Tinh toan dong ILFC hoc kit cau be china thanh mong chju tac dung cua tai trong song no
Dynamic Analysis of structural Liquid Storage Tanks of thin the effects of the blast wave loads
Ngay nhan bai: 15/12/2014 Ngay sCiia bai: 20/01/2015 Ngay chap nhan dang; 05/02/2015
Lu'dng Si Hoang, Vu Ngoc Quang
T 6 M T A T :
Bai bao da phan tich be chira chat long dat not chiu tac dyng cua tai trpng song no. H^ ket cau - chat long lam vi^c trong dieu ki^n bai toati phing. Thuat giai cua bai toan du^rc xay dung iren ca sa phuang phap phan tCr hmi han (PTHH), mien ket cau ducfc rcri rac hoa thanh cac phan tu thanh phang, mien long thanh cac phan tti tam giac phang.
Chuong trinh tnay tinh duoc viet bang ngon ngu lap trinh Matlab de phan tich ung xii dpng luc hgc mien long len ket cau.
Tir khoa: BS chiia chat long, song no, tuang tac ran - long, phuong phap phan tu hihi han.
ABSTRACT:
This paper analysis the Liquid Storage Tanks on the ground the effects ofthe blast wave loads. Structural - fluid system working in a flat condition problem. The solution of the problem based on the finite element method, the structural domain into a flat bar elements, liquid domain into a flat tnangular element. Computer program developed Matlab language to analyse the dynamics responses of liquid to structiual domain.
Keywords: Liquid storage tanks, shock waves, interactive solid - liquif, finite element method.
ThS Linrag ST Hoang, PGS.TS Vu Ngpc Quang HQC vi?n Ky thuat Quan sir
Email: [email protected] - 0983 302 944
1. Dat bai toan, gi& thiet tinh toan
Kh^o sdt be chiJTa chat ldng dat noi, be chu'a c6 ket c^u m6ng chju tac dung cua ap lUc song no (hinh 1) C3n xac d m h bien dang, ngi liic cCia k^t cau be ch<^ cung n h i / ap lUc ciia chat ldng tde dung l^n be chu'a. Oe g i i i bai toan dat ra se sCf dung phuong phap phan tCr huU han (PTHH) vh thiSa nhan cac gia thiet:
- Chat I6ng khong nhcrt, khong xoay, n6n dUOc, mat do thay doi rat it va chuyen v j n h d ;
- Khong tinh den anh hu'dng cua lire khoi trong chat long va song tr^n bi mat tU do;
- Vat li§u ket cau b l chu'a dan hoi tuyen tinh, cdn chuyen vi va bi^n dang tai diem bat ky cua ket cau be \i nhd;
- He ket cau b^ - chcSt Idng l^m viec trong dieu kien cOa bai todn phang;
- Li4n ket giu'a ket du be vdi nen \h lien ket goi tu'a.
AP(t)
Hmh 1. Md hinh khio sat he ket cau be - chit I6ng 2. PhUtfng trinh PTHH tong quat d e phan tich dong liTc hoc be chiJTa chat Idng
He khdo sat g o m 2 mi4n con' mien cua ket c^u be va mien Idng.
