• Khoa hpc Ky thu4t va CAng nghe
Bai toan t6i iru kk cau dan phang sir (iung phan tich try-c tiep CO xet 6k di^u kien rang buoc ve tan so dao dong neng
2 2020 ng3> chu;
Ha Manh H u n - . Trinmg \"ift Hung=
, .nrr,g .Un Jiin^ va . o-:, r^hcp Tn.mg / V I'Oc -V.i' •/t"'.'.' A ' p - j f . i i e tr-.nh Tnn'^g T>ai hoc Thuv hn
, . , - > -.(pn iv.iv chap 111'
•n ptun hicn 2! 2 211:1'. ngav nh;in phan bien . • -' - > ' - ' • -- -
in dani2 10 4 2020
^'""f^f^ -• dan thep chju cac t6 hop tai t r ^ n g I rone biii bao ^a^. cae i;.c uia trinh hii> cjch i h i i i lap %a giai quvet b^i toan loi uu ^ ^ ^ ^ -^ ^^^^ ^. ^^^ ^ < „ ^.^^
k h i c nhau n. M l den dicu ki^n r i n s bu.V ^i• i:in M'. dao d^np neng. 1 him ticn 1 . J " ^ j ^ ^ ^ h ^ua cong t r i n h UHR w phi u i v i n nnh. phi dan hAi cua ki-t cfiu. Ham muc tieu cua biii toan to, iru J , | ^ ^ ^ .^ ^ , ^ ^ , ^ ^,x ^^.^.„g dirvc d.m Klan hoa nhu ham tone khiii IU^HR- Cac dieu ki^n rang buyc cua hM loan k ^^^^ ^,. ^ ^ ^ , ^^ 1^^^
dO, Mr d y n t va tan MI dao dOnc rienj;. Thuat toan tien hoa vi phan dirge sirdung OL ^ thep phflnn 111 Ihanh dirgr xem v i i di- minh h9a cho nghien cini nay.
Tif khda: dAn th6p. phan tich t r y r n i p . lien hoa \\ phan. toi uu.
(. hi ^d olnin Umi: IA
Kel cm dan la niCn trong nhiing loai ket c.ki dugc sir d\ing pho bien hign na\ nhii kha niing \ut,n nhjp icm. hinh ihue dvp \a phong phii. phal huy loi da kha nang ciia \at liC-u nen khoi lucmg nh?... \ icc thiet ke dan thep hien nay thuimg dui,Te ap dyng theo each tiep can gian tiep \ ai 2 bunc ihii-i kc nham co the \ei Jen ac linh chat phi tuyen hinh hpc cua kel cau \a phi dan hoi cua \al Ii^'u 0 buoc dau lien, nin l\rc cua cac Ihanh dan dirge \ac dinh dua Iren phan tich tuyen tinh Jan hoi. Ti> cac npi lue da dupc tinh loan nay, ining huae thu hai cae thanh dan sc dtrpc ihiet ke rieng le hing \ lec .\^ dyng C.K cong ihirc ccS \el den cac img xir phi luyen cua ki'l cau dupc cung cap trong cae tieu chuan hien hanh nhu \IS(.' LRFD [1], Eurocode [ 2 ] . . Phucmg phap ihiei ke iruyen thong nav co nhieu uu diem nhu thiei ke nil nhanh, dim gian va ket qua co dp chinh xac chap nhan dupc. Tnv nhicn, v iec tiep can gian tiep nhu tren khien cho cac img \ u eua loan bp kei cau khong duoc mo ta mgt each chinh xac \goai ra, tinh luong thich cua cac phan tu rieng Iciloi vai loan hi-Ihong cQng khiing duac dam bao De khac ph\ic cac nhuoc dicni na\. gan da\ cac phuong phap phan tich inie iii'p duac nhieu nha khoa hoc chii \ nghien ^uu mo ra humig Ji mai irong ihiet ke kei cju dan ihep noi r'eng va cong tnnh \ a \ dtmg noi chung L u diem cua phan t i c tnic tiep la linh loan duac kh.i na!';; ^hm lai cua '.oan P • eong trinh cime nhu ca,. ini^; \ i i phi uivcp ,. ,.: cone tnnh irong cjc gi.u di>an dan hoi v j 111:0 • I'an ho: 1-6]
Dc phat huy hieu qua cong lac thigt kg, thiet ke toi uu cuni! dupc quan tam nghien ciru va ap dung rong rai trong ket ciu dan thep. Uu difim cua lhi§t ke toi tru la no cho phep dua ra cac giai phap Ihifit kfi c6 chi phi ve xay dung thap h(Tn rat nhik so vai cac phuong phap thilt ke Ihoiig ihutmg ma cac yeu ciu v^ thiSt kl d6i vai cong trinh vin dugc dam bao. Tiiy thupc vao muc dich cira nha thiet ke ma bai loan 161 uu thanh dan co the chia ra lam 3 loai co ban la t6i uu ti4t dien (sizing optimization), toi uu hinh hpc (shape optimization) hay toi uu vat lieu (topology optimization).
