chpc.ut.ac.ir of blast-induced shock waves on...chpc.ut.ac.ir
Transcript of chpc.ut.ac.ir of blast-induced shock waves on...chpc.ut.ac.ir
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J- j1 01Z ) uLS 4 r -I s lt LJ J~ Y4 )~ )LJ L 4 jlf -I I) s)~ 1
ss1 rli ~ j1 IJ4ltS JoAts ~I s4)u ~1r ~~ 4 Jtl)xl ~lt5
[r ] gt-o)ltS (-1 ) )lil -I 6r rli) sLa)13 ) bull IZ ~1 sL rlt5 r4lt-i1 jgt
)~I sjl5 Y~ -~ wl~ ) LI bullL1b ~J xIJ 1 3000 0 C ~) sy
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) ~ ) ~I)~)j 4)gtl JlL tt middotPI ~lt5 ~~ J)~~
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Email smohamUtacir
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[11middot1]
1 m ~yo~ bulllo
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1 1) s L=5 lo j ul~ sly 1 IS I) xj
[I1Wr1]
p(t) = P e -110 (I)
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~I) b I) i 1 IS oS ( Pm Ie) - )L=5
[11] 1 - ~~ h~ y X) srY rill J-122
0=965 (W3) lW (r)R
J~ ~li cS~J~ - AJ~ jL r) ~~ ~yI
[ I0] IS 1) ltc)lgt )b
pSI J~ ~ ss uLfgt sly JLu ltIIt I xj u) - x~
ap +y(xeJilJ +Pf(xB)ii f 0 (f)ax x )I-J j1 ~ )L=5) J~ ) )19 oLDI p
ii I J~ o)~ ampr iJl J~ 0 ts i
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sv ltIIJ s [11 s)~1 sly ~ ~ I) JJo [r] Hunter Geers ~b I~I sl 01-1
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ISjl Ji sLiJ) ~I~ ~rU 4 ltl1
bulljl ) j P = HP pP P = 12 Jl-raquo) ) r
umu~) -i ~ -i N P IS = JIl UN N 12
4middot))) 0)L1 Ojl)) uLS~ Jl-raquo) JI IS)I)
ulol-o lSI Ojl ~ 1S1r ~)l3 ) jI bull )lAl
Jl-gt 1S1r 1 oum NN ouN
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IS )jlr I IS~I I~ 41)1 S j ~~ ~L
-i IS)~I 1Sil 4 (W) (~) ui)1 ~ j1
~ir ) -j fir M iF + c p2 + (K + Kj)p2 _S~M jiM
+0 UN tv + M N aM + c(~ It + [sJ~YpQ - pH = 0
( )
Jl-gt ) I 1S)li1U~) -i 1Yo) Q PISlA lt)I
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r JSjl
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dV (fl)
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IS 1 ri )b - )~li ) -i ~s-1
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x -i- Ii ~ 0)5 ~ P 1) (f) 41)1
(~s-k -i yip ~ jl u)5 )iir 4) df
L bull )5 ~ (0) 41)1 Lj uLA 4 I lL
) -i Jl-gt )I IS~ J~ 1S1r $jgt 41)1
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I y a (I apJK p +P K P - ax -p ax 0
) JlI 41)1 IA~ jI bull )lA14
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~i r)
~ (1 y J I Blip apJdVup -p+--p + -_shy1[ K P Kf Pfax ax (V)
+ 1P (J ft + p) d S = 0 fo 01c1
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r
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fAT
) jgt jgt- )lJ )li jgt- oj )) ~I
Jk )~I tJi1 107 s )~)) Ij Iri
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210 GPa$~ J 7800 kglm3 )~ ~
) ci~ gt)) 360 MPa ~
l
ill
[ Explo51 veIgt Charge
~ R lSloodurr Libullbull uo)
(AI)
pressure pulse at plate center 50
4()
m
OOOStOO 1008-1)4 200B-04 lt)08-04
(5)
(y)
standoff point ~ 1 -4~~ (AI) ~
b~o)o30gr iz1i)i~lt(y) b~O)o
~ Jgt jf 30 em d1i)) TNT
s1~sI~ )agt WI y ~ s)13 ~
J-I ~ ) s~ J-o ABAQUS ) )p- S4R
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I em )~ ~ lAgt ~ AC3D8R li ltI sI~ a
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cb )) s)~I J~ gt )) sIr l ~)
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1)) 1Si uJ~ J-o ~s1 s1A)lJ ltI 4lJ
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srJI~I )I )) Ymiddot (r ~~) srJI~I J 4l1iJ-1) lt4S ~L yr )l ~~
)) Sri )~ ltI (J~) ~s1 ~t ir ~I ~
I~ ci~ gt
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ss ~ l~l )) ~~ 4lL J-I ))
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0)1 )~I Iu 2 mm L 25 em )j ~
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)) )~I jgtjAA))u 1s~ b03 bull)- )13
I jgt jAA )) ~~) 11 ~L ))r
)j sl Ai 1-I ) ltI 4lJ s~ 1 ())) )
cb u s)k ltI ) J 20 em Jk 25 em
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li bulliL l 1 uLS bull ~ 0)1 4A J-1~
~1)1 1 -)lJ )l ~L sIr 1 bullI bull )13
1S1 ~1) J-I ~ r ) )LOI (n(I)(1)
5427 MPaAt ~ - e Ii ~~ Pm S )lJ
)11 Ii -)lJ )b ~i ) ltI 2975 liS
y1i 1 bullI fgt) () jS ) ~r r
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~ 1 JLgt
)1gt ~~~ )IS bull aL d$ 1gt0Lo
~41S II ~)- 111gt y )1 gtI~
)) J j --gt r r ~ ) 0ts ~ ))
r1r 0ts ~ r1 1fL 1 bull amp-) (f) ~
41S 191 mm
4 I) ~1 bulllol ) is) ~ li s4j)1 iSlr
~ n iSlr d$ ~~ s~ ~I) r
~II 1 rj )~I 1 ~ iSlorb -6i 0ts ~
~IS~lQI
a iS1orb -6i ) jS ~ iSlr Nuriek
[A]I bull)b )~ I) r J)
(7l = 0425Clgtc + 0227 (I )
~ s iSyI~ $ ~L t ~1)rI))
rLwI r ri ~I) )1 d$ 1 iSlrb -6i iSlr
[ ] l11S) ~I iSlIIgtlltgtl
$c 10 (n) 1rrtl(pCl)lll
C1y 1)~ P bull iSl orb ~ tt r
rj ~ ~ S D H rfgt 111 ~~ JS is) r d$ ltNs --gtr)1 0Lj - )W ~
~ I ~ lltgt1 )) rfgt )~IS iSr-fJlftl ~
[ r ] 10Lj lJ ~rj
1()= fP()dt (n)
Ns 1m2 --gt)iris~ ~I) jlli 0 1 IS d$
[ ] ) i ) ll9
1=5760 Will (W) r (rr)
-gtb iSlr 1 m --gtr R kg --gtr W d$
~ isaLgt ~5r CJ- ~~~4 IO
rfgt 0 1gt1- )) ~b I j i )) )
~i ) ~ JS iSlr 110 ~ r~ l )
)gt)~ oll- r1 iSlr bull ~1- is 111gt y1)4 r)ll
r= 125 em = 492 in t=2mm=0079 in W= 30 gr R 30 em P = 1025 kg I m3 = 64 pef Oy = 360 MPa 52 ksi IO = 876 Ns = 1969 Ibs
l1 IS) 142 mm 4 056 in ~
d$ ) IS ci ~)) 0001 s rJlil 0Lj r1rl
)W jl ~L bA jLw J51 ~~ 01 Jltgt )) IS
(~ ~)
jlJW(b Jl4wJW(a ~s~fs
JUS
)br ~ lt11 J )) ~ y iS1IIgt0ts
sr- Jc - ~ JS Jj )~IS
b)) ~ d$ -1l)r1 ~ middot4 ~ll bA 1iI ci 1 jI ) li ~ )) )~I
~li r1 ~lgt ~ ) 0 Jlo Jl-- jl ~
d$ ) IS Jt1 (f rlSai1 ri-) isr is)) ~1
~li r1 j) jl bull )~I D d$ 1 ~ rl
)i ~li Jgtb ~IS )r rts1 0l
0001 s 1 ~~ ci~ jS ~ jS )) ~
1 bull 1 0~ (f) ~ )) ~ iSW ) jI
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6E P P 2 X 2l(I-x) (J= pm
a p2 C 2 (I-v)
c ~)L9 p ~ ~~ Jlo E ) )gt lt45 n shy
~ sl) rr-gtltgt ltJ~ xI)gtr 41 )I) lt45 1
(rv)X= m
~~ ~I rr- m lojli 8 )1)gt lt45
fO-)gt AIl- )11 sl) 1
E = 21 e 11 Pa = 439 e 9 psf Pp= 7800 kg m3 48695 pef Pm = 5427 MPa = 11334468 psf
P = 1025 kg 1m3 = 64 pef c = 1463 mls 4800 fils V 03 8=2975ls m=3206psf x= 2851
89698 ksf )I) Cla)~ (r7) J~ jl~)1~
Ak)l lt45 )J )w ~1 s- ~ 4295 MPa ~
jI lt45 1 ltSII~ ~ ~gt )~ )~ )11 gtsshy(4176 MPa) 1 bulllo1 gt ~ sltgt ~
shy oJII OM -1lt10OM bullbull
(11
-WjS)srlulo-ulSo~)) f~
U1b0 ~~ cSJ J~t ~J~ lNT )~I jI r1 5 (Z I o-j )11 )gt
~ r))5f gt~14 ~~~ s) ~li gt~ ltSIrlt1 11) 4 ~l bulli ~ Lil
03 gt~14 ~ sl ~ AIl- )11)gt gt sshy2 )~I JoY)gt 2 mm G 4 X 025 m
) ~ jSyo 30 em ul)gt lNT r )-I )gt (1 i AIl- Lilo )~1 61) gt r sshy
bull)1s ))))) I~ JoY)) ~~~ 4shy ~ gt~I)w 4 ~~ ) ~i
Jlo Jl ~ s~1 )s- Jlo 20 em JJ
)) ~ bulll J 10 em u(j )) bullbull~
bulljL 5- ~ s)Iil 1A0W1tY gtrsshy
s )11 ~ Rajendran b s~) ~I)
[7] 1 ~ )~
(rf)(1 =0541lt1gtc -0433
~ 065 in )I) )15 ~ ~I) )11 ltJLI ) lt45
~i s- gt ~ 166 mm
~~~ sl) ~ ~I) ji Jones ll
ul) 41 t ~ sl )b w jSyo 015 ~
[ ] 1 ) )11 ~ lt45 1 o)b
(1 0817lt1gtc (ro)
)15 ~ sl) Jones ~ ~ ~ )-~
264 JgtL 104 in (rO) ~I) ~~ )-I yo
~i s- gt ~ mm
~ ltSIrlt1 11) )s-~)l lt45 )Lo)w
sjLJlo ~l 4 ~gt ~ ~ s1A ~ xgtli ltSIrlt1 11) s lAr )11 4 lagt s- ul) s)o
sgtltgt ~l jl 5raquo)1 x)li ~ 11) 5f
bulllagt s- ~
s) ~ )~I r~r- ) (0) Js ))
s )J )w ) s- oul 0001 S jl ~~
1 ~ )) yo - ~ LA w jl gt s- o~gt
Ii- s s)Lo ~ )s- )4j ~ so6- )J ~
)1Jc s1 ~~yo jlLAy )gt
S jIs ~4 ~ w ~l3 y 61 Iilsshy
JS s-sr ~ )lj1
utraquo) -wsj) ~u~ lJj O~
0001 s
)I) ~ yo )gt r- ) ~jSl
~jSl sl o)b w sl) 1 4176 MPa
1 ~~ JtU xi ltSIrlt1 ~1) jl eTa r- 0
[ ]
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m ~ I jki
~~~ lol bull ))) ISjL JAo 4~ J)lgt1
AI) rs ltlSI) 1S)j I~ Jones
~ IS) bull )~I ~ 9 ~ (V) Js )) ~) ~ )6 lA ) rs bullAIL OOOls jI ~
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y sfbl ~ ~Ir lamp ~ ~Irs ~ ))gt
4~
JiIJi ~ Pr )) ~ 9 ~ ~Plo
~Plo 1SJi lSI bull)i1) wGtA lo 143502 MPa
) )) )ij ~I) ~ wGtA Pr )) ~ [IJI
214EPp Pm 2 X (I-x)
cr =0867 2 2P c
)~ 1 (n) ~I) lo ~I) )1 ISUI~
I 99389 ksf )I) a a )li (rn J jl ~
~ jl ~~ ~ ~i rs ) ~ 4759 MPa
1 IS))amp JAo
~ IIgt uJ I) Y yl yj )~1 1 ~)Y bti1 ~Lul A IIgt ~~ ) -~
-1 rs ~ JJ jI ~ ISU JAo ~ )1 ))
middot4 ltsA)) 1SLs jacket ~~ jl ~
roA 4 ltr)) 1 )j )~I I bull ISjLJAo
4 ~~ bS Jb lSI) uJJ )rs ~li
4 TNT ~ bull)lo ~ ~~ ISlIzLgtt
4Ji jI s I )1 ~ 19 )) ~ ))li
liz JJ Jb ) rs -ili roJ 4 4Ji ~l )r rs
10 ) x4 Jb 1 80 cm ~ibS IO m ~
) sfbl ~ ~Ir ~ bull Gil gtIgt )1 ~ ( m
I) I) roS bull) rs ci )ii)) )br oS JJ r
)lampI)lJ ~loj ~)Ik- w lo J~
~ 4 ~ Pr ~ )~I ~ 4A ) s-Ihj )
Jilb middot4 rs k- JL lo )~I ~I ~I -
1 r- ~Pr IS~ i) 1 (I) Js
)1 ~Plo 1 bull 1) (7) Js )) loj ~
1 163 mm )IJi IS ~
wGtA Pr Js ~ lSI) Nurick ~~
[A]I)j w) ~ ~
(7 =0471lt1gt +0001 ((A)
1 ~ wGtA lSI) ~ ltS-I 14 lt1gt
~i rs ) ~ rj ~I) jI ~I ISU~I ltJLI)
[ J
lt1gt = 01 2t 2 (4abpCT y )1I2
r~J6~~~ ba ~I))I))
~crI))~~~
a = 15 em = 591 in b = 125 cm 492 in
~~ ~4 k- J1gtlo 1t0i ~b lSI)
1 Pr)) s I )) ~~y ry -
01 4Jl ~ j1 ) rgt 1 L )) lgt
Jb- r pound ~ I) Jb- w )1 ) ~i ) ~ 21) ~Igt ~4J )) ~ rs ~ 6 x 5 cm
01 131 Ns = 2945 Ihs
Pr IS ~ 17270 )I) ltfgt r ~r~
~1 rs ) ~ 163 mm 4 064 in ~
- ~ wGtA lSI) Rajendran ltS-IrU ~I) lol
[17] I)) w)
(71 =0553lt1gt +0741
b ~Igt ~I) )1 jb ) 0 = 0813 in 207 mm
- Js~~ Jones ~~~ ltJLI )
r ~ J6 ~ 4 ~ wGtA lSI) t
[1 J I)j w) ~ 12
(l =095 [(1+06637lt1gt2)112 -1] (rl)
~ )1 Pr IS ~ lSI) Jones ~~ 1lJ
) ~ 250 mm J)L 098 in (r) ~I) ~
4 ltS-Igt )~ Jlbi Nurick ~I) )IJi~ ~1 rs
~~ r- Rajendaran ~~ ))b IS))amp JAo
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Time (IJIt)
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~ ~ ~ r1 ~I ~ ~yO Aigt
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rA~ 0 I JG
bulliJ 1oS1W ~ Jw 18ti ~ J~
Model
Charge weight
W(kg)
Distance between charge and pipe
R(m)
Max VonshyMisesstres5
(Numerical)
(MPa)
Max Von-Mises stress
(from Eq (26raquo
(circular plate)
Max Von-Mises stress
(from Eq (32raquo
(rectansular plate)
Max deflection
(Numerical)
d (mm)
Nurick
prediction
(Eq (20raquo
de (mm)
Rajendran
prediction
(Eq (24raquo
de (mm)
Jones
prediction
(Eq (25raquo
de (mm)
Nurick
p ediction
(Eq (28raquo
dr (mm)
Rajendran
prediction
(Eq (30raquo
dr (mm)
Jones
prediction
(Eq (31raquo
dr (mm)
E -
Al
A2
A3
A4 foshy
100
100
100
100
8
12
16
20
40010
33308
25492
20005 ---shy
30320
19470
14212
11131 ------~--
33596
21573
15748
12333
1839
1029
772
591
1808
1328
1079
925 -----shy
1587
975
658
462 ------shy
3044
2121
1641
1345 -____--shy
1923
1340
1038
851
2991
2307
1951
1732
2355
1453
1005
743 ___--shy-shy -
II- A 1509 8 27044 13467 14922 543 706 183 924 584 1419 403
A6 5094 12 25610 14645 16227 753 946 489 13 86 876 1762 778
A7 12074 16 27600 15376 17038 863 1186 795 1848 1168 2105 1195
AS 23581 20 28723 15884 17600 1004 1427 1101 2310 1460 2447 1635
E Bl 100 8 38561 27941 30960 1408 1387 683 2012 1272 2602 1103
B2 100 12 29289 18014 19960 1002 1069 279 1402 887 2150 612
II- B3 100 16 2181 13 186 14610 671 905 070 1085 687 1915 391
B4 100 20 17079 10348 11466 545 803 -060 889 563 1770 273
Cl 100 8 3693 26060 28876 1306 1237 126 15oJ 951 2601 557
sect C2 100 12 2569 16855 18676 889 1000 -176 1047 663 2263 288 N
II- C3 100 16 18871 12365 13701 624 877 -332 810 514 2088 177
C4 100 20 14761 9721 10771 490 8Ql -429 664 421 1979 121
E DI 100 8 33846 24578 27234 1174 1195 -276 12 II 767 2743 313
on D2 100 12 22817 15938 17660 778 1004 -519 844 536 2470 157
N II- OJ 100 16 16739 11713 12978 545 905 -645 653 415 2329 095
D4 100 20 13083 9220 10216 438 844 -723 535 341 2241 064
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I - Cole R H (1948) Underwater explosions NJ USA Princeton University Press
2 - Smith P D and Hetherington J G (1994) Blast and ballistic loading of structures Butterworthshy
Heinemann
3 - Chung M and Brett J (1997) Assessment of underwater blast effects on scaled submerged cylindrical
objects DSTO Aeronautical and Maritime Research Laboratory
4 - Huang H and Wang Y F (1970) Transient interactions of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 48 No1 PP 228-235
5 - Huang H and Wang Y F (1971) Early-time interaction of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 50 No3 PP 885-891
6 - Geers T L and Hunter K S (2002) An integrated wave-effects model for an underwater explosion
bubble Journal ofAcoustical Society ofAmerica Vol III No4 PP 1584-1601
7 - Nurick GN and Martin 1 B (1989) Defurmation of thin plates subjected to impulsive loading-a review
Part I theoritical consideration International Journal ofImpact Engineering Vol 8 No2 PP159-170
8 - Nurick G N and Martin 1 B (1989) Deformation of thin plates subjected to impulsive loading-a review
Part II experimental studies International Journal ofImpact Engineering Vol 8 No2 PP171-186
9 - Teeling-Smith RG and Nurick G N (1991) Deformation and rupture of blast loaded circular platesshy
predictions and experiments International Journal ofImpact Engineering Vol 11 No1 PP77-9
10 - Rajendran R and Narasimhan K (2006) Deformation and fracture behaviour of plate specimens
subjected to underwater explosion-a review International Journal ofImpact Engineering Vol 32 PP1945shy
1963
II - Rajendran R and Narasimhan K (2001) Linear elastic shock response of plane plates subjected to
underwater explosion International Journal ofImpact Engineering Vol 25 PP 493-506
12middot Bangash RY H (1993) Impact and explosion Oxford Blackwell scientific publications
13 bull Lam KY long l and Wang Q X (2003) Dynamic response of a laminated pipeline on the seabed
subjected to underwater shock Composites Part B Vol 34 PP 59-66
14 - Zong l Lam K Y (2000) The flexUral response of a submarine pipeline to an underwater explosion
bubble Journal ofQlJshore Mechanics and Arctic Engineering Vol 122 PP 194middot199
15 - ABAQUS Users Manual (2003) Ver 64
16 - Rajendran R and Narasimhan K (200 I) Performance evaluation of HSLA steel subjected to underwater
explosion ASM Journal ofMaterials Engineering and Performance Vol 10 PP 66-74
jiA )~ lI~liNIl ~ ~ ~11SAt IIjl
1- Explosion 2- High explosive
3- Pressure pulse 4- Shock wave
5middot Bubble pulse 6- Cavitation
7- Peak pressure 8- Coupled acoustic-structural medium analysis
9- Compressible 10- Volumetric drag
11- Inviscid 12- Bulk modulus
)3 Radiating acoustic boundary 14middot Transient analysis
15middot Weak form 16middot Traction
17- Mass proportional damping factor 18- Discretize
19- Strain interpolator 20- Explicit dynamic integration
21- Nonreflecting 22- Impulse
23middot VonmiddotMises 24- Inverse mass number
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4 I) ~1 bulllol ) is) ~ li s4j)1 iSlr
~ n iSlr d$ ~~ s~ ~I) r
~II 1 rj )~I 1 ~ iSlorb -6i 0ts ~
~IS~lQI
a iS1orb -6i ) jS ~ iSlr Nuriek
[A]I bull)b )~ I) r J)
(7l = 0425Clgtc + 0227 (I )
~ s iSyI~ $ ~L t ~1)rI))
rLwI r ri ~I) )1 d$ 1 iSlrb -6i iSlr
[ ] l11S) ~I iSlIIgtlltgtl
$c 10 (n) 1rrtl(pCl)lll
C1y 1)~ P bull iSl orb ~ tt r
rj ~ ~ S D H rfgt 111 ~~ JS is) r d$ ltNs --gtr)1 0Lj - )W ~