Theo [1], ciing vdi cac gid thiet cua bai todn da thiet ldp dUOC phUdng trinh c h u y i n dSng tong quat de phan tich ddng lu'c hoc he k i t cau be - chat Idng lam viec dong thdi nhU sau:
r [Ml i(iii|(uii rra [oiirMi^
UKl -[Lnf{ull
'[[0] [Bl J({plJ
{SI
= 0,0)
7.2015BOniI[|S
trong do: [Kl,[Mj,[Cl la ma trdn do ciJlng, ma Iran khdi lUOng vd ma trdn can cua cua toan he ket cdu be, cac ma tran nay duac hinh thanh tit dc m a t r a n c o n [Klg,[MJe,[Cle cua tat ca cacPTHH mien ketcau; W lavec t o tai trong ngoai quy nut ciJa he ket cau, no duoc hinh thdnh tir cac vec t o con {Q)e doi vdi mdi phan t i l ; (u| la vec t o chuyen vi niit cua he k i t cau, nd diipc hinh thanh til cac vec t o chuyen vj niit [ul^ cOa tat ca phan tif k i t cau. [Al va [B] la ma tran khdi lUOng va ma tran dd cung cda toan mien Idng, cdc ma trdn nay duoc h1nh thdnh tir cdc ma trdn con [Ale,[Big <^"3 tat cd cac PTHH chat long; [L] la ma trdn dUoc hinh thanh tir ma tran con [Ll^ cda cdc PTHH chat Idng cd bien t i l p xiic vdi phan tCr mien ket cau va goi la ma trdn lien ket; pf la khoi lUOng rieng cua chat ldng; {p) la vec t o dp lUc nut cua todn mien long, nd dUOc hinh thanh tif cac vec to con {pig la vec t o dp lUc nut cua mdi phan t i l mien Idng 2 . 1 . Xiy diTng c^c ma t r ^ n phin tit hCTu han
Trong bai bdo ndy mien ket cau be se dUoc rdi rac hda thanh cac phan tirthanh phSng, cdn mien Idng duoc rdi rac hda thdnh cac phan t i l tam gidc phling (hinh 2).
Hinh 2. Mo hmh M khio sjt da iuac rcH rac hoa thanh uc PIHH trong he toa 3b long the (x,y) 2.1.1. Xay d u n g cdc ma t r a n PTHH ciia mien Idng
Khao sat phan t i l chat Idng dang tam gidc p h i n g cd 3 d i l m niit trong he tpa do tong the (x,y), (hinh 3)
Hinh 3. Phan tir tam gidc phang thudc mien Idng Vec t o dp luc nut ciia phan tin
( p ) e = [ P l P2 P 3 ] ^ - (2) Ma trdn hdm dang ciia phan tCn
[N]e = [Ni N2 N3], (3) trong dd:
N | - — ( a i + bix + qy), 1 = 1^3. (4) vdi' A - di6n tich phan t i l ,
a, = X 2 y 3 - X 3 y 2 ; b, = y 2 - y 3 ; c i = X 3 - x 2 ; a 2 = ' < 3 y i - ' < i y 3 ; b 2 - y 3 - y i ; C2 = X ] - X 3 ; a 3 = ' < i y 2 - ' < 2 y i . b 3 - y ] - y 2 ; C3 = X 2 - x , .
Ap luc plx.y) thuoc phan tir duac xap xi bdng bieu thilc:
p(x,y) = [NJe{p}e.
• Ma tran k h o i l u p n g p h a n t i l chat Idng d u o o [ A ] e = ^ J[N]J[N]edV,
Do chi4u day t ciia phan tir ia khdng doi nen (f [ A ] e = ' ^ | [ N ] e [ N ] e d S ,
Ap dung cong thilc [3]
fJ(Ni)"(Nj)P(N,,}Vdxdy^ " ' P ; ' ^ ' 2A.