Trong bai toan toi uu tiet dien, tiet dien ciia cac thanh dan la cac bien thiet kk va dugc lira chon sao cho tong gia Ihanh xay dung hoac long khoi lugng ciia ca he dugc toi thieu hoa ma van dam bao cac dieu kien ve thiet ke. Bai toan toi uu ket cau dan se tro nen phirc tap voi do phi tuyen cao khi cac img xu phi tuyen tinh. phi dan hoi ciia cong trinh dugc xet den. Trong truong hgp nay, cac Ihuat loan meta ha-rit-tic thuong dugc sir dung de giai bai loan loi uu [7-9], Mgl so ihuai toan meta ha-ril-lic hieu qua cao trong viec giai quyet cac bai loan loi uu liet dien cua dan ihep la; ti^n hoa vi phan (DitTerenlial Evolution - DE). toi uu bay dan (Particle S\^a^m fJplimization - PSO), giai thual di truySn (Genetic Mgonthm - GA), thuiii toan bay ong (Bee)..
i ac dieu kien rang buiiL trong bai loan 161 uii iigt dien tt.ep tlimmg duac giai han la cac dicu h e I. ii'iig do ihco cac 16 hop lai trong d -'ii, j , , . JL 11.U Jiuan Ben eanh do dc cai ihien b na ca I tnii. va ngan chan cac hien tucn
yen vi 1 trong
ng. eac
S!SSl!«\fciVr-"'^'"°-
Khoa hpc Ky thu$t va Cong ngh^ i
Optimisation of planar trusses using direct design considering
frequency constraints
M a n h H u n g Ha'*, \ ' i e t H u n g T r u o n g - ' Faculty of Building and Indiiiinal Consiniciion.
Natiimal University of Civil Engineering
•Faculty of Civil Engineering. Thuyloi Cniversily Received 17 Febuary 2020; accepted 10Apnl2020 Abstract:
In this paper, the a u t h o r s p r e s e n t e d the m e t h o d to establish and solve the optimisation of steel trusses subjected to several load c o m b i n a t i o n s a n d frequency constraints. A direct design was employed to account for the non-geometric non-linear b e h a v i o u r of the s t r u c t u r e . The objective function of the optimisation p r o b l e m was the total cost of the s t r u c t u r e which was simplified as a function of total weight. T h e c o n s t r a i n t s of the optimisation included the strength a n d serviceability conditions, a n d s t r u c t u r a l frequency r e q u i r e m e n t s . T h e differential evolution a l g o r i t h m was applied to solve the proposed optimisation p r o b l e m . .A 10-bar p l a n a r truss v\'as studied to illustrate this w o r k .
Keywords: differential evolution, direct design, optimisation, steel t r u s s .
Classification number: IA
rang buoc dgng rat can dugc xet den trong cac bai loan toi uu [10], De thirc hien dieu nay, cac dieu ki?n rang bugc ve tan so dao dgng rieng ciia ket cau dugc xet den. Mgl so nghien ciru not bat ve bai loan toi uu dan ihep co dieu ki^n rang bugc la tan so dao dgng rieng co the ke den nhu P.H Anh [11]. Kaveh v a Z o l g h a d r [ ! 2 ] . Far^ihchin va cs [ U ] . . Tuy so lugng cac nghien cim ve loi uu dan thep chiu dieu kien rang bugc la cae to hgp lai trgng ho3c la lan so dao dgng rieng ciia ket cau kha nhieu, nhimg Iheo hieu biel ciia tac gia chua co mpt nghien ciiu nao xel den cac dieu kiC*n rang bugc neu tren mgl each dong then, Dieu nay khien cho cac nghien cim toi uu \ c kcl cau dan co khoang trong can dugc bo khuyet
Trong nghien ciiu nay. cac tac gia trinh bay bai loan toi uu dan thep co dieu kien rang bugc, gom ca dieu kien rang bugc ve chuyen vi va cuimg dg dudi cac lo hgp lai trgng khac nhau va dieu kien rang bugc ve tan so dao dgng rieng ciia kel cau. Ham muc lieu ctia bai loan toi uu dugc dem gian hoa nhu ham long khoi lugng. Cac dieu ki^n rang buge ve cuong dp V a sir dung dugc xac dinh dua vao phan tich trye Hep cho phep xet den cac tinh chat phi tuyen hinh hpc ciia ket cau va phi tuyen vat lieu. Thuat loan lien hoa vi phan dugc sir dung de giai bai loan toi uu de ra. Dan thep phang 10 thanh duoc xem xet de minh hga cho nghien ciru nay.
