG IURP XOWUDVRQLF WHVWLQJ 87  DQG LWV OHQJWK c  PP LV REWDLQHGE\PHDQVRIWKHPDJQHWLFSDUWLFOHLQVSHFWLRQWHFKQLTXH 07 DVUHSRUWHGLQ>@7KHRXWVLGHUDGLXVDQGWKH WKLFNQHVVRIWKHF\OLQGHUDUHro in DQGB inUHVSHFWLYHO\VRWKDWWKHLQWHUQDOUDGLXVLVri in7DEOHVKRZV WKHPDWHULDOSURSHUWLHVXVHGLQWKHDVVHVVPHQW)RUDPRUHGHWDLOHGGHVFULSWLRQRIWKHSUREOHPWKHUHDGHULVUHIHUUHGWR >@ 7DEOH0DWHULDOSURSHUWLHVRIWKHVWHHOLQ³&DVH6WXG\´ 3URSHUW\

0DJQLWXGH




3RLVVRQ¶VUDWLRǂ



0LQLPXPVSHFLILHG\LHOGVWUHVVı\V NVL 



)UDFWXUHWRXJKQHVV.PDW NVLLQ 



 7KLQZDOOHGF\OLQGHUVROXWLRQV B/ro  DUHXVHGWRFRPSXWHWKHKRRS ım DQGWKURXJKZDOOEHQGLQJ ıb  FRPSRQHQWVRIWKHSULPDU\VWUHVVDWWKHFHQWUHRIWKHXQFUDFNHGF\OLQGHUXVLQJHTXDWLRQV ' DQG ' LQ>@

1331

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

Vm

Pri B

Vb

  Pro ª B §B· §B· º «   ¨ ¸   ¨ ¸ » ksi 03D  ro  ri « ri © ri ¹ © ri ¹ »¼ ¬

ksi 03D 



 

 

'XHWRLWVVPDOOYDOXHLQFRPSDULVRQWRWKHPHPEUDQHVWUHVVFRPSRQHQWVmWKHEHQGLQJVWUHVV Vb LVQHJOHFWHGLQ WKHDVVHVVPHQW$3DUWLDO6DIHW\)DFWRURQORDGRILVXVHGLQWKHVROXWLRQSURYLGHGLQ>@7KXVLQWKHDVVHVVPHQWV UHSRUWHGKHUHım 03D  03DLVXVHGWRPDNHUHVXOWVGLUHFWO\FRPSDUDEOHWRWKHEHQFKPDUNUHVXOWV LQ>@ 5HVLGXDOVWUHVVHVDUHDFFRXQWHGIRUPHDQVRIDXQLIRUPPHPEUDQHVXUIDFHUHVLGXDOVWUHVVGLVWULEXWLRQ7KHVLPSOH DQGFRQVHUYDWLYHDSSURDFKHVDUHJLYHQLQHTXDWLRQV    

V r y V rys Rr ZLWKV rys V ys  'V ys  $3,  ª

§ ¨ ©

V r y PLQ «V ys  ¨   «¬

V r y V ys  5 

V ref Vf

º · ¸ V ys »  %6  ¸ »¼ ¹ 

 

 

 