We-~^ -
(5) c dinh tir cdng thilc
(6)
chuyen ve dang:
vdl: t - chieu day cua phan tif, cf - toe do am dien tich phan t i l
• Matran d o c i i n g phan t i l duoc xac d m h tU cong thi [Ble = J (^[N]e](V[Nle)dV - t J (V-[N]^l(V[N]e)dS,
(8)
ing chdt idng; A
^J
"<-[N]e"
r x tlNle L ^
l e n ta
"r-N, ex cNi . ^y
CO
^2 dx ,"N2
• y
rNjl
cv ,-N3 ' y . V[N]eT i r b i l u thiic ham dang cua phan tir chat Idng.cd dk 1 , ck 1
—!- = — b | , —'- = — c,, 1 ^ 1 - 3 dx 2A c'y 2A Vdy suy ra
r b ] b , + c i c i bib2 + c,C2 b-|b3+ciC3 [ N e = ^ | ' ^ 2 b l + C 2 C i b2b2 + C2C2 b2b3 + C2C3
i^b3bi-c3C| b3b2+c3C2 b3b3+C3C3 2.1.2. X i y d U n g cac ma t r a n PTHH cua mien k e t cau
y ' •> . y '
a, Trong he loa do cue bo
0
b, Trong he toa do chung H h * 5. Phan tli Ihanh phang diiu uon ciing ven keo - nen (mien ket cau) Khao sdt phan tif thanh chiu udn cung l<eo - nen trong mat phina Jf,y Ky h l | u fxm, y^r) la he true toa do cue bo cua phan tU, con feyj la he toa do tfing quat (hinh 5 ). Goi u la chuyen ui doc true phan tir, v\i c h u y i n vj vuong goc vai true thanh, (Via gdc xoay, ju.'g la vec tochuyeiiSOBWnOOl 7-2015
i niit cua phan tCf theo p h u o n g cdc true toa do cue bq. Thira nhdn trong ud trinh chju lire cac trang thai keo - nen {tUong dtig vdi u) va uon :ilong ling vdl V, 0 ] cua phan t i r l d khdng dnh hudng l l n nhau.
Trong he t m e toa d p cue b d vec t o chuyen vi nOt va ma t r | n hdm lang cda phdn tir thanh eo dang:
{ u ) e = t " l m Vim ^ m " 2 m "21^ 92m
Nl-
rong Nim
0 0 6 : L
0 0
N i m N3m dx dx la chi^u dai pha
N4m 0 0 t u .
0
Nsm dNsm dx
0
Nem dx
01)
0 12 -61 0
2 -ei
61 if 0 -61 4|2 IK],=
trong dd: B = — ; L - la chl^u dai phan tU; l,F- m d men quan tinh va dign tich t i ^ t dien phdn t i i ; [B^vle - " i 3 tran bi^n dang<huy4n yi; [Ov|l - ma trdn vat lieu cua phdn tU.
• Ma trdn can phan t i r t h a n h duoc xeic dinh:
[C],= Jc,[Ni;[N]^dV,
|2 • N6m
Chuydn yi tai mpt d i l m bit ky tren phan t i i "e" dupe n^i suy theo i/ec to ehuyen yi nut cua ncj theo bi^u thiic:
{u} = [N]e{u}e, (13) trongdd; [u} = [u v 9]'''.
Sau day se dan ra cdc cdng thilc tfnh cuoi ciing ciia ma trdn khoi liTcfng, ma trdn d d ciitig, ma tran cdn vd vec t o tdl trong quy niit do lUc b l mdt gdy ra ddi vdi phSn t i r t h a n h .
• Ma trdn khoi lupng phan t i l thanh duoc xdc dmh
trong do. e^ - he so can cua vdt Ii4u cua phan t u .
Tuy nhien trong thUc t e ti'nh todn ma tran cdn ciia he thudng tinh theo t d hpp tuyen tinh cOa ma tran khoi luong vd ma tran d o ciTng ciia he k i t cau.
• Vec t o tdi trong quy niit cua phan t i l :
TrUdng hpp tdi trong phdn bd d i u vudng gdc vdi true thanh
[M]e=fPs[NllKdV,
H=
(14)
-13L trong do: p j - khoi luong rieng cii^n tieh tiet dien phan tiJ
• Ma trdn dp eiing phdn tir thanh duoc xac djnh:
0 ~22L 41"
vdt lieu; L - la chi^u dai phdn t i i ; F -
W e = J [ B » J [ D v l l [ B c v l . < l V ,
(Q)e-J[NlI{PbU<iS, S
( Q ) , - { P b ) [ o { i ^ L ^ 0 1 1 Trong cae eong thUc (14), (15), (16)'
(17)
12 J
i (17) ma trdn ham dang cda
(18) dupe bieu dien d dang rut gpn
Nim 0 0 N4n, 0 0 . 0 N3m N4m 0 Ngm Ngm Ma tran ehuyen he true toa dd cue bo sang he toa do t ^ n g the:
cos a sin a [N],
i n a c o s a 0 0
cosa - s i n a
veil, a - la gdc giUa true oxm ciia hg toa d p cue b d va true ox eua h^ toa d p tdng th4.