TM^l Idp bal toan ldi uti ddn Ui6p
Tong khoi lugng ciia ket cau dugc chgn la ham muc lieu ciia bai loan va dugc toi thieu hoa theo phuang trinh (1).
Miniyl,\)^pT} 1 y^L \ (1)
trong do P la khoi lucmg rieng ciia vat lieu; "^ ={y\^yl^•••^yd) la vec ta bien ihiet ke, cung chinh la di?n tich tiet dien ciia cac thanh dan: d la so lugng bien thiel ke; t/, la so thanh dan trong nhom phan tir thanh thu /; iy la chieu dai ciia thanh dan thuy trong nhom phan lir thii /. Trong bai loan thiet ke CO bien la bien lien tuc thi bien thiel ke }',{' -1.••><'') dugc chgn trong khoang gia tri cho truac [>','"",>',"'"]. Trong bai loan ihiet ke co bien ia bien roi rac thi >', dugc chgn lir mgt tap hgp cac gia tri rcri rac cho truoc.
Doi vdi lo hgp trang thai giai han cuong dg, bang viec su dung phan lich true tiep cho phep tinh loan kha nang chju tai ciia ca cong trinh. dieu kien rang bugc dugc the hien bang cong thirc iZ).
C" =1 - < 0 (2)
trong do R^ la kha nang chiu tai ciia ket cau doi vai to hgp lai trgng Ihii k va 5^ la hieu img do to hgp tai irgng c u o n g do thu A- eay ra.
I Kfioa /IOC Ky thuit va C6ng nghi
DOI VOI to hiTp trang thai giai han su dung Jieu K\-cr\ vc ehuven VI sOduoc xem vet ihiSng qua cong thuc (3i
S t.'i I ^ . —. - I <(), i -1 -•-•>-
V
trong do '»! la sti nui dan dugc xetdieukicn ehuven \ i . A xa s- la chiivcn vi va giai han chuyi-n vi cua nut thu ' lutmg ung vol to hvTp irang thai gidi han •iu dung ihu /,
i)icu kivn rang buiv vi- lan M> <^io dimg nene cua kel cau dugc the bicn n h u ( 4 i
(•'•' ^ — : L - | < ( ) . \...nm l-^'
iroii^ido lUn 1.1 M'ii.in-od.io done neng duiTC veldi-n. . ' r, va / . lu Lin s o d j o dgng neng I h u / c i i a ki'l cau vagi J in cho phep cua no
Ooi \ a i b.!i loan loi uu lO dicu kien rang buoc a ircn. de ap dyng cic ihu^t toan nieUi ho-ril-lic ciuing la can su dung cac kv ihii.it di- \ u Iv cae dieu kii-n rang hwetc Trong nghien cuu luiv. phuinig phap ham phal dugc su dyng do kv thuat n.iv khii dmi gum \ a hicu qua m cho hau het eac loai ring bupc khac nhau Khi i\i\ ham muc ueu cua hai man dugc MCl 1,11 nhu v u r
nrtitMnrtimm'"!"""'""" » a P "
IhiKi. ...an lion !-».. >• r l > - " " ' " " ,.,„„ trong k M p h . , m,nl> [l-t] ^.. J."«-- ^"'f -"'"f, , „ „ „ do CO c i c bai
„h,;-u J.mg Ku u...n .oi m kluc n •• • - ^^^ , | „ , j , ,o.in ,oanl.-.,.m>.>J..nl.V n . l M Noi Ju",-
c : . „ n . range g , a c i n . , . « n , * l - „ n , c . . c o
" „ „ l ^ I = ( k 0 j i - u / * : - a - / ' I ' ^ ' I trong do'
/', l|n,.>M(.-.Oll II. \ V , „ , , | , . 0 ] |
(5)
(6)