~ I ~ lltgt1 )) rfgt )~IS iSr-fJlftl ~
[ r ] 10Lj lJ ~rj
1()= fP()dt (n)
Ns 1m2 --gt)iris~ ~I) jlli 0 1 IS d$
[ ] ) i ) ll9
1=5760 Will (W) r (rr)
-gtb iSlr 1 m --gtr R kg --gtr W d$
~ isaLgt ~5r CJ- ~~~4 IO
rfgt 0 1gt1- )) ~b I j i )) )
~i ) ~ JS iSlr 110 ~ r~ l )
)gt)~ oll- r1 iSlr bull ~1- is 111gt y1)4 r)ll
r= 125 em = 492 in t=2mm=0079 in W= 30 gr R 30 em P = 1025 kg I m3 = 64 pef Oy = 360 MPa 52 ksi IO = 876 Ns = 1969 Ibs
l1 IS) 142 mm 4 056 in ~
d$ ) IS ci ~)) 0001 s rJlil 0Lj r1rl
)W jl ~L bA jLw J51 ~~ 01 Jltgt )) IS
(~ ~)
jlJW(b Jl4wJW(a ~s~fs
JUS
)br ~ lt11 J )) ~ y iS1IIgt0ts
sr- Jc - ~ JS Jj )~IS
b)) ~ d$ -1l)r1 ~ middot4 ~ll bA 1iI ci 1 jI ) li ~ )) )~I
~li r1 ~lgt ~ ) 0 Jlo Jl-- jl ~
d$ ) IS Jt1 (f rlSai1 ri-) isr is)) ~1
~li r1 j) jl bull )~I D d$ 1 ~ rl
)i ~li Jgtb ~IS )r rts1 0l
0001 s 1 ~~ ci~ jS ~ jS )) ~
1 bull 1 0~ (f) ~ )) ~ iSW ) jI
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6E P P 2 X 2l(I-x) (J= pm
a p2 C 2 (I-v)
c ~)L9 p ~ ~~ Jlo E ) )gt lt45 n shy
~ sl) rr-gtltgt ltJ~ xI)gtr 41 )I) lt45 1
(rv)X= m
~~ ~I rr- m lojli 8 )1)gt lt45
fO-)gt AIl- )11 sl) 1
E = 21 e 11 Pa = 439 e 9 psf Pp= 7800 kg m3 48695 pef Pm = 5427 MPa = 11334468 psf
P = 1025 kg 1m3 = 64 pef c = 1463 mls 4800 fils V 03 8=2975ls m=3206psf x= 2851
89698 ksf )I) Cla)~ (r7) J~ jl~)1~
Ak)l lt45 )J )w ~1 s- ~ 4295 MPa ~
jI lt45 1 ltSII~ ~ ~gt )~ )~ )11 gtsshy(4176 MPa) 1 bulllo1 gt ~ sltgt ~
shy oJII OM -1lt10OM bullbull
(11
-WjS)srlulo-ulSo~)) f~
U1b0 ~~ cSJ J~t ~J~ lNT )~I jI r1 5 (Z I o-j )11 )gt
~ r))5f gt~14 ~~~ s) ~li gt~ ltSIrlt1 11) 4 ~l bulli ~ Lil
03 gt~14 ~ sl ~ AIl- )11)gt gt sshy2 )~I JoY)gt 2 mm G 4 X 025 m
) ~ jSyo 30 em ul)gt lNT r )-I )gt (1 i AIl- Lilo )~1 61) gt r sshy
bull)1s ))))) I~ JoY)) ~~~ 4shy ~ gt~I)w 4 ~~ ) ~i
Jlo Jl ~ s~1 )s- Jlo 20 em JJ
)) ~ bulll J 10 em u(j )) bullbull~
bulljL 5- ~ s)Iil 1A0W1tY gtrsshy
s )11 ~ Rajendran b s~) ~I)
[7] 1 ~ )~
(rf)(1 =0541lt1gtc -0433
~ 065 in )I) )15 ~ ~I) )11 ltJLI ) lt45
~i s- gt ~ 166 mm
~~~ sl) ~ ~I) ji Jones ll
ul) 41 t ~ sl )b w jSyo 015 ~
[ ] 1 ) )11 ~ lt45 1 o)b
(1 0817lt1gtc (ro)
)15 ~ sl) Jones ~ ~ ~ )-~
264 JgtL 104 in (rO) ~I) ~~ )-I yo
~i s- gt ~ mm
~ ltSIrlt1 11) )s-~)l lt45 )Lo)w
sjLJlo ~l 4 ~gt ~ ~ s1A ~ xgtli ltSIrlt1 11) s lAr )11 4 lagt s- ul) s)o
sgtltgt ~l jl 5raquo)1 x)li ~ 11) 5f
bulllagt s- ~
s) ~ )~I r~r- ) (0) Js ))
s )J )w ) s- oul 0001 S jl ~~
1 ~ )) yo - ~ LA w jl gt s- o~gt
Ii- s s)Lo ~ )s- )4j ~ so6- )J ~
)1Jc s1 ~~yo jlLAy )gt
S jIs ~4 ~ w ~l3 y 61 Iilsshy
JS s-sr ~ )lj1
utraquo) -wsj) ~u~ lJj O~
0001 s
)I) ~ yo )gt r- ) ~jSl
~jSl sl o)b w sl) 1 4176 MPa
1 ~~ JtU xi ltSIrlt1 ~1) jl eTa r- 0
[ ]
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m ~ I jki
~~~ lol bull ))) ISjL JAo 4~ J)lgt1
AI) rs ltlSI) 1S)j I~ Jones
~ IS) bull )~I ~ 9 ~ (V) Js )) ~) ~ )6 lA ) rs bullAIL OOOls jI ~
~Ijl Pr ~ liz y ~ )S )b ~ )rs
~ ~ gtIA Jlii ~ )) lol ~Irs
y sfbl ~ ~Ir lamp ~ ~Irs ~ ))gt
4~
JiIJi ~ Pr )) ~ 9 ~ ~Plo
~Plo 1SJi lSI bull)i1) wGtA lo 143502 MPa
) )) )ij ~I) ~ wGtA Pr )) ~ [IJI
214EPp Pm 2 X (I-x)
cr =0867 2 2P c
)~ 1 (n) ~I) lo ~I) )1 ISUI~
I 99389 ksf )I) a a )li (rn J jl ~
~ jl ~~ ~ ~i rs ) ~ 4759 MPa
1 IS))amp JAo
~ IIgt uJ I) Y yl yj )~1 1 ~)Y bti1 ~Lul A IIgt ~~ ) -~
-1 rs ~ JJ jI ~ ISU JAo ~ )1 ))
middot4 ltsA)) 1SLs jacket ~~ jl ~
roA 4 ltr)) 1 )j )~I I bull ISjLJAo
4 ~~ bS Jb lSI) uJJ )rs ~li
4 TNT ~ bull)lo ~ ~~ ISlIzLgtt
4Ji jI s I )1 ~ 19 )) ~ ))li
liz JJ Jb ) rs -ili roJ 4 4Ji ~l )r rs
10 ) x4 Jb 1 80 cm ~ibS IO m ~
) sfbl ~ ~Ir ~ bull Gil gtIgt )1 ~ ( m
I) I) roS bull) rs ci )ii)) )br oS JJ r
)lampI)lJ ~loj ~)Ik- w lo J~
~ 4 ~ Pr ~ )~I ~ 4A ) s-Ihj )
Jilb middot4 rs k- JL lo )~I ~I ~I -
1 r- ~Pr IS~ i) 1 (I) Js
)1 ~Plo 1 bull 1) (7) Js )) loj ~
1 163 mm )IJi IS ~
wGtA Pr Js ~ lSI) Nurick ~~
[A]I)j w) ~ ~
(7 =0471lt1gt +0001 ((A)
1 ~ wGtA lSI) ~ ltS-I 14 lt1gt
~i rs ) ~ rj ~I) jI ~I ISU~I ltJLI)
[ J
lt1gt = 01 2t 2 (4abpCT y )1I2
r~J6~~~ ba ~I))I))
~crI))~~~
a = 15 em = 591 in b = 125 cm 492 in
~~ ~4 k- J1gtlo 1t0i ~b lSI)
1 Pr)) s I )) ~~y ry -
01 4Jl ~ j1 ) rgt 1 L )) lgt
Jb- r pound ~ I) Jb- w )1 ) ~i ) ~ 21) ~Igt ~4J )) ~ rs ~ 6 x 5 cm
01 131 Ns = 2945 Ihs
Pr IS ~ 17270 )I) ltfgt r ~r~
~1 rs ) ~ 163 mm 4 064 in ~
- ~ wGtA lSI) Rajendran ltS-IrU ~I) lol
[17] I)) w)
(71 =0553lt1gt +0741
b ~Igt ~I) )1 jb ) 0 = 0813 in 207 mm
- Js~~ Jones ~~~ ltJLI )
r ~ J6 ~ 4 ~ wGtA lSI) t
[1 J I)j w) ~ 12
(l =095 [(1+06637lt1gt2)112 -1] (rl)
~ )1 Pr IS ~ lSI) Jones ~~ 1lJ
) ~ 250 mm J)L 098 in (r) ~I) ~
4 ltS-Igt )~ Jlbi Nurick ~I) )IJi~ ~1 rs
~~ r- Rajendaran ~~ ))b IS))amp JAo
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l )-Iy ~ ltS4)l sts ~ st ~4 jl
~ IS l~ IS ciJ )U)l )br-f w) - 41 s~1
1 )U 10 1 6 )l 0 jL ~4 ~I - ~
bOj ~I~ - ~~~ ~I jI )l I~
I) I) ~ 91)01 lli )1gt - IS JI- jl ~
JI- jl -i ~ l)I Jilo bulll~ IS JIo ciJ
)l D JIo ~s1 ~ ) - ~ 91)01
ri=- s y Sir br li )-I s=raquo ~ ~ )l t ~ )-I ~ ~ l~ IS Jwl rlSu1
~ 11slj ~ - JI IS li~ IS Jraquo ~1 jI
9r ~ l)-II jl )-Iy li)l 4)) ~ ~1
ciJ )U )l r ~lgt u-l4 I ~~ l IS )U
IS ~l t ~ s) s es I bOj l~ ~
rlY 10 )-I )l ~ ~4 IS r-Jlii Lj 10 l
bull1 0002 s y1y bull
~L st JIo ~l ~ () J~ )l
r-oL riO li 6 4 st ~ 1 0101 bull
JI~ )-I )l lil 0 s)lS Ili D li A 4~ -
~ (in (I) ~I) jl ~ ~flo
~ Jraquo 4 bull ~ ltS~ ~I) I 0lli1 4 LS
~ t ~ )i ~ ~ 4 y1y )i ~ sl o)b
12 JIgt~)i ~ ~ y1yJgtr 4 ~ Nuriek ~I)S )1 - 1 0 6 Jgtr y1y
s~ es I Sly s~ ~l ~ Ib l A Sly
(25 em) ~ st 6 )l 41 bulllAl IS l -
i l rmiddot llgt )l1 ~~~ byr ~I)
Sly l IS s)amp ~l )I 5s ~)l fmiddot li imiddot llgt ( 1 15 em) ~4 st 6 Sly
~ )) imiddot li rmiddot llgt )~ st 6 Sly ~))
bull ~ IS )1gt 100 ~ Slamp ~l I 5s R lao = 60 4 )~II 1 em 6 4~ Sly
r)Y li)b sgt~ s )lj ~~ )l IS
0101 (A8 li A5 st JIo) () J~ )) i ~l
(TNT j ~ ~ ) u19 JI)I 4~ II 1
- ~ )l lol l4 IS JI)I LS ~
li)Ili ~ 4 slj 9)tgt1 ~l bull l) )) oJ
bullIgttgt JI)I 4 IS 1 )-I ~l )tJ1 kLi ~
() st jgt )l ~l1S J-AgtIS LS ~
A st JIo sly ~ - ~ ()
)-I r)Y l) IS bull1 6 )l ~ J-li ~ S)
) - ~1 ~ 91)01 ~4 ~b 1 ~
l IS JIo 0jL ~I 22 m uli li sl oljl-I
r-oL 25 2 bull 15 bull 1 sUt6 4 t ~ IS Oly 100 kg TNT o~ DlL lil D ~lgt1
jl sr-o 20 16 12 8 JI )l ~ 6 A Sly
r l jl y1y u19 4 ~6kLA)l ~ ~
~ Sly Ut JIo )-I y ojs 1 bull bull lb 1) (i
slA- j 4 TNT bull~ OlL bull 1 em Igttgt 4 bull1 bull r)Y sr-o 20 l 8 J1)lJ
ollo tL - u19 ~ 41 olAgt sly IS sl olj -
~I ~yen kLi ( R lao = 60 ) 1 60 y1y 0~
bull ciJ )U )) 152 grem3 Ar TNT)~ bull1
~ to )-s)~)ls~)lj sgtLj ~)li
jl bulllli1 4 ~ ~ fr ~ )~I J-- ~
)~ IS JLs1 P(t) Pm - byr r~ ~I) 100
s )lj sgtLj ~)li olj~ sly (A) JS )l
1) Sr-o rmiddot A u19)l 100 kg TNT - b~r
360
~
ii ~
R=20m
20
lU
0 0 I 20
Time (IJIt)
IOOkg IJ s~)ut)IoJ
rmiddot A JgtI J~ ~)ll A~
TNT
)wgt r )lj )u )wgt loj )l IS l ~yen ~4
)l sgtloj 10 ~ IS )1 100 I)) l IS Jgt) s~ es l ~ IS J1 )~I uJ 11107 s llgt
LA r li ~ 11 ~ gtJY )U )) to -
)iu )l bull l)b 385 MPa y1y ~ IS ST 52
~ 4 S4R~J f WI nmiddotmiddot 4~ l~ IS ciJ
AC3D8R WI iiAmiddotmiddot 4JI- ~ 01 m llgt
s- ~ li~ IS slj-o 02 m llgt ~ 4 bull ~ raquo 100 4 ~ JL JiL JI- jL
~~ )l Ut u )-I ~ li~ IS ~~ -
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~I Jlgtu
0tS ~ )l ( f) l ( ) -S1As)l
0 )lI-SlI))l )~I-S) d ) uJb ~
)l (1 ~ r-- )l 0tS ~ oaC ltIS) s J -SlA l -SIr bull~ ollo )IJ JoIs
ltIS )1gt 01A lil bulll ~to pgtA 4 (t25 l tl)uJ
~15 0tS ~ l rlljl 4 l)lt5 )UI
)l ltIS s~)l 01 lt5 lA)b r1jl ~~~ lt5
l d bTr 0tS~ )~I J- )1 ulS I
bTr 0tS ~ )1 rs )l 30 lgtgt (ti) I em
-slAl -sIr 1 (tl5) 25 em l d
-st gtI~ )1gt d 0tS ~ r1 -i )l
~lt5~
A4 Jlo(d A3 Jlo(e
0lo) 04~)l (25 em l) D (l em l)
)~I -s) d ) oIil ~ l -sIr (0002 s) rlll
1 o~ olb 0l lA uJ
~ () () -slAsI l) ~ )l
jI ~ uJ r JIraquoI bli -r )l ltIS 1
-S )l1 lil lt5 ~ r1chll bull1 r lp
)ts r-gtu 4 )lz9 ~)l ~t s (s
~~ r~l~ ltIS uJ b ~ d ~ )lo)
0loj )l l lt5 ~4 ltIS ~4 1 )~I J- d uJ
lJbL uJ ~ -s) ~ ~j ~ 0002 s )c
middot~4
A2 Jc(b Al Jc (a
D4 Jc(d D3 Jlo(e D2 Jlo(b
)~Isr) 411 eo~ u_)~ 25 em 6 Irs 411 sIr 0002 s
00 05 10
o~----------
12 --------------
Dl Jc(a
~1ol)1) ~~~ ~
05 10 15 20
16 --__________J
r 2 5 2
I 5
II
12m from l()()kgof TNT
12 5
tl t I 5 I
8m from IOOmiddotkg of TNT
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20m from IOO-kgof TNT
loS (~ shy)j )~I JL s~~ siL ~ 4llii r1 )~
~I) ~ ol I~I jyi-o s1A OjL J~ )~ 1
~l ~ 1 ol ~lii ~ sU~ ~
~ ~ oL ~ ~ JlL ) ltcent~ 1Jlb1 ~
)~I o~ JlL kbU sl) sgt~ JIo JlS J~
jyi-o s1A 4lJ sIr 1 ~ s1A jL r i r)
4lJ -h9 ~ ~ -h9 ~ srb ~ Jgtlao I) ~i ~I
Jb 4lJ -h9 ~ ~ Jgtr ~ ~~
~ ~l Nuriek ~ J- f~ Jgtr Ir 12
r1 ~~ db ~ ~)b s~~ ~l ~ ~~~
JoIs )~ ~ )l ~~ ~lj ~I )gt IS 1 IS) ~~ 411 jL l )~I Jgt du ~ Igt ~
~ (~ Jlblgt ji ~ L tt= 411 4 I~ )l lS U Irj l Jlblgt fs)j ejL Jl1
rj eb ~)y ~ ~ ~yO 1)-0 ci~ lS
IS 1 tamp~ 41~~ J110Lj )l ~
4 ejL JlI ~~ 4bt1) ~ ~ ~ r1
~)~I Jgt )1 du
00 05 10 u o~--~----~--~----~
-8
125
12
115 It
16m from IOO-kgof TNT
l AS) As1A JIo 1 sr ji (6) Js )
uo ~ ~ ) Js r1 ) IJIl ltr)r (AS
1 em ~ ~ uJ sIr )~I s) ~ ) uJ 6
60 rlr R I ao ~ IS )~I ~ s1AJb sIr
JiI1gt yS11gt J~I ~ r1 )~ Jlb~ 0~ I) IJ)~
1 -WI) 4S ~1gt (0002 S 0Lj )~) ~ ~
0 05 15
0
-2 E R8-4shy RI2 c 0 -6 RI6
8 =
R20 ~ 0 10
-2 1-_____________---1
- )ltiil lIbSI1So ~ )I~ 0 JSj
Rlao =60
~I ~~ ~ IS ~ Jlbl ) r1 )~
1 sL )~I ~ ~b sIr ~ )l
~lj R lao ~I )~ IS R 411 4 LI (13S3 MPa)
411 r- 0~ ~ bull1 ao 41 ~ ~
~~ ~ ~~ 4 IS 1 r1 i lc IS ~~
uu 411 4 4i Lj ~lj s )l yS11gt
uu 411 ~ )l JItgtlS U rlr~ ~~ 411
) 0Lj -)l ~ rj eb ~~ JItgtlS
~ ~ ~ r1 ~I ~ ~yO Aigt
)~I Jgt )1 d13 ~ jL Jl1 ~~ bL)
~(R)
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rA~ 0 I JG
bulliJ 1oS1W ~ Jw 18ti ~ J~
Model
Charge weight
W(kg)
Distance between charge and pipe
R(m)
Max VonshyMisesstres5
(Numerical)
(MPa)
Max Von-Mises stress
(from Eq (26raquo
(circular plate)
Max Von-Mises stress
(from Eq (32raquo
(rectansular plate)
Max deflection
(Numerical)
d (mm)
Nurick
prediction
(Eq (20raquo
de (mm)
Rajendran
prediction
(Eq (24raquo
de (mm)
Jones
prediction
(Eq (25raquo
de (mm)
Nurick
p ediction
(Eq (28raquo
dr (mm)
Rajendran
prediction
(Eq (30raquo
dr (mm)
Jones
prediction
(Eq (31raquo
dr (mm)
E -
Al
A2
A3
A4 foshy
100
100
100
100
8
12
16
20
40010
33308
25492
20005 ---shy
30320
19470
14212
11131 ------~--
33596
21573
15748
12333
1839
1029
772
591
1808
1328
1079
925 -----shy
1587
975
658
462 ------shy
3044
2121
1641
1345 -____--shy
1923
1340
1038
851
2991
2307
1951
1732
2355
1453
1005
743 ___--shy-shy -
II- A 1509 8 27044 13467 14922 543 706 183 924 584 1419 403
A6 5094 12 25610 14645 16227 753 946 489 13 86 876 1762 778
A7 12074 16 27600 15376 17038 863 1186 795 1848 1168 2105 1195
AS 23581 20 28723 15884 17600 1004 1427 1101 2310 1460 2447 1635
E Bl 100 8 38561 27941 30960 1408 1387 683 2012 1272 2602 1103
B2 100 12 29289 18014 19960 1002 1069 279 1402 887 2150 612
II- B3 100 16 2181 13 186 14610 671 905 070 1085 687 1915 391
B4 100 20 17079 10348 11466 545 803 -060 889 563 1770 273
Cl 100 8 3693 26060 28876 1306 1237 126 15oJ 951 2601 557
sect C2 100 12 2569 16855 18676 889 1000 -176 1047 663 2263 288 N
II- C3 100 16 18871 12365 13701 624 877 -332 810 514 2088 177
C4 100 20 14761 9721 10771 490 8Ql -429 664 421 1979 121
E DI 100 8 33846 24578 27234 1174 1195 -276 12 II 767 2743 313
on D2 100 12 22817 15938 17660 778 1004 -519 844 536 2470 157
N II- OJ 100 16 16739 11713 12978 545 905 -645 653 415 2329 095
D4 100 20 13083 9220 10216 438 844 -723 535 341 2241 064
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I - Cole R H (1948) Underwater explosions NJ USA Princeton University Press
2 - Smith P D and Hetherington J G (1994) Blast and ballistic loading of structures Butterworthshy
Heinemann
3 - Chung M and Brett J (1997) Assessment of underwater blast effects on scaled submerged cylindrical
objects DSTO Aeronautical and Maritime Research Laboratory
4 - Huang H and Wang Y F (1970) Transient interactions of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 48 No1 PP 228-235
5 - Huang H and Wang Y F (1971) Early-time interaction of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 50 No3 PP 885-891
6 - Geers T L and Hunter K S (2002) An integrated wave-effects model for an underwater explosion
bubble Journal ofAcoustical Society ofAmerica Vol III No4 PP 1584-1601
7 - Nurick GN and Martin 1 B (1989) Defurmation of thin plates subjected to impulsive loading-a review
Part I theoritical consideration International Journal ofImpact Engineering Vol 8 No2 PP159-170
8 - Nurick G N and Martin 1 B (1989) Deformation of thin plates subjected to impulsive loading-a review
Part II experimental studies International Journal ofImpact Engineering Vol 8 No2 PP171-186
9 - Teeling-Smith RG and Nurick G N (1991) Deformation and rupture of blast loaded circular platesshy
predictions and experiments International Journal ofImpact Engineering Vol 11 No1 PP77-9
10 - Rajendran R and Narasimhan K (2006) Deformation and fracture behaviour of plate specimens
subjected to underwater explosion-a review International Journal ofImpact Engineering Vol 32 PP1945shy
1963
II - Rajendran R and Narasimhan K (2001) Linear elastic shock response of plane plates subjected to
underwater explosion International Journal ofImpact Engineering Vol 25 PP 493-506
12middot Bangash RY H (1993) Impact and explosion Oxford Blackwell scientific publications
13 bull Lam KY long l and Wang Q X (2003) Dynamic response of a laminated pipeline on the seabed
subjected to underwater shock Composites Part B Vol 34 PP 59-66
14 - Zong l Lam K Y (2000) The flexUral response of a submarine pipeline to an underwater explosion
bubble Journal ofQlJshore Mechanics and Arctic Engineering Vol 122 PP 194middot199
15 - ABAQUS Users Manual (2003) Ver 64
16 - Rajendran R and Narasimhan K (200 I) Performance evaluation of HSLA steel subjected to underwater
explosion ASM Journal ofMaterials Engineering and Performance Vol 10 PP 66-74
jiA )~ lI~liNIl ~ ~ ~11SAt IIjl
1- Explosion 2- High explosive
3- Pressure pulse 4- Shock wave
5middot Bubble pulse 6- Cavitation
7- Peak pressure 8- Coupled acoustic-structural medium analysis
9- Compressible 10- Volumetric drag
11- Inviscid 12- Bulk modulus
)3 Radiating acoustic boundary 14middot Transient analysis
15middot Weak form 16middot Traction
17- Mass proportional damping factor 18- Discretize
19- Strain interpolator 20- Explicit dynamic integration
21- Nonreflecting 22- Impulse
23middot VonmiddotMises 24- Inverse mass number
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middot iI~
~rU lSi~ )5 41)1 4 lSI ojl JlJJ) i) j1
) r
IvSsadV + IvucPSu Ii dV
(W)+ Iv pSu ij dV
+ L pSundS - J Sumiddot( dS 0 Sft 51
ss-l ~ $r- IS 1 ~ Sf ))IS
J) (J )r J 0jl $r- -i ~ Jb -i
- Jl-gt sr=-~ )l1 )I P il j1 ~~
a c 0)L)~ P [JLgt - Ojl )s n Oil
1 - bull ) IV l I bullsr- fgt~ ~ r sr- r
IS ~ ( jl )) Ji ~l it (0jl lSI uI ~ I~ u10l-0 DUm jl r )l1 ~