Cac ma tran phdn t i r c h u y i n t i f he tpa d p cue b d sang he toa d o tong t h i seed dang:
[K]e=[G]^[K]e[G]e;
[M]e = [Gll£M]e[Gle;
[Cle=[G]J[C]e[Gle;
{Q)e=[G]J{Q}e,
(20) (21) (22) (23) trong dd' [K]g,[M]g,[C]e - tuang itng la ma tran dp cilng, ma tran khdi lupng va ma trdn edn phdn tir trong he toa dp tong t h i ; {Q}g - Id vec t d
tdl trong quy niit cOa phan tir trong h^ toa d p tong the.
2 . 1 3 . Ma t r | n lien k e t ciia p h a n tuT
0 " 0 ^ a, Trong hf Iga do cue bo b, Trong h? toa d^ long quat
Hinh 6. Phan til Iam giac (mien I6ng] tiep xiic vdi phan tii thanh (mifn k^t cau) Khdo sdt phdn tir tam gidc m i l n Idng eo eanh V 2 t i l p xOc vdi phdn tif thanh m i l n k i t cdu {hinh 6). Chpn he true toa do cue bd [Xm,yn>) vdi gdc cua nd tai nut l va true Xm triing vdi canh l -2 cua phdn tif tam gidc (va triing vdi true ciia phan tirthanh)
Trong h@ true tpa do cue b6, ma tran lien k i t dUoc xdc dinh bdi cdng thilc:
duoc cdc ma trdn cho toan mien ket cau b^ vd mien Idng.
3. P h u o n g p h a p g i d i b i i t o a n d a o d o n g ciT&ng bile ciia ket du Theo [1,4] lua ehpn phUcmg phdp tieh phdn trUc tiep eiia Newmark d e g i a i he phuong trinh { l ) . T r e n co sd cdc thuat toan nhan duaetCfcac mue tren, nhom tac gia dd lap chuong trinh tinh bai toan b l chila chiu tde dung cda tdi trong ddng va duoc v i l t bdng ngdn ngO ldp trinh MATLAB 2009a.
Trong thuc t l tinh toan ma tran cdn cua he t h u d n g t i n h theo to hflp t u y l n linh eiia ma tran khdi lupng va ma trdn do cutig ciia h&, theo cdng thiic.
[C] = a [ M ] + p [ K ] , (30) trong dd a v a ^ J I d c d c h & s d c d n Rayleigh.Cdchesd nay Hen he vdi t j sfi
edn 4 bSng phuang trinh:
[L]g= j [N]V[NledS = tJ[NlIn'''[|N(]edL, (24)
ip m^}
(31)trong d d :
S g ] ' la dien tich b l mdt tiep xiic giila hai phan t i i ,
L - c h i l u dai true thanh ket cdu vd cung la chieu dai canh 1-2 eiia p h a n t i r t a m g i d e mien Idng;
[Nig - ma trdn hdm dang cua phdn t i l ket cau dang thanh (ma trdn nit gon, cdng thirc (18));
[ N i g - m a trdn ham dang ciia phan tir tam gidc thudc m i l n Idng;
n - Id vie t o phdp t u y l n ciia b l mdt t i l p xuc, ed hUdng di ra ngodi be mat phan tif chat Idng, trong he true toa do cue bd thi, n=[ 0 1 ] .
