2 bending operations

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Page 1: 2 Bending Operations
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SNOITAREPO GNIDNEB FO SEPYT

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secnawollA gnidneB

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SUIDAR DNEB

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uidaR dneB .niM s

suidaR dneB .nim no tnemtaerT taeH fo tceffE

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taeH fo tceffE suidaR dneB .nim no tnemtaerT

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fo tceffE ,lairetaM tnemtaerT taeH ssenkcihT teehS ,

noitceriD dneB dna no eht suidaR dneB .nim

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) s ( ssenkcihT pirtS no gnidnepeD iidaR gnidneB elbissimdA .niM

lairetaM dezilamroN ro delaennA H detaerT tae denedrah niarts ro

srebiF gnilloR oT ylevitaleR gnidneB fo eniL esiwssorC gnolA esiwssorC gnolA

munimulA 0.0 s 3.0 s 3.0 s 8.0 reppoC delaennA 0.0 s 3.0 s 0.1 s 0.2

)uC%76( ssarB 0.0 s 3.0 s 4.0 s 8.0 leetS ytilauQ 0.0 s 3.0 s 2.0 s 5.0

.IIV tS 32 0.0 s 4.0 s 4.0 8.0 01 C

2 tS ,1 tS 02 C..…51 C s 1.0 s 5.0 s 5.0 s 0.1 3 tS 03C..…52 C s 2.0 s 6.0 s 6.0 s 2.1 4 tS 04 C..…53 C s 3.0 s 8.0 s 8.0 s 5.1 5 tS 05 C..…54C s 5.0 s 0.1 s 0.1 s 7.1 6 tS 06C..…55 C s 7.0 3.1 s s 3.1 s 0.2 7 tS

munimularuD tfoS s 0.1 s 5.1 s 5.1 s 5.2 munimularuD draH s 0.2 s 0.3 s 0.3 s 0.4 syollA muisengaM C°003 ot pu detaeH noitidnoc dloc nI

nMgM s 0.2 s 0.3 s 0.7 s 0.9 7lAgM s 0.2 s 0.3 s 0.5

muinatiT C° 073……002 ot detaeH nI noitidnoc dloc s 5.0 s 0.2 0.3 s s 0.5

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suidaR dneB .nim eht etaluclaC ot ealumroF :reteiD egroeG retfA

𝑅 𝑛𝑖𝑚

s � 1

2 Z - 1 %02 < Z roF

𝑅 𝑛𝑖𝑚

s �

(1 � 𝑍)2

(2 𝑍 � 𝑍2) %02 > Z roF

erehW

R nim mm ,suidaR dneB .niM s teehS mm ,ssenkcihT Z aerA fo noitcudeR egatnecreP )lairetam teehs eht fo tset elisnet morf(

erehw ,R 𝛂 dna suidar looT elgna Ro , αo dna suidar deriuqeR elgna 𝛔s lairetam teehs fo htgnerts dleiY E teehs fo suludoM s'gnuoY

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SLOOT GNIMROF FO SUIDAR

8 ERUGIF - .sloot gnidneb fo gninoisnemid dednemmocer yllareneG 8

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fo snoisnemiDslooT gnimroF

epyT looT

)36 .giF( snoisnemiD ]mm[ ssenkcihT lairetaM

1 ot pU 2…1 3…2 4…3 5…4 6…5 7…6 8…7 01…8 III ,II ,I rM 3 5 7 9 01 11 21 31 51

I h 4 7 11 51 81 22 52 82 63…23 1 H 02 03 04 54 55 56 07 08 09 II t 3 4 5 6 8 01 51 02 52

]mm[ htgnel metS )III ;36 .giF( k noisnemiD «05…52 51 02 52 52

57…05 02 52 03 03 53 53 001…57 52 03 53 53 04 04 04 04 051…001 03 53 04 04 05 05 05 05 06 002…051 04 54 55 55 06 56 56 56 08

]mm[ htgnel metS tneiciffeoc n )III dna II ;36 .giF( 52 ot pU 01,0 80,0 80,0 70,0 70,0 60,0 60,0 50,0 50,0

52 - 05 51,0 01,0 01,0 80,0 80,0 70,0 70,0 60,0 60,0 05 - 001 81,0 51,0 51,0 01,0 01,0 90,0 90,0 80,0 80,0 001 - 002 02,0 81,0 81,0 21,0 21,0 11,0 11,0 01,0 01,0

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eiD dna hcnuP gnidneB .teB ecnaraelC

Z .nim = S .xam dna Z xam = S xam + n . S

:erehW Z ,eid dna hcnuP .teb ecnaraelc ehT = S xam = ,teehs fo ssenkciht .xam N = elbaT evoba eht morf eulav

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gnirpS - kcaB

eht ,gnidneb latem teehs gniruD .tneb gnieb sti retfa kcab gnirps fo eerged niatrec a sah latem llA dna noisnet ni si suidar dneb roiretxe eht dna noisserpmoc rednu si latem tneb eht fo suidar roiretni

,yticitsale ’slatem eht ot euD .dehcterts dna tneb gnieb sti retfa epahs lanigiro sti ot kcab og ot sdnet ti fo tnuoma niatrec a tibihxe ,noitamrofed ot detcejbus nehw ,slatem llA .kcab gnirps sa wonk si siht

iwollof eht no sdneped gnidneb latem teehs ni kcab gnirps fo tnuoma ehT .yrevocer citsale .srotcaf gn

gnidneb latem teehs ni kcab gnirps gnitceffa srotcaF .