V Ol ff .., ./ \ a (7,, la cac tham si- phal tucmg ung \ 6i cac dieu kivn ning huge \ e eucmg dp. chuyen vi va tan so dao dpng rieng f o n g thuc (5) cho ihay rang, neu mot thiet ke nia V1 ph,?m dieu kicn rang bupc thi hani muc Ueu iuong ung '-e diu'i egng ihem mot gia tn ggi la gia In phal tuong ung cho VI phijmi do Do qua trinh tin uu la toi ihieu hoa ham m\ic tieu, cac thiet ke vi pham Jieu kien rang buoc sc dan djn bl loai bo
111,1 in i.iia Lac iham-.0 phai nav khong nhu thugc \ JO D.LI loan loi vm. luv nhicn thuifng J u o . lav gia in du lon n h i m loai K)cac ii-ici ki' i^' vi pham \ a ^in ^on lai cac lliiii ke-ihoa mail 1.11 ca ^ae dicu Men -ui:.: i^uoc Irou'^ nghien LJU n;.
cac Iham ^o plijl duoc lav bang lu uim
€[> , „ ] • ' = ' -
..d (7) , •, , i , lin luot la gia Iri
• ™ i ^ ' ' " ' ' ' V " ' " ; ' ' ; ; . : , •w™:Wi.can.6iuunay
, I0) = , .+,W(0.1]Mv,,„-A;.,.),/ = l,...,rf (8) ironudo --om/iO.!] la s6 llwc chpn ngSu nh.en trong klioang ,ir o'dC-n I 0 thS he thir ( r + l ) . Mong iing v m ca the thir * irong quin lliS, x.(r). mpt ca t h i m m dirge tao ra bang pliep dot hien nliir sau:
• . - - v . ' I . F 4 v , , r ) - M . ) ] (5) irong do, r ,/•„;•, la ba s6 tir nhien dirge chgn ngau nhien thoa
man^di^u kien 1< r,*r,^ r.^k < NP- F la he s6 k h u k h dai thuong dugc chgn trong khoang (0,1). Trong nghien ciru nay chpn F = 0,7. Trong cong ihirc (9), n6u xay ra trucmg hop mpt bi^n s6 u ciia vec to u v u g l ra ngoai k h o a n g gia tri cua no [•^mir'"'''i,maJ thi u nhan gia tri bien no vi pham. TCr ca the u. mgt ca th6 moi, v, duoc tao ra bang each lai ghep vai x,(0 Iheo nguyen tac sau'
k h i r a w 4 0 , l ] < O - (iQ) .T,,(f) khi ra«t/[0,ll>O-
trong do Cr la tham so lai ghep co gia tri irong k h o a n g (0,1).
Thyc hien so sanh ham muc tieu ciia v va xft). ca the nao CO gia tri ham muc lieu nho hon se la ca the thir k trong quan t h e o the he thir (/+!)
Luu y rang, trong p h u o n g trinh (9). ca the x,. ( 0 dan[
d u a c ehon la ngau nhien trong quan the T u a n g ung v a irutmg hgp nay ta goi la ky thual ' D E ' r a n d / l ' Tuy nhien ncii \ . l O d u g c chon la ea the tut nhat trong quan th£ thi I.
CO k> ibuat "DEbe-ii 1' Day la 2 k\ thual dot bidn duoi su dung long rai hien nay Diem khac biet gifja 2 ky thua jy 1.1 o kh.t niuvj lim kiem long quat \ a tot ,j-, hoi lu cii qua ;rinh toi uu Lu '.he, ky thual 'DF rand iuv iri lAi si da u.iiig cua quan ihe ^a kha nang lun n,,,,, ^ ^ ^ . hon ky thual "DL best I i u y n b i e n . k l " - ' u n kiOm I
KHOAHOC \ I CONG M G H E - V "
Khoa hpc Ky thu$t va Cong ngh^ •
phuang va loc do hgi lu ciia ky thual "DE rand 1' lai kem hem "DEbesL 1".