ZKHUHy LVWKHORFDOFRRUGLQDWHIRUWKHVWUHVVGLVWULEXWLRQDORQJWKHRXWHUVXUIDFHDQGLVPHDVXUHGIURPWKHZHOGFHQWUH DQGSHUSHQGLFXODUWRWKHVHDPGLUHFWLRQ,QHTXDWLRQ  Rr LVDUHGXFWLRQIDFWRUDFFRXQWLQJWKHHIIHFWRQUHVLGXDO VWUHVVHV RI WKH WHVW SUHVVXUH $FFRUGLQJ WR WKH $3,  SURFHGXUH (TV ( LQ >@  IRU WKLV FDVH Rr  7KH HOHYDWLRQRIWKHPHPEUDQHUHVLGXDOVWUHVVLQ$3,¨ıys ksi 03DLVJLYHQLQ(T(LQ>@ZLWKıys LQ WKLVFRGHEHLQJWKHPLQLPXPVSHFLILHG\LHOGVWUHVV,QHTXDWLRQ  ıref DQGıf DUHWKHUHIHUHQFHVWUHVVDQGWKHIORZ VWUHVVUHVSHFWLYHO\,Q%6DQG5ıys LQHTXDWLRQV  VKRXOGEHWDNHQDVWKHPHDQ\LHOGVWUHVVLQFRQWUDVWWR WKHPLQLPXPVSHFLILHG\LHOGVWUHVV+RZHYHUDV>@GRHVQRWSURYLGHPHDQ\LHOGVWUHVVGDWDWKHPLQLPXPVSHFLILHG \LHOGVWUHVVKDVEHHQXVHGLQVWHDGZKHQDSSO\LQJ%6DQG5DQGWKLVLVGLVFXVVHGODWHU )LJXUHVKRZVWKHUDQJHRIDSSOLFDWLRQRIWKH6,)VROXWLRQVJLYHQLQHDFKSURFHGXUHIRUDF\OLQGHUZLWKDVHPL HOOLSWLFDOLQWHUQDOFUDFN,WLVZRUWKQRWLQJWKDWWKHUDQJHVRIDSSOLFDWLRQIRUWKH6,)VROXWLRQVGLIIHUVLJQLILFDQWO\ DPRQJWKHSURFHGXUHV)RUWKLVFDVH5LQFOXGHVVROXWLRQVIRURQO\DOLPLWHGUDQJHRIrm/BEXWSURYLGHVDVRXUFH UHIHUHQFH IRU KLJKHU rm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r UHVXOWVIRUGLIIHUHQWVROXWLRQVDVDIXQFWLRQRIWKHQRUPDOL]HGFUDFNGHSWK a/B &\OLQGHU VROXWLRQVDUHVKRZQLQWKHILJXUHIRUERWK%6DQG$3,7ZRVHWVRIVXUIDFHEUHDNLQJIODWSODWHVROXWLRQVDUH DOVR LQFOXGHG IRU %6  ,Q %6  WHQVLOH IRUFHV FDQ EH DSSOLHG YLD SLQ MRLQWHG RU IL[HG JULS FRQGLWLRQV Lr HVWLPDWHVIRUWKHJHRPHWU\XQGHUDQDO\VLVDUHVKRZQLQ7DEOH5HVXOWVIURP$3, F\OLQGHU DQG5 F\OLQGHU JOREDO DUHLGHQWLFDO,QFRQWUDVW%6 F\OLQGHU HVWLPDWHVDUHXSWRKLJKHUWKDQWKRVHIRU$3,DQG5 )RUODUJHUFUDFNVWKHGLIIHUHQFHDPRQJWKHVHVROXWLRQVGRHVQRWFKDQJHVLJQLILFDQWO\7KH%6>)ODWSODWH)L[HG

1332

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

*ULS )* DQG3LQ/RDGHG 3/ @VROXWLRQVDUHWKHPRVWSHVVLPLVWLFZLWKGLIIHUHQFHVZLWKLQ )* DQG 3/  $VVKRZQLQ)LJGLIIHUHQFHVDUHODUJHUIRUKLJKHUa/B YDOXHV 

 )LJ6WUHVVLQWHQVLW\IDFWRUUDQJHVRIDSSOLFDWLRQIRUDF\OLQGHUZLWKDQ LQWHUQDOVHPLHOOLSWLFDOD[LDOIODZ*UHHQGRWUHSUHVHQWVFDVHXQGHUDQDO\VLV 7DEOH6ROXWLRQVXVHGLQWKHDVVHVVPHQWIRUµ&DVHVWXG\¶///LPLWORDG565HIHUHQFH6WUHVV 363ULPDU\VWUHVVHV666HFRQGDU\VWUHVVHV**OREDO//RFDO7:7KLFNZDOOHG 3URFHGXUH

*HRPHWU\

6,)

5HIHUHQFH6WUHVV/LPLWORDG

5

3ODWH

,9





&\OLQGHU



,9

%6

3ODWH

0

3 56 



&\OLQGHU

0

3

$3,

&\OLQGHU

& 36 

' 56 

& 66 

 7DEOH3ODVWLFFROODSVHSDUDPHWHU /U UHVXOWVIRU³&DVH6WXG\´)3)ODW3ODWH)*)L[HG JULS3/3LQORDGHG&\O&\OLQGHUVROXWLRQ**OREDO//RFDO 6ROXWLRQ