15 ~ os j uLS A
ISjl Ji sLiJ) ~I~ ~rU 4 ltl1
bulljl ) j P = HP pP P = 12 Jl-raquo) ) r
umu~) -i ~ -i N P IS = JIl UN N 12
4middot))) 0)L1 Ojl)) uLS~ Jl-raquo) JI IS)I)
ulol-o lSI Ojl ~ 1S1r ~)l3 ) jI bull )lAl
Jl-gt 1S1r 1 oum NN ouN
U -i I~
bull)lA1 (A) ~I) 1S)lfIS~ 4I) op = HP3pP ~I)
~r
OA)
IS )jlr I IS~I I~ 41)1 S j ~~ ~L
-i IS)~I 1Sil 4 (W) (~) ui)1 ~ j1
~ir ) -j fir M iF + c p2 + (K + Kj)p2 _S~M jiM
+0 UN tv + M N aM + c(~ It + [sJ~YpQ - pH = 0
( )
Jl-gt ) I 1S)li1U~) -i 1Yo) Q PISlA lt)I
ojl ) uLS ~ IS)I) U~)) -i 1Yo) M N
I))~
cPQ =J l~ HI HQ dV I V PI Kj
M PQ = I _I_HI HQ dV O) j v K
j
KPQ i
r JSjl
1 HI HI dS 0
(H)
KPQ=J V
~aHP aHQ PI ax ax
dV (fl)
~ 5) r J~ )~ P Jl-gt 0) 1
~ ISlA~ (J (cr r ~ 1gt1 r lri)
~ 1 cSl I~ b 10) IiL
) r r~ ~I Agt lId r-i Jl-gt
xlr~
(0)
middot~4 r Jl-gt ITsJ4 J K r
ui)1 I IS ss-1 ~ i l ltlgtli ~ i)
S ISlA 4-gtli ri -i I~ r ~r IS~ (0) (f)
) ~ r) ylb
~~s-i )I )~ j)1foxI )) Sfp
~ IS 11gt ) Jil If~l ~s-ij) Sfi
IS 1 ri )b - )~li ) -i ~s-1
bull)5 Jl1 IS) 1 ~s~sect I) ~6u 4-gtli
J I) [JLgt -i ~6u 4-gtli jI cS)~ ltr11l
~
r- uLA 4 J-ilh) 41)1 ltr1~1 1S1r It shy
1)lfrJlil ~ 1Sr JI~I )) bull)lA1 )
x -i- Ii ~ 0)5 ~ P 1) (f) 41)1
(~s-k -i yip ~ jl u)5 )iir 4) df
L bull )5 ~ (0) 41)1 Lj uLA 4 I lL
) -i Jl-gt )I IS~ J~ 1S1r $jgt 41)1
~1
I y a (I apJK p +P K P - ax -p ax 0
) JlI 41)1 IA~ jI bull )lA14
-i ~s-l ~ 1S1r s~ I~ JIgt r- -i
~i r)
~ (1 y J I Blip apJdVup -p+--p + -_shy1[ K P Kf Pfax ax (V)
+ 1P (J ft + p) d S = 0 fo 01c1
~rU rj u -i aJ CJ ISlAI)~ u1 )) IS
r
(A)[A] ()I ~[f3 y]
0 = -p+ 2Pr ~P K
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fAT
) jgt jgt- )lJ )li jgt- oj )) ~I
Jk )~I tJi1 107 s )~)) Ij Iri
)13 ~rgt ))Ji ltI S ~l ~
210 GPa$~ J 7800 kglm3 )~ ~
) ci~ gt)) 360 MPa ~
l
ill
[ Explo51 veIgt Charge
~ R lSloodurr Libullbull uo)
(AI)
pressure pulse at plate center 50
4()
m
OOOStOO 1008-1)4 200B-04 lt)08-04
(5)
(y)
standoff point ~ 1 -4~~ (AI) ~
b~o)o30gr iz1i)i~lt(y) b~O)o
~ Jgt jf 30 em d1i)) TNT
s1~sI~ )agt WI y ~ s)13 ~
J-I ~ ) s~ J-o ABAQUS ) )p- S4R
~ ) ci~ gt)) 1 em )~ IAWI
~ ~s1)agt WI IIAmiddotmiddot ~ J~
I em )~ ~ lAgt ~ AC3D8R li ltI sI~ a
I p )) s~ J-o J-11 lSiL s~ J-o
cb )) s)~I J~ gt )) sIr l ~)
Tie ) ltI ~ )J-I ojL J~ S~
master ~Ic ltI 4lJ ~ ~I ~ ~ foJS slave ~ Ic ltI 4lJ ~ L )) J~ ~ sl iL IA lS ~ ~ y~ ) LI
1)) 1Si uJ~ J-o ~s1 s1A)lJ ltI 4lJ
~lS ~r S ~~))~ b-r J~
s ~ I b03 bullwlla J-I )) ~I ltI ~ ~
bull) 1S)r )~I jI ~li )lJ 41 J~ ~
MNM Iv pNN N M dV
SPM r H P n-middotNM dS Js Js
IN Iv 3NmiddotCT dV
C~~ Iv U c P NN N M dV (IY)
pN f NN t dS (I A) s
bull1 r ~)l ~l tt u ~j jl bull )lA1 ~ Ii ltof ) l)~
srJI~I )I )) Ymiddot (r ~~) srJI~I J 4l1iJ-1) lt4S ~L yr )l ~~
)) Sri )~ ltI (J~) ~s1 ~t ir ~I ~
I~ ci~ gt
JJamp ~jll ~
ISI 0xl) ~ oSt IS) Y )~IIS)X
ss ~ l~l )) ~~ 4lL J-I ))
6 1NT ~ )li )~I I u rf js
lS ~ l J ABAQUS A
J-I )l u ~ r~ ~I) sgtr ~ 1 r )) js sl rb ~ ) ~lio )) )p- ))
0)1 )~I Iu 2 mm L 25 em )j ~
))u )r )) 30 gr )li ltI 1NT ~
~ il ~ ))b ) ~ ril 30 em uij
)) )~I jgtjAA))u 1s~ b03 bull)- )13
I jgt jAA )) ~~) 11 ~L ))r
)j sl Ai 1-I ) ltI 4lJ s~ 1 ())) )
cb u s)k ltI ) J 20 em Jk 25 em
)~I J-I 1 0 em ult)l J~ s4=-i1 )lgt
))b)
~Ji J-~li)) S)lJ Ii ~)l
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li bulliL l 1 uLS bull ~ 0)1 4A J-1~
~1)1 1 -)lJ )l ~L sIr 1 bullI bull )13
1S1 ~1) J-I ~ r ) )LOI (n(I)(1)
5427 MPaAt ~ - e Ii ~~ Pm S )lJ
)11 Ii -)lJ )b ~i ) ltI 2975 liS
y1i 1 bullI fgt) () jS ) ~r r
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~ 1 JLgt
)1gt ~~~ )IS bull aL d$ 1gt0Lo
~41S II ~)- 111gt y )1 gtI~
)) J j --gt r r ~ ) 0ts ~ ))
r1r 0ts ~ r1 1fL 1 bull amp-) (f) ~
41S 191 mm
4 I) ~1 bulllol ) is) ~ li s4j)1 iSlr
~ n iSlr d$ ~~ s~ ~I) r
~II 1 rj )~I 1 ~ iSlorb -6i 0ts ~
~IS~lQI
a iS1orb -6i ) jS ~ iSlr Nuriek
[A]I bull)b )~ I) r J)
(7l = 0425Clgtc + 0227 (I )
~ s iSyI~ $ ~L t ~1)rI))
rLwI r ri ~I) )1 d$ 1 iSlrb -6i iSlr
[ ] l11S) ~I iSlIIgtlltgtl
$c 10 (n) 1rrtl(pCl)lll
C1y 1)~ P bull iSl orb ~ tt r
rj ~ ~ S D H rfgt 111 ~~ JS is) r d$ ltNs --gtr)1 0Lj - )W ~
~ I ~ lltgt1 )) rfgt )~IS iSr-fJlftl ~
[ r ] 10Lj lJ ~rj
1()= fP()dt (n)
Ns 1m2 --gt)iris~ ~I) jlli 0 1 IS d$
[ ] ) i ) ll9
1=5760 Will (W) r (rr)
-gtb iSlr 1 m --gtr R kg --gtr W d$
~ isaLgt ~5r CJ- ~~~4 IO
rfgt 0 1gt1- )) ~b I j i )) )
~i ) ~ JS iSlr 110 ~ r~ l )
)gt)~ oll- r1 iSlr bull ~1- is 111gt y1)4 r)ll
r= 125 em = 492 in t=2mm=0079 in W= 30 gr R 30 em P = 1025 kg I m3 = 64 pef Oy = 360 MPa 52 ksi IO = 876 Ns = 1969 Ibs
l1 IS) 142 mm 4 056 in ~
d$ ) IS ci ~)) 0001 s rJlil 0Lj r1rl
)W jl ~L bA jLw J51 ~~ 01 Jltgt )) IS
(~ ~)
jlJW(b Jl4wJW(a ~s~fs
JUS
)br ~ lt11 J )) ~ y iS1IIgt0ts
sr- Jc - ~ JS Jj )~IS
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~li r1 ~lgt ~ ) 0 Jlo Jl-- jl ~
d$ ) IS Jt1 (f rlSai1 ri-) isr is)) ~1
~li r1 j) jl bull )~I D d$ 1 ~ rl
)i ~li Jgtb ~IS )r rts1 0l
0001 s 1 ~~ ci~ jS ~ jS )) ~
1 bull 1 0~ (f) ~ )) ~ iSW ) jI
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6E P P 2 X 2l(I-x) (J= pm
a p2 C 2 (I-v)
c ~)L9 p ~ ~~ Jlo E ) )gt lt45 n shy
~ sl) rr-gtltgt ltJ~ xI)gtr 41 )I) lt45 1
(rv)X= m
~~ ~I rr- m lojli 8 )1)gt lt45
fO-)gt AIl- )11 sl) 1
E = 21 e 11 Pa = 439 e 9 psf Pp= 7800 kg m3 48695 pef Pm = 5427 MPa = 11334468 psf
P = 1025 kg 1m3 = 64 pef c = 1463 mls 4800 fils V 03 8=2975ls m=3206psf x= 2851
89698 ksf )I) Cla)~ (r7) J~ jl~)1~
Ak)l lt45 )J )w ~1 s- ~ 4295 MPa ~
jI lt45 1 ltSII~ ~ ~gt )~ )~ )11 gtsshy(4176 MPa) 1 bulllo1 gt ~ sltgt ~
shy oJII OM -1lt10OM bullbull
(11
-WjS)srlulo-ulSo~)) f~
U1b0 ~~ cSJ J~t ~J~ lNT )~I jI r1 5 (Z I o-j )11 )gt
~ r))5f gt~14 ~~~ s) ~li gt~ ltSIrlt1 11) 4 ~l bulli ~ Lil
03 gt~14 ~ sl ~ AIl- )11)gt gt sshy2 )~I JoY)gt 2 mm G 4 X 025 m
) ~ jSyo 30 em ul)gt lNT r )-I )gt (1 i AIl- Lilo )~1 61) gt r sshy
bull)1s ))))) I~ JoY)) ~~~ 4shy ~ gt~I)w 4 ~~ ) ~i
Jlo Jl ~ s~1 )s- Jlo 20 em JJ
)) ~ bulll J 10 em u(j )) bullbull~
bulljL 5- ~ s)Iil 1A0W1tY gtrsshy
s )11 ~ Rajendran b s~) ~I)
[7] 1 ~ )~
(rf)(1 =0541lt1gtc -0433
~ 065 in )I) )15 ~ ~I) )11 ltJLI ) lt45
~i s- gt ~ 166 mm
~~~ sl) ~ ~I) ji Jones ll
ul) 41 t ~ sl )b w jSyo 015 ~
[ ] 1 ) )11 ~ lt45 1 o)b
(1 0817lt1gtc (ro)
)15 ~ sl) Jones ~ ~ ~ )-~
264 JgtL 104 in (rO) ~I) ~~ )-I yo
~i s- gt ~ mm
~ ltSIrlt1 11) )s-~)l lt45 )Lo)w
sjLJlo ~l 4 ~gt ~ ~ s1A ~ xgtli ltSIrlt1 11) s lAr )11 4 lagt s- ul) s)o
sgtltgt ~l jl 5raquo)1 x)li ~ 11) 5f
bulllagt s- ~
s) ~ )~I r~r- ) (0) Js ))
s )J )w ) s- oul 0001 S jl ~~
1 ~ )) yo - ~ LA w jl gt s- o~gt
Ii- s s)Lo ~ )s- )4j ~ so6- )J ~
)1Jc s1 ~~yo jlLAy )gt
S jIs ~4 ~ w ~l3 y 61 Iilsshy
JS s-sr ~ )lj1
utraquo) -wsj) ~u~ lJj O~
0001 s
)I) ~ yo )gt r- ) ~jSl
~jSl sl o)b w sl) 1 4176 MPa
1 ~~ JtU xi ltSIrlt1 ~1) jl eTa r- 0
[ ]
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m ~ I jki
~~~ lol bull ))) ISjL JAo 4~ J)lgt1
AI) rs ltlSI) 1S)j I~ Jones
~ IS) bull )~I ~ 9 ~ (V) Js )) ~) ~ )6 lA ) rs bullAIL OOOls jI ~
~Ijl Pr ~ liz y ~ )S )b ~ )rs
~ ~ gtIA Jlii ~ )) lol ~Irs
y sfbl ~ ~Ir lamp ~ ~Irs ~ ))gt
4~
JiIJi ~ Pr )) ~ 9 ~ ~Plo
~Plo 1SJi lSI bull)i1) wGtA lo 143502 MPa
) )) )ij ~I) ~ wGtA Pr )) ~ [IJI
214EPp Pm 2 X (I-x)
cr =0867 2 2P c
)~ 1 (n) ~I) lo ~I) )1 ISUI~
I 99389 ksf )I) a a )li (rn J jl ~
~ jl ~~ ~ ~i rs ) ~ 4759 MPa
1 IS))amp JAo
~ IIgt uJ I) Y yl yj )~1 1 ~)Y bti1 ~Lul A IIgt ~~ ) -~
-1 rs ~ JJ jI ~ ISU JAo ~ )1 ))
middot4 ltsA)) 1SLs jacket ~~ jl ~
roA 4 ltr)) 1 )j )~I I bull ISjLJAo
4 ~~ bS Jb lSI) uJJ )rs ~li
4 TNT ~ bull)lo ~ ~~ ISlIzLgtt
4Ji jI s I )1 ~ 19 )) ~ ))li
liz JJ Jb ) rs -ili roJ 4 4Ji ~l )r rs
10 ) x4 Jb 1 80 cm ~ibS IO m ~
) sfbl ~ ~Ir ~ bull Gil gtIgt )1 ~ ( m
I) I) roS bull) rs ci )ii)) )br oS JJ r
)lampI)lJ ~loj ~)Ik- w lo J~
~ 4 ~ Pr ~ )~I ~ 4A ) s-Ihj )
Jilb middot4 rs k- JL lo )~I ~I ~I -
1 r- ~Pr IS~ i) 1 (I) Js
)1 ~Plo 1 bull 1) (7) Js )) loj ~
1 163 mm )IJi IS ~
wGtA Pr Js ~ lSI) Nurick ~~
[A]I)j w) ~ ~
(7 =0471lt1gt +0001 ((A)
1 ~ wGtA lSI) ~ ltS-I 14 lt1gt
~i rs ) ~ rj ~I) jI ~I ISU~I ltJLI)
[ J
lt1gt = 01 2t 2 (4abpCT y )1I2
r~J6~~~ ba ~I))I))
~crI))~~~
a = 15 em = 591 in b = 125 cm 492 in
~~ ~4 k- J1gtlo 1t0i ~b lSI)
1 Pr)) s I )) ~~y ry -
01 4Jl ~ j1 ) rgt 1 L )) lgt
Jb- r pound ~ I) Jb- w )1 ) ~i ) ~ 21) ~Igt ~4J )) ~ rs ~ 6 x 5 cm
01 131 Ns = 2945 Ihs
Pr IS ~ 17270 )I) ltfgt r ~r~
~1 rs ) ~ 163 mm 4 064 in ~
- ~ wGtA lSI) Rajendran ltS-IrU ~I) lol
[17] I)) w)
(71 =0553lt1gt +0741
b ~Igt ~I) )1 jb ) 0 = 0813 in 207 mm
- Js~~ Jones ~~~ ltJLI )
r ~ J6 ~ 4 ~ wGtA lSI) t
[1 J I)j w) ~ 12
(l =095 [(1+06637lt1gt2)112 -1] (rl)
~ )1 Pr IS ~ lSI) Jones ~~ 1lJ
) ~ 250 mm J)L 098 in (r) ~I) ~
4 ltS-Igt )~ Jlbi Nurick ~I) )IJi~ ~1 rs
~~ r- Rajendaran ~~ ))b IS))amp JAo
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l )-Iy ~ ltS4)l sts ~ st ~4 jl
~ IS l~ IS ciJ )U)l )br-f w) - 41 s~1
1 )U 10 1 6 )l 0 jL ~4 ~I - ~
bOj ~I~ - ~~~ ~I jI )l I~
I) I) ~ 91)01 lli )1gt - IS JI- jl ~
JI- jl -i ~ l)I Jilo bulll~ IS JIo ciJ
)l D JIo ~s1 ~ ) - ~ 91)01
ri=- s y Sir br li )-I s=raquo ~ ~ )l t ~ )-I ~ ~ l~ IS Jwl rlSu1
~ 11slj ~ - JI IS li~ IS Jraquo ~1 jI
9r ~ l)-II jl )-Iy li)l 4)) ~ ~1
ciJ )U )l r ~lgt u-l4 I ~~ l IS )U
IS ~l t ~ s) s es I bOj l~ ~
rlY 10 )-I )l ~ ~4 IS r-Jlii Lj 10 l
bull1 0002 s y1y bull
~L st JIo ~l ~ () J~ )l
r-oL riO li 6 4 st ~ 1 0101 bull
JI~ )-I )l lil 0 s)lS Ili D li A 4~ -
~ (in (I) ~I) jl ~ ~flo
~ Jraquo 4 bull ~ ltS~ ~I) I 0lli1 4 LS
~ t ~ )i ~ ~ 4 y1y )i ~ sl o)b
12 JIgt~)i ~ ~ y1yJgtr 4 ~ Nuriek ~I)S )1 - 1 0 6 Jgtr y1y
s~ es I Sly s~ ~l ~ Ib l A Sly
(25 em) ~ st 6 )l 41 bulllAl IS l -
i l rmiddot llgt )l1 ~~~ byr ~I)
Sly l IS s)amp ~l )I 5s ~)l fmiddot li imiddot llgt ( 1 15 em) ~4 st 6 Sly
~ )) imiddot li rmiddot llgt )~ st 6 Sly ~))
bull ~ IS )1gt 100 ~ Slamp ~l I 5s R lao = 60 4 )~II 1 em 6 4~ Sly
r)Y li)b sgt~ s )lj ~~ )l IS
0101 (A8 li A5 st JIo) () J~ )) i ~l
(TNT j ~ ~ ) u19 JI)I 4~ II 1
- ~ )l lol l4 IS JI)I LS ~
li)Ili ~ 4 slj 9)tgt1 ~l bull l) )) oJ
bullIgttgt JI)I 4 IS 1 )-I ~l )tJ1 kLi ~
() st jgt )l ~l1S J-AgtIS LS ~
A st JIo sly ~ - ~ ()
)-I r)Y l) IS bull1 6 )l ~ J-li ~ S)
) - ~1 ~ 91)01 ~4 ~b 1 ~
l IS JIo 0jL ~I 22 m uli li sl oljl-I
r-oL 25 2 bull 15 bull 1 sUt6 4 t ~ IS Oly 100 kg TNT o~ DlL lil D ~lgt1
jl sr-o 20 16 12 8 JI )l ~ 6 A Sly
r l jl y1y u19 4 ~6kLA)l ~ ~
~ Sly Ut JIo )-I y ojs 1 bull bull lb 1) (i
slA- j 4 TNT bull~ OlL bull 1 em Igttgt 4 bull1 bull r)Y sr-o 20 l 8 J1)lJ
ollo tL - u19 ~ 41 olAgt sly IS sl olj -
~I ~yen kLi ( R lao = 60 ) 1 60 y1y 0~
bull ciJ )U )) 152 grem3 Ar TNT)~ bull1
~ to )-s)~)ls~)lj sgtLj ~)li
jl bulllli1 4 ~ ~ fr ~ )~I J-- ~
)~ IS JLs1 P(t) Pm - byr r~ ~I) 100
s )lj sgtLj ~)li olj~ sly (A) JS )l
1) Sr-o rmiddot A u19)l 100 kg TNT - b~r
360
~
ii ~
R=20m
20
lU
0 0 I 20
Time (IJIt)
IOOkg IJ s~)ut)IoJ
rmiddot A JgtI J~ ~)ll A~
TNT
)wgt r )lj )u )wgt loj )l IS l ~yen ~4
)l sgtloj 10 ~ IS )1 100 I)) l IS Jgt) s~ es l ~ IS J1 )~I uJ 11107 s llgt
LA r li ~ 11 ~ gtJY )U )) to -
)iu )l bull l)b 385 MPa y1y ~ IS ST 52
~ 4 S4R~J f WI nmiddotmiddot 4~ l~ IS ciJ
AC3D8R WI iiAmiddotmiddot 4JI- ~ 01 m llgt
s- ~ li~ IS slj-o 02 m llgt ~ 4 bull ~ raquo 100 4 ~ JL JiL JI- jL
~~ )l Ut u )-I ~ li~ IS ~~ -
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~I Jlgtu
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0 )lI-SlI))l )~I-S) d ) uJb ~
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ltIS )1gt 01A lil bulll ~to pgtA 4 (t25 l tl)uJ
~15 0tS ~ l rlljl 4 l)lt5 )UI
)l ltIS s~)l 01 lt5 lA)b r1jl ~~~ lt5
l d bTr 0tS~ )~I J- )1 ulS I
bTr 0tS ~ )1 rs )l 30 lgtgt (ti) I em
-slAl -sIr 1 (tl5) 25 em l d
-st gtI~ )1gt d 0tS ~ r1 -i )l
~lt5~
A4 Jlo(d A3 Jlo(e
0lo) 04~)l (25 em l) D (l em l)
)~I -s) d ) oIil ~ l -sIr (0002 s) rlll
1 o~ olb 0l lA uJ
~ () () -slAsI l) ~ )l
jI ~ uJ r JIraquoI bli -r )l ltIS 1
-S )l1 lil lt5 ~ r1chll bull1 r lp
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~~ r~l~ ltIS uJ b ~ d ~ )lo)
0loj )l l lt5 ~4 ltIS ~4 1 )~I J- d uJ
lJbL uJ ~ -s) ~ ~j ~ 0002 s )c
middot~4
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D4 Jc(d D3 Jlo(e D2 Jlo(b
)~Isr) 411 eo~ u_)~ 25 em 6 Irs 411 sIr 0002 s
00 05 10
o~----------
12 --------------
Dl Jc(a
~1ol)1) ~~~ ~
05 10 15 20
16 --__________J
r 2 5 2
I 5
II
12m from l()()kgof TNT
12 5
tl t I 5 I
8m from IOOmiddotkg of TNT
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20m from IOO-kgof TNT
loS (~ shy)j )~I JL s~~ siL ~ 4llii r1 )~
~I) ~ ol I~I jyi-o s1A OjL J~ )~ 1
~l ~ 1 ol ~lii ~ sU~ ~
~ ~ oL ~ ~ JlL ) ltcent~ 1Jlb1 ~
)~I o~ JlL kbU sl) sgt~ JIo JlS J~
jyi-o s1A 4lJ sIr 1 ~ s1A jL r i r)
4lJ -h9 ~ ~ -h9 ~ srb ~ Jgtlao I) ~i ~I
Jb 4lJ -h9 ~ ~ Jgtr ~ ~~
~ ~l Nuriek ~ J- f~ Jgtr Ir 12
r1 ~~ db ~ ~)b s~~ ~l ~ ~~~
JoIs )~ ~ )l ~~ ~lj ~I )gt IS 1 IS) ~~ 411 jL l )~I Jgt du ~ Igt ~
~ (~ Jlblgt ji ~ L tt= 411 4 I~ )l lS U Irj l Jlblgt fs)j ejL Jl1
rj eb ~)y ~ ~ ~yO 1)-0 ci~ lS
IS 1 tamp~ 41~~ J110Lj )l ~
4 ejL JlI ~~ 4bt1) ~ ~ ~ r1
~)~I Jgt )1 du
00 05 10 u o~--~----~--~----~
-8
125
12
115 It
16m from IOO-kgof TNT
l AS) As1A JIo 1 sr ji (6) Js )
uo ~ ~ ) Js r1 ) IJIl ltr)r (AS
1 em ~ ~ uJ sIr )~I s) ~ ) uJ 6
60 rlr R I ao ~ IS )~I ~ s1AJb sIr
JiI1gt yS11gt J~I ~ r1 )~ Jlb~ 0~ I) IJ)~
1 -WI) 4S ~1gt (0002 S 0Lj )~) ~ ~
0 05 15
0
-2 E R8-4shy RI2 c 0 -6 RI6
8 =
R20 ~ 0 10
-2 1-_____________---1
- )ltiil lIbSI1So ~ )I~ 0 JSj
Rlao =60
~I ~~ ~ IS ~ Jlbl ) r1 )~
1 sL )~I ~ ~b sIr ~ )l
~lj R lao ~I )~ IS R 411 4 LI (13S3 MPa)
411 r- 0~ ~ bull1 ao 41 ~ ~
~~ ~ ~~ 4 IS 1 r1 i lc IS ~~
uu 411 4 4i Lj ~lj s )l yS11gt
uu 411 ~ )l JItgtlS U rlr~ ~~ 411
) 0Lj -)l ~ rj eb ~~ JItgtlS
~ ~ ~ r1 ~I ~ ~yO Aigt
)~I Jgt )1 d13 ~ jL Jl1 ~~ bL)
~(R)
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rA~ 0 I JG
bulliJ 1oS1W ~ Jw 18ti ~ J~
Model
Charge weight
W(kg)
Distance between charge and pipe
R(m)
Max VonshyMisesstres5
(Numerical)
(MPa)
Max Von-Mises stress
(from Eq (26raquo
(circular plate)
Max Von-Mises stress
(from Eq (32raquo
(rectansular plate)
Max deflection
(Numerical)
d (mm)
Nurick
prediction
(Eq (20raquo
de (mm)
Rajendran
prediction
(Eq (24raquo
de (mm)
Jones
prediction
(Eq (25raquo
de (mm)
Nurick
p ediction
(Eq (28raquo
dr (mm)
Rajendran
prediction
(Eq (30raquo
dr (mm)
Jones
prediction
(Eq (31raquo
dr (mm)
E -
Al
A2
A3
A4 foshy
100
100
100
100
8
12
16
20
40010
33308
25492
20005 ---shy
30320
19470
14212
11131 ------~--
33596
21573
15748
12333
1839
1029
772
591
1808
1328
1079
925 -----shy
1587
975
658
462 ------shy
3044
2121
1641
1345 -____--shy
1923
1340
1038
851
2991
2307
1951
1732
2355
1453
1005
743 ___--shy-shy -
II- A 1509 8 27044 13467 14922 543 706 183 924 584 1419 403
A6 5094 12 25610 14645 16227 753 946 489 13 86 876 1762 778
A7 12074 16 27600 15376 17038 863 1186 795 1848 1168 2105 1195
AS 23581 20 28723 15884 17600 1004 1427 1101 2310 1460 2447 1635
E Bl 100 8 38561 27941 30960 1408 1387 683 2012 1272 2602 1103
