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(1)

1398Q=y@'h}QWu=Qta|UOvyt

|:viCW=OO=}'121115"X'1/2|xQ=tW'352|xQwO

|UQQ@ QO OwOLt <=RH= VwQ C}r@=k |@=}RQ=

ResearchNote

COW pt=a QO M=QwU w jQw |=vyB Q}F-=D Q=OlQD jQw QO VvD

OWQ= T=vWQ |a}iQ =[QOtLt Q=}O=DU=xO=RQ=tat s=yQB O=@; hHv '|tqU= O=R; x=oWv=O 'O=@;hHv OL=w 'u=Qta |UOvyt xwQo

|v}@V}B |=Q@ xm CU= VvD COW pt=a 'CUmW l}v=mt QO syt |=yQ}eDt R= |m}

Qou=}@ 'VvD COW pt=a "OwW|t xO=iDU= xOQwNlQD w[a |xOv=t|k=@ Qta w lQD OWQ C@Uv 'VvD COW pt=a QO Q=PoQ}F-=D pt=wa R= |m} "CU= lQD lwv h=Q]= |=yVvD R= xDU@ pL hrDNt |=yVwQ x@ u=QoWywSB \UwD xm CU= jQw |=vyB x@ lQD pw]

VwQ C}r@=k |UQQ@ 'Q[=L Q=DWwv hOy "CU= xOW |UQQ@ CvQwr \U@ VwQ xrtH QO |}=Hx@=H pQDvm |Q=PoQ=@ CLD |=yjQw |=vyB Q}F-=D |@=}RQ= |=Q@ OwOLt <=RH= |OOa Cw=iDt lQD |=ypw] w O=a@= C@Uv =@ |=yjQw 'Qw_vt u}= |=Q@ "CU= VvD COW pt=a VvD COW pt=a w |R=UpOt lQD lwv QO u}mD <=RH= R= xO=iDU= =@ OwOLt <=RH= VwQ x@

xm OyO|t u=Wv Q[=L |xar=]t "CU= xOW x@U=Lt lQD VQDUo VwQ R= xO=iDU= =@

pL |=yVwQ R= pY=L G}=Dv =@ |@wN Ck@=]t 'xOWQmP VwQ R= xOt; CUOx@ G}=Dv

|=yxrY=i =@ M=QwU OwHw QF= |UQQ@ x@ 'xt=O= QO "OQ=O =yVywSB Q}=U QO OwHwt |xDU@

xOW xDN=OQB O=a@= hrDNt C@Uv =@ |=yjQw QO VvD COW pt=a QO lQD lwv R= hrDNt QO xm |}=yM=QwU |=Q@ VvD COW pt=a QO M=QwU Q}F-=D xm OyO|t u=Wv G}=Dv "CU=

"CU= R}J=v 'Ov=xDiQo Q=Qk lQD lwv R= jQw |=vyB 10 R= V}@ |}xrY=i

[email protected] [email protected]

<=RH= 'OwOLt <=RH= VwQ 'VvD COW pt=a '|RmQt lQD =@ jQw %|O}rm u=oS=w

"lQD VQDUo VwQ 'u}mD

xtOkt "1

QO R}v |OOa |=yVwQ 'OW VvD COW pt=a QO jQw |=vyB Q}F-=D |xrUt |=Q@

VwQ '|OOa |=yVwQ xrtH R= "OvQ=O |a}Uw OQ@Q=m VvD COW pt=a |x@U=Lt pt=a |x@U=Lt x@ Ov=wD|t hrDNt |=yVwQ R= xO=iDU= =@ xm CU= OwOLt <=RH=

|SQv= |=v@t Q@ xm |}=yVwQ x@ u=wD|t Qw@Rt |=yVwQ R= "OR=OQB@ VvD COW

[9^]'wQ}v pQDvm CLD³lQD VQDUo VwQ^[⁸^]'²|DNU jDWt VwQ %Ovv=t 'OvDUy R}v w^[¹⁰^]'⁵sQ=yJ l} |x]kv |}=Hx@=H VwQ^[¹⁰^]'⁴|}=Hx@=H |oDU@ty VwQ

|x@U=Lt |=Q@ R}v |Qo}O |=yVwQ "OQm xQ=W= ^[¹¹^]'⁶lQD |R=Ht Q=DU@ VwQ

[13]'^J p=QoDv= VwQ^[¹²^]'⁷wQ}v VwQ %Ovv=t 'CU= xOW x=Q= VvD COW pt=a

|}=Hx@=H |=yVwQ =} w^[¹⁶^]'|v}mD Vy=m VwQ^[^15w14^]'⁸|}=Hx@=H |@=}uwQ@ VwQ

|oOWR=@ Owt |=Q@ VvD COW pt=a 'u; R= xO=iDU= =@ xm VvD |@=}uwQ@ w⁹|}xQo

[17]"OwW|t x@U=Lt |Oqwi jQw QO lQD xDN=OQB QwmPt |=yVwQ R= |O=OaD |xU}=kt x@ R}v 2016 |Qo}O Q=DWwv QO