/U

3HUFHQWDJHGLIIHUHQFH $3, 

%6 )3)* 





%6 )33/ 





%6 &\O 





$3, &\O 



QD

5 &\O 





1333

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

 )LJ3ODVWLFFROODSVHUDWLR Lr IRUWKHVROXWLRQVSURYLGHGLQWKHWKUHHVWDQGDUGV9HUWLFDOGDVKHGOLQHVKRZVUHVXOWVIRUµ&DVH6WXG\¶

)UDFWXUH SDUDPHWHU Kr  HVWLPDWHV IRU SULPDU\ DQG VHFRQGDU\ ORDGV DQG WKH SODVWLFLW\ LQWHUDFWLRQ IDFWRU 9  DUH VKRZQ LQ 7DEOH  ,W LV REVHUYHG WKDW WKH SULPDU\ ORDG FRPSRQHQWV KrP  DUH LQ YHU\ FORVH DJUHHPHQW 6LJQLILFDQW GLIIHUHQFHVEHWZHHQ$3,VHFRQGDU\ORDGV KrS HVWLPDWHVDQG5%6SUHGLFWLRQVDUHIRXQGEXWWKLVLVODUJHO\ EHFDXVHWKHUHVLGXDOVWUHVVXVHGLQ$3,LVKLJKHUWKDQWKDWXVHGIRUWKH%65FDOFXODWLRQVDVDUHVXOWVRIWKH DGGLWLRQRI¨ıys LQHTXDWLRQ  $VVKRZQLQWKH7DEOHIRUWKHFDVHRI5%6WKHUDWLRRIWKHIUDFWXUHSDUDPHWHU IRUVHFRQGDU\ORDGVWRWKDWRISULPDU\ORDGV KrS/KrP LVDOPRVWWKHVDPHDVWKHUDWLRRIWKHPHPEUDQHUHVLGXDOVWUHVVHV WRWKHDSSOLHGPHPEUDQHVWUHVV Vyr/V VKRZLQJWKDWIRUWKLVVLPSOLILHGFDVHWKHVDPH6,)VROXWLRQLVXVHGIRUWKH SUHVVXUHPHPEUDQHVWUHVVDQGWKHUHVLGXDOVWUHVV$GLIIHUHQFHRIEHWZHHQKrS/KrPDQGVyr/VLVREVHUYHGLQ$3, LQGLFDWLQJWKDWWKH6,)VROXWLRQVXVHGIRUWKHSULPDU\DQGVHFRQGDU\ORDGVGLIIHUDOWKRXJKQRWVLJQLILFDQWO\ 7DEOH)UDFWXUHSDUDPHWHUUHVXOWVIRUSULPDU\ .U3 DQGVHFRQGDU\ .U6 ORDGVIRU³&DVH6WXG\´ 

5

%6

$3,

KrP







K

S r







KrS/KrP







Vyr/V







9







 7DEOHVKRZVWKHUHVXOWVRIWKHDVVHVVPHQWIRUWKHVXUIDFH ‫ ׋‬R DQGGHHSHVWSRLQWV ‫ ׋‬R RIWKHD[LDOO\RULHQWHG LQWHUQDOFUDFNERWKLQFOXGLQJDQGH[FOXGLQJWKHHIIHFWRIUHVLGXDOVWUHVVHV8VLQJWKH$3,VROXWLRQDVDQDUELWUDU\ UHIHUHQFHZKHQDXQLIRUPUHVLGXDOVWUHVVHVGLVWULEXWLRQLVWDNHQLQWRDFFRXQWKrVROXWLRQVDUHZLWKLQIRUWKH GHHSHVWSRLQWDQGZLWKLQIRUWKHVXUIDFHSRLQW,IUHVLGXDOVWUHVVHVDUHQHJOHFWHGVROXWLRQVDUHZLWKLQDQG DWWKHGHHSHVWDQGWKHVXUIDFHSRLQWUHVSHFWLYHO\'LIIHUHQFHVLQLrVROXWLRQVDUHZLWKLQ7KHODUJHVWGLIIHUHQFHV DULVHVEHWZHHQ%6DOLPLWORDGDSSURDFKDQGWKHVROXWLRQVSURYLGHGE\5DQG$3,ZKLFKDUHEDVHGRQD UHIHUHQFHVVWUHVVDSSURDFKDQGDUHH[SUHVVHGE\VLPLODUHTXDWLRQV)LJVKRZVWKHVHUHVXOWVZLWKLQWKH2SWLRQ IDLOXUHDVVHVVPHQWGLDJUDP )$'    

1334

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

7DEOH3ODVWLFFROODSVHSDUDPHWHU /U DQGIUDFWXUHSDUDPHWHUUHVXOWV .U IRU³&DVH6WXG\´ 5HVLGXDOVWUHVVHV





3HUFHQWDJHGLIIHUHQFH $3, 

Deepest point

Lr

Kr

Lr 

Kr

$3,





QD

QD

5









%6









Surface point

/U

.U

Lr 

Kr

$3,





QD

QD

R6









%6









1RUHVLGXDOVWUHVVHV





3HUFHQWDJHGLIIHUHQFH $3, 

Deepest point

/U

.U

Lr 

Kr

$3,





QD

QD

R6









%6









Surface point

/U

.U

Lr 

Kr

$3,





QD

QD

5









%6











 o

)LJ$VVHVVPHQWUHVXOWVRIµ&DVHVWXG\¶DWWKHVXUIDFH ‫  ׋‬DQGGHHSHVW o SRLQW ‫  ׋‬ORFDWLRQVZLWKDQGZLWKRXWWKHHIIHFWRIUHVLGXDOVWUHVVHV

,WZDVQRWHGDERYHDQGVKRZQLQ(T  WKDW$3,>@UHFRPPHQGVDQHOHYDWLRQDERYHWKHPLQLPXPVSHFLILHG \LHOGVWUHQJWKWRDFFRXQWIRUWKHW\SLFDOHOHYDWLRQRIPDWHULDOSURSHUWLHVDERYHPLQLPXPUHTXLUHPHQWV,Q)LJWKH UHGV\PEROVVKRZWKH$3,VROXWLRQVLIWKLVHOHYDWLRQLVQRWFRQVLGHUHG,WLVREVHUYHGWKDWWKHSRLQWVDUHVKLIWHG GRZQZDUGVDQGWKHKrVROXWLRQVDWWKHGHHSHVWSRLQWZKHUHFRQGLWLRQVDUHPRVWVHYHUHGLIIHUE\OHVVWKDQIURP WKHRWKHUVROXWLRQV8VLQJWKHVDPHYDOXHRIWKHPHPEUDQHUHVLGXDOVWUHVVDVWKDWLQ5%6SURFHGXUHV$3, HVWLPDWHVKrS/KrP ZLWKVyr/V  VHH7DEOH 