Vi in minh tioa
Ddn phdng 10 thanh
De minh hga cho bai toan loi uu co xet den dieu kien rang bugc la tan so dao dgng rieng. trong phan nay chiing la se xem xel mgt dim phSng 10 thanh nhu trong hinh 1 N'hip dan la 9.144 (mm). Tai trgng lac dung gom tinh tai DL . hoat tai LL va tai Irgng gio IV duac quy ve thanh cac tai tap trung tai cac nut dan. Gia tri ciia DL, LL \a U' lan lugt la 400 (kN), 300 (kN) va 300 (kN) Vat lieu co cuong do chay la F^ =344.1 MPa va mo dun dan hoi la E^lOQGPa.
Tai trgng khoi tap trung, ma.-is, diing de tinh lan so dao dgng neng ciia ket cau duac gia thiel dai lai niit dan va co khoi lugng la 454 (kg). Khoi lugng rieng ciia vat lieu ia 7.850 (kg/m^).
Bai loan toi uu co 10 bien thiet ke la tiet dien cac Ihanh dan dugc chpn trong khoang gia trj [64,5: 22.580.6]
(mnr). Dieu ki?n rang bugc g6m" 2 dieu kien ve cucmg dp luong irng vai l6 hgp tai trgng (1.6DL +1,2/,L) va {12DL + \,6W + 0.5LL)\ ! difiu kien ve chuyen vi luong ung vai to hgp (I, ODL + 0.71^ + 0,5LL) vai giai han chuydn VI eua cac niii dan theo phuang ngang khong vugt qua /i/400
= 22.86 (mm) vai h la chieu cao ciia tang; 3 dieu kien ve lan so dao dgng rieng. yj > 7 . /-, > 15 v a f\>20{H=) vdi Ti-.A ^^ fi '^ -^ t^" so dao dgng neng dau lien ciia ket cau.
Cac to hgp tai trgng dugc xet den trong bai loan dua theo tieu chuan AISC-LRFD ciia My [1]. Phiin m^m phan tich phi luyen PAAP se duac sir dung de linh loan img xu phi tuyen ciia kcl cau nham danh gia dieu kien rang buoc Chi liet vc phan mem PAAP doc gia co the tim dpc trong cac lai lieu [3. 4. 8, 9]. Cac thong so ap dung ctia thuat loan DE dugc lya chpn nhu sau: so bien thiet ke (cfj la 10. quy mo quan the {NP) la 25, s6 thg he t6i da {Ma.\lleralion) la 4.000.
bien dp dpi bien (F) bang 0,7, xae suat lai ghep (O") bang 0,6. Luu y rang, viec lya chgn cac tham so NP. F va O- co anh huong den ket qua cua chuong trinh lot uu. Vi du. neu
\P chgn ldn se giup qua trinh toi uu tranh bi toi uu cue bg lot hon nhimg lai hgi tu cham han va ton nhieu thai gian tinh loan. Do vay, tiiy thugc vao lirng bai loan loi uu khac nhau ma cac gia tri nay can lua chgn mgl each thich hgp.
Trong trucmg hgp nghien eiru nay, cac gia tri ciia cac tham so dugc lya chgn dua tren sy tham khao tai lieu [3]. Dieu kien dimg lai ciia chuong trinh loi iru la khi so the he toi da dat den gia tn cho inidc. hoac khi gia In cua ham muc tieu khong thay doi trong 1.000 th£ he lien tuc.
Hinh 1. Dan phang 10 thanh.
Kit qud tinh loan vd trao ddi
Ba trudng hgp bai loan toi uu dugc xem xet la: (1) Tat ca cac dieu kien rang bugc dugc xel, (2) Cac dieu ki?n rang bugc ve tan so khong dugc \el den vii (3) Chi xet cae dieu kien rang bugc ve tan so. Dc \c\ den yeu to ngau nhien ciia cac giai thuat meta ha-ril-lic, chirang trinh toi uu dugc chay 10 lan dgc lap, Chi kcl qua tdi uu tot nhat dugc trinh bay trong bang 1 Dua vao bang 1 ta co the thay r^ng, khi xel lat ca cac dieu kien rang buge, gia tri Idi uu tim duge ciia dan la 675,54 (kg), ldn hon kha nhieu so vai hai trudng hgp edn lai. Dieu nay cho thay rang, bai loan tdi uii khdng chiu sy anh hudng ldn ciia tai ea cac dieu kien rang bugc vc cucmg do, chuyen vj va tan sd dao dgng neng. Hay ndi mdt each khac, cac dieu kien rang bupc nay deu ddng vai trd quan trpng trong bai loan tdi uu dang xet. Do do. viec xet den tat ca cac dieu kien \e cudng do, chuyen v i va tan sd dao dgng rieng la can thiet trong bai loan tdi uu ket cau dan.