\w@Qt VvD COW pt=a^[¹⁹^]'1990 p=U QO |WywSB QO u}vJty^[¹⁸^]"CU= xOW lQD =@ jQw QO VvD COW pt=a R}v w OwOLt jQw l} QO M=QwU |x@r lQD x@

p@=kQ}e |=y|oDN}Uo Q=JO 'u=tR QwQt x@ =yxR=U xm OvyO|t u=Wv C=ar=]t QO u; CUmW ?Hwt Ov=wD|t xa]k l} QO R}Q |=ylQD OwHw "OvwW|t |Q=_Dv=

|QDW}@ |oO=t; QDnQR@ pw] =@ |=ylQD "OwW |L=Q] VvD R= QDlJwm |}=yVvD w lQD lwv h=Q]= QO VvD QDq=@ COW R= |W=v Qt= u}= xm OvQ=O VQDUo |=Q@

R= lQD lwv h=Q]= QO VvQm =} VvD u=O}t u=}@ |=Q@^[¹^]"CU= jQw Ctw=kt Vy=m 'xOQ=w VvD R= |a@=D xm OwW|t xO=iDU=¹^{SIF or K} VvD COW pt=a Q}eDt jQw |=vyB Q}F-=D |xar=]t x@ hrDNt u=QoWywSB "CU= jQw |=vyB R}v w lQD pw]

`@=wD R= xO=iDU= =@^[⁴²^]'=yu; R= |NQ@ 'xvwtv |=Q@ "Ov=xDN=OQB VvD COW pt=a QO C=}[Qi |NQ@ uDiQo Q_vQO =@ =} w^[⁵^]'CvQwr \U@ R= xO=iDU= =@ =} w |Q}= VvD COW pt=a QO jQw |=vyB Q}F-=D uO=O u=Wv |=Q@ =Q |YNWt \@=wQ^[^7w6^]'xOvvmxO=U xDU@ pL |x=Q= x@ QHvt xm xOW xQ=W= |=yVwQ Q@ xwqa "Ov=xOQm x=Q= VvD pwUt xOvU}wv

"1396 4 10 VQ}PB '1396 3 16 x}LqY= '1395 11 27 Ci=}QO %M}Q=D

DOI:10.24200/J30.2018.1867.2040

(2)

"""|UQQ@QOOwOLt<=RH=VwQC}r@=k|@=}RQ=

"Ot; Oy=wN CUOx@ 2^apw] x@ |RmQt lQD l} w^W OwOLt |=vyB =@ jQw l}

|=yx@r |wQ Q@ |WQ@ |=yVvD 'uQ=kD p}rO x@^[¹^]'1982 p=U QO |WywSB T=U=Q@

pt=a QO |yHwD p@=k CmQ=Wt 'lQD =@ |R=wt |=yVvD w OvDUy QiY^CDw^AB

|xOW`]k |=yVN@ QO |}x@r |=yVvD QF= uDiQo xO}O=v =@ "OvQ=Ov VvD COW lQD w^W OwOLt |=vyB =@ |=yjQw |=Q@ =Q 2 |x]@=Q OQ@Q=m |xvt=O u=wD|t 'jQw

"O=O VQDUo 2^apw] x@ |RmQt '2 |x]@=Q QO⁽W^a)?UL Q@ CQ=@a xm CU=O}B 2 w 1 |=yx]@=Q |xU}=kt R=

Qo= xm |Qw]x@ &CU= VvD COW pt=a QO jQw OwOLt |=vyB Q}F-=D |xOvQ}oQ@QO 1 |x]@=Q CQwYx@ 2 |x]@=Q 'OwOLt=v |=yjQw QO Ovm p}t QiY CtU x@⁽W^a)

3 |x]@=Q CQwYx@ OwOLt |=yjQw QO VvD COW pt=a 'u}=Q@=v@ "OW Oy=wN xO=U

%OwW|t xDWwv

KI = p

a ' (3⁾

|}xar=]t QO "CU= jQw OwOLt |=vyB QF= x@ \w@Qt K}LYD ?}Q[^''u; QO xm l} CQwYx@ K}LYD ?}Q[ 'CW=ov `@=wD R= xO=iDU= =@ ^[⁵^]'1971 p=U QO u=ty QO |Qo}O VywSB QO 'TBU w xOt; CUOx@⁽W^a)?UL Q@ |}xrtHOvJ 4 |x]@=Q CQwYx@ |@wN |@Uv CkO =@ Q}N= |}xrtHOvJ K}LYD ?}Q[^[⁶^]'p=U