1335

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

 )LJ$VVHVVPHQWUHVXOWVRIµ&DVHVWXG\¶DWWKHVXUIDFH ࢥ R DQGGHHSHVWSRLQW ࢥ R ORFDWLRQVZLWKDQGZLWKRXWWKHHIIHFWRIUHVLGXDOVWUHVVHV5HGV\PEROVVKRZV DVVHVVPHQWXVLQJPHPEUDQHUHVLGXDOVWUHVVHVDVUHFRPPHQGHGLQ5%6

Triangles: API 579, 2007 (Red: RS field as in R6-BS7910) Squares: BS 7910, 2013 (Global Plate solution - SIF Cylinder)(Green: Thick cylinder soltuion) Stars: R6, 2014 (Blue: VM yield criterion)

 

$3,2SW %652SW

 

.U .,.PDW

 o

Solid: I=90 , residual stresses o Hollow: I=0 , residual stresses o Crossed: I=90 , no residual stresses o Semi-Solid: I=0 , no residual stresses

       

















/U 33/

 o

o

)LJ$VVHVVPHQWUHVXOWVRIµ&DVHVWXG\¶DWWKHVXUIDFH ‫  ׋‬DQGGHHSHVWSRLQW ‫  ׋‬ ORFDWLRQVZLWKDQGZLWKRXWWKHHIIHFWRIUHVLGXDOVWUHVVHV&RQGLWLRQVDQGSORWWHG

)LJXUHVKRZVUHVXOWVIRUWZRDGGLWLRQDOFRQGLWLRQV DGMXVWLQJWKHSLSHGLPHQVLRQVDQGYDOXHRIWKHDSSOLHG LQWHUQDOSUHVVXUH P WRNHHSWKHVDPHDSSOLHGPHPEUDQHVWUHVVDQGREWDLQDUDWLRrm/B WKDWILWVZLWKLQWKHWKLFNSLSH 6,)VROXWLRQVUDQJH )LJ  DGRSWLQJWKH9RQ0LVHV\LHOGFULWHULRQ 7KHH[WUHPHYDOXHVrm/B DQGrm/B ZHUHXVHGLQWKHFRPSDULVRQWRDVVHVVWKHHIIHFWRQWKHUHVXOWVDQG WKHYDOXHRIPZDVREWDLQHGDFFRUGLQJO\IURP(T  7KHUHVXOWVIRUWKHVHFDVHVGLIIHUE\OHVVWKDQLQLrDQG DQGLQKrDWWKHEDVHDQGWKHHGJHRIWKHFUDFNUHVSHFWLYHO\$VDUHVXOWHVWLPDWHVIRUrm/B DUH RQO\SORWWHGLQWKHILJXUH,QFRPSDULVRQZLWKWKHIODWSODWHVROXWLRQVUHVXOWVIRUFRQGLWLRQDUHKLJKHULQWHUPVRI

1336

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

SODVWLFFROODSVHSDUDPHWHU Lr ZLWKLQDQGORZHULQWHUPVRIWKHIUDFWXUHSDUDPHWHU Kr ZLWKGLIIHUHQFHVRI OHVVWKDQIRUWKHHGJHRIWKHFUDFNDQGZLWKLQDWWKHEDVHRIWKHIODZ )RUFRQGLWLRQLr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