Trong h^ true ix-^ym), tren eanh 1-2 ciia phan tif c h i t Idng, dp luc tai diem bat ky plXj^) dUoc ndi suy qua dp lUc niit tai nut 1 vd mit 2 nhU sau:
p(Xm) = [N]e(ple. (25) trong d d
l p ) e = t P l P 2 ] ^ ; (26) [ N ] e = [ N i m N 2 m ] ; (27) vdi: Nim = l - - ^ ; N i m ^ — -
im L ^"^ L
Khai t n l n cdng thiic (26) vd thuc hien tieh phdn, ta cd:
L f o 21 3L 0 9 - 2 L l ^
H . = S|.0 9 2L 0 2, -3LJ • ™
Chuyen tif he toa dp cue bd sang he tpa d d tong the se cd dang:
[ L l e - [ G ] J [ L ) e (29) Sir dung cdc thii tuc eiia phudng phdp "dp ciing trUc t i l p " trong
phUOTig phdp PTHH [3,4], tren eo sd cdc ma tran phdn tif d tren ta se t h u
voi. (i)j,(i}j - la 2 tan sd dao ddng thdp nhat ^ | , 4 j - t y s d c a n t u c j n g u n g . T h e o [ 5 ] k i e n n g h l s i f d u n g t 9 s 6 c d n ^ = 2 % ( b l t h e p ) , ^ = 5 % { b l W tdng) cho cac mode dao ddng ciia cd hi,
4 . Tfnh t o d n sd
D l nghien ctlu vd thdy rd dnh hUdng cua mien Idng den dao ddng be chira khi chiu tac dung eiia tai trong ddng Id sdng n6, ta se tinh bi chila vdi hai trudng hop, be khong co chat Idng (trUdng hop 1) vd be co chat Idng (trUdng hdp 2).
Dlnhlu^
aflO
MCday Hinh 7. Mo hinh tinh be Chila
Be chiia hinh chif nhat kfch thudc 6x6m, chieu day day, tudng, n6c b l la 0,5m {hlnh 7). Ddc trUng vat lieu eiia ket cdu; md dun ddn hoi E=27xlO'MPa, khdi lUong rieng p^ = 2500kg/m^ he so poisson u = 0,3.
Chat Idng trong be cd khoi lupng rieng pf =1000 k g / m ^ vdn tde dm thanh trong chat Idng Cf =1500m/s.
Be chiia chiu tde dung eiia tdi trpng sdng nd lan t r u y i n trin mat ddt, tinh tai thdi d i l m sdng tdi gap ket cau b l chu'a va sinh ra sdng phdn xa vdl sieu dp sdng xung kich la 16,5ST/m^ (khdng xet den hi&n tuong sdng chdy bao), t h d i gian duy Iri pha nen T = 0 , 1 S S; Ap lire sdng nd phdnb6 d i u ben tudng trdi theo quy luat [2].
2 A p ( , ) = , 6 . 5 5 . [ , - ^ ] , T „ M6 hinh ti'nh cho bai toan the hien uin hlnh 8.
82
Hinh 8: Mo hinh tinh oJa be diua da dUoc loi rac hoa thanh cac PIKH K i t qua chuyen vi ngang ciia diem dinh t u d n g be (mit 72) theo thdi gian (tUOng ilng v& trUdng hop 1 va 2) the hien trong hinh 9; bleu d o chuyin vi cua k i t cau b l tai t h d i diem t=0,2l s irng vdi t r u d n g hop l vd 2 the hien trong hinh 10.