%CU= xOW u=}@

' = r

sec aW (4⁾

"Ov=xOW h}QaD QDV}B 4 |x]@=Q |=yQ}eDt

VvD COW pt=a |x@U=Lt |=Q@ lQD VQDUo VwQ "3

COW pt=a |x@U=Lt |=Q@ xm CU= |SQv= |x}=B Q@ |WwQ 'lQD VQDUo VwQ

[9^]%Ovm|t xO=iDU= 5 |x]@=Q R= |wDUt VvD |=yjQw QO VvD

KI =p

EG (5⁾

6 |x]@=Q R= xm CU= |WvQm |SQv= |R=UO=R; MQv^Gw u=UWm pwOt^E'u; QO xm

[9^]%O};|t CUOx@

G = U₂ U₁

B 2^a ⁽6⁾

|WvQm |SQv= ?}DQDx@Û²wÛ¹w Ct=N[^B'wU l} R= lQD wtvâ'u; QO xm Qou=}@ '6 |x]@=Q GQNt QO 2 OOa "OvDUy 2^{a + a}w 2âpw] x@lQD =@ |=yjQw pt=a |x@U=Lt =@ xm CU= K[=w "CU= lQD |wU wO QO wtv R= |W=v lQD pm wtv R= xO=iDU= =@ =Q K}LYD ?}Q[ u=wD|t |oO=Ux@ 'xOW QmP VwQ x@ VvD COW VvD Q=Okt 'wQ}v pQDvm |Q=PoQ=@ Q}R |=yjQw QO xm =Hv; R= "OQw; CUOx@ 3 |x]@=Q x@ 3 |x]@=Q R= VvD COW pt=a |x@U=Lt 'OQ=O |D@=F Q=Okt |Q=PoQ=@ |=yx@r QO '|}=Hx@=H pQDvm |Q=PoQ=@ Q}R |=yjQw QO xm |r=L QO &CU= s=Hv= p@=k |oO=U '3 |x]@=Q QOQ=Okt 'Q[=L |xar=]t QO "CU= Q}eDt |Q=PoQ=@ |x@r pw] QO VvD xm CU= xOt; CUOx@ 7 |x]@=Q R= jQw |x@r QO VvD Q=Okt R= |Q}ou}ov=}t =@

xDWwv jQw |x@r QO u}ov=}t VvD ?UL Q@ jQw |WvQm |SQv= |x@U=Lt T=U=Q@

%OwW|t

ave= U₁

12W B (7⁾

COW pt=a |x@U=Lt |=Q@ xOW s=Hv= C=ar=]t QDW}@ "OW x@U=Lt^[²⁰^]'|}x@r CU= xOW s=Hv= |}=yjQw |wQ Q@ lQD VQDUo VwQ w OwOLt <=RH= VwQ =@ VvD Q@ OwOLt <=RH= VwQ =@ |D=ar=]t w xOw@ wQ}v pQDvm VwQ x@ =yu; |Q=PoQ=@ xm wQ u}= R= "CU= xOWv s=Hv= |}=Hx@=H pQDvm VwQ x@ |Q=PoQ=@ =@ |=yjQw |wQ

|Q=PoQ=@ =@ |=yjQw VvD COW p}rLD |=Q@ OwOLt <=RH= VwQ C}=im |UQQ@

VwQ C}=im |UQQ@ 'Q[=L Q=DWwv hOy "OUQ|t Q_v x@ |QwQ[ |}=Hx@=H pQDvm

|Q=PoQ=@ CLD |=yjQw |=vyB Q}F-=D |@=}RQ= |=Q@¹⁰u}mD OwOLt <=RH= |OOa

|=yC@Uv =@ |=yjQw Qw_vt u}= |=Q@ "CU= VvD COW pt=a QO |}=Hx@=H pQDvm R= xO=iDU= =@ OwOLt <=RH= VwQ x@ lQD pw] hrDNt |=yC@Uv R}v w O=a@= hrDNt VQDUo VwQ R= xO=iDU= =@ VvD COW pt=a w |R=UpOt lQD lwv QO u}mD <=RH=

u}@ Q[=L VywSB QO xar=]t OQwt lQD pw] |=yC@Uv "CU= xOW x@U=Lt lQD

<=RH= `wv R= u}mD OwOLt <=RH= R= jQw |OOa |R=UpOt |=Q@ "CU= 0 8 =D 0 1 xOW xO=iDU= lQD lwv h=Q]= QO^[²³²¹^]'¹¹^QPE sQ=yJ l} |x]kv OwOLt

"CU=

pL |=yVwQ x@ VvD COW pt=a QO jQw |=vyB QF= "2

VvD CLD 2^apw] x@ lQD =@ OwOLt=v |=vyB =@ jQw l} QO VvD COW pt=a

xDU@

[1]%OwW|t h}QaD 1 |x]@=Q j@=]t|WWm

KI = p

a (1⁾

|xrUt |xDU@ pL "CU= |oOWR=@ Owt |oOQwNlQD pw= Owt Qou=}@^I'u; QO xm

"CU= Q=wWO |tm xO}J}B |RQt \}=QW OwHw p}rO x@ lQD =@ OwOLt |=vyB =@ jQw

=yjQw xvwou}= pL x@ Ov=wD|t xOvvmxO=U |=yZQi |NQ@ uO=O Q=Qk 'p=L u}= =@

jQw R= |DtUk u=wD|t =Q Q=OlQD OwOLt |=vyB =@ jQw l} 'p=Ft |=Q@ "Ovm ltm Oa@ x@ jQw |=vyB OQm ZQi 1 pmW j@=]t |r=wDt |=ylQD =@ OwOLt=v |=vyB =@