 )LJ5HVHUYH)DFWRUVRQ/RDGIRU¶&DVHVWXG\¶&RPSDULVRQRIDVVHVVPHQWSURFHGXUHHVWLPDWLRQV



 )LJ&ULWLFDOFUDFNVL]HHVWLPDWLRQVIRU¶&DVHVWXG\¶&RPSDULVRQRIDVVHVVPHQWSURFHGXUHHVWLPDWHV

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

1337

3.2. Case study 2 &DVHVWXG\LVDFUDFNOLNHIODZWKDWKDVEHHQIRXQGRQWKHRXWVLGHVXUIDFHRIDSLSHDWWKHZHOGWRHRIWKHJLUWK ZHOGSLSH)LJ E 7KHVHDPLVDVLQJOH9JURRYHZHOGDQGWKHIODZLVSDUDOOHOWRWKHZHOGVHDP7KHSLSHLVPDGH RI6$*UDGH%VWHHODQGGHVLJQHGDVSHU$60(%FRGH)XOO\RSHUDWLRQDOFRQGLWLRQVDUHUHDFKHGZKHQ 7 R&7KHSLSHZDVGHVLJQHGWRVXVWDLQ03DRILQWHUQDOSUHVVXUHDWR&DQGKDGQRWEHHQVXEMHFWWRSRVWZHOG KHDWWUHDWPHQW 3:+7 DWWKHWLPHRIIDEULFDWLRQ QRUHOD[DWLRQRIUHVLGXDOVWUHVVHV 7KHGHWHFWHGIODZGHSWKLVD  PP7KHRXWVLGHUDGLXVDQGWKHWKLFNQHVVRIWKHF\OLQGHUDUHro PPDQGB PPUHVSHFWLYHO\ ,QWHUQDOSUHVVXUHDQGJOREDOEHQGLQJGXHWRWKHORFDWLRQRIWKHIODZ PLGZD\EHWZHHQVXSSRUWVZKLFKDUHDWD GLVWDQFHDSDUWRIP DUHWDNHQLQWRDFFRXQW7KHVHOHFWHGKHDWLQSXWFRUUHVSRQGVWRVKLHOGHGPHWDODUFZHOGLQJ 60$: PHWDODUFZHOGLQJ 00$ SDVVHVUHFRUGHGDVE -RXOHVPP7DEOHVKRZVWKHPDWHULDOSURSHUWLHV XVHGLQWKHDVVHVVPHQW 7DEOH0DWHULDOSURSHUWLHVRIWKHVWHHOLQ³&DVH6WXG\´ 3URSHUW\

0DJQLWXGH




3RLVRQ¶VUDWLRȞ



0LQLPXPVSHFLILHG\LHOGVWUHVVıys 03D 



)UDFWXUHWRXJKQHVVKmat 03DP. 



 )LJXUH  VKRZV WKH UDQJH RI DSSOLFDWLRQ IRU WKH 6,) VROXWLRQV IRU µ&DVH VWXG\ ¶ D F\OLQGHU ZLWK D IXOO\ FLUFXPIHUHQWLDOH[WHUQDOFUDFNIRUHDFKSURFHGXUH)RUWKHFDVHXQGHUDQDO\VLV JUHHQGRW WKH6,)VROXWLRQVSURYLGHG E\5LVRXWWKHUDQJHRIDSSOLFDWLRQWKXVDIODWSODWHVROXWLRQZDVXVHGIRUDVVHVVPHQWSXUSRVH+RZHYHUDVIRU&DVH VWXG\5SURYLGHVDVRXUFHUHIHUHQFHIRUVROXWLRQVIRUODUJHUrm/BDQGWKHVHVROXWLRQVDUHFRQWDLQHGLQ5FRGH

 )LJ6WUHVVLQWHQVLW\IDFWRUUDQJHVRIDSSOLFDWLRQIRUDF\OLQGHUZLWKDQ H[WHUQDOFLUFXPIHUHQWLDOIODZ*UHHQGRWUHSUHVHQWVFDVHXQGHUDQDO\VLV

7DEOHVKRZVWKH6,)DQGUHIHUHQFHVWUHVVOLPLWORDGVROXWLRQVXVHGLQWKLVFDVHVWXG\,QWKLVSUREOHPWKHWUHDWPHQW RIVHFRQGDU\VWUHVVHV LHUHVLGXDOVWUHVVHV LVGRQHE\XVLQJDQRQXQLIRUPVWUHVVGLVWULEXWLRQDFURVVWKHWKLFNQHVVRI WKHSLSHLQFRQWUDVWWRµ&DVHVWXG\¶ZKHUHDFRQVWDQWUHVLGXDOVWUHVVGLVWULEXWLRQZDVXVHG  

1338

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

7DEOH6ROXWLRQVXVHGLQWKHDVVHVVPHQWIRUµ&DVHVWXG\¶///LPLWORDG565HIHUHQFH6WUHVV 3URFHGXUH

5HIHUHQFH

*HRPHWU\

6,)

5

3ODWH

,9RU ,9





&\OLQGHU



,9 // 

%6

&\OLQGHU

0

3 56 

$3,

&\OLQGHU

&

' 56 

6WUHVVRU/LPLWORDG

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µOLQHDU¶DQGD VHOIHTXLOLEUDWLQJFRPSRQHQW%RWK%6DQG5RQO\FRQVLGHUZDOOWKLFNQHVVHIIHFWVLQDQRUPDOL]HGOLQHDUKHDW LQSXW GHILQLWLRQ ZKLOH $3,  53$60( ))6 H[SOLFLWO\ LQFRUSRUDWH WKLFNQHVV WHUP LQ WKH UHVLGXDO VWUHVV IRUPXODWLRQXSWRDWKLFNQHVVRIPP7KHWUDQVYHUVHUHVLGXDOVWUHVVHVVXJJHVWHGIRUWKHGLIIHUHQWSURFHGXUHVDUH VKRZQLQ)LJ