B2 100 12 29289 18014 19960 1002 1069 279 1402 887 2150 612
II- B3 100 16 2181 13 186 14610 671 905 070 1085 687 1915 391
B4 100 20 17079 10348 11466 545 803 -060 889 563 1770 273
Cl 100 8 3693 26060 28876 1306 1237 126 15oJ 951 2601 557
sect C2 100 12 2569 16855 18676 889 1000 -176 1047 663 2263 288 N
II- C3 100 16 18871 12365 13701 624 877 -332 810 514 2088 177
C4 100 20 14761 9721 10771 490 8Ql -429 664 421 1979 121
E DI 100 8 33846 24578 27234 1174 1195 -276 12 II 767 2743 313
on D2 100 12 22817 15938 17660 778 1004 -519 844 536 2470 157
N II- OJ 100 16 16739 11713 12978 545 905 -645 653 415 2329 095
D4 100 20 13083 9220 10216 438 844 -723 535 341 2241 064
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I - Cole R H (1948) Underwater explosions NJ USA Princeton University Press
2 - Smith P D and Hetherington J G (1994) Blast and ballistic loading of structures Butterworthshy
Heinemann
3 - Chung M and Brett J (1997) Assessment of underwater blast effects on scaled submerged cylindrical
objects DSTO Aeronautical and Maritime Research Laboratory
4 - Huang H and Wang Y F (1970) Transient interactions of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 48 No1 PP 228-235
5 - Huang H and Wang Y F (1971) Early-time interaction of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 50 No3 PP 885-891
6 - Geers T L and Hunter K S (2002) An integrated wave-effects model for an underwater explosion
bubble Journal ofAcoustical Society ofAmerica Vol III No4 PP 1584-1601
7 - Nurick GN and Martin 1 B (1989) Defurmation of thin plates subjected to impulsive loading-a review
Part I theoritical consideration International Journal ofImpact Engineering Vol 8 No2 PP159-170
8 - Nurick G N and Martin 1 B (1989) Deformation of thin plates subjected to impulsive loading-a review
Part II experimental studies International Journal ofImpact Engineering Vol 8 No2 PP171-186
9 - Teeling-Smith RG and Nurick G N (1991) Deformation and rupture of blast loaded circular platesshy
predictions and experiments International Journal ofImpact Engineering Vol 11 No1 PP77-9
10 - Rajendran R and Narasimhan K (2006) Deformation and fracture behaviour of plate specimens
subjected to underwater explosion-a review International Journal ofImpact Engineering Vol 32 PP1945shy
1963
II - Rajendran R and Narasimhan K (2001) Linear elastic shock response of plane plates subjected to
underwater explosion International Journal ofImpact Engineering Vol 25 PP 493-506
12middot Bangash RY H (1993) Impact and explosion Oxford Blackwell scientific publications
13 bull Lam KY long l and Wang Q X (2003) Dynamic response of a laminated pipeline on the seabed
subjected to underwater shock Composites Part B Vol 34 PP 59-66
14 - Zong l Lam K Y (2000) The flexUral response of a submarine pipeline to an underwater explosion
bubble Journal ofQlJshore Mechanics and Arctic Engineering Vol 122 PP 194middot199
15 - ABAQUS Users Manual (2003) Ver 64
16 - Rajendran R and Narasimhan K (200 I) Performance evaluation of HSLA steel subjected to underwater
explosion ASM Journal ofMaterials Engineering and Performance Vol 10 PP 66-74
jiA )~ lI~liNIl ~ ~ ~11SAt IIjl
1- Explosion 2- High explosive
3- Pressure pulse 4- Shock wave
5middot Bubble pulse 6- Cavitation
7- Peak pressure 8- Coupled acoustic-structural medium analysis
9- Compressible 10- Volumetric drag
11- Inviscid 12- Bulk modulus
)3 Radiating acoustic boundary 14middot Transient analysis
15middot Weak form 16middot Traction
17- Mass proportional damping factor 18- Discretize
19- Strain interpolator 20- Explicit dynamic integration
21- Nonreflecting 22- Impulse
23middot VonmiddotMises 24- Inverse mass number
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ill
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4 I) ~1 bulllol ) is) ~ li s4j)1 iSlr
~ n iSlr d$ ~~ s~ ~I) r
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a iS1orb -6i ) jS ~ iSlr Nuriek
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rj ~ ~ S D H rfgt 111 ~~ JS is) r d$ ltNs --gtr)1 0Lj - )W ~
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1=5760 Will (W) r (rr)
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rfgt 0 1gt1- )) ~b I j i )) )
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r= 125 em = 492 in t=2mm=0079 in W= 30 gr R 30 em P = 1025 kg I m3 = 64 pef Oy = 360 MPa 52 ksi IO = 876 Ns = 1969 Ibs
l1 IS) 142 mm 4 056 in ~
d$ ) IS ci ~)) 0001 s rJlil 0Lj r1rl
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d$ ) IS Jt1 (f rlSai1 ri-) isr is)) ~1
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6E P P 2 X 2l(I-x) (J= pm
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E = 21 e 11 Pa = 439 e 9 psf Pp= 7800 kg m3 48695 pef Pm = 5427 MPa = 11334468 psf
P = 1025 kg 1m3 = 64 pef c = 1463 mls 4800 fils V 03 8=2975ls m=3206psf x= 2851
89698 ksf )I) Cla)~ (r7) J~ jl~)1~
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03 gt~14 ~ sl ~ AIl- )11)gt gt sshy2 )~I JoY)gt 2 mm G 4 X 025 m
) ~ jSyo 30 em ul)gt lNT r )-I )gt (1 i AIl- Lilo )~1 61) gt r sshy
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ul) 41 t ~ sl )b w jSyo 015 ~
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(1 0817lt1gtc (ro)
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1 ~~ JtU xi ltSIrlt1 ~1) jl eTa r- 0
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) )) )ij ~I) ~ wGtA Pr )) ~ [IJI
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cr =0867 2 2P c
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4 ~~ bS Jb lSI) uJJ )rs ~li
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4Ji jI s I )1 ~ 19 )) ~ ))li
liz JJ Jb ) rs -ili roJ 4 4Ji ~l )r rs
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r~J6~~~ ba ~I))I))
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a = 15 em = 591 in b = 125 cm 492 in
~~ ~4 k- J1gtlo 1t0i ~b lSI)
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01 4Jl ~ j1 ) rgt 1 L )) lgt
Jb- r pound ~ I) Jb- w )1 ) ~i ) ~ 21) ~Igt ~4J )) ~ rs ~ 6 x 5 cm
01 131 Ns = 2945 Ihs
Pr IS ~ 17270 )I) ltfgt r ~r~
~1 rs ) ~ 163 mm 4 064 in ~
- ~ wGtA lSI) Rajendran ltS-IrU ~I) lol
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(71 =0553lt1gt +0741
b ~Igt ~I) )1 jb ) 0 = 0813 in 207 mm
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(l =095 [(1+06637lt1gt2)112 -1] (rl)
~ )1 Pr IS ~ lSI) Jones ~~ 1lJ
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r l jl y1y u19 4 ~6kLA)l ~ ~
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ollo tL - u19 ~ 41 olAgt sly IS sl olj -
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bull ciJ )U )) 152 grem3 Ar TNT)~ bull1
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jl bulllli1 4 ~ ~ fr ~ )~I J-- ~
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1) Sr-o rmiddot A u19)l 100 kg TNT - b~r
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20
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0 0 I 20
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)l sgtloj 10 ~ IS )1 100 I)) l IS Jgt) s~ es l ~ IS J1 )~I uJ 11107 s llgt
LA r li ~ 11 ~ gtJY )U )) to -
)iu )l bull l)b 385 MPa y1y ~ IS ST 52
~ 4 S4R~J f WI nmiddotmiddot 4~ l~ IS ciJ
AC3D8R WI iiAmiddotmiddot 4JI- ~ 01 m llgt
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loS (~ shy)j )~I JL s~~ siL ~ 4llii r1 )~
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~ (~ Jlblgt ji ~ L tt= 411 4 I~ )l lS U Irj l Jlblgt fs)j ejL Jl1
rj eb ~)y ~ ~ ~yO 1)-0 ci~ lS
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uo ~ ~ ) Js r1 ) IJIl ltr)r (AS
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1 sL )~I ~ ~b sIr ~ )l
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411 r- 0~ ~ bull1 ao 41 ~ ~
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uu 411 4 4i Lj ~lj s )l yS11gt
uu 411 ~ )l JItgtlS U rlr~ ~~ 411
) 0Lj -)l ~ rj eb ~~ JItgtlS
~ ~ ~ r1 ~I ~ ~yO Aigt
)~I Jgt )1 d13 ~ jL Jl1 ~~ bL)
~(R)
PDF created with pdf Factory Pro trial version wwwpdffactorycom
rA~ 0 I JG
bulliJ 1oS1W ~ Jw 18ti ~ J~
Model
Charge weight
W(kg)
Distance between charge and pipe
R(m)
Max VonshyMisesstres5
(Numerical)
(MPa)
Max Von-Mises stress
(from Eq (26raquo
(circular plate)
Max Von-Mises stress
(from Eq (32raquo
(rectansular plate)
Max deflection
(Numerical)
d (mm)
Nurick
prediction
(Eq (20raquo
de (mm)
Rajendran
prediction
(Eq (24raquo
de (mm)
Jones
prediction
(Eq (25raquo
de (mm)
Nurick
p ediction
(Eq (28raquo
dr (mm)
Rajendran
prediction
(Eq (30raquo
dr (mm)
Jones
prediction
(Eq (31raquo
dr (mm)
E -
Al
A2
A3
A4 foshy
100
100
100
100
8
12
16
20
40010
33308
25492
20005 ---shy
30320
19470
14212
11131 ------~--
33596
21573
15748
12333
1839
1029
772
591
1808
1328
1079
925 -----shy
1587
975
658
462 ------shy
3044
2121
1641
1345 -____--shy
1923
1340
1038
851
2991
2307
1951
1732
2355
1453
1005
743 ___--shy-shy -
II- A 1509 8 27044 13467 14922 543 706 183 924 584 1419 403
A6 5094 12 25610 14645 16227 753 946 489 13 86 876 1762 778
A7 12074 16 27600 15376 17038 863 1186 795 1848 1168 2105 1195
AS 23581 20 28723 15884 17600 1004 1427 1101 2310 1460 2447 1635
E Bl 100 8 38561 27941 30960 1408 1387 683 2012 1272 2602 1103
B2 100 12 29289 18014 19960 1002 1069 279 1402 887 2150 612
II- B3 100 16 2181 13 186 14610 671 905 070 1085 687 1915 391
B4 100 20 17079 10348 11466 545 803 -060 889 563 1770 273
Cl 100 8 3693 26060 28876 1306 1237 126 15oJ 951 2601 557
sect C2 100 12 2569 16855 18676 889 1000 -176 1047 663 2263 288 N
II- C3 100 16 18871 12365 13701 624 877 -332 810 514 2088 177
C4 100 20 14761 9721 10771 490 8Ql -429 664 421 1979 121
E DI 100 8 33846 24578 27234 1174 1195 -276 12 II 767 2743 313
on D2 100 12 22817 15938 17660 778 1004 -519 844 536 2470 157
N II- OJ 100 16 16739 11713 12978 545 905 -645 653 415 2329 095
D4 100 20 13083 9220 10216 438 844 -723 535 341 2241 064
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I - Cole R H (1948) Underwater explosions NJ USA Princeton University Press
2 - Smith P D and Hetherington J G (1994) Blast and ballistic loading of structures Butterworthshy
Heinemann
3 - Chung M and Brett J (1997) Assessment of underwater blast effects on scaled submerged cylindrical
objects DSTO Aeronautical and Maritime Research Laboratory
4 - Huang H and Wang Y F (1970) Transient interactions of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 48 No1 PP 228-235
5 - Huang H and Wang Y F (1971) Early-time interaction of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 50 No3 PP 885-891
6 - Geers T L and Hunter K S (2002) An integrated wave-effects model for an underwater explosion
bubble Journal ofAcoustical Society ofAmerica Vol III No4 PP 1584-1601
7 - Nurick GN and Martin 1 B (1989) Defurmation of thin plates subjected to impulsive loading-a review
Part I theoritical consideration International Journal ofImpact Engineering Vol 8 No2 PP159-170
8 - Nurick G N and Martin 1 B (1989) Deformation of thin plates subjected to impulsive loading-a review
Part II experimental studies International Journal ofImpact Engineering Vol 8 No2 PP171-186
9 - Teeling-Smith RG and Nurick G N (1991) Deformation and rupture of blast loaded circular platesshy
predictions and experiments International Journal ofImpact Engineering Vol 11 No1 PP77-9
10 - Rajendran R and Narasimhan K (2006) Deformation and fracture behaviour of plate specimens
subjected to underwater explosion-a review International Journal ofImpact Engineering Vol 32 PP1945shy
1963
II - Rajendran R and Narasimhan K (2001) Linear elastic shock response of plane plates subjected to
underwater explosion International Journal ofImpact Engineering Vol 25 PP 493-506
12middot Bangash RY H (1993) Impact and explosion Oxford Blackwell scientific publications
13 bull Lam KY long l and Wang Q X (2003) Dynamic response of a laminated pipeline on the seabed
subjected to underwater shock Composites Part B Vol 34 PP 59-66
14 - Zong l Lam K Y (2000) The flexUral response of a submarine pipeline to an underwater explosion
bubble Journal ofQlJshore Mechanics and Arctic Engineering Vol 122 PP 194middot199
15 - ABAQUS Users Manual (2003) Ver 64
16 - Rajendran R and Narasimhan K (200 I) Performance evaluation of HSLA steel subjected to underwater
explosion ASM Journal ofMaterials Engineering and Performance Vol 10 PP 66-74
jiA )~ lI~liNIl ~ ~ ~11SAt IIjl
1- Explosion 2- High explosive
3- Pressure pulse 4- Shock wave
5middot Bubble pulse 6- Cavitation
7- Peak pressure 8- Coupled acoustic-structural medium analysis
9- Compressible 10- Volumetric drag
11- Inviscid 12- Bulk modulus
)3 Radiating acoustic boundary 14middot Transient analysis
15middot Weak form 16middot Traction
17- Mass proportional damping factor 18- Discretize
19- Strain interpolator 20- Explicit dynamic integration
21- Nonreflecting 22- Impulse
23middot VonmiddotMises 24- Inverse mass number
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~ 1 JLgt
)1gt ~~~ )IS bull aL d$ 1gt0Lo
~41S II ~)- 111gt y )1 gtI~
)) J j --gt r r ~ ) 0ts ~ ))
r1r 0ts ~ r1 1fL 1 bull amp-) (f) ~
41S 191 mm
4 I) ~1 bulllol ) is) ~ li s4j)1 iSlr
~ n iSlr d$ ~~ s~ ~I) r
~II 1 rj )~I 1 ~ iSlorb -6i 0ts ~
~IS~lQI
a iS1orb -6i ) jS ~ iSlr Nuriek
[A]I bull)b )~ I) r J)
(7l = 0425Clgtc + 0227 (I )
~ s iSyI~ $ ~L t ~1)rI))
rLwI r ri ~I) )1 d$ 1 iSlrb -6i iSlr
[ ] l11S) ~I iSlIIgtlltgtl
$c 10 (n) 1rrtl(pCl)lll
C1y 1)~ P bull iSl orb ~ tt r
rj ~ ~ S D H rfgt 111 ~~ JS is) r d$ ltNs --gtr)1 0Lj - )W ~
~ I ~ lltgt1 )) rfgt )~IS iSr-fJlftl ~
[ r ] 10Lj lJ ~rj
1()= fP()dt (n)
Ns 1m2 --gt)iris~ ~I) jlli 0 1 IS d$
[ ] ) i ) ll9
1=5760 Will (W) r (rr)
-gtb iSlr 1 m --gtr R kg --gtr W d$
~ isaLgt ~5r CJ- ~~~4 IO
rfgt 0 1gt1- )) ~b I j i )) )
~i ) ~ JS iSlr 110 ~ r~ l )
)gt)~ oll- r1 iSlr bull ~1- is 111gt y1)4 r)ll
r= 125 em = 492 in t=2mm=0079 in W= 30 gr R 30 em P = 1025 kg I m3 = 64 pef Oy = 360 MPa 52 ksi IO = 876 Ns = 1969 Ibs
l1 IS) 142 mm 4 056 in ~
d$ ) IS ci ~)) 0001 s rJlil 0Lj r1rl
)W jl ~L bA jLw J51 ~~ 01 Jltgt )) IS
(~ ~)
jlJW(b Jl4wJW(a ~s~fs
JUS
)br ~ lt11 J )) ~ y iS1IIgt0ts
sr- Jc - ~ JS Jj )~IS
b)) ~ d$ -1l)r1 ~ middot4 ~ll bA 1iI ci 1 jI ) li ~ )) )~I
~li r1 ~lgt ~ ) 0 Jlo Jl-- jl ~
d$ ) IS Jt1 (f rlSai1 ri-) isr is)) ~1
~li r1 j) jl bull )~I D d$ 1 ~ rl
)i ~li Jgtb ~IS )r rts1 0l
0001 s 1 ~~ ci~ jS ~ jS )) ~
1 bull 1 0~ (f) ~ )) ~ iSW ) jI
PDF created with pdf Factory Pro trial version WINWpdffactorycom
6E P P 2 X 2l(I-x) (J= pm
a p2 C 2 (I-v)
c ~)L9 p ~ ~~ Jlo E ) )gt lt45 n shy
~ sl) rr-gtltgt ltJ~ xI)gtr 41 )I) lt45 1
(rv)X= m
~~ ~I rr- m lojli 8 )1)gt lt45
fO-)gt AIl- )11 sl) 1
E = 21 e 11 Pa = 439 e 9 psf Pp= 7800 kg m3 48695 pef Pm = 5427 MPa = 11334468 psf
P = 1025 kg 1m3 = 64 pef c = 1463 mls 4800 fils V 03 8=2975ls m=3206psf x= 2851