"OwW|t xDio lQD pw] |R=wt

[42^]'u=QoWywSB |NQ@ \UwD 1 pmW |r=wDt |=ylQD =@ OwOLt=v jQw pL =@

2 |x]@=Q CQwYx@ OwOLt=v jQw QO VvD COW pt=a '|Q}= VvD `@=wD R= xO=iDU= =@

[1]%OW x=Q=

KI = p a

rW

atan( aW) (2⁾

QDV}B =yQ}eDt Q}=U w CU= |r=wDt |=ylQD RmQt =D RmQt |xrY=i^W 'u; QO xm 'OwW `]k^CDw^AB|=DU=Q QO 1 pmW QO OwOLt=v jQw Qo= "Ov=xOW h}QaD

[1^]"|WWm |=yVvD CLD OwOLt=v jQw "1 pmW

(3)

1/2|xQ=tW'352|xQwO'1398Q=y@h}QWu=Qta|UOvyt

[23]"|}xQo 8 VwoQ=yJ sQ=yJ l} |x]kv u}mD OwOLt <RH "4 pmW

"lQD =@ jQw R= |DtUk OwOLt <=RH= pOt "5 pmW

"|Ov@xm@W x@ OwOLt <=RH= pOt C}U=UL "6 pmW

u}= "CU= xDiQo Q=Qk 1 |xQo R= \w@Qt `r[ pw] sQ=yJ l} |xrY=i QO 8 w 5 u}= R= "OwW|t 1 |xQo QO VvD |oOWu}mD ?Hwt OwOLt <RH X=N Vv}J xO=O Q=Qk jQw QO |}xvwo x@ u}mD OwOLt <=RH= 'lQD =@ jQw |R=UpOt |=Q@ 'wQ QO u}mD OwOLt <=RH= uDiQo Q=Qk |xwLv "OwW `k=w lQD lwv Q@ 1 xQo xm 'OvwW|t

"CU= xOW xO=O u=Wv^ShQL =@ 5 pmW QO lQD lwv h=Q]=

QO "OyO|t u=Wv =Q lQD =@ jQw l} OwOLt <=RH= pOt R= |DtUk '5 pmW jQw |x@r QO |}=Hx@=H pQDvm `wv R= |Q=PoQ=@ R= |W=v lQD |oOWR=@ 'hr=5 pmW lQD lwv h=Q]= QO u}mD <=RH= C}akwt '?5 pmW QO 'u}vJty "OwW|t xOy=Wt

|=Q@ ?U=vt |=yu=tr= O=OaD uDi=} |=Q@ "OwW|t xOy=Wt |QDW}@ |}=tvnQR@ =@

=yu=tr= O=OaD x@ C@Uv C}U=UL p}rLD CLD lQD =@ jQw pOt 'j}kO G}=Dv O}rwD hrDNt O=OaD =@ jQw OwOLt <=RH= pOt |=Q@ K}LYD ?}Q[ '6 pmW "CiQo Q=Qk

"VvD \UwDt Q=Okt =@ |R=UpOt VvD |xU}=kt "2 pmW

"CN=wvm} |}=Hx@=H CLD |RmQt lQD =@ jQw "3 pmW

QDV}B =yQ}eDt Q}=U w CU= jQw |Q=PoQ=@ |x@r QO VvD u}ov=}t^ave'u; QO xm VwQ x@ C=@U=Lt R= xOt; CUOx@ G}=Dv |xU}=kt =@ 'xt=O= QO "Ov=xOW h}QaD xO=O u=Wv 3 |x]@=Q QO u}ov=}t VvD R= xO=iDU= VwQ |}=Q=m '`H=Qt QO xOWO=}

jQw |=Q@ u}ov=}t VvD =@ jQw |x@r QO VvD `}RwD Q=Owtv '2 pmW QO "CU= xOW

B =1^cm'^{L =}60^cm'^{W =}50^cmO=a@= =@ 3 pmW QO xOW xO=O u=Wv

"CU= xOW xU}=kt^{E =}210⁷C=YNWt w

C}U=UL p}rLD w xar=]t OQwt |=ypOt C=YNWt "4

Q=Ri=sQv R= |Oa@ wO OwOLt <=RH= VwQ x@ |R=UpOt |=Q@ 'Q[=L |xar=]t QO u=UWm jQw l} '|UQQ@OQwt jQw "CU= xOW xO=iDU=¹²Twm=@; OwOLt <=RH=

pw] w^W |=vyB x@ jQw l} '3 pmW "CU= xOw@ |RmQt lQD =@ uoty l}BwQDwR}=

w |rYit `wv R=^A|xQo QO |RQt \}=QW "OyO|t u=Wv =Q 2^apw] x@ lQD =@^L 'jQw |}q=@ |x@r "CU= |mDre `wv R= jQw |v}}=B |x@r QO OwHwt |=yxQo Q}=U QO

"OQ=O 3 pmW j@=]t^yQwLt O=ODt= QO CN=wvm} |}=Hx@=H

|=Q@ "CU= xOW xO=iDU= |}xQo 8 VwoQ=yJ OwOLt <RH R= '|R=UpOt |=Q@

`wv R= lQD lwv h=Q]= QO xDiQoQ=Qk <=RH= 'lQD lwv QO VvD |oOWu}mD uOQm pOt

"OvOW ?=NDv= |rwtat `wv R= <=RH= Q}=U w 4 pmW sQ=yJ l} |x]kv u}mD <=RH=

|=yxQo w `q[= \Uw QO 7 w 6 |=yxQo '4 pmW QO xOWxO=O u=Wv u}mD <RH QO

(4)