htgnerts lairetam rehgiH .1 lairetam rennihT .2 suludom s'gnuoY rewoL .3 suidar eid regraL .4 ecnaraelc leets epiw retaerG .5 eniltuo trap ni ytiralugerri sseL .6 ruotnoc ecafrus trap rettalF .7

dengised eb nac loot sserp a ,emit yreve tcefrep ti teg ot elba reven lliw elgna dneb ,gnipmats latem nI.tnetsisnoc yltcefrep eb reven lliw ti hguoht selgna dneb elbatpecca ekam ot tliub dna

dohtem tnereffid ynam era erehT tnereffid yb detpoda s srekam loot ni kcab gnirps eht emocrevo ot nihtiw tnemtsujda gnikam elihw ylefas ,ylkciuq ,ylisae ti ekam ot woh si yek ehT .gnidneb latem teehs

etasnepmoc ot ytiliba eht gnivah elihw sserp eht lacinahcem dna ssenkciht lioc ni secnereffid ronim.emit emas eht ta seitreporp

loot evissergorp ni kcab gnirps gnimocrevO

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,elgna eht dneb revo ,suidar dneb lanretxe eht gninioc sa hcuS .tsap eht ni sdohtem ynam deirt Iht llA .cte ecnaraelc gnidneb ecuder eht deirt I litnu ti ot noitulos evitceffe na edivorp yllaer t’nac ese

.ngised ym ni sloot evissergorp deeps hgih eht lla tsomla rof gnisu ylippah m’I hcihw dohtem gniwollof

0.2 R a htiw teehs leets kciht mm 0.1 a gnidneb era uoy yas s’teL .1 giF nI ehT .suidar dneb lanretnisi enil lartuen eht fo htgnel ot refeR .mm 729.3 htgnel knalb talf .enil lartuen eht etupmoc ot woh rof

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54 A .2 giF nI erp eerged - ot esoppus si gnidneb eht ,dneb eerged 09 eht erofeb decalp eb ot si dneb ,kcab gnirps eht emocrevo oT ) tra eerged 54 eht fo htgnel ( .noitisop detaluclac 5369.1 eht morf trats

.a2 .giF eeS .mm 50.0 yb yawa evom ot sah noitacol eht

giF nI eht ot euD .lausu sa dneb eerged 09 A .3

ffo - 09 raen ta eb lliw elgna tneb eht ,enil trats tes.kcab sgnirps latem eht retfa ressel ro eerged

edis elbatsujda na fo ngised eht gniwohS .4 giF ronim yna rof elgna tneb eht enut enif ot mac

ciht ni secnereffid .seitreporp dna ssenk

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.elif eht ni dnuof ton saw 26dIr DI pihsnoitaler htiw trap egami ehT

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SNOITALUCLAC ERUSSERP GNIMROF DNA GNIDNEB

yam yehT .serusserp gnimrof dna gnidneb fo noitaluclac rof dezilitu era salumrof lareveS .dezilitu gnidneb fo epyt eht htiw yrav

1. V a ni gnidneB - ralugnatcer htiw ,eid ssorc - :noitces

W ereh :

kv = seulav regral( 5.2 ot 57.0 ,rotcaf gninepo eid era rellams rof tW eciv dna soitar A .)asrev 33.1 rof desu si eulav a .ssenkciht latem semit 8 fo gninepo eid

W = tneb eht fo htdiw - noitrop pu L = neewteb ecnatsid 8 .giF ees( stroppus lairetam - )25 S = 8 elbaT( htgnerts elisnet etamitlu - )01

U a ni gnidneB .2 - gnirps a htiw deppiuqe ,eid - :dap erusserp dedaol

erehw

kU = 01 ot 4.0 ,rotcaf gninepo eid RE = 8 .giF ees( egde eid ,suidar - )35 RD = fo mottob ,suidar U lennahc P dap = gnirps fo erusserp - troppus dedaol

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.3 :)gninioc( gnimottob htiw gnidneB

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4. :noitaluclac erusserp seid gnidneb epiW

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:swollof sa si gnidneb yrator ni devlovni erusserp eht fo noitaluclaC .5

erehw TS = lairetam demrof eht fo htgnerts elisneT L = RP + TP + B

8 .giF rep seulav rehto lla - .55

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ecrof gnidneB bF .7.61 V a ni gnidneB 1 - eid depahs

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ygolonimreT

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suidaR dneB muminiM

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.tnoc suidaR dneB muminiM

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E eff snoisulcnI detagnolE fo tc

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gnirpS gnidneB ni kcab

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rotcaF kcab gnirpS

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kcab gnirpS evitageN

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kcab gnirpS gnicudeR rof sdohteM

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eiD cisaB - snoitarepO gnidneB

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nommoC rehtO snoitarepO gnidneB

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gnimroF daeB

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snoitarepO gnignalF

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lloR - ssecorP gnimroF

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snoitarepO gnidneB ebuT

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noitarepO gnihctertS

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ngiseD egnalF

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noitazilitU sehctoN

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noitartnecnoC ssertS