89698 ksf )I) Cla)~ (r7) J~ jl~)1~
Ak)l lt45 )J )w ~1 s- ~ 4295 MPa ~
jI lt45 1 ltSII~ ~ ~gt )~ )~ )11 gtsshy(4176 MPa) 1 bulllo1 gt ~ sltgt ~
shy oJII OM -1lt10OM bullbull
(11
-WjS)srlulo-ulSo~)) f~
U1b0 ~~ cSJ J~t ~J~ lNT )~I jI r1 5 (Z I o-j )11 )gt
~ r))5f gt~14 ~~~ s) ~li gt~ ltSIrlt1 11) 4 ~l bulli ~ Lil
03 gt~14 ~ sl ~ AIl- )11)gt gt sshy2 )~I JoY)gt 2 mm G 4 X 025 m
) ~ jSyo 30 em ul)gt lNT r )-I )gt (1 i AIl- Lilo )~1 61) gt r sshy
bull)1s ))))) I~ JoY)) ~~~ 4shy ~ gt~I)w 4 ~~ ) ~i
Jlo Jl ~ s~1 )s- Jlo 20 em JJ
)) ~ bulll J 10 em u(j )) bullbull~
bulljL 5- ~ s)Iil 1A0W1tY gtrsshy
s )11 ~ Rajendran b s~) ~I)
[7] 1 ~ )~
(rf)(1 =0541lt1gtc -0433
~ 065 in )I) )15 ~ ~I) )11 ltJLI ) lt45
~i s- gt ~ 166 mm
~~~ sl) ~ ~I) ji Jones ll
ul) 41 t ~ sl )b w jSyo 015 ~
[ ] 1 ) )11 ~ lt45 1 o)b
(1 0817lt1gtc (ro)
)15 ~ sl) Jones ~ ~ ~ )-~
264 JgtL 104 in (rO) ~I) ~~ )-I yo
~i s- gt ~ mm
~ ltSIrlt1 11) )s-~)l lt45 )Lo)w
sjLJlo ~l 4 ~gt ~ ~ s1A ~ xgtli ltSIrlt1 11) s lAr )11 4 lagt s- ul) s)o
sgtltgt ~l jl 5raquo)1 x)li ~ 11) 5f
bulllagt s- ~
s) ~ )~I r~r- ) (0) Js ))
s )J )w ) s- oul 0001 S jl ~~
1 ~ )) yo - ~ LA w jl gt s- o~gt
Ii- s s)Lo ~ )s- )4j ~ so6- )J ~
)1Jc s1 ~~yo jlLAy )gt
S jIs ~4 ~ w ~l3 y 61 Iilsshy
JS s-sr ~ )lj1
utraquo) -wsj) ~u~ lJj O~
0001 s
)I) ~ yo )gt r- ) ~jSl
~jSl sl o)b w sl) 1 4176 MPa
1 ~~ JtU xi ltSIrlt1 ~1) jl eTa r- 0
[ ]
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m ~ I jki
~~~ lol bull ))) ISjL JAo 4~ J)lgt1
AI) rs ltlSI) 1S)j I~ Jones
~ IS) bull )~I ~ 9 ~ (V) Js )) ~) ~ )6 lA ) rs bullAIL OOOls jI ~
~Ijl Pr ~ liz y ~ )S )b ~ )rs
~ ~ gtIA Jlii ~ )) lol ~Irs
y sfbl ~ ~Ir lamp ~ ~Irs ~ ))gt
4~
JiIJi ~ Pr )) ~ 9 ~ ~Plo
~Plo 1SJi lSI bull)i1) wGtA lo 143502 MPa
) )) )ij ~I) ~ wGtA Pr )) ~ [IJI
214EPp Pm 2 X (I-x)
cr =0867 2 2P c
)~ 1 (n) ~I) lo ~I) )1 ISUI~
I 99389 ksf )I) a a )li (rn J jl ~
~ jl ~~ ~ ~i rs ) ~ 4759 MPa
1 IS))amp JAo
~ IIgt uJ I) Y yl yj )~1 1 ~)Y bti1 ~Lul A IIgt ~~ ) -~
-1 rs ~ JJ jI ~ ISU JAo ~ )1 ))
middot4 ltsA)) 1SLs jacket ~~ jl ~
roA 4 ltr)) 1 )j )~I I bull ISjLJAo
4 ~~ bS Jb lSI) uJJ )rs ~li
4 TNT ~ bull)lo ~ ~~ ISlIzLgtt
4Ji jI s I )1 ~ 19 )) ~ ))li
liz JJ Jb ) rs -ili roJ 4 4Ji ~l )r rs
10 ) x4 Jb 1 80 cm ~ibS IO m ~
) sfbl ~ ~Ir ~ bull Gil gtIgt )1 ~ ( m
I) I) roS bull) rs ci )ii)) )br oS JJ r
)lampI)lJ ~loj ~)Ik- w lo J~
~ 4 ~ Pr ~ )~I ~ 4A ) s-Ihj )
Jilb middot4 rs k- JL lo )~I ~I ~I -
1 r- ~Pr IS~ i) 1 (I) Js
)1 ~Plo 1 bull 1) (7) Js )) loj ~
1 163 mm )IJi IS ~
wGtA Pr Js ~ lSI) Nurick ~~
[A]I)j w) ~ ~
(7 =0471lt1gt +0001 ((A)
1 ~ wGtA lSI) ~ ltS-I 14 lt1gt
~i rs ) ~ rj ~I) jI ~I ISU~I ltJLI)
[ J
lt1gt = 01 2t 2 (4abpCT y )1I2
r~J6~~~ ba ~I))I))
~crI))~~~
a = 15 em = 591 in b = 125 cm 492 in
~~ ~4 k- J1gtlo 1t0i ~b lSI)
1 Pr)) s I )) ~~y ry -
01 4Jl ~ j1 ) rgt 1 L )) lgt
Jb- r pound ~ I) Jb- w )1 ) ~i ) ~ 21) ~Igt ~4J )) ~ rs ~ 6 x 5 cm
01 131 Ns = 2945 Ihs
Pr IS ~ 17270 )I) ltfgt r ~r~
~1 rs ) ~ 163 mm 4 064 in ~
- ~ wGtA lSI) Rajendran ltS-IrU ~I) lol
[17] I)) w)
(71 =0553lt1gt +0741
b ~Igt ~I) )1 jb ) 0 = 0813 in 207 mm
- Js~~ Jones ~~~ ltJLI )
r ~ J6 ~ 4 ~ wGtA lSI) t
[1 J I)j w) ~ 12
(l =095 [(1+06637lt1gt2)112 -1] (rl)
~ )1 Pr IS ~ lSI) Jones ~~ 1lJ
) ~ 250 mm J)L 098 in (r) ~I) ~
4 ltS-Igt )~ Jlbi Nurick ~I) )IJi~ ~1 rs
~~ r- Rajendaran ~~ ))b IS))amp JAo
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l )-Iy ~ ltS4)l sts ~ st ~4 jl
~ IS l~ IS ciJ )U)l )br-f w) - 41 s~1
1 )U 10 1 6 )l 0 jL ~4 ~I - ~
bOj ~I~ - ~~~ ~I jI )l I~
I) I) ~ 91)01 lli )1gt - IS JI- jl ~
JI- jl -i ~ l)I Jilo bulll~ IS JIo ciJ
)l D JIo ~s1 ~ ) - ~ 91)01
ri=- s y Sir br li )-I s=raquo ~ ~ )l t ~ )-I ~ ~ l~ IS Jwl rlSu1
~ 11slj ~ - JI IS li~ IS Jraquo ~1 jI
9r ~ l)-II jl )-Iy li)l 4)) ~ ~1
ciJ )U )l r ~lgt u-l4 I ~~ l IS )U
IS ~l t ~ s) s es I bOj l~ ~
rlY 10 )-I )l ~ ~4 IS r-Jlii Lj 10 l
bull1 0002 s y1y bull
~L st JIo ~l ~ () J~ )l
r-oL riO li 6 4 st ~ 1 0101 bull
JI~ )-I )l lil 0 s)lS Ili D li A 4~ -
~ (in (I) ~I) jl ~ ~flo
~ Jraquo 4 bull ~ ltS~ ~I) I 0lli1 4 LS
~ t ~ )i ~ ~ 4 y1y )i ~ sl o)b
12 JIgt~)i ~ ~ y1yJgtr 4 ~ Nuriek ~I)S )1 - 1 0 6 Jgtr y1y
s~ es I Sly s~ ~l ~ Ib l A Sly
(25 em) ~ st 6 )l 41 bulllAl IS l -
i l rmiddot llgt )l1 ~~~ byr ~I)
Sly l IS s)amp ~l )I 5s ~)l fmiddot li imiddot llgt ( 1 15 em) ~4 st 6 Sly
~ )) imiddot li rmiddot llgt )~ st 6 Sly ~))
bull ~ IS )1gt 100 ~ Slamp ~l I 5s R lao = 60 4 )~II 1 em 6 4~ Sly
r)Y li)b sgt~ s )lj ~~ )l IS
0101 (A8 li A5 st JIo) () J~ )) i ~l
(TNT j ~ ~ ) u19 JI)I 4~ II 1
- ~ )l lol l4 IS JI)I LS ~
li)Ili ~ 4 slj 9)tgt1 ~l bull l) )) oJ
bullIgttgt JI)I 4 IS 1 )-I ~l )tJ1 kLi ~
() st jgt )l ~l1S J-AgtIS LS ~
A st JIo sly ~ - ~ ()
)-I r)Y l) IS bull1 6 )l ~ J-li ~ S)
) - ~1 ~ 91)01 ~4 ~b 1 ~
l IS JIo 0jL ~I 22 m uli li sl oljl-I
r-oL 25 2 bull 15 bull 1 sUt6 4 t ~ IS Oly 100 kg TNT o~ DlL lil D ~lgt1
jl sr-o 20 16 12 8 JI )l ~ 6 A Sly
r l jl y1y u19 4 ~6kLA)l ~ ~
~ Sly Ut JIo )-I y ojs 1 bull bull lb 1) (i
slA- j 4 TNT bull~ OlL bull 1 em Igttgt 4 bull1 bull r)Y sr-o 20 l 8 J1)lJ
ollo tL - u19 ~ 41 olAgt sly IS sl olj -
~I ~yen kLi ( R lao = 60 ) 1 60 y1y 0~
bull ciJ )U )) 152 grem3 Ar TNT)~ bull1
~ to )-s)~)ls~)lj sgtLj ~)li
jl bulllli1 4 ~ ~ fr ~ )~I J-- ~
)~ IS JLs1 P(t) Pm - byr r~ ~I) 100
s )lj sgtLj ~)li olj~ sly (A) JS )l
1) Sr-o rmiddot A u19)l 100 kg TNT - b~r
360
~
ii ~
R=20m
20
lU
0 0 I 20
Time (IJIt)
IOOkg IJ s~)ut)IoJ
rmiddot A JgtI J~ ~)ll A~
TNT
)wgt r )lj )u )wgt loj )l IS l ~yen ~4
)l sgtloj 10 ~ IS )1 100 I)) l IS Jgt) s~ es l ~ IS J1 )~I uJ 11107 s llgt
LA r li ~ 11 ~ gtJY )U )) to -
)iu )l bull l)b 385 MPa y1y ~ IS ST 52
~ 4 S4R~J f WI nmiddotmiddot 4~ l~ IS ciJ
AC3D8R WI iiAmiddotmiddot 4JI- ~ 01 m llgt
s- ~ li~ IS slj-o 02 m llgt ~ 4 bull ~ raquo 100 4 ~ JL JiL JI- jL
~~ )l Ut u )-I ~ li~ IS ~~ -
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~I Jlgtu
0tS ~ )l ( f) l ( ) -S1As)l
0 )lI-SlI))l )~I-S) d ) uJb ~
)l (1 ~ r-- )l 0tS ~ oaC ltIS) s J -SlA l -SIr bull~ ollo )IJ JoIs
ltIS )1gt 01A lil bulll ~to pgtA 4 (t25 l tl)uJ
~15 0tS ~ l rlljl 4 l)lt5 )UI
)l ltIS s~)l 01 lt5 lA)b r1jl ~~~ lt5
l d bTr 0tS~ )~I J- )1 ulS I
bTr 0tS ~ )1 rs )l 30 lgtgt (ti) I em
-slAl -sIr 1 (tl5) 25 em l d
-st gtI~ )1gt d 0tS ~ r1 -i )l
~lt5~
A4 Jlo(d A3 Jlo(e
0lo) 04~)l (25 em l) D (l em l)
)~I -s) d ) oIil ~ l -sIr (0002 s) rlll
1 o~ olb 0l lA uJ
~ () () -slAsI l) ~ )l
jI ~ uJ r JIraquoI bli -r )l ltIS 1
-S )l1 lil lt5 ~ r1chll bull1 r lp
)ts r-gtu 4 )lz9 ~)l ~t s (s
~~ r~l~ ltIS uJ b ~ d ~ )lo)
0loj )l l lt5 ~4 ltIS ~4 1 )~I J- d uJ
lJbL uJ ~ -s) ~ ~j ~ 0002 s )c
middot~4
A2 Jc(b Al Jc (a
D4 Jc(d D3 Jlo(e D2 Jlo(b
)~Isr) 411 eo~ u_)~ 25 em 6 Irs 411 sIr 0002 s
00 05 10
o~----------
12 --------------
Dl Jc(a
~1ol)1) ~~~ ~
05 10 15 20
16 --__________J
r 2 5 2
I 5
II
12m from l()()kgof TNT
12 5
tl t I 5 I
8m from IOOmiddotkg of TNT
PDF created with pdfFactory Pro trial version wwwpdffactorvcom
20m from IOO-kgof TNT
loS (~ shy)j )~I JL s~~ siL ~ 4llii r1 )~
~I) ~ ol I~I jyi-o s1A OjL J~ )~ 1
~l ~ 1 ol ~lii ~ sU~ ~
~ ~ oL ~ ~ JlL ) ltcent~ 1Jlb1 ~
)~I o~ JlL kbU sl) sgt~ JIo JlS J~
jyi-o s1A 4lJ sIr 1 ~ s1A jL r i r)
4lJ -h9 ~ ~ -h9 ~ srb ~ Jgtlao I) ~i ~I
Jb 4lJ -h9 ~ ~ Jgtr ~ ~~
~ ~l Nuriek ~ J- f~ Jgtr Ir 12
r1 ~~ db ~ ~)b s~~ ~l ~ ~~~
JoIs )~ ~ )l ~~ ~lj ~I )gt IS 1 IS) ~~ 411 jL l )~I Jgt du ~ Igt ~
~ (~ Jlblgt ji ~ L tt= 411 4 I~ )l lS U Irj l Jlblgt fs)j ejL Jl1
rj eb ~)y ~ ~ ~yO 1)-0 ci~ lS
IS 1 tamp~ 41~~ J110Lj )l ~
4 ejL JlI ~~ 4bt1) ~ ~ ~ r1
~)~I Jgt )1 du
00 05 10 u o~--~----~--~----~
-8
125
12
115 It
16m from IOO-kgof TNT
l AS) As1A JIo 1 sr ji (6) Js )
uo ~ ~ ) Js r1 ) IJIl ltr)r (AS
1 em ~ ~ uJ sIr )~I s) ~ ) uJ 6
60 rlr R I ao ~ IS )~I ~ s1AJb sIr
JiI1gt yS11gt J~I ~ r1 )~ Jlb~ 0~ I) IJ)~
1 -WI) 4S ~1gt (0002 S 0Lj )~) ~ ~
0 05 15
0
-2 E R8-4shy RI2 c 0 -6 RI6
8 =
R20 ~ 0 10
-2 1-_____________---1
- )ltiil lIbSI1So ~ )I~ 0 JSj
Rlao =60
~I ~~ ~ IS ~ Jlbl ) r1 )~
1 sL )~I ~ ~b sIr ~ )l
~lj R lao ~I )~ IS R 411 4 LI (13S3 MPa)
411 r- 0~ ~ bull1 ao 41 ~ ~
~~ ~ ~~ 4 IS 1 r1 i lc IS ~~
uu 411 4 4i Lj ~lj s )l yS11gt
uu 411 ~ )l JItgtlS U rlr~ ~~ 411
) 0Lj -)l ~ rj eb ~~ JItgtlS
~ ~ ~ r1 ~I ~ ~yO Aigt
)~I Jgt )1 d13 ~ jL Jl1 ~~ bL)
~(R)
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rA~ 0 I JG
bulliJ 1oS1W ~ Jw 18ti ~ J~
Model
Charge weight
W(kg)
Distance between charge and pipe
R(m)
Max VonshyMisesstres5
(Numerical)
(MPa)
Max Von-Mises stress
(from Eq (26raquo
(circular plate)
Max Von-Mises stress
(from Eq (32raquo
(rectansular plate)
Max deflection
(Numerical)
d (mm)
Nurick
prediction
(Eq (20raquo
de (mm)
Rajendran
prediction
(Eq (24raquo
de (mm)
Jones
prediction
(Eq (25raquo
de (mm)
Nurick
p ediction
(Eq (28raquo
dr (mm)
Rajendran
prediction
(Eq (30raquo
dr (mm)
Jones
prediction
(Eq (31raquo
dr (mm)
E -
Al
A2
A3
A4 foshy
100
100
100
100
8
12
16
20
40010
33308
25492
20005 ---shy
30320
19470
14212
11131 ------~--
33596
21573
15748
12333
1839
1029
772
591
1808
1328
1079
925 -----shy
1587
975
658
462 ------shy
3044
2121
1641
1345 -____--shy
1923
1340
1038
851
2991
2307
1951
1732
2355
1453
1005
743 ___--shy-shy -
II- A 1509 8 27044 13467 14922 543 706 183 924 584 1419 403
A6 5094 12 25610 14645 16227 753 946 489 13 86 876 1762 778
A7 12074 16 27600 15376 17038 863 1186 795 1848 1168 2105 1195
AS 23581 20 28723 15884 17600 1004 1427 1101 2310 1460 2447 1635
E Bl 100 8 38561 27941 30960 1408 1387 683 2012 1272 2602 1103
B2 100 12 29289 18014 19960 1002 1069 279 1402 887 2150 612
II- B3 100 16 2181 13 186 14610 671 905 070 1085 687 1915 391
B4 100 20 17079 10348 11466 545 803 -060 889 563 1770 273
Cl 100 8 3693 26060 28876 1306 1237 126 15oJ 951 2601 557
sect C2 100 12 2569 16855 18676 889 1000 -176 1047 663 2263 288 N
II- C3 100 16 18871 12365 13701 624 877 -332 810 514 2088 177
C4 100 20 14761 9721 10771 490 8Ql -429 664 421 1979 121
E DI 100 8 33846 24578 27234 1174 1195 -276 12 II 767 2743 313
on D2 100 12 22817 15938 17660 778 1004 -519 844 536 2470 157
N II- OJ 100 16 16739 11713 12978 545 905 -645 653 415 2329 095
D4 100 20 13083 9220 10216 438 844 -723 535 341 2241 064
PDF created with pdfFactory Pro trial version wwwpdffactorycom
I - Cole R H (1948) Underwater explosions NJ USA Princeton University Press
2 - Smith P D and Hetherington J G (1994) Blast and ballistic loading of structures Butterworthshy
Heinemann
3 - Chung M and Brett J (1997) Assessment of underwater blast effects on scaled submerged cylindrical
objects DSTO Aeronautical and Maritime Research Laboratory
4 - Huang H and Wang Y F (1970) Transient interactions of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 48 No1 PP 228-235
5 - Huang H and Wang Y F (1971) Early-time interaction of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 50 No3 PP 885-891
6 - Geers T L and Hunter K S (2002) An integrated wave-effects model for an underwater explosion
bubble Journal ofAcoustical Society ofAmerica Vol III No4 PP 1584-1601
7 - Nurick GN and Martin 1 B (1989) Defurmation of thin plates subjected to impulsive loading-a review
Part I theoritical consideration International Journal ofImpact Engineering Vol 8 No2 PP159-170
8 - Nurick G N and Martin 1 B (1989) Deformation of thin plates subjected to impulsive loading-a review
Part II experimental studies International Journal ofImpact Engineering Vol 8 No2 PP171-186
9 - Teeling-Smith RG and Nurick G N (1991) Deformation and rupture of blast loaded circular platesshy
predictions and experiments International Journal ofImpact Engineering Vol 11 No1 PP77-9
10 - Rajendran R and Narasimhan K (2006) Deformation and fracture behaviour of plate specimens
subjected to underwater explosion-a review International Journal ofImpact Engineering Vol 32 PP1945shy
1963
II - Rajendran R and Narasimhan K (2001) Linear elastic shock response of plane plates subjected to
underwater explosion International Journal ofImpact Engineering Vol 25 PP 493-506
12middot Bangash RY H (1993) Impact and explosion Oxford Blackwell scientific publications
13 bull Lam KY long l and Wang Q X (2003) Dynamic response of a laminated pipeline on the seabed
subjected to underwater shock Composites Part B Vol 34 PP 59-66
14 - Zong l Lam K Y (2000) The flexUral response of a submarine pipeline to an underwater explosion
bubble Journal ofQlJshore Mechanics and Arctic Engineering Vol 122 PP 194middot199
15 - ABAQUS Users Manual (2003) Ver 64
16 - Rajendran R and Narasimhan K (200 I) Performance evaluation of HSLA steel subjected to underwater
explosion ASM Journal ofMaterials Engineering and Performance Vol 10 PP 66-74
jiA )~ lI~liNIl ~ ~ ~11SAt IIjl
1- Explosion 2- High explosive
3- Pressure pulse 4- Shock wave
5middot Bubble pulse 6- Cavitation
7- Peak pressure 8- Coupled acoustic-structural medium analysis
9- Compressible 10- Volumetric drag
11- Inviscid 12- Bulk modulus
)3 Radiating acoustic boundary 14middot Transient analysis
15middot Weak form 16middot Traction
17- Mass proportional damping factor 18- Discretize
19- Strain interpolator 20- Explicit dynamic integration
21- Nonreflecting 22- Impulse
23middot VonmiddotMises 24- Inverse mass number
PDF created with pdf Factory Pro trial version wwwpdffactorvcom
6E P P 2 X 2l(I-x) (J= pm
a p2 C 2 (I-v)
c ~)L9 p ~ ~~ Jlo E ) )gt lt45 n shy
~ sl) rr-gtltgt ltJ~ xI)gtr 41 )I) lt45 1
(rv)X= m
~~ ~I rr- m lojli 8 )1)gt lt45
fO-)gt AIl- )11 sl) 1
E = 21 e 11 Pa = 439 e 9 psf Pp= 7800 kg m3 48695 pef Pm = 5427 MPa = 11334468 psf
P = 1025 kg 1m3 = 64 pef c = 1463 mls 4800 fils V 03 8=2975ls m=3206psf x= 2851
89698 ksf )I) Cla)~ (r7) J~ jl~)1~
Ak)l lt45 )J )w ~1 s- ~ 4295 MPa ~
jI lt45 1 ltSII~ ~ ~gt )~ )~ )11 gtsshy(4176 MPa) 1 bulllo1 gt ~ sltgt ~
shy oJII OM -1lt10OM bullbull
(11
-WjS)srlulo-ulSo~)) f~
U1b0 ~~ cSJ J~t ~J~ lNT )~I jI r1 5 (Z I o-j )11 )gt
~ r))5f gt~14 ~~~ s) ~li gt~ ltSIrlt1 11) 4 ~l bulli ~ Lil
03 gt~14 ~ sl ~ AIl- )11)gt gt sshy2 )~I JoY)gt 2 mm G 4 X 025 m
) ~ jSyo 30 em ul)gt lNT r )-I )gt (1 i AIl- Lilo )~1 61) gt r sshy
bull)1s ))))) I~ JoY)) ~~~ 4shy ~ gt~I)w 4 ~~ ) ~i
Jlo Jl ~ s~1 )s- Jlo 20 em JJ
)) ~ bulll J 10 em u(j )) bullbull~
bulljL 5- ~ s)Iil 1A0W1tY gtrsshy
s )11 ~ Rajendran b s~) ~I)
[7] 1 ~ )~
(rf)(1 =0541lt1gtc -0433
~ 065 in )I) )15 ~ ~I) )11 ltJLI ) lt45
~i s- gt ~ 166 mm
~~~ sl) ~ ~I) ji Jones ll
ul) 41 t ~ sl )b w jSyo 015 ~
[ ] 1 ) )11 ~ lt45 1 o)b
(1 0817lt1gtc (ro)
)15 ~ sl) Jones ~ ~ ~ )-~
264 JgtL 104 in (rO) ~I) ~~ )-I yo
~i s- gt ~ mm
~ ltSIrlt1 11) )s-~)l lt45 )Lo)w
sjLJlo ~l 4 ~gt ~ ~ s1A ~ xgtli ltSIrlt1 11) s lAr )11 4 lagt s- ul) s)o
sgtltgt ~l jl 5raquo)1 x)li ~ 11) 5f
bulllagt s- ~
s) ~ )~I r~r- ) (0) Js ))
s )J )w ) s- oul 0001 S jl ~~
1 ~ )) yo - ~ LA w jl gt s- o~gt
Ii- s s)Lo ~ )s- )4j ~ so6- )J ~
)1Jc s1 ~~yo jlLAy )gt
S jIs ~4 ~ w ~l3 y 61 Iilsshy
JS s-sr ~ )lj1