[5^]"`HQt G}=Dv =@ Q[=L |xar=]t G}=Dv |rm |xU}=kt "7 pmW

"jQw O=a@= C@Uv ?UL Q@ K}LYD ?}Q[ "8 pmW

QO "OW x@U=Lt lQD VQDUo VwQx@ K}LYD ?}Q[ '3 VN@ |=yx]@=Q j@=]t 2^{a =}20^cm|w=Ut lQD pw] '^{L =}60^cm|w=Ut jQw pw] '=ypOt |xty 3 pwOH QO G}=Dv "OW xDiQo Q_v QO^{a =}0 001^cmpO=at lQD wtv u=R}t w

"CU= xOW x=Q= hrDNt O=a@= C@Uv =@ |=yjQw |=Q@

pt=a |x@U=Lt w u}mD OwOLt <=RH= pOt p}rLD 'OwW|t x_Lqt xmv=vJ

\U@ VwQ R= pY=L G}=Dv x@ |m}ORv Q=}U@ G}=Dv lQD VQDUo VwQ x@ VvD COW

\U@ VwQ R= xO=iDU= =@^[⁵^]`HQt G}=Dv 'CU= |vDio "OyO|t CUOx@^[⁵^]'CvQwr

|=yxrY=i x@ |r=wDt |=ylQD =@ OwOLt=v pw] w^W|=vyB =@ jQw l} |=Q@ CvQwr CUOx@ G}=Dv QDy@ |xU}=kt |=Q@ "CU= xOt; CUOx@ CN=wvm} |}=Hx@=H CLD^L C@Uv ?UL Q@ K}LYD ?}Q[ |=yQ=Owtv '^[⁵^]`HQt G}=Dv w Q[=L VwQ R= xOt;

Qw]u=ty "7 pmW Ov=xOW s}UQD hrDNt O=a@= C@Uv =@ |=yjQw |=Q@ lQD pw]

u}=Q@=v@ w OvDUy l}ORv sy x@ Q=}U@ xOWQmP VwQ wO G}=Dv 'OwW|t xOy=Wt xm

|=Q@ |@wN C}r@=k 'u}mD OwOLt <=RH= |R=UpOt x=Qty x@ lQD VQDUo VwQ

?}Q[ Q=Owtv '8 pmW QO "OQ=O hrDNt |=yjQw QO VvD COW pt=a |x@U=Lt xOy=Wt lQD pw] hrDNt |=yC@Uv |=Q@ jQw O=a@= C@Uv ?UL Q@ K}LYD

\ki '1 R= QDnQR@ O=a@= C@Uv =@ |=yjQw K}LYD ?}Q[ 'u; j@=]t xm OwW|t u; QO |}x_Lqt p@=k Q}F-=D 'jQw O=a@= C@Uv w CU= lQD pw] C@Uv R= |a@=D O=a@= C@Uv V}=Ri= =@ 1 R= QDlJwm O=a@= C@Uv =@ |=yjQw |=Q@ u}vJty "OQ=Ov 'QDW}@ pw] =@ |=ylQD |=Q@ u; C=Q}}eD MQv w O@=}|t V}=Ri= K}LYD ?}Q[ 'jQw

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a(cm) U1^(N:cm) ^U2^(N:cm) ^'

0 000001 6 7680459010⁶ 6 7680456210⁶ 1 1028 0 00001 6 7680459010⁶ 6 7680430910⁶ 1 1047 0 0001 6 7680459010⁶ 6 7680176410⁶ 1 1079 0 001 6 7680459010⁶ 6 7677632710⁶ 1 1079 0 01 6 7680459010⁶ 6 7652198810⁶ 1 1079

"K}LYD ?}Q[ QO uwU=wB ?}Q[ Q}F-=D "2 pwOH

U1^(N:cm) ^U2^(N:cm) ^'

0 6 7680459010⁶ 6 7677632710⁶ 1 1079 0 1 6 7680793510⁶ 6 7677967310⁶ 1 1079 0 2 6 7681404210⁶ 6 7678578210⁶ 1 1079

"CU= |a@Qt w s_vt ,qt=m |Ov@Vt '=ypOt |t=tD QO "OyO|t u=Wv =Q <=RH=

'Q[=L Q=DWwv QO xOWp}rLD |=ypOt |t=tD QO jQw Ct=N[ w |v=UWm pwOt

"CU= xOW xDiQo Q_v QO 1^cmw 210⁷cm^N2 pO=at ?}DQD x@

2000R= V}@=@|=ypOtG}=Dv|=Q@|@U=vt |}=Qosy'OwW|txOy=Wt xmv=vJ

|xm@W l} 'QDq=@ CkO =@ |H}=Dv x@ |@=}CUO |=Q@ 'p=Lu}= =@ "OQ=O OwHw <RH

|=y|R=UpOt Q}=U |=Q@ O=a@= =@ |rOt QO OwOLt <RH 12000 0 50 5^cm lQD VQDUo VwQ C}U=UL u=R}t |UQQ@ |=Q@ |}=yp}rLD 'u}vJty "OW ?=NDv=