 )LJ7UDQVYHUVHUHVLGXDOVWUHVVSURILOHVSUHVFULEHGE\$3, $QQH[( %6 $SSHQGL[4 DQG5 6HF,9 

$VLPSOHDQGUDSLGDSSURDFKWRDVVHVVVWUHVVLQWHQVLW\IDFWRUVROXWLRQVIRUERWKSULPDU\DQGVHFRQGDU\ORDGVLVWR WDNHLQWRDFFRXQWVWUHVVJUDGLHQWVE\OLQHDULVLQJWKHVWUHVVILHOGRYHUWKHIODZGHSWKaDQGVSOLWWLQJLWLQWRPHPEUDQH WHQVLOH DQGEHQGLQJFRPSRQHQWV7KHPHWKRGRIOLQHDULVDWLRQVKRXOGEHSHVVLPLVWLFLQWKDW6,)VDUHRYHUHVWLPDWHG >@ )LJXUHVKRZVWKHVWUHVVOLQHDULVDWLRQDSSURDFKXVHGDVVXJJHVWHGLQ5DQG%6,WLVREVHUYHGWKDWWKHUH DUHFRPSUHVVLYHUHVLGXDOVWUHVVHVRYHUWKHFRPSOHWHFUDFNIDFHJLYLQJDSRVLWLYHPHPEUDQHVWUHVV Qm DQGDQHJDWLYH EHQGLQJFRPSRQHQW Qb 

1339

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

 )LJ6WUHVVOLQHDULVDWLRQDSSURDFKXVHGWRDVVHVVUHVLGXDOVWUHVVFUDFNGULYLQJIRUFH

)LJXUHVDQGVKRZVWKHILWWLQJDSSURDFKXVHGWRHYDOXDWHWKH6,)IRUWKHFDVHXQGHUDQDO\VLV7KLUGRUGHU )LJ  DQGDIRXUWKRUGHU )LJ SRO\QRPLDOILWVDUHXVHGWRREWDLQ6,)VZLWK5>@DQG$3,>@UHVSHFWLYHO\,Q RUGHUWRFRPSDUHVROXWLRQVRIWKHGLIIHUHQWDSSURDFKHVVXJJHVWHGLQWKHFRGHVWKHOLQHDULVDWLRQDSSURDFKLVXVHGWR REWDLQ6,)VZLWK%6>@ $VVHVVPHQW UHVXOWV DUH VKRZQ LQ 7DEOH  DQG )LJ  $V VKRZQ UHVLGXDO VWUHVVHV KDYH D VLJQLILFDQW HIIHFW RQ IUDFWXUHSDUDPHWHUUHVXOWV8QLIRUPUHVLGXDOVWUHVVHVSURGXFHWKHPRVWSHVVLPLVWLFUHVXOWVZKHUHDVWKHQRQXQLIRUP GLVWULEXWLRQVXVXDOO\KDYHDPLOGHUHIIHFW,WLVZRUWKPHQWLRQLQJWKDWDSSOLFDWLRQRIERWK5DQG%6OHDGVWR FRPSUHVVLYHVHFRQGDU\VWUHVVLQWHQVLW\IDFWRUVDQGIRUDVVHVVPHQWSXUSRVHVWKHFRQWULEXWLRQWRWKHIUDFWXUHGULYLQJ S IRUFHLVWKHQQHJOHFWHG Kr  

 )LJ7KLUGRUGHUSRO\QRPLDOILWWRDVVHVVUHVLGXDOVWUHVVFUDFNGULYLQJIRUFHDVVXJJHVWHGLQ5 ,9 DQGLQ%6 4 

1340

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342



WKRUGHUSRO\QRPLDOILW $3, $3,/LQHDUFRPSRQHQW VPVE



$3,6HOI(TXLOLEUDWLQJFRPS

  7

V5

 

&RHIILFLHQW 9DOXH  V

 

V



V



V



V



 







]%





Crack

 )LJ)RXUWKRUGHUSRO\QRPLDOILWWRDVVHVVUHVLGXDOVWUHVVFUDFNGULYLQJIRUFHDVVXJJHVWHGLQ$3, (E 

 )LJ$VVHVVPHQWUHVXOWVRI¶&DVHVWXG\¶DWWKHGHHSHVWSRLQWORFDWLRQZLWKDQGZLWKRXWWKHHIIHFW UHVLGXDOVWUHVVHV&RPSDULVRQVRIXVLQJDXQLIRUPDQGDQRQXQLIRUPUHVLGXDOVWUHVVSURILOHDUHVKRZQ

)URP7DEOHLWLVREVHUYHGWKDWLr VROXWLRQVDUHZLWKLQRIHDFKRWKHU5Kr VROXWLRQVZHUHXSWRDQG DQG%6Kr VROXWLRQVZHUHXSWRDQGZLWKDQGZLWKRXW56UHVSHFWLYHO\LQFRPSDULVRQZLWK$3, VROXWLRQV7KHGLIIHUHQFHLQ6,)GXHWRSULPDU\VWUHVVHVLVZLWKLQEXWPXFKJUHDWHUGLIIHUHQFHVRFFXUZLWK56 EHFDXVHRIERWKGLIIHUHQFHVLQ56OHYHOVLQWKHFRGHVDQGGLIIHUHQFHVLQWKH6,)VROXWLRQDSSURDFKHV    