utraquo) -wsj) ~u~ lJj O~
0001 s
)I) ~ yo )gt r- ) ~jSl
~jSl sl o)b w sl) 1 4176 MPa
1 ~~ JtU xi ltSIrlt1 ~1) jl eTa r- 0
[ ]
PDF created with pdf Factory Pro trial version wwwpdffactorvcom
m ~ I jki
~~~ lol bull ))) ISjL JAo 4~ J)lgt1
AI) rs ltlSI) 1S)j I~ Jones
~ IS) bull )~I ~ 9 ~ (V) Js )) ~) ~ )6 lA ) rs bullAIL OOOls jI ~
~Ijl Pr ~ liz y ~ )S )b ~ )rs
~ ~ gtIA Jlii ~ )) lol ~Irs
y sfbl ~ ~Ir lamp ~ ~Irs ~ ))gt
4~
JiIJi ~ Pr )) ~ 9 ~ ~Plo
~Plo 1SJi lSI bull)i1) wGtA lo 143502 MPa
) )) )ij ~I) ~ wGtA Pr )) ~ [IJI
214EPp Pm 2 X (I-x)
cr =0867 2 2P c
)~ 1 (n) ~I) lo ~I) )1 ISUI~
I 99389 ksf )I) a a )li (rn J jl ~
~ jl ~~ ~ ~i rs ) ~ 4759 MPa
1 IS))amp JAo
~ IIgt uJ I) Y yl yj )~1 1 ~)Y bti1 ~Lul A IIgt ~~ ) -~
-1 rs ~ JJ jI ~ ISU JAo ~ )1 ))
middot4 ltsA)) 1SLs jacket ~~ jl ~
roA 4 ltr)) 1 )j )~I I bull ISjLJAo
4 ~~ bS Jb lSI) uJJ )rs ~li
4 TNT ~ bull)lo ~ ~~ ISlIzLgtt
4Ji jI s I )1 ~ 19 )) ~ ))li
liz JJ Jb ) rs -ili roJ 4 4Ji ~l )r rs
10 ) x4 Jb 1 80 cm ~ibS IO m ~
) sfbl ~ ~Ir ~ bull Gil gtIgt )1 ~ ( m
I) I) roS bull) rs ci )ii)) )br oS JJ r
)lampI)lJ ~loj ~)Ik- w lo J~
~ 4 ~ Pr ~ )~I ~ 4A ) s-Ihj )
Jilb middot4 rs k- JL lo )~I ~I ~I -
1 r- ~Pr IS~ i) 1 (I) Js
)1 ~Plo 1 bull 1) (7) Js )) loj ~
1 163 mm )IJi IS ~
wGtA Pr Js ~ lSI) Nurick ~~
[A]I)j w) ~ ~
(7 =0471lt1gt +0001 ((A)
1 ~ wGtA lSI) ~ ltS-I 14 lt1gt
~i rs ) ~ rj ~I) jI ~I ISU~I ltJLI)
[ J
lt1gt = 01 2t 2 (4abpCT y )1I2
r~J6~~~ ba ~I))I))
~crI))~~~
a = 15 em = 591 in b = 125 cm 492 in
~~ ~4 k- J1gtlo 1t0i ~b lSI)
1 Pr)) s I )) ~~y ry -
01 4Jl ~ j1 ) rgt 1 L )) lgt
Jb- r pound ~ I) Jb- w )1 ) ~i ) ~ 21) ~Igt ~4J )) ~ rs ~ 6 x 5 cm
01 131 Ns = 2945 Ihs
Pr IS ~ 17270 )I) ltfgt r ~r~
~1 rs ) ~ 163 mm 4 064 in ~
- ~ wGtA lSI) Rajendran ltS-IrU ~I) lol
[17] I)) w)
(71 =0553lt1gt +0741
b ~Igt ~I) )1 jb ) 0 = 0813 in 207 mm
- Js~~ Jones ~~~ ltJLI )
r ~ J6 ~ 4 ~ wGtA lSI) t
[1 J I)j w) ~ 12
(l =095 [(1+06637lt1gt2)112 -1] (rl)
~ )1 Pr IS ~ lSI) Jones ~~ 1lJ
) ~ 250 mm J)L 098 in (r) ~I) ~
4 ltS-Igt )~ Jlbi Nurick ~I) )IJi~ ~1 rs
~~ r- Rajendaran ~~ ))b IS))amp JAo
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l )-Iy ~ ltS4)l sts ~ st ~4 jl
~ IS l~ IS ciJ )U)l )br-f w) - 41 s~1
1 )U 10 1 6 )l 0 jL ~4 ~I - ~
bOj ~I~ - ~~~ ~I jI )l I~
I) I) ~ 91)01 lli )1gt - IS JI- jl ~
JI- jl -i ~ l)I Jilo bulll~ IS JIo ciJ
)l D JIo ~s1 ~ ) - ~ 91)01
ri=- s y Sir br li )-I s=raquo ~ ~ )l t ~ )-I ~ ~ l~ IS Jwl rlSu1
~ 11slj ~ - JI IS li~ IS Jraquo ~1 jI
9r ~ l)-II jl )-Iy li)l 4)) ~ ~1
ciJ )U )l r ~lgt u-l4 I ~~ l IS )U
IS ~l t ~ s) s es I bOj l~ ~
rlY 10 )-I )l ~ ~4 IS r-Jlii Lj 10 l
bull1 0002 s y1y bull
~L st JIo ~l ~ () J~ )l
r-oL riO li 6 4 st ~ 1 0101 bull
JI~ )-I )l lil 0 s)lS Ili D li A 4~ -
~ (in (I) ~I) jl ~ ~flo
~ Jraquo 4 bull ~ ltS~ ~I) I 0lli1 4 LS
~ t ~ )i ~ ~ 4 y1y )i ~ sl o)b
12 JIgt~)i ~ ~ y1yJgtr 4 ~ Nuriek ~I)S )1 - 1 0 6 Jgtr y1y
s~ es I Sly s~ ~l ~ Ib l A Sly
(25 em) ~ st 6 )l 41 bulllAl IS l -
i l rmiddot llgt )l1 ~~~ byr ~I)
Sly l IS s)amp ~l )I 5s ~)l fmiddot li imiddot llgt ( 1 15 em) ~4 st 6 Sly
~ )) imiddot li rmiddot llgt )~ st 6 Sly ~))
bull ~ IS )1gt 100 ~ Slamp ~l I 5s R lao = 60 4 )~II 1 em 6 4~ Sly
r)Y li)b sgt~ s )lj ~~ )l IS
0101 (A8 li A5 st JIo) () J~ )) i ~l
(TNT j ~ ~ ) u19 JI)I 4~ II 1
- ~ )l lol l4 IS JI)I LS ~
li)Ili ~ 4 slj 9)tgt1 ~l bull l) )) oJ
bullIgttgt JI)I 4 IS 1 )-I ~l )tJ1 kLi ~
() st jgt )l ~l1S J-AgtIS LS ~
A st JIo sly ~ - ~ ()
)-I r)Y l) IS bull1 6 )l ~ J-li ~ S)
) - ~1 ~ 91)01 ~4 ~b 1 ~
l IS JIo 0jL ~I 22 m uli li sl oljl-I
r-oL 25 2 bull 15 bull 1 sUt6 4 t ~ IS Oly 100 kg TNT o~ DlL lil D ~lgt1
jl sr-o 20 16 12 8 JI )l ~ 6 A Sly
r l jl y1y u19 4 ~6kLA)l ~ ~
~ Sly Ut JIo )-I y ojs 1 bull bull lb 1) (i
slA- j 4 TNT bull~ OlL bull 1 em Igttgt 4 bull1 bull r)Y sr-o 20 l 8 J1)lJ
ollo tL - u19 ~ 41 olAgt sly IS sl olj -
~I ~yen kLi ( R lao = 60 ) 1 60 y1y 0~
bull ciJ )U )) 152 grem3 Ar TNT)~ bull1
~ to )-s)~)ls~)lj sgtLj ~)li
jl bulllli1 4 ~ ~ fr ~ )~I J-- ~
)~ IS JLs1 P(t) Pm - byr r~ ~I) 100
s )lj sgtLj ~)li olj~ sly (A) JS )l
1) Sr-o rmiddot A u19)l 100 kg TNT - b~r
360
~
ii ~
R=20m
20
lU
0 0 I 20
Time (IJIt)
IOOkg IJ s~)ut)IoJ
rmiddot A JgtI J~ ~)ll A~
TNT
)wgt r )lj )u )wgt loj )l IS l ~yen ~4
)l sgtloj 10 ~ IS )1 100 I)) l IS Jgt) s~ es l ~ IS J1 )~I uJ 11107 s llgt
LA r li ~ 11 ~ gtJY )U )) to -
)iu )l bull l)b 385 MPa y1y ~ IS ST 52
~ 4 S4R~J f WI nmiddotmiddot 4~ l~ IS ciJ
AC3D8R WI iiAmiddotmiddot 4JI- ~ 01 m llgt
s- ~ li~ IS slj-o 02 m llgt ~ 4 bull ~ raquo 100 4 ~ JL JiL JI- jL
~~ )l Ut u )-I ~ li~ IS ~~ -
PDF created with pdf Factory Pro trial version wwwpdffactorvcom
~I Jlgtu
0tS ~ )l ( f) l ( ) -S1As)l
0 )lI-SlI))l )~I-S) d ) uJb ~
)l (1 ~ r-- )l 0tS ~ oaC ltIS) s J -SlA l -SIr bull~ ollo )IJ JoIs
ltIS )1gt 01A lil bulll ~to pgtA 4 (t25 l tl)uJ
~15 0tS ~ l rlljl 4 l)lt5 )UI
)l ltIS s~)l 01 lt5 lA)b r1jl ~~~ lt5
l d bTr 0tS~ )~I J- )1 ulS I
bTr 0tS ~ )1 rs )l 30 lgtgt (ti) I em
-slAl -sIr 1 (tl5) 25 em l d
-st gtI~ )1gt d 0tS ~ r1 -i )l
~lt5~
A4 Jlo(d A3 Jlo(e
0lo) 04~)l (25 em l) D (l em l)
)~I -s) d ) oIil ~ l -sIr (0002 s) rlll
1 o~ olb 0l lA uJ
~ () () -slAsI l) ~ )l
jI ~ uJ r JIraquoI bli -r )l ltIS 1
-S )l1 lil lt5 ~ r1chll bull1 r lp
)ts r-gtu 4 )lz9 ~)l ~t s (s
~~ r~l~ ltIS uJ b ~ d ~ )lo)
0loj )l l lt5 ~4 ltIS ~4 1 )~I J- d uJ
lJbL uJ ~ -s) ~ ~j ~ 0002 s )c
middot~4
A2 Jc(b Al Jc (a
D4 Jc(d D3 Jlo(e D2 Jlo(b
)~Isr) 411 eo~ u_)~ 25 em 6 Irs 411 sIr 0002 s
00 05 10
o~----------
12 --------------
Dl Jc(a
~1ol)1) ~~~ ~
05 10 15 20
16 --__________J
r 2 5 2
I 5
II
12m from l()()kgof TNT
12 5
tl t I 5 I
8m from IOOmiddotkg of TNT
PDF created with pdfFactory Pro trial version wwwpdffactorvcom
20m from IOO-kgof TNT
loS (~ shy)j )~I JL s~~ siL ~ 4llii r1 )~
~I) ~ ol I~I jyi-o s1A OjL J~ )~ 1
~l ~ 1 ol ~lii ~ sU~ ~
~ ~ oL ~ ~ JlL ) ltcent~ 1Jlb1 ~
)~I o~ JlL kbU sl) sgt~ JIo JlS J~
jyi-o s1A 4lJ sIr 1 ~ s1A jL r i r)
4lJ -h9 ~ ~ -h9 ~ srb ~ Jgtlao I) ~i ~I
Jb 4lJ -h9 ~ ~ Jgtr ~ ~~
~ ~l Nuriek ~ J- f~ Jgtr Ir 12
r1 ~~ db ~ ~)b s~~ ~l ~ ~~~
JoIs )~ ~ )l ~~ ~lj ~I )gt IS 1 IS) ~~ 411 jL l )~I Jgt du ~ Igt ~
~ (~ Jlblgt ji ~ L tt= 411 4 I~ )l lS U Irj l Jlblgt fs)j ejL Jl1
rj eb ~)y ~ ~ ~yO 1)-0 ci~ lS
IS 1 tamp~ 41~~ J110Lj )l ~
4 ejL JlI ~~ 4bt1) ~ ~ ~ r1
~)~I Jgt )1 du
00 05 10 u o~--~----~--~----~
-8
125
12
115 It
16m from IOO-kgof TNT
l AS) As1A JIo 1 sr ji (6) Js )
uo ~ ~ ) Js r1 ) IJIl ltr)r (AS
1 em ~ ~ uJ sIr )~I s) ~ ) uJ 6
60 rlr R I ao ~ IS )~I ~ s1AJb sIr
JiI1gt yS11gt J~I ~ r1 )~ Jlb~ 0~ I) IJ)~
1 -WI) 4S ~1gt (0002 S 0Lj )~) ~ ~
0 05 15
0
-2 E R8-4shy RI2 c 0 -6 RI6
8 =
R20 ~ 0 10
-2 1-_____________---1
- )ltiil lIbSI1So ~ )I~ 0 JSj
Rlao =60
~I ~~ ~ IS ~ Jlbl ) r1 )~
1 sL )~I ~ ~b sIr ~ )l
~lj R lao ~I )~ IS R 411 4 LI (13S3 MPa)
411 r- 0~ ~ bull1 ao 41 ~ ~
~~ ~ ~~ 4 IS 1 r1 i lc IS ~~
uu 411 4 4i Lj ~lj s )l yS11gt
uu 411 ~ )l JItgtlS U rlr~ ~~ 411
) 0Lj -)l ~ rj eb ~~ JItgtlS
~ ~ ~ r1 ~I ~ ~yO Aigt
)~I Jgt )1 d13 ~ jL Jl1 ~~ bL)
~(R)
PDF created with pdf Factory Pro trial version wwwpdffactorycom
rA~ 0 I JG
bulliJ 1oS1W ~ Jw 18ti ~ J~
Model
Charge weight
W(kg)
Distance between charge and pipe
R(m)
Max VonshyMisesstres5
(Numerical)
(MPa)
Max Von-Mises stress
(from Eq (26raquo
(circular plate)
Max Von-Mises stress
(from Eq (32raquo
(rectansular plate)
Max deflection
(Numerical)
d (mm)
Nurick
prediction
(Eq (20raquo
de (mm)
Rajendran
prediction
(Eq (24raquo
de (mm)
Jones
prediction
(Eq (25raquo
de (mm)
Nurick
p ediction
(Eq (28raquo
dr (mm)
Rajendran
prediction
(Eq (30raquo
dr (mm)
Jones
prediction
(Eq (31raquo
dr (mm)
E -
Al
A2
A3
A4 foshy
100
100
100
100
8
12
16
20
40010
33308
25492
20005 ---shy
30320
19470
14212
11131 ------~--
33596
21573
15748
12333
1839
1029
772
591
1808
1328
1079
925 -----shy
1587
975
658
462 ------shy
3044
2121
1641
1345 -____--shy
1923
1340
1038
851
2991
2307
1951
1732
2355
1453
1005
743 ___--shy-shy -
II- A 1509 8 27044 13467 14922 543 706 183 924 584 1419 403
A6 5094 12 25610 14645 16227 753 946 489 13 86 876 1762 778
A7 12074 16 27600 15376 17038 863 1186 795 1848 1168 2105 1195
AS 23581 20 28723 15884 17600 1004 1427 1101 2310 1460 2447 1635
E Bl 100 8 38561 27941 30960 1408 1387 683 2012 1272 2602 1103
B2 100 12 29289 18014 19960 1002 1069 279 1402 887 2150 612
II- B3 100 16 2181 13 186 14610 671 905 070 1085 687 1915 391
B4 100 20 17079 10348 11466 545 803 -060 889 563 1770 273
Cl 100 8 3693 26060 28876 1306 1237 126 15oJ 951 2601 557
sect C2 100 12 2569 16855 18676 889 1000 -176 1047 663 2263 288 N
II- C3 100 16 18871 12365 13701 624 877 -332 810 514 2088 177
C4 100 20 14761 9721 10771 490 8Ql -429 664 421 1979 121
E DI 100 8 33846 24578 27234 1174 1195 -276 12 II 767 2743 313
on D2 100 12 22817 15938 17660 778 1004 -519 844 536 2470 157
N II- OJ 100 16 16739 11713 12978 545 905 -645 653 415 2329 095
D4 100 20 13083 9220 10216 438 844 -723 535 341 2241 064
PDF created with pdfFactory Pro trial version wwwpdffactorycom
I - Cole R H (1948) Underwater explosions NJ USA Princeton University Press
2 - Smith P D and Hetherington J G (1994) Blast and ballistic loading of structures Butterworthshy
Heinemann
3 - Chung M and Brett J (1997) Assessment of underwater blast effects on scaled submerged cylindrical
objects DSTO Aeronautical and Maritime Research Laboratory
4 - Huang H and Wang Y F (1970) Transient interactions of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 48 No1 PP 228-235
5 - Huang H and Wang Y F (1971) Early-time interaction of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 50 No3 PP 885-891
6 - Geers T L and Hunter K S (2002) An integrated wave-effects model for an underwater explosion
bubble Journal ofAcoustical Society ofAmerica Vol III No4 PP 1584-1601
7 - Nurick GN and Martin 1 B (1989) Defurmation of thin plates subjected to impulsive loading-a review
Part I theoritical consideration International Journal ofImpact Engineering Vol 8 No2 PP159-170
8 - Nurick G N and Martin 1 B (1989) Deformation of thin plates subjected to impulsive loading-a review
Part II experimental studies International Journal ofImpact Engineering Vol 8 No2 PP171-186
9 - Teeling-Smith RG and Nurick G N (1991) Deformation and rupture of blast loaded circular platesshy
predictions and experiments International Journal ofImpact Engineering Vol 11 No1 PP77-9
10 - Rajendran R and Narasimhan K (2006) Deformation and fracture behaviour of plate specimens
subjected to underwater explosion-a review International Journal ofImpact Engineering Vol 32 PP1945shy
1963
II - Rajendran R and Narasimhan K (2001) Linear elastic shock response of plane plates subjected to
underwater explosion International Journal ofImpact Engineering Vol 25 PP 493-506
12middot Bangash RY H (1993) Impact and explosion Oxford Blackwell scientific publications
13 bull Lam KY long l and Wang Q X (2003) Dynamic response of a laminated pipeline on the seabed
subjected to underwater shock Composites Part B Vol 34 PP 59-66
14 - Zong l Lam K Y (2000) The flexUral response of a submarine pipeline to an underwater explosion
bubble Journal ofQlJshore Mechanics and Arctic Engineering Vol 122 PP 194middot199
15 - ABAQUS Users Manual (2003) Ver 64
16 - Rajendran R and Narasimhan K (200 I) Performance evaluation of HSLA steel subjected to underwater
explosion ASM Journal ofMaterials Engineering and Performance Vol 10 PP 66-74
jiA )~ lI~liNIl ~ ~ ~11SAt IIjl
1- Explosion 2- High explosive
3- Pressure pulse 4- Shock wave
5middot Bubble pulse 6- Cavitation
7- Peak pressure 8- Coupled acoustic-structural medium analysis
9- Compressible 10- Volumetric drag
11- Inviscid 12- Bulk modulus
)3 Radiating acoustic boundary 14middot Transient analysis
15middot Weak form 16middot Traction
17- Mass proportional damping factor 18- Discretize
19- Strain interpolator 20- Explicit dynamic integration
21- Nonreflecting 22- Impulse
23middot VonmiddotMises 24- Inverse mass number
PDF created with pdf Factory Pro trial version wwwpdffactorvcom
m ~ I jki
~~~ lol bull ))) ISjL JAo 4~ J)lgt1
AI) rs ltlSI) 1S)j I~ Jones
~ IS) bull )~I ~ 9 ~ (V) Js )) ~) ~ )6 lA ) rs bullAIL OOOls jI ~
~Ijl Pr ~ liz y ~ )S )b ~ )rs
~ ~ gtIA Jlii ~ )) lol ~Irs
y sfbl ~ ~Ir lamp ~ ~Irs ~ ))gt
4~
JiIJi ~ Pr )) ~ 9 ~ ~Plo
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rA~ 0 I JG
bulliJ 1oS1W ~ Jw 18ti ~ J~
Model
Charge weight
W(kg)
Distance between charge and pipe
R(m)
Max VonshyMisesstres5
(Numerical)
(MPa)
Max Von-Mises stress
(from Eq (26raquo
(circular plate)
Max Von-Mises stress
(from Eq (32raquo
(rectansular plate)
Max deflection
(Numerical)
d (mm)
Nurick
prediction
(Eq (20raquo
de (mm)
Rajendran
prediction
(Eq (24raquo
de (mm)
Jones
prediction
(Eq (25raquo
de (mm)
Nurick
p ediction
(Eq (28raquo
dr (mm)
Rajendran
prediction
(Eq (30raquo
dr (mm)
Jones
prediction
(Eq (31raquo
dr (mm)
E -
Al
A2
A3
A4 foshy
100
100
100
100
8
12
16
20
40010
33308
25492
20005 ---shy
30320
19470
14212
11131 ------~--
33596
21573
15748
12333
1839
1029
772
591
1808
1328
1079
925 -----shy
1587
975
658
462 ------shy
3044
2121
1641
1345 -____--shy
1923
1340
1038
851
2991
2307
1951
1732
2355
1453
1005
743 ___--shy-shy -
II- A 1509 8 27044 13467 14922 543 706 183 924 584 1419 403
A6 5094 12 25610 14645 16227 753 946 489 13 86 876 1762 778
A7 12074 16 27600 15376 17038 863 1186 795 1848 1168 2105 1195
AS 23581 20 28723 15884 17600 1004 1427 1101 2310 1460 2447 1635
E Bl 100 8 38561 27941 30960 1408 1387 683 2012 1272 2602 1103
B2 100 12 29289 18014 19960 1002 1069 279 1402 887 2150 612
II- B3 100 16 2181 13 186 14610 671 905 070 1085 687 1915 391
B4 100 20 17079 10348 11466 545 803 -060 889 563 1770 273
Cl 100 8 3693 26060 28876 1306 1237 126 15oJ 951 2601 557
sect C2 100 12 2569 16855 18676 889 1000 -176 1047 663 2263 288 N
II- C3 100 16 18871 12365 13701 624 877 -332 810 514 2088 177
C4 100 20 14761 9721 10771 490 8Ql -429 664 421 1979 121
E DI 100 8 33846 24578 27234 1174 1195 -276 12 II 767 2743 313
on D2 100 12 22817 15938 17660 778 1004 -519 844 536 2470 157
N II- OJ 100 16 16739 11713 12978 545 905 -645 653 415 2329 095
D4 100 20 13083 9220 10216 438 844 -723 535 341 2241 064
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I - Cole R H (1948) Underwater explosions NJ USA Princeton University Press
2 - Smith P D and Hetherington J G (1994) Blast and ballistic loading of structures Butterworthshy
Heinemann
3 - Chung M and Brett J (1997) Assessment of underwater blast effects on scaled submerged cylindrical
objects DSTO Aeronautical and Maritime Research Laboratory
4 - Huang H and Wang Y F (1970) Transient interactions of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 48 No1 PP 228-235
5 - Huang H and Wang Y F (1971) Early-time interaction of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 50 No3 PP 885-891