'=Hv}= QO "CU= xOW x=Q= 1 pwOH QO G}=Dv xm OW s=Hv= ^a lQD wtv Q=Okt x@

%CU= xOW x=Q= xvwtv |=Q@ 1 pwOH R= pw= Q]U x@ \w@Qt C=@U=Lt C=}RH

G = 6 7680456210⁶ 6 7680459010⁶

120 000001 ⁼140000

K =p

E G =p

210⁷140000⁼1673320 0530

ave= U₁

12W B =6 7680459010⁶

12501 ⁼270721 8360

; = K p

a= 1673320 053

270721 8360^p 10 ⁼1 1028

"OW xDiQo Q_v QO =ylQD |=Q@ 0 001^cmpO=at |wtv '1 pwOH x@ xHwD =@

?}Q[ Q}F-=D u=R}t |UQQ@ x@ 'lQD wtv w |Ov@xm@W ?U=vt u=R}t ?=NDv= R= TB

|=Q@ 6 |r= 3 \@=wQ 'CU= |vDio &OW xDN=OQB K}LYD ?}Q[ QO ' uwU=wB CU= QDnQR@ Q=}U@ lQD pw] x@ C@Uv jQw O=a@= xm C}=yv|@ O=a@= =@ |}=yjQw QO &OvDU}v uwU=wB ?}Q[ `@=D 6 |r= 3 \@=wQ p}rO u}ty x@ CU= xDi=} xaUwD Q=PoQ}F-=D G}=Dv QO CU= umtt uwU=wB ?}Q[ 'OwOLt O=a@= =@ |=yjQw QO xm |r=L Q}F-=D uwU=wB ?}Q[ R}v OwOLt |=yjQw QO xm OyO|t u=Wv 2 pwOH G}=Dv "OW=@

"OQ=Ov VvD COW pt=a Q=Okt QO |}x_Lqt p@=k

|OOa G}=Dv "5

C@Uv =@ |=ylQD =@ 2 0 w 1 5 '1 0 '0 8 '0 6 '0 4 O=a@= C@Uv =@ |=yjQw

|R=UpOt 3 pmW j@=]t |RQt \}=QW =@ xm 0 8 =D 0 1 jQw |=vyB x@ lQD pw]

C}U=UL |=yp}rLD x@ xHwD =@ "OvOW p}rLD OwOLt <=RH= VwQ =@ 'OvOw@ xOW 'TBU "OW xDiQo Q_v QO 0 50 5^cmO=a@= x@ <=RH= R= |}xm@W 'xDiQo s=Hv=

(5)

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0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 2^a=W

1 5282 1 1703 0 9858 0 8887 0 8476 0 8531 0 9002 0 9660 Q[=L VywSB

L=W =0 4 1 1651 0 9837 0 8907 0 8488 0 8512 0 8977 0 9651 ^[⁵^]`HQt

1 6910 1 3405 1 1451 1 0379 0 9853 0 9704 0 9779 0 9924 Q[=L VywSB

L=W =0 6 1 6884 1 3302 1 1465 1 0395 0 9860 0 9698 0 9767 0 9953 ^[⁵^]`HQt

1 7934 1 4345 1 2430 1 1305 1 0703 1 0245 1 0071 1 0007 Q[=L VywSB

L=W =0 8 1 7977 1 4302 1 2419 1 1279 1 0685 1 0233 1 0070 0 9953 ^[⁵^]`HQt

1 8106 1 4777 1 2887 1 1712 1 0954 1 0478 1 0191 1 0039 Q[=L VywSB

L=W =1=0 1 8077 1 4721 1 2930 1 1721 1 0977 1 0488 1 0163 1 0000 ^[⁵^]`HQt

1 8188 1 4919 1 3066 1 1889 1 1110 1 0584 1 0245 1 0051 Q[=L VywSB _{L=W =}1 5 1 8087 1 4953 1 3047 1 1860 1 1116 1 0581 1 0233 1 0047 ^[⁵^]`HQt

1 8164 1 4888 1 3039 1 1869 1 1094 1 0577 1 0241 1 0048 Q[=L VywSB

L=W =2⁼0 1 8087 1 4953 1 3047 1 1860 1 1116 1 0581 1 0233 1 0047 ^[⁵^]`HQt

"CU= xOW G=QNDU= u=oOvU}wv \UwD^[⁵^]`HQt QO OwHwt Q=Owtv |wQ R=^[⁵^]`HQt x@ \w@Qt O=Oa= %xHwD

"VvD COW pt=a QO lQD lwv R= M=QwU |xrY=i Q}F-=D "10 pmW V}@ |xrY=i QO xm |}=yM=QwU |=Q@ VvD COW pt=a QO M=QwU Q}F-=D xm OwW|t