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

1341

7DEOH$VVHVVPHQWUHVXOWVIRUµ&DVHVWXG\¶(IIHFWRIµ/HYHO¶DQGµ/HYHO¶UHVLGXDOVWUHVVHIIHFWLQ Kr LQFOXGHG3HUFHQWDJHGLIIHUHQFHZLWKUHVSHFWWR$3,HVWLPDWLRQVLQSDUHQWKHVLV 

/U



1R5HVLGXDO6WUHVVHV

.U

$3,





5

  

  

%6

  

  



8QLIRUP5HVLGXDO6WUHVVSURILOH /HYHO 

$3,





5

  

  

%6

  

  



1RQXQLIRUP5HVLGXDO6WUHVVSURILOH /HYHO 

$3,





5

  

  

%6

  

   

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rs KDYH EHHQ VKRZQ WR SURGXFH VLJQLILFDQW GLIIHUHQFHV LQ Kr HVWLPDWHV +RZHYHUXVLQJWKHVDPHDSSURDFKWRDFFRXQWIRUUHVLGXDOVWUHVVHVUHGXFHVWKHVHGLIIHUHQFHVFRQVLGHUDEO\ 7KH PDLQ GLIIHUHQFHV LQ Kr VROXWLRQV DULVH IURP GLIIHUHQFHV LQ 6,) IRUPXODWLRQ VROXWLRQV DQG WKH WUHDWPHQW RI VHFRQGDU\ VWUHVVHV 7KH QRQXQLIRUP UHVLGXDO VWUHVV SURILOH VXJJHVWHG LQ $3,  LV FRQVLGHUDEO\ GLIIHUHQW WR WKDW UHFRPPHQGHGLQ5%6:KHQWKHFUDFNOLHVRQWKHH[WHUQDOVLGHRIWKHSLSHF\OLQGHUDVLQµ&DVH6WXG\¶D FRPSUHVVLYHUHVLGXDOVWUHVVFRPSRQHQWLVJLYHQE\5%6ZKHUHDVDWHQVLOHUHVLGXDOVWUHVVSURILOHLVREWDLQHGE\ PHDQVRIWKHGLVWULEXWLRQVXJJHVWHGE\$3,7KLVKDVDKXJHLPSDFWRQWKHDVVHVVPHQWUHVXOWV)RUH[DPSOH DOWKRXJKWKHDSSURDFKXVHGZLWK5DQG$3,WRDVVHVV6,)VLVVLPLODULWLVREVHUYHGWKDWWKHVHYHULW\RIWKHGHIHFW S LVXQFKDQJHG DV Kr   LWLVVHWWR]HUR ZKHQDSSO\LQJWKHQRQXQLIRUPUHVLGXDOVWUHVVSURILOHDVVXJJHVWHGLQ5%6  FRPSUHVVLYHVWUHVVHVRQWKHDUHDZKHUHWKHFUDFNOLHV ZKHUHDVDQLQFUHDVHGVHYHULW\LVREWDLQHGZKHQDSSO\LQJ WKH$3,UHVLGXDOVWUHVVSURILOH WHQVLOHVWUHVVHVRQWKHDUHDZKHUHWKHFUDFNOLHV  6LJQLILFDQWGLIIHUHQFHVLQLr VROXWLRQVDULVHGXHWRWKHDYDLODELOLW\RIJHRPHWU\VSHFLILFVROXWLRQV$GMXVWLQJWKH SLSHGLPHQVLRQVDQGYDOXHRIWKHDSSOLHGLQWHUQDOSUHVVXUH P WRNHHSWKHVDPHDSSOLHGPHPEUDQHVWUHVVDQGREWDLQD UDWLRrm/B WKDWILWVZLWKLQWKHWKLFNSLSH6,)VROXWLRQUDQJH )LJ OHGWRUHVXOWVLQJRRGDJUHHPHQWZLWKHDFKRWKHU &RQFOXVLRQV ,QWKLVZRUNUHVXOWVEDVHGRQRIWKHPRVWFRPPRQO\XVHG)LWQHVV)RU6HUYLFHSURFHGXUHVKDYHEHHQFRPSDUHG WRDVVHVVWKHVLJQLILFDQFHRIGHIHFWVE\IRFXVLQJRQ6,)DQGSODVWLFFROODSVHVROXWLRQV7KHVDPHORDGLQJFRQGLWLRQV