6 - Geers T L and Hunter K S (2002) An integrated wave-effects model for an underwater explosion
bubble Journal ofAcoustical Society ofAmerica Vol III No4 PP 1584-1601
7 - Nurick GN and Martin 1 B (1989) Defurmation of thin plates subjected to impulsive loading-a review
Part I theoritical consideration International Journal ofImpact Engineering Vol 8 No2 PP159-170
8 - Nurick G N and Martin 1 B (1989) Deformation of thin plates subjected to impulsive loading-a review
Part II experimental studies International Journal ofImpact Engineering Vol 8 No2 PP171-186
9 - Teeling-Smith RG and Nurick G N (1991) Deformation and rupture of blast loaded circular platesshy
predictions and experiments International Journal ofImpact Engineering Vol 11 No1 PP77-9
10 - Rajendran R and Narasimhan K (2006) Deformation and fracture behaviour of plate specimens
subjected to underwater explosion-a review International Journal ofImpact Engineering Vol 32 PP1945shy
1963
II - Rajendran R and Narasimhan K (2001) Linear elastic shock response of plane plates subjected to
underwater explosion International Journal ofImpact Engineering Vol 25 PP 493-506
12middot Bangash RY H (1993) Impact and explosion Oxford Blackwell scientific publications
13 bull Lam KY long l and Wang Q X (2003) Dynamic response of a laminated pipeline on the seabed
subjected to underwater shock Composites Part B Vol 34 PP 59-66
14 - Zong l Lam K Y (2000) The flexUral response of a submarine pipeline to an underwater explosion
bubble Journal ofQlJshore Mechanics and Arctic Engineering Vol 122 PP 194middot199
15 - ABAQUS Users Manual (2003) Ver 64
16 - Rajendran R and Narasimhan K (200 I) Performance evaluation of HSLA steel subjected to underwater
explosion ASM Journal ofMaterials Engineering and Performance Vol 10 PP 66-74
jiA )~ lI~liNIl ~ ~ ~11SAt IIjl
1- Explosion 2- High explosive
3- Pressure pulse 4- Shock wave
5middot Bubble pulse 6- Cavitation
7- Peak pressure 8- Coupled acoustic-structural medium analysis
9- Compressible 10- Volumetric drag
11- Inviscid 12- Bulk modulus
)3 Radiating acoustic boundary 14middot Transient analysis
15middot Weak form 16middot Traction
17- Mass proportional damping factor 18- Discretize
19- Strain interpolator 20- Explicit dynamic integration
21- Nonreflecting 22- Impulse
23middot VonmiddotMises 24- Inverse mass number
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r l jl y1y u19 4 ~6kLA)l ~ ~
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R20 ~ 0 10
-2 1-_____________---1
- )ltiil lIbSI1So ~ )I~ 0 JSj
Rlao =60
~I ~~ ~ IS ~ Jlbl ) r1 )~
1 sL )~I ~ ~b sIr ~ )l
~lj R lao ~I )~ IS R 411 4 LI (13S3 MPa)
411 r- 0~ ~ bull1 ao 41 ~ ~
~~ ~ ~~ 4 IS 1 r1 i lc IS ~~
uu 411 4 4i Lj ~lj s )l yS11gt
uu 411 ~ )l JItgtlS U rlr~ ~~ 411
) 0Lj -)l ~ rj eb ~~ JItgtlS
~ ~ ~ r1 ~I ~ ~yO Aigt
)~I Jgt )1 d13 ~ jL Jl1 ~~ bL)
~(R)
PDF created with pdf Factory Pro trial version wwwpdffactorycom
rA~ 0 I JG
bulliJ 1oS1W ~ Jw 18ti ~ J~
Model
Charge weight
W(kg)
Distance between charge and pipe
R(m)
Max VonshyMisesstres5
(Numerical)
(MPa)
Max Von-Mises stress
(from Eq (26raquo
(circular plate)
Max Von-Mises stress
(from Eq (32raquo
(rectansular plate)
Max deflection
(Numerical)
d (mm)
Nurick
prediction
(Eq (20raquo
de (mm)
Rajendran
prediction
(Eq (24raquo
de (mm)
Jones
prediction
(Eq (25raquo
de (mm)
Nurick
p ediction
(Eq (28raquo
dr (mm)
Rajendran
prediction
(Eq (30raquo
dr (mm)
Jones
prediction
(Eq (31raquo
dr (mm)
E -
Al
A2
A3
A4 foshy
100
100
100
100
8
12
16
20
40010
33308
25492
20005 ---shy
30320
19470
14212
11131 ------~--
33596
21573
15748
12333
1839
1029
772
591
1808
1328
1079
925 -----shy
1587
975
658
462 ------shy
3044
2121
1641
1345 -____--shy
1923
1340
1038
851
2991
2307
1951
1732
2355
1453
1005
743 ___--shy-shy -
II- A 1509 8 27044 13467 14922 543 706 183 924 584 1419 403
A6 5094 12 25610 14645 16227 753 946 489 13 86 876 1762 778
A7 12074 16 27600 15376 17038 863 1186 795 1848 1168 2105 1195
AS 23581 20 28723 15884 17600 1004 1427 1101 2310 1460 2447 1635
E Bl 100 8 38561 27941 30960 1408 1387 683 2012 1272 2602 1103
B2 100 12 29289 18014 19960 1002 1069 279 1402 887 2150 612
II- B3 100 16 2181 13 186 14610 671 905 070 1085 687 1915 391
B4 100 20 17079 10348 11466 545 803 -060 889 563 1770 273
Cl 100 8 3693 26060 28876 1306 1237 126 15oJ 951 2601 557
sect C2 100 12 2569 16855 18676 889 1000 -176 1047 663 2263 288 N
II- C3 100 16 18871 12365 13701 624 877 -332 810 514 2088 177
C4 100 20 14761 9721 10771 490 8Ql -429 664 421 1979 121
E DI 100 8 33846 24578 27234 1174 1195 -276 12 II 767 2743 313
on D2 100 12 22817 15938 17660 778 1004 -519 844 536 2470 157
N II- OJ 100 16 16739 11713 12978 545 905 -645 653 415 2329 095
D4 100 20 13083 9220 10216 438 844 -723 535 341 2241 064
PDF created with pdfFactory Pro trial version wwwpdffactorycom
I - Cole R H (1948) Underwater explosions NJ USA Princeton University Press
2 - Smith P D and Hetherington J G (1994) Blast and ballistic loading of structures Butterworthshy
Heinemann
3 - Chung M and Brett J (1997) Assessment of underwater blast effects on scaled submerged cylindrical
objects DSTO Aeronautical and Maritime Research Laboratory
4 - Huang H and Wang Y F (1970) Transient interactions of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 48 No1 PP 228-235
5 - Huang H and Wang Y F (1971) Early-time interaction of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 50 No3 PP 885-891
6 - Geers T L and Hunter K S (2002) An integrated wave-effects model for an underwater explosion
bubble Journal ofAcoustical Society ofAmerica Vol III No4 PP 1584-1601
7 - Nurick GN and Martin 1 B (1989) Defurmation of thin plates subjected to impulsive loading-a review
Part I theoritical consideration International Journal ofImpact Engineering Vol 8 No2 PP159-170
8 - Nurick G N and Martin 1 B (1989) Deformation of thin plates subjected to impulsive loading-a review
Part II experimental studies International Journal ofImpact Engineering Vol 8 No2 PP171-186
9 - Teeling-Smith RG and Nurick G N (1991) Deformation and rupture of blast loaded circular platesshy
predictions and experiments International Journal ofImpact Engineering Vol 11 No1 PP77-9
10 - Rajendran R and Narasimhan K (2006) Deformation and fracture behaviour of plate specimens
subjected to underwater explosion-a review International Journal ofImpact Engineering Vol 32 PP1945shy
1963
II - Rajendran R and Narasimhan K (2001) Linear elastic shock response of plane plates subjected to
underwater explosion International Journal ofImpact Engineering Vol 25 PP 493-506
12middot Bangash RY H (1993) Impact and explosion Oxford Blackwell scientific publications
13 bull Lam KY long l and Wang Q X (2003) Dynamic response of a laminated pipeline on the seabed
subjected to underwater shock Composites Part B Vol 34 PP 59-66
14 - Zong l Lam K Y (2000) The flexUral response of a submarine pipeline to an underwater explosion
bubble Journal ofQlJshore Mechanics and Arctic Engineering Vol 122 PP 194middot199
15 - ABAQUS Users Manual (2003) Ver 64
16 - Rajendran R and Narasimhan K (200 I) Performance evaluation of HSLA steel subjected to underwater
explosion ASM Journal ofMaterials Engineering and Performance Vol 10 PP 66-74
jiA )~ lI~liNIl ~ ~ ~11SAt IIjl
1- Explosion 2- High explosive
3- Pressure pulse 4- Shock wave
5middot Bubble pulse 6- Cavitation
7- Peak pressure 8- Coupled acoustic-structural medium analysis
9- Compressible 10- Volumetric drag
11- Inviscid 12- Bulk modulus
)3 Radiating acoustic boundary 14middot Transient analysis
15middot Weak form 16middot Traction
17- Mass proportional damping factor 18- Discretize
19- Strain interpolator 20- Explicit dynamic integration
21- Nonreflecting 22- Impulse
23middot VonmiddotMises 24- Inverse mass number
PDF created with pdf Factory Pro trial version wwwpdffactorvcom
~I Jlgtu
0tS ~ )l ( f) l ( ) -S1As)l
0 )lI-SlI))l )~I-S) d ) uJb ~
)l (1 ~ r-- )l 0tS ~ oaC ltIS) s J -SlA l -SIr bull~ ollo )IJ JoIs
ltIS )1gt 01A lil bulll ~to pgtA 4 (t25 l tl)uJ
~15 0tS ~ l rlljl 4 l)lt5 )UI
)l ltIS s~)l 01 lt5 lA)b r1jl ~~~ lt5
l d bTr 0tS~ )~I J- )1 ulS I
bTr 0tS ~ )1 rs )l 30 lgtgt (ti) I em
-slAl -sIr 1 (tl5) 25 em l d
-st gtI~ )1gt d 0tS ~ r1 -i )l
~lt5~
A4 Jlo(d A3 Jlo(e
0lo) 04~)l (25 em l) D (l em l)
)~I -s) d ) oIil ~ l -sIr (0002 s) rlll
1 o~ olb 0l lA uJ
~ () () -slAsI l) ~ )l
jI ~ uJ r JIraquoI bli -r )l ltIS 1
-S )l1 lil lt5 ~ r1chll bull1 r lp
)ts r-gtu 4 )lz9 ~)l ~t s (s
~~ r~l~ ltIS uJ b ~ d ~ )lo)
0loj )l l lt5 ~4 ltIS ~4 1 )~I J- d uJ
lJbL uJ ~ -s) ~ ~j ~ 0002 s )c
middot~4
A2 Jc(b Al Jc (a
D4 Jc(d D3 Jlo(e D2 Jlo(b
)~Isr) 411 eo~ u_)~ 25 em 6 Irs 411 sIr 0002 s
00 05 10
o~----------
12 --------------
Dl Jc(a
~1ol)1) ~~~ ~
05 10 15 20
16 --__________J
r 2 5 2
I 5
II
12m from l()()kgof TNT
12 5
tl t I 5 I
8m from IOOmiddotkg of TNT
PDF created with pdfFactory Pro trial version wwwpdffactorvcom
20m from IOO-kgof TNT
loS (~ shy)j )~I JL s~~ siL ~ 4llii r1 )~
~I) ~ ol I~I jyi-o s1A OjL J~ )~ 1
~l ~ 1 ol ~lii ~ sU~ ~
~ ~ oL ~ ~ JlL ) ltcent~ 1Jlb1 ~
)~I o~ JlL kbU sl) sgt~ JIo JlS J~
jyi-o s1A 4lJ sIr 1 ~ s1A jL r i r)
4lJ -h9 ~ ~ -h9 ~ srb ~ Jgtlao I) ~i ~I
Jb 4lJ -h9 ~ ~ Jgtr ~ ~~
~ ~l Nuriek ~ J- f~ Jgtr Ir 12
r1 ~~ db ~ ~)b s~~ ~l ~ ~~~
JoIs )~ ~ )l ~~ ~lj ~I )gt IS 1 IS) ~~ 411 jL l )~I Jgt du ~ Igt ~
~ (~ Jlblgt ji ~ L tt= 411 4 I~ )l lS U Irj l Jlblgt fs)j ejL Jl1
rj eb ~)y ~ ~ ~yO 1)-0 ci~ lS
IS 1 tamp~ 41~~ J110Lj )l ~
4 ejL JlI ~~ 4bt1) ~ ~ ~ r1
~)~I Jgt )1 du
00 05 10 u o~--~----~--~----~
-8
125
12
115 It
16m from IOO-kgof TNT
l AS) As1A JIo 1 sr ji (6) Js )
uo ~ ~ ) Js r1 ) IJIl ltr)r (AS
1 em ~ ~ uJ sIr )~I s) ~ ) uJ 6
60 rlr R I ao ~ IS )~I ~ s1AJb sIr
JiI1gt yS11gt J~I ~ r1 )~ Jlb~ 0~ I) IJ)~
1 -WI) 4S ~1gt (0002 S 0Lj )~) ~ ~
0 05 15
0
-2 E R8-4shy RI2 c 0 -6 RI6
8 =
R20 ~ 0 10
-2 1-_____________---1
- )ltiil lIbSI1So ~ )I~ 0 JSj
Rlao =60
~I ~~ ~ IS ~ Jlbl ) r1 )~
1 sL )~I ~ ~b sIr ~ )l
~lj R lao ~I )~ IS R 411 4 LI (13S3 MPa)
411 r- 0~ ~ bull1 ao 41 ~ ~
~~ ~ ~~ 4 IS 1 r1 i lc IS ~~
uu 411 4 4i Lj ~lj s )l yS11gt
uu 411 ~ )l JItgtlS U rlr~ ~~ 411
) 0Lj -)l ~ rj eb ~~ JItgtlS
~ ~ ~ r1 ~I ~ ~yO Aigt
)~I Jgt )1 d13 ~ jL Jl1 ~~ bL)
~(R)
PDF created with pdf Factory Pro trial version wwwpdffactorycom
rA~ 0 I JG
bulliJ 1oS1W ~ Jw 18ti ~ J~
Model
Charge weight
W(kg)
Distance between charge and pipe
R(m)
Max VonshyMisesstres5
(Numerical)
(MPa)
Max Von-Mises stress
(from Eq (26raquo
(circular plate)
Max Von-Mises stress
(from Eq (32raquo
(rectansular plate)
Max deflection
(Numerical)
d (mm)
Nurick
prediction
(Eq (20raquo
de (mm)
Rajendran
prediction
(Eq (24raquo
de (mm)
Jones
prediction
(Eq (25raquo
de (mm)
Nurick
p ediction
(Eq (28raquo
dr (mm)
Rajendran
prediction
(Eq (30raquo
dr (mm)
Jones
prediction
(Eq (31raquo
dr (mm)
E -
Al
A2
A3
A4 foshy
100
100
100
100
8
12
16
20
40010
33308
25492
20005 ---shy
30320
19470
14212
11131 ------~--
33596
21573
15748
12333
1839
1029
772
591
1808
1328
1079
925 -----shy
1587
975
658
462 ------shy
3044
2121
1641
1345 -____--shy
1923
1340
1038
851
2991
2307
1951
1732
2355
1453
1005
743 ___--shy-shy -
II- A 1509 8 27044 13467 14922 543 706 183 924 584 1419 403
A6 5094 12 25610 14645 16227 753 946 489 13 86 876 1762 778
A7 12074 16 27600 15376 17038 863 1186 795 1848 1168 2105 1195
AS 23581 20 28723 15884 17600 1004 1427 1101 2310 1460 2447 1635
E Bl 100 8 38561 27941 30960 1408 1387 683 2012 1272 2602 1103
B2 100 12 29289 18014 19960 1002 1069 279 1402 887 2150 612
II- B3 100 16 2181 13 186 14610 671 905 070 1085 687 1915 391
B4 100 20 17079 10348 11466 545 803 -060 889 563 1770 273
Cl 100 8 3693 26060 28876 1306 1237 126 15oJ 951 2601 557
sect C2 100 12 2569 16855 18676 889 1000 -176 1047 663 2263 288 N
II- C3 100 16 18871 12365 13701 624 877 -332 810 514 2088 177
C4 100 20 14761 9721 10771 490 8Ql -429 664 421 1979 121
E DI 100 8 33846 24578 27234 1174 1195 -276 12 II 767 2743 313
on D2 100 12 22817 15938 17660 778 1004 -519 844 536 2470 157
N II- OJ 100 16 16739 11713 12978 545 905 -645 653 415 2329 095
D4 100 20 13083 9220 10216 438 844 -723 535 341 2241 064
PDF created with pdfFactory Pro trial version wwwpdffactorycom
I - Cole R H (1948) Underwater explosions NJ USA Princeton University Press
2 - Smith P D and Hetherington J G (1994) Blast and ballistic loading of structures Butterworthshy
Heinemann
3 - Chung M and Brett J (1997) Assessment of underwater blast effects on scaled submerged cylindrical
objects DSTO Aeronautical and Maritime Research Laboratory
4 - Huang H and Wang Y F (1970) Transient interactions of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 48 No1 PP 228-235
5 - Huang H and Wang Y F (1971) Early-time interaction of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 50 No3 PP 885-891
6 - Geers T L and Hunter K S (2002) An integrated wave-effects model for an underwater explosion
bubble Journal ofAcoustical Society ofAmerica Vol III No4 PP 1584-1601
7 - Nurick GN and Martin 1 B (1989) Defurmation of thin plates subjected to impulsive loading-a review
Part I theoritical consideration International Journal ofImpact Engineering Vol 8 No2 PP159-170
8 - Nurick G N and Martin 1 B (1989) Deformation of thin plates subjected to impulsive loading-a review
Part II experimental studies International Journal ofImpact Engineering Vol 8 No2 PP171-186
9 - Teeling-Smith RG and Nurick G N (1991) Deformation and rupture of blast loaded circular platesshy
predictions and experiments International Journal ofImpact Engineering Vol 11 No1 PP77-9
10 - Rajendran R and Narasimhan K (2006) Deformation and fracture behaviour of plate specimens
subjected to underwater explosion-a review International Journal ofImpact Engineering Vol 32 PP1945shy
1963
II - Rajendran R and Narasimhan K (2001) Linear elastic shock response of plane plates subjected to
underwater explosion International Journal ofImpact Engineering Vol 25 PP 493-506
12middot Bangash RY H (1993) Impact and explosion Oxford Blackwell scientific publications
13 bull Lam KY long l and Wang Q X (2003) Dynamic response of a laminated pipeline on the seabed
subjected to underwater shock Composites Part B Vol 34 PP 59-66
14 - Zong l Lam K Y (2000) The flexUral response of a submarine pipeline to an underwater explosion
bubble Journal ofQlJshore Mechanics and Arctic Engineering Vol 122 PP 194middot199
15 - ABAQUS Users Manual (2003) Ver 64
16 - Rajendran R and Narasimhan K (200 I) Performance evaluation of HSLA steel subjected to underwater
explosion ASM Journal ofMaterials Engineering and Performance Vol 10 PP 66-74
jiA )~ lI~liNIl ~ ~ ~11SAt IIjl
1- Explosion 2- High explosive
3- Pressure pulse 4- Shock wave
5middot Bubble pulse 6- Cavitation