Bang 1 Ket qua toi u'u tot nhat.
Til a di(u buocdin^
W'ii 365i3
rejw
m%
MiO
\iii.m Ki'6y
lii^D rSDg Kbong 1^1 cdc dicu ring bujc
H,50 370.55 126.45 276,05 M,50 226.25 M,50
elan so
klfn Chi t i l cic a/k k l ^ ling bofc \l Iin u 1 143,6(1 52DJ3 i.ni.io 483,73 64.50 i50J4 727,75 'W,4K
I Khoa hpc Ky tt}u$t va C6ng ngtif
Hinh 2 trinh bay duimg cong hgi tu cua 3 bai toan loi ini. Bai loan xel dieu kien rang bucx v c tdn >d cd tdc do td' uu nhanh hon 2 bai loan kia V 3 dung - v" • • vong I3p eua qua tnnh ldi uu khoang hon LOOO .i" Bai ".»an \ e i tJt ca cac dicu ki?n rang buoc hgi ly cham nhat va dung iai '-.hi -o vong l^piren 3 5lK). Dieu nav co nghTa la, vice xet den dieu ki^n riing bugc hao gdm ca tan ^d dao dgng n e n g . cuimg do V a chuy en \ j khicn cho bai loan idi uu tro nen phirc lap h m rat nhieu so vai \ ifc chi xel tan sd dao dgng rieng. Noi mgi each kh-ii. bai loan tdi uu duoc \ c m \ e i trong bdi bao nay cd tinh phirc tap cao him rat nhicu so \cn bai loan ldi iru chi xel tan vd dao ddng neng
2000 1.KO0 1 ^ 0
•C 1.400
3 1200 I LOOO
:: 800
- Xo I o n bo J K U b c n m g b u ^ - Kbocig Ifl dicu ben rang b t w \ e tic 10 ,
•- \ : ' ' : ibennngbuoc \ e l i n w i
\
500 1.000 L500 :.ooo :K' SovcagUpqiulrmhio
3.000 i 5 0 0 4jOOO
Hinh 2 Oiro^g cong h^i i^ cua bai toan loi iru h^ dan 10 thanh.
1*1 Intii
\ g h i e n cmi da trinh bay mgl dang bai loan tdi uu mdi cho i-lm ihep trong ilo co \ei den cac dieu kien rang bugc v e chuv cn VI \ ,i cuong i.\c' dudi cac to hgp lai trgng khac nhau V J dieu ki^n rang bugc v e tan so dao dgng rieng ciia ket cau.
Ham myc lieu cua bai loan ldi uu la ham long khdi luong.
Cac dieu ki^n rang bugc v e cudng dp va sir dung dugc xac d|nh dya \ a o phan lich trye liep cho phep xet den cac tinh chat phi luvcn hinh hgc cua ket cau va phi luy^n vat lieu.
Thugi loan lien hda vi phan dugc sir dung de giai bai loan idi uu de ra. Ket qua phan tich dan thep phang 10 thanh cho Uiay cac dieu kien rang bugc \ e cudng d o . chuyen v j v a t i n sd dao dpng rieng deu anh hudng ldn den ket qua toi uu cho nen can phai dugc xeni xel. Ben canh do, bai loan tdi uu cd xet tai ca dieu kicn rang budc v e chuyen v i, c u o n g do v a i J r sd dao dgng neng co linh phuc tap cao hem rai nhieu so M>
bai toan chi xet i,in so dao dpng rieng Dieu nay mo ra mo"
Idp bill lo.tn mm \ c tdi uu ki-l c.'iu dan co mil-' phir^ "ap . hem va cCine thuv u wi, ..ic b;;^ l o . ; . loi uu d"i '• - den truoc do
TM UEU TMM (MO
H l s c - L R I D l l "
,„.• ofSlo
••Dc^ 1 structures
Eiiiopt^i"!
| , | , . s i g a s - l - l Eurtx-ode 3 l:ral>l•
- pan 1.1 f c n t r a l rales and ralo "•' ™ '
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