"CU= R}J=v 'Ov=xDiQo Q=Qk lQD lwv R= jQw |=vyB 10 R=

|Q}oxH}Dv "6

Q}F-=D |UQQ@ |=Q@ OwOLt <=RH= |OOa VwQ C}r@=k |@=}RQ= x@ 'Q[=L Q=DWwv QO xDN=OQB VvD COW pt=a QO |}=Hx@=H pQDvm CLD |RmQt lQD =@ |=yjQw |=vyB

|=yx@r QO VvD Q=Okt |}=Hx@=H pQDvm |Q=PoQ=@ Q}R jQw QO xm =Hv; R= "CU= xOW u}ov=}t VvD R= VvD COW pt=a |x@U=Lt |=Q@ 'CU}v CN=wvm} |Q=PoQ=@

|=yC@Uv w 2 0 |r= 0 4 O=a@= |=yC@Uv =@ M=QwU uwO@ |=yjQw "OW xO=iDU=

|x@r QO OL=w |}=Hx@=H CLD 0 8 |r= 0 1 R= jQw |=vyB x@ lQD pw] hrDNt 0 6 O=a@= |=yC@Uv =@ Q=OM=QwU |=yjQw p}rLD x@ 'xt=O= QO "OvOW p}rLD jQw

"lQD lwv h=Q]= QO M=QwU |=Q=O jQw "9 pmW

VvD COW pt=a QO lQD lwv h=Q]= QO M=QwU OwHw Q}F-=D "1"5 lwv h=Q]= QO pmW |}xQ}=O M=QwU l} OwHw Q}F-=D |@=}RQ= x@ '|vwvm VN@ QO Qw_vt u}O@ "CU= xOW xDN=OQB lQD VQDUo VwQ x@ VvD COW pt=a QO lQD Q]k w lQD pw] =@ 'hrDNt lQD lwv =D M=QwU |xrY=i w O=a@= C@Uv =@ |=yjQw w 1^cmM=QwU Q]k =ypOt |t=tD QO "OvOW p}rLD 9 pmW j@=]t C@=F M=QwU

"OW xDiQo Q_v QO 20^cmQo}O Q=@ w 12^cmQ=@ l} lQD pw]

M=QwU Q]k 2^rw M=QwU |x@r =D lQD lwv |xrY=i Qou=}@^d '9 pmW QO 'VvD COW pt=a QO lQD lwv h=Q]= QO M=QwU OwHw Q}F-=D |xOy=Wt |=Q@ "CU=

10 pmW j@=]t VvD COW pt=a QO lQD lwv R= M=QwU |xrY=i Q}F-=D Q=Owtv lwv |m}ORv QO M=QwU l} OwHw 'OwW|t xOy=Wt 9 pmW QO xmv=vJ "OW sUQ lQD lwv |xrY=i xJ Qy w OwW|t VvD COW pt=a Q=Okt V}=Ri= Ea=@ lQD xOy=Wt u}vJty "Ovm|t =O}B Vy=m K}LYD ?}Q[ Q=Okt 'OwW QDW}@ M=QwU =D

(6)

=@ hrDNt |=yjQw QO VvD COW pt=a u}tND QO |@wN C}=im 'u}ov=}t VvD

|=yjQw K}LYD ?}Q[ xm OyO|t u=Wv G}=Dv "OQ=O lQD pw] Cw=iDt |=yC@Uv O=a@= C@Uv w CU= lQD pw] C@Uv R= |a@=D \ki '1 R= QDnQR@ O=a@= C@Uv =@

=@ |=yjQw |wQ Q@ xOWs=Hv= |=y|UQQ@ QO "OQ=Ov u; QO |}x_Lqt p@=k Q}F-=D jQw Ea=@ lQD lwv h=Q]= QO M=QwU OwHw xm OW xOy=Wt 'lQD lwv h=Q]= QO M=QwU xOt;CUOx@ G}=Dv x@ xHwD =@ u}vJty "OwW|t VvD COW pt=a Q=Okt V}=Ri=

QO xm |}=yM=QwU |=Q@ VvD COW pt=a QO M=QwU Q}F-=D xm Ci=}QO u=wD|t

|=yp}rLD "CU= R}J=v 'Ov=xDiQo Q=Qk lQD lwv R= jQw |=vyB 10 R= V}@ |xrY=i COW pt=a Q=Okt QO uwU=wB ?}Q[ R}J=v Q}F-=D Qou=}@ R}v xOWs=Hv= C}U=UL

"CU= VvD

R= 'lQD lwv QO |oOWu}mD |OOa |R=UpOt |=Q@ "CU= xOW xDN=OQB 1 5 w

|Ov@xm@W 'C}U=UL |=yp}rLD s=Hv= =@ "OW xO=iDU= sQ=yJ l} |x]kv <=RH=

w VvD COW pt=a '=ypOt p}rLD R= TB w u}}aD =yjQw |R=UpOt |=Q@ |@U=vt

"OW x@U=Lt lQD VQDUo VwQ x@ jQw |=vyB Q}F-=D x@ \w@Qt K}LYD ?}Q[ R}v pw] wtv Q=Okt 'C}U=UL |=yp}rLD R= Qo}O |QU l} s=Hv= =@ 'QwmPt VwQ QO

|=ypOt p}rLD "OW ?=NDv= 0 001^cmu=R}t x@ |Oa@ |=y|R=UpOt QO lQD

|x@U=Lt w lQD lwv h=Q]= QO u}mD <=RH= =@ M=QwU uwO@ |=yjQw OwOLt <=RH=

VwQ R= pY=L G}=Dv xm OyO|t u=Wv lQD VQDUo VwQ x@ K}LYD ?}Q[

\UwD xDi=}xaUwD CvQwr \U@ VwQ R= pY=L G}=Dv =@ |@wN j@=]D QO 'xOWQmP R= xO=iDU= R}v w u}mD OwOLt <=RH= |OOa VwQ 'u}=Q@=v@ "CU= u=QoWywSB Q}=U