1342

N.O. Larrosa and R.A. Ainsworth / Procedia Engineering 130 (2015) 1327 – 1342

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x 7KH$3,VWDQGDUGFRQWDLQHGVROXWLRQVIRUWKHODUJHVWUDQJHRIGLPHQVLRQVIRUWKHFDVHVXQGHUDQDO\VLV x Lr UHVXOWVGHULYHGE\%6DUHKLJKHUWKDQWKHRWKHUFRGHV x 'LIIHUHQFHVLQ6,)IRUPXODWLRQVROXWLRQV9IDFWRUDQGUHVLGXDOVWUHVVHVOHDGWRVLJQLILFDQWYDULDWLRQVLQ.U VROXWLRQV x ,Q5%6D/HYHOWUHDWPHQWRIUHVLGXDOVWUHVVHVDVVXPHVWKDWWKHPDJQLWXGHRIZHOGLQJUHVLGXDOVWUHVVLV WKHPHDQ\LHOGVWUHQJWKRIWKHSDUHQWPDWHULDO$3,SURYLGHVDQHOHYDWLRQRIWKHHIIHFWLYH\LHOGVWUHQJWKDERYH WKHVSHFLILHGPLQLPXP\LHOGVWUHQJWKWRDFFRXQWIRUWKHW\SLFDOHOHYDWLRQRIDFWXDOSURSHUWLHVDERYHPLQLPXP UHTXLUHPHQWV x )RU&DVHVWXG\WKH/HYHOQRQXQLIRUPUHVLGXDOVWUHVVGLVWULEXWLRQVXJJHVWHGE\$3,IRUWKHVSHFLILFOHYHO RIKHDWLQSXWJLYHQLVVLJQLILFDQWO\GLIIHUHQWIURPWKRVHLQ5DQG%6 x %RWKDVWUHVVOLQHDULVDWLRQDSSURDFKDQGDSRO\QRPLDOILWWLQJSURFHGXUHDUHVXJJHVWHGLQ5DQG%6WR DVVHVVVWUHVVLQWHQVLW\IDFWRUVLQIODWSODWHV x %66,)VROXWLRQVZHUHDVVHVVHGLQWKLVZRUNLQWHUPVRIEHQGLQJDQGPHPEUDQHVWUHVV5DQG$3, VROXWLRQVDUHSUHVHQWHGLQWHUPVRIZHLJKWIXQFWLRQVDOORZLQJVWUHVVLQWHQVLW\IDFWRUVWREHHYDOXDWHGIRUDUELWUDU\ VWUHVVILHOGV x 7KHVWUHVVOLQHDULVDWLRQDSSURDFKLVTXLFNDQGHDV\DQGSURYLGHVDVDWLVIDFWRU\SUHOLPLQDU\VROXWLRQ x 7KHSRO\QRPLDOFXUYHILWWLQJDSSURDFKXVHGLQµ&DVH6WXG\¶WRDVVHVVWKHKr VROXWLRQE\PHDQVRI5DQG$3, XVXDOO\UHTXLUHVILWWLQJWKHVWUHVVILHOGE\WKWKRUGHUSRO\QRPLDOV)RUVRPHJHRPHWULHVQXPHULFDO LQWHJUDWLRQIRUWKHFDOFXODWLRQRIWKHSIF LVDOVRQHHGHG 7KLVSDSHULVSDUWRIDQRQJRLQJSURMHFWDQGWKHVHDUHSUHOLPLQDU\UHVXOWV $FNQRZOHGJHPHQWV 7KHDXWKRUVZLVKWRDFNQRZOHGJHSDUWIXQGLQJIRUWKLVUHVHDUFKIURP%3WKURXJKWKH%3,QWHUQDWLRQDO&HQWUHIRU $GYDQFHG0DWHULDOV3URYLVLRQRIVRIWZDUHE\7:,(')(QHUJ\DQG4XHVW,QWHJULW\LVJUDWHIXOO\DFNQRZOHGJHG 5HIHUHQFHV >@ >@ >@ >@ >@ >@

$PHULFDQ3HWUROHXP,QVWLWXWH$PHULFDQ6RFLHW\RI0HFKDQLFDO(QJLQHHUV$3,$60())65HFRPPHQGHGSUDFWLFHIRUILWQHVV IRUVHUYLFH$3, %6*XLGHWRPHWKRGVIRUDVVHVVLQJWKHDFFHSWDELOLW\RIIODZVLQPHWDOOLFVWUXFWXUHV%ULWLVK6WDQGDUG,QVWLWXWLRQ/RQGRQ8.  55HYLVLRQ$VVHVVPHQWRIWKHLQWHJULW\RIVWUXFWXUHVFRQWDLQLQJGHIHFWV(')(QHUJ\*ORXFHVWHU8. $3,$60())6)LWQHVVIRUVHUYLFH([DPSOHSUREOHPPDQXDO$3, &UDFNZLVH$XWRPDWLRQRI)UDFWXUHDQG)DWLJXH$VVHVVPHQW3URFHGXUHV %6 IRU(QJLQHHULQJ&ULWLFDO$VVHVVPHQW (UHQ6+DGOH\,DQG1LNELQ.'LIIHUHQFHVLQWKHDVVHVVPHQWRISODVWLFFROODSVHLQ%6DQG5)LWQHW))6 SURFHGXUHV$PHULFDQ6RFLHW\RI0HFKDQLFDO(QJLQHHUV3UHVVXUH9HVVHOVDQG3LSLQJ'LYLVLRQ3939ROSS±