7- Peak pressure 8- Coupled acoustic-structural medium analysis
9- Compressible 10- Volumetric drag
11- Inviscid 12- Bulk modulus
)3 Radiating acoustic boundary 14middot Transient analysis
15middot Weak form 16middot Traction
17- Mass proportional damping factor 18- Discretize
19- Strain interpolator 20- Explicit dynamic integration
21- Nonreflecting 22- Impulse
23middot VonmiddotMises 24- Inverse mass number
PDF created with pdf Factory Pro trial version wwwpdffactorvcom
20m from IOO-kgof TNT
loS (~ shy)j )~I JL s~~ siL ~ 4llii r1 )~
~I) ~ ol I~I jyi-o s1A OjL J~ )~ 1
~l ~ 1 ol ~lii ~ sU~ ~
~ ~ oL ~ ~ JlL ) ltcent~ 1Jlb1 ~
)~I o~ JlL kbU sl) sgt~ JIo JlS J~
jyi-o s1A 4lJ sIr 1 ~ s1A jL r i r)
4lJ -h9 ~ ~ -h9 ~ srb ~ Jgtlao I) ~i ~I
Jb 4lJ -h9 ~ ~ Jgtr ~ ~~
~ ~l Nuriek ~ J- f~ Jgtr Ir 12
r1 ~~ db ~ ~)b s~~ ~l ~ ~~~
JoIs )~ ~ )l ~~ ~lj ~I )gt IS 1 IS) ~~ 411 jL l )~I Jgt du ~ Igt ~
~ (~ Jlblgt ji ~ L tt= 411 4 I~ )l lS U Irj l Jlblgt fs)j ejL Jl1
rj eb ~)y ~ ~ ~yO 1)-0 ci~ lS
IS 1 tamp~ 41~~ J110Lj )l ~
4 ejL JlI ~~ 4bt1) ~ ~ ~ r1
~)~I Jgt )1 du
00 05 10 u o~--~----~--~----~
-8
125
12
115 It
16m from IOO-kgof TNT
l AS) As1A JIo 1 sr ji (6) Js )
uo ~ ~ ) Js r1 ) IJIl ltr)r (AS
1 em ~ ~ uJ sIr )~I s) ~ ) uJ 6
60 rlr R I ao ~ IS )~I ~ s1AJb sIr
JiI1gt yS11gt J~I ~ r1 )~ Jlb~ 0~ I) IJ)~
1 -WI) 4S ~1gt (0002 S 0Lj )~) ~ ~
0 05 15
0
-2 E R8-4shy RI2 c 0 -6 RI6
8 =
R20 ~ 0 10
-2 1-_____________---1
- )ltiil lIbSI1So ~ )I~ 0 JSj
Rlao =60
~I ~~ ~ IS ~ Jlbl ) r1 )~
1 sL )~I ~ ~b sIr ~ )l
~lj R lao ~I )~ IS R 411 4 LI (13S3 MPa)
411 r- 0~ ~ bull1 ao 41 ~ ~
~~ ~ ~~ 4 IS 1 r1 i lc IS ~~
uu 411 4 4i Lj ~lj s )l yS11gt
uu 411 ~ )l JItgtlS U rlr~ ~~ 411
) 0Lj -)l ~ rj eb ~~ JItgtlS
~ ~ ~ r1 ~I ~ ~yO Aigt
)~I Jgt )1 d13 ~ jL Jl1 ~~ bL)
~(R)
PDF created with pdf Factory Pro trial version wwwpdffactorycom
rA~ 0 I JG
bulliJ 1oS1W ~ Jw 18ti ~ J~
Model
Charge weight
W(kg)
Distance between charge and pipe
R(m)
Max VonshyMisesstres5
(Numerical)
(MPa)
Max Von-Mises stress
(from Eq (26raquo
(circular plate)
Max Von-Mises stress
(from Eq (32raquo
(rectansular plate)
Max deflection
(Numerical)
d (mm)
Nurick
prediction
(Eq (20raquo
de (mm)
Rajendran
prediction
(Eq (24raquo
de (mm)
Jones
prediction
(Eq (25raquo
de (mm)
Nurick
p ediction
(Eq (28raquo
dr (mm)
Rajendran
prediction
(Eq (30raquo
dr (mm)
Jones
prediction
(Eq (31raquo
dr (mm)
E -
Al
A2
A3
A4 foshy
100
100
100
100
8
12
16
20
40010
33308
25492
20005 ---shy
30320
19470
14212
11131 ------~--
33596
21573
15748
12333
1839
1029
772
591
1808
1328
1079
925 -----shy
1587
975
658
462 ------shy
3044
2121
1641
1345 -____--shy
1923
1340
1038
851
2991
2307
1951
1732
2355
1453
1005
743 ___--shy-shy -
II- A 1509 8 27044 13467 14922 543 706 183 924 584 1419 403
A6 5094 12 25610 14645 16227 753 946 489 13 86 876 1762 778
A7 12074 16 27600 15376 17038 863 1186 795 1848 1168 2105 1195
AS 23581 20 28723 15884 17600 1004 1427 1101 2310 1460 2447 1635
E Bl 100 8 38561 27941 30960 1408 1387 683 2012 1272 2602 1103
B2 100 12 29289 18014 19960 1002 1069 279 1402 887 2150 612
II- B3 100 16 2181 13 186 14610 671 905 070 1085 687 1915 391
B4 100 20 17079 10348 11466 545 803 -060 889 563 1770 273
Cl 100 8 3693 26060 28876 1306 1237 126 15oJ 951 2601 557
sect C2 100 12 2569 16855 18676 889 1000 -176 1047 663 2263 288 N
II- C3 100 16 18871 12365 13701 624 877 -332 810 514 2088 177
C4 100 20 14761 9721 10771 490 8Ql -429 664 421 1979 121
E DI 100 8 33846 24578 27234 1174 1195 -276 12 II 767 2743 313
on D2 100 12 22817 15938 17660 778 1004 -519 844 536 2470 157
N II- OJ 100 16 16739 11713 12978 545 905 -645 653 415 2329 095
D4 100 20 13083 9220 10216 438 844 -723 535 341 2241 064
PDF created with pdfFactory Pro trial version wwwpdffactorycom
I - Cole R H (1948) Underwater explosions NJ USA Princeton University Press
2 - Smith P D and Hetherington J G (1994) Blast and ballistic loading of structures Butterworthshy
Heinemann
3 - Chung M and Brett J (1997) Assessment of underwater blast effects on scaled submerged cylindrical
objects DSTO Aeronautical and Maritime Research Laboratory
4 - Huang H and Wang Y F (1970) Transient interactions of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 48 No1 PP 228-235
5 - Huang H and Wang Y F (1971) Early-time interaction of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 50 No3 PP 885-891
6 - Geers T L and Hunter K S (2002) An integrated wave-effects model for an underwater explosion
bubble Journal ofAcoustical Society ofAmerica Vol III No4 PP 1584-1601
7 - Nurick GN and Martin 1 B (1989) Defurmation of thin plates subjected to impulsive loading-a review
Part I theoritical consideration International Journal ofImpact Engineering Vol 8 No2 PP159-170
8 - Nurick G N and Martin 1 B (1989) Deformation of thin plates subjected to impulsive loading-a review
Part II experimental studies International Journal ofImpact Engineering Vol 8 No2 PP171-186
9 - Teeling-Smith RG and Nurick G N (1991) Deformation and rupture of blast loaded circular platesshy
predictions and experiments International Journal ofImpact Engineering Vol 11 No1 PP77-9
10 - Rajendran R and Narasimhan K (2006) Deformation and fracture behaviour of plate specimens
subjected to underwater explosion-a review International Journal ofImpact Engineering Vol 32 PP1945shy
1963
II - Rajendran R and Narasimhan K (2001) Linear elastic shock response of plane plates subjected to
underwater explosion International Journal ofImpact Engineering Vol 25 PP 493-506
12middot Bangash RY H (1993) Impact and explosion Oxford Blackwell scientific publications
13 bull Lam KY long l and Wang Q X (2003) Dynamic response of a laminated pipeline on the seabed
subjected to underwater shock Composites Part B Vol 34 PP 59-66
14 - Zong l Lam K Y (2000) The flexUral response of a submarine pipeline to an underwater explosion
bubble Journal ofQlJshore Mechanics and Arctic Engineering Vol 122 PP 194middot199
15 - ABAQUS Users Manual (2003) Ver 64
16 - Rajendran R and Narasimhan K (200 I) Performance evaluation of HSLA steel subjected to underwater
explosion ASM Journal ofMaterials Engineering and Performance Vol 10 PP 66-74
jiA )~ lI~liNIl ~ ~ ~11SAt IIjl
1- Explosion 2- High explosive
3- Pressure pulse 4- Shock wave
5middot Bubble pulse 6- Cavitation
7- Peak pressure 8- Coupled acoustic-structural medium analysis
9- Compressible 10- Volumetric drag
11- Inviscid 12- Bulk modulus
)3 Radiating acoustic boundary 14middot Transient analysis
15middot Weak form 16middot Traction
17- Mass proportional damping factor 18- Discretize
19- Strain interpolator 20- Explicit dynamic integration
21- Nonreflecting 22- Impulse
23middot VonmiddotMises 24- Inverse mass number
PDF created with pdf Factory Pro trial version wwwpdffactorvcom
rA~ 0 I JG
bulliJ 1oS1W ~ Jw 18ti ~ J~
Model
Charge weight
W(kg)
Distance between charge and pipe
R(m)
Max VonshyMisesstres5
(Numerical)
(MPa)
Max Von-Mises stress
(from Eq (26raquo
(circular plate)
Max Von-Mises stress
(from Eq (32raquo
(rectansular plate)
Max deflection
(Numerical)
d (mm)
Nurick
prediction
(Eq (20raquo
de (mm)
Rajendran
prediction
(Eq (24raquo
de (mm)
Jones
prediction
(Eq (25raquo
de (mm)
Nurick
p ediction
(Eq (28raquo
dr (mm)
Rajendran
prediction
(Eq (30raquo
dr (mm)
Jones
prediction
(Eq (31raquo
dr (mm)
E -
Al
A2
A3
A4 foshy
100
100
100
100
8
12
16
20
40010
33308
25492
20005 ---shy
30320
19470
14212
11131 ------~--
33596
21573
15748
12333
1839
1029
772
591
1808
1328
1079
925 -----shy
1587
975
658
462 ------shy
3044
2121
1641
1345 -____--shy
1923
1340
1038
851
2991
2307
1951
1732
2355
1453
1005
743 ___--shy-shy -
II- A 1509 8 27044 13467 14922 543 706 183 924 584 1419 403
A6 5094 12 25610 14645 16227 753 946 489 13 86 876 1762 778
A7 12074 16 27600 15376 17038 863 1186 795 1848 1168 2105 1195
AS 23581 20 28723 15884 17600 1004 1427 1101 2310 1460 2447 1635
E Bl 100 8 38561 27941 30960 1408 1387 683 2012 1272 2602 1103
B2 100 12 29289 18014 19960 1002 1069 279 1402 887 2150 612
II- B3 100 16 2181 13 186 14610 671 905 070 1085 687 1915 391
B4 100 20 17079 10348 11466 545 803 -060 889 563 1770 273
Cl 100 8 3693 26060 28876 1306 1237 126 15oJ 951 2601 557
sect C2 100 12 2569 16855 18676 889 1000 -176 1047 663 2263 288 N
II- C3 100 16 18871 12365 13701 624 877 -332 810 514 2088 177
C4 100 20 14761 9721 10771 490 8Ql -429 664 421 1979 121
E DI 100 8 33846 24578 27234 1174 1195 -276 12 II 767 2743 313
on D2 100 12 22817 15938 17660 778 1004 -519 844 536 2470 157
N II- OJ 100 16 16739 11713 12978 545 905 -645 653 415 2329 095
D4 100 20 13083 9220 10216 438 844 -723 535 341 2241 064
PDF created with pdfFactory Pro trial version wwwpdffactorycom
I - Cole R H (1948) Underwater explosions NJ USA Princeton University Press
2 - Smith P D and Hetherington J G (1994) Blast and ballistic loading of structures Butterworthshy
Heinemann
3 - Chung M and Brett J (1997) Assessment of underwater blast effects on scaled submerged cylindrical
objects DSTO Aeronautical and Maritime Research Laboratory
4 - Huang H and Wang Y F (1970) Transient interactions of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 48 No1 PP 228-235
5 - Huang H and Wang Y F (1971) Early-time interaction of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 50 No3 PP 885-891
6 - Geers T L and Hunter K S (2002) An integrated wave-effects model for an underwater explosion
bubble Journal ofAcoustical Society ofAmerica Vol III No4 PP 1584-1601
7 - Nurick GN and Martin 1 B (1989) Defurmation of thin plates subjected to impulsive loading-a review
Part I theoritical consideration International Journal ofImpact Engineering Vol 8 No2 PP159-170
8 - Nurick G N and Martin 1 B (1989) Deformation of thin plates subjected to impulsive loading-a review
Part II experimental studies International Journal ofImpact Engineering Vol 8 No2 PP171-186
9 - Teeling-Smith RG and Nurick G N (1991) Deformation and rupture of blast loaded circular platesshy
predictions and experiments International Journal ofImpact Engineering Vol 11 No1 PP77-9
10 - Rajendran R and Narasimhan K (2006) Deformation and fracture behaviour of plate specimens
subjected to underwater explosion-a review International Journal ofImpact Engineering Vol 32 PP1945shy
1963
II - Rajendran R and Narasimhan K (2001) Linear elastic shock response of plane plates subjected to
underwater explosion International Journal ofImpact Engineering Vol 25 PP 493-506
12middot Bangash RY H (1993) Impact and explosion Oxford Blackwell scientific publications
13 bull Lam KY long l and Wang Q X (2003) Dynamic response of a laminated pipeline on the seabed
subjected to underwater shock Composites Part B Vol 34 PP 59-66
14 - Zong l Lam K Y (2000) The flexUral response of a submarine pipeline to an underwater explosion
bubble Journal ofQlJshore Mechanics and Arctic Engineering Vol 122 PP 194middot199
15 - ABAQUS Users Manual (2003) Ver 64
16 - Rajendran R and Narasimhan K (200 I) Performance evaluation of HSLA steel subjected to underwater
explosion ASM Journal ofMaterials Engineering and Performance Vol 10 PP 66-74
jiA )~ lI~liNIl ~ ~ ~11SAt IIjl
1- Explosion 2- High explosive
3- Pressure pulse 4- Shock wave
5middot Bubble pulse 6- Cavitation
7- Peak pressure 8- Coupled acoustic-structural medium analysis
9- Compressible 10- Volumetric drag
11- Inviscid 12- Bulk modulus
)3 Radiating acoustic boundary 14middot Transient analysis
15middot Weak form 16middot Traction
17- Mass proportional damping factor 18- Discretize
19- Strain interpolator 20- Explicit dynamic integration
21- Nonreflecting 22- Impulse
23middot VonmiddotMises 24- Inverse mass number
PDF created with pdf Factory Pro trial version wwwpdffactorvcom
I - Cole R H (1948) Underwater explosions NJ USA Princeton University Press
2 - Smith P D and Hetherington J G (1994) Blast and ballistic loading of structures Butterworthshy
Heinemann
3 - Chung M and Brett J (1997) Assessment of underwater blast effects on scaled submerged cylindrical
objects DSTO Aeronautical and Maritime Research Laboratory
4 - Huang H and Wang Y F (1970) Transient interactions of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 48 No1 PP 228-235
5 - Huang H and Wang Y F (1971) Early-time interaction of spherical acoustic waves and a cylindrical
elastic shell The Journal ofthe Acoustical Society ofAmerica Vol 50 No3 PP 885-891
6 - Geers T L and Hunter K S (2002) An integrated wave-effects model for an underwater explosion
bubble Journal ofAcoustical Society ofAmerica Vol III No4 PP 1584-1601
7 - Nurick GN and Martin 1 B (1989) Defurmation of thin plates subjected to impulsive loading-a review
Part I theoritical consideration International Journal ofImpact Engineering Vol 8 No2 PP159-170
8 - Nurick G N and Martin 1 B (1989) Deformation of thin plates subjected to impulsive loading-a review
Part II experimental studies International Journal ofImpact Engineering Vol 8 No2 PP171-186
9 - Teeling-Smith RG and Nurick G N (1991) Deformation and rupture of blast loaded circular platesshy
predictions and experiments International Journal ofImpact Engineering Vol 11 No1 PP77-9
10 - Rajendran R and Narasimhan K (2006) Deformation and fracture behaviour of plate specimens
subjected to underwater explosion-a review International Journal ofImpact Engineering Vol 32 PP1945shy
1963
II - Rajendran R and Narasimhan K (2001) Linear elastic shock response of plane plates subjected to
underwater explosion International Journal ofImpact Engineering Vol 25 PP 493-506
12middot Bangash RY H (1993) Impact and explosion Oxford Blackwell scientific publications
13 bull Lam KY long l and Wang Q X (2003) Dynamic response of a laminated pipeline on the seabed
subjected to underwater shock Composites Part B Vol 34 PP 59-66
14 - Zong l Lam K Y (2000) The flexUral response of a submarine pipeline to an underwater explosion
bubble Journal ofQlJshore Mechanics and Arctic Engineering Vol 122 PP 194middot199
15 - ABAQUS Users Manual (2003) Ver 64
16 - Rajendran R and Narasimhan K (200 I) Performance evaluation of HSLA steel subjected to underwater
explosion ASM Journal ofMaterials Engineering and Performance Vol 10 PP 66-74
jiA )~ lI~liNIl ~ ~ ~11SAt IIjl
1- Explosion 2- High explosive
3- Pressure pulse 4- Shock wave
5middot Bubble pulse 6- Cavitation
7- Peak pressure 8- Coupled acoustic-structural medium analysis
9- Compressible 10- Volumetric drag
11- Inviscid 12- Bulk modulus
)3 Radiating acoustic boundary 14middot Transient analysis
15middot Weak form 16middot Traction
17- Mass proportional damping factor 18- Discretize
19- Strain interpolator 20- Explicit dynamic integration
21- Nonreflecting 22- Impulse
23middot VonmiddotMises 24- Inverse mass number
PDF created with pdf Factory Pro trial version wwwpdffactorvcom