=yCWwv=B

1. stress intensity factor 2. stiness derivative method 3. crack extension technique 4. displacement correlation method 5. quarter point displacement method 6. virtual crack closure technique 7. force method

8. displacement extrapolation method 9. nodal displacement method 10. singular nite element 11. quarter point elements (QPE) 12. Abaqus

^References

`@=vt

1. Broek, D., Elementary Engineering Fracture Mechanics, 3d Edition, Boston (1982).

2. Irwin, G.R. \Crack extension force for a part-through crack in a plate", Journal of Applied Mechanics, 29(4), pp. 651-654 (Dec., 1962).

3. Koiter, W.T. \An innite row of collinear cracks in an innite elastic sheet", Ingenieur-Archiv, 28(1), pp. 168- 172 (Jan.,1959).

4. Westergaard, H.M. \Bearing pressures and cracks", Journal of Applied Mechanics, 6, pp. A49-A53 (1939).

5. Isida, M. \Eect of width and length on stress intensity factors of internally cracked plates under various bound- ary conditions", International Journal of Fracture Me- chanics, 7(3), pp. 301-316 (Sep., 1971).

6. Feddersen, C.E. \Evaluation and prediction of the resid- ual strength of center cracked panels", American Society for Testing and Materials, STP 486, pp. 50-78 (1971).

7. Feddersen, C.E. \Discussion", American Society for Testing and Materials, STP 410, pp. 77-79 (1967).

8. Parks, D.M. \A stiness derivative nite element technique for determination of crack tip stress intensity

factors", International Journal of Fracture Mechanics, 10(4), pp. 487-502 (Dec.,1974).

9. Heyliger, P.R. \On conventional and quarter-point mixed elements in linear elastic fracture mechanics", En- gineering Fracture Mechanics, 31(1), pp. 157-171 (1988).

10. Truman, K.Z. and Fehl, B.D. \An evaluation of fracture mechanics quarter-point displacement techniques used for computing stress intensity factors", Engineer- ing Structures, 21(5), pp. 406-415 (1999).

11. Fawaz, S. \Application of the virtual crack closure technique to calculate stress intensity factors for through cracks with an elliptical crack front", Engineering Frac- ture Mechanics, 59(3), pp. 327-342 (Feb., 1998).

12. Morais, A.B. \Calculation of stress intensity factors by the force method", Engineering Fracture Mechanics, 74(5), pp. 739-750 (2006).

13. Courtin, S., Gardin, C., Bezine, G. and et al. \Advan- tages of the J-integral approach for calculating stress intensity factors when using the commercial nite element software ABAQUS", Engineering Fracture Mechanics, 72(4), pp. 2174-2185 (Sep., 2005).

14. Guinea, G.V., Planas, J. and Elices, M. \KI evaluation by the displacement extrapolation technique", Engineer- ing Fracture Mechanics, 66(3), pp. 243-255 (2000).

15. Kuizhu, X. \Numerical determination of stress intensity factors using ABAQUS", Proceeding of the ASME Pres- sure Vessels and Piping Conference (July, 2014).

16. Zafosnik, B., Ulbin, M. and Flasker, J. \Deternination of dierent fracture modes stress intensity factor with crack extension method", University of Maribor, Slove- nia (2000).

17. Wang, D., Yin, Y., Wang, Y. and et al. \Determina- tion of stress intensity factor for mode I fatigue crack based on nite element analysis", Engineering Fracture Mechanics, 138, pp. 118-126 (2015).

18. Qian, G., Gonzalez-Albuixech, V.F., Nienegger, M. and et al. \Comparison of KI calculation methods", Engi- neering Fracture Mechanics, 156, pp. 52-67 (2016).

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1/2|xQ=tW'352|xQwO'1398Q=y@h}QWu=Qta|UOvyt

19. Lai, J. and Schijve, J. \The stress intensity factor of hole edge cracks in a nite width plate", International Journal of Fracture, 46(3), pp. R37-R42 (1990).

20. Mingming, W., Xiangjun, Z. and Ming, Y. \Stress intensity factor of dierent width plates with edge crack", Ap- plied Mechanics and Materials, 415, pp. 602-605 (2013).

21. Ingraea, A.R. and Manu, C. \Quarter-point elements for curved cracked fronts", Computer and Structures, 17(2), pp. 227-231 (1983).

22. Banks-Sills, L. and Sherman, D. \Comparison of methods for calculating stress intensity factors with quarter- point elements", International Journal of Fracture, 32(2), pp. 127-140 (Oct., 1986).

23. Nejati, M., Paluszny, A. and Zimmerman, R.W. \On the use of quarter-point tetrahedral nite elements in linear elastic fracture mechanics", Engineering Fracture Me- chanics, 144, pp. 194-221 (2015).