ih 9:06 thi chuydn vi ngang Iheo thcA gian, tai mit 72 ling voi rniong hop 1 va 2 {ty le x lir')
Hinh 12:{)6 thi luc cat theo thoi gian, tai mat c3t day img vA tmdng hop 1 v^ 2 Tren cdc hinh 11 va 12 the hien rd quy luat b i l n thien theo t h d i gian cua ndi lUc d d n g trong ket cau (tai mat cdt day) ling vdi hai t r u d n g hpp Id khde nhau rat Idn. Dieu nay eho thay khi be chifa cd ehdt Idng ehiu tde d u n g cda tdi trong d o n g la sdng nd thi dnh hUdng ciia khoi chat Idng trong be chiia den qud trinh dao d d n g h^ ket edu be - ehdt ldng Id rdt Idn. Gid t n m d m e n , lue cat theo thoi gian ldn nhat ifng vdi t n i d n g hpp 1 Id M<M«M=91,93Tm (tai t h d i d i l m t=0,18s); Qn»yrhi=36,24T (tai thdi d i l m t = 0 , l Ss). Gid tri momen, lUe cdt theo thdi gian Idn nhat eiia IrUdng hpp 2 Id MmMM=l02,93Tm (tai thdi d i l m t=0,21s); Q™,nu=62,83T {tai thdi d i l m t=0,21s).
Ap luc mien Idng len ket cau, tai thdi d i l m t=0,21s t h i hien trong hinh 13.
I
(trudng hpp 1) (trUdng hop 2) Hinli 10: Bieu do chuyen vicija ket cSu be, tai thcii diem 1=0,215 TCr do t h i vd cdc bieu d o chuyen vi ta nhan thay, bien dp ehuyen vi ngang tai dinh tUdng b l {nut 72) cCia trudng hop 1 ( b l khong cd ehat Idng) Icm hem so vcri t r u d n g hpp 2 (be cd chila chat Idng), gia tri ehuyen vj ngang Idn nhat tai dinh t u d n g be (niit 72) Ung vdi truejng hop l la Unhi=0,64cm {lai thcfi d i e m t=0,21s); trUdng hpp 2 Id u,ih3=0,60cm (tai thdi a i m t=0,21s)
K i t qud m d men vd lUc cdt tai mat cdt day Iheo thdi gian lan lUot the h i ^ trong cac hinh 11 vd 12.
I-
1"
-
1 fli
—11
/ l -
[ —•— Truonq hop 2 j
_J.. t _.
-.A",. —
^ ' " - - ' — -^
—^- ^ i— -, -
Hinh 11: Bo Ihl mfimen theo tha gian, tai mat cit day ling vol tnrrnig hop 1 v J ;
(MPa)
Hmh 13: Bieu do ap luc mien long len ket cau (mrcmg hop 2], tai thcri diem tM),21s(ty leu 10') 5. Ket tuan
Trong nghien cilu nay da xay dung m d hinh tinh be chila vdi m d hinh phdng theo phUctng phap phdn tir hCftj han. Ddng thdi xay dpng cdc ma tran phan tif huU han ciia he ket cau be he thanh, mdi trudng Idng trong be chiia la cde phan tif tam giac phang. Qua dd xay dung duoe thudt todn va ehUcmg trinh tinh. Khdo sdt bdi loan k i t cau be chila he thanh chju tde dyng eua tdi trpng sdng no vdi hai trUdng hpp (be khdng ehua ehat ldng va be cd chiia chat Idng), k i t qud so cho thay khi be chila cd chat Idng chiu tde dung ciia tdl trong ddng la sdng no Ihi dnh hudng cira khdi chat Idng trong be chifa d i n qua trinh dao ddng he ket eau b l - chat Idng la rdt Idn. Vi vay Irong qua trinh tinh loan, thiet ke be ehCia chiu tac dung ciia tdi trong dong can thiet phai ke den anh hUcffig ddng hoc eiia khdi chat long len k i t cau be chda.
TAILIEU THAM KHAO
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3. Chii()u6cthSn9(1997),ffliW5p/ii^pyM(tfhu!ih(7n,Nhaxuatban Khoa hgcvaky thuat 4. Bathe KJ (1996), Finite element procedures - Part one,twn Prentice Hall International I n t ,
Englewood Ciilfi.
5 EurcKodeS iWS): Design provisions of earthguakerenstance of structures, Part 4 Silos, lanks ondpipelines European CommitteeforStandardization,Bmssels.
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