laaa KHOA HOC - CONG NGH?
Tom tat: Bii bio gi&i thieu phifong dn tidp can giai tich de xdc dinh dang nghigm hiin eua do vdng tuyin tinh eua tim gia cwang bdng he thong swan ting cw&ng theo hat phwang. Cic phwang trinh chu dgo eua tim dugc thiit lip dt/a trdn ly thuyit biin dang trugt bgc nhat kit hgp v&i mdt ky thugt san tic dung sw&n cil tiin. Giii bii toin bing phwang phip Galerkin di nhan dugc kit qui do vdng tuyin tinh dwai dgng hien. Anh huang cua sd Itfgng, kich thw&c swan tang ctf&ng t&i do vdng cua tim eung dwgc khao sat chi tiit.
Abstract; 77J/S paper presents an analytical approach to determine the explicit solution form , of linear deflection of lattice stiffened plate. The ' governing equations are established by using the first order shear deformation theory and ^ improved smeared stiffeners technique. These ( equabons are solved by Galerkin method and deflection is obtained in explicit form. Effects of quantity, geometric parameters of stiffener on the linear deflection of plate are also ••
Keywords: Stiffened plate. Anisotropic structure. First order shear deformation plate theory.
I . M d ' D A U
Cae k i t eau tdm d u p e gia c u d n g b i n g he thong cac s u d n tang e u d n g leeh tam la dgng k i t c l u d u y c s u dyng pho bien trong n h i l u nganh ky thugt.
Trong eae cdng trinh giao thdng chung d u y c s u dung lam cac ban mgt eau t r y e (dj) h u d n g n h l m t l i u u hda giua trpng l u p n g va kha nang ehju l y e cda k i t eau.
Ky thugt san tde dung ciia s u d n tang cudng theo cac phuang cho ly t h u y l t tam co dien dupe d l x u l t bdi Lekhnistky. Trong nhiing nam g i n day, n h i l u tdc gia da s u dyng ky thugt nay de phat t r i l n cho nhieu k i t cau cd hinh dgng va ldm bang cac logi vat lieu khac nhau. Cd the k l d i n mpt so cdng trinh ddng chii y gan ddy: Bfch va cac cdng s y [1-3], Dung va Nam [4], Nam va cac cdng s y [5] da s u dyng ky thugt san deu tae dyng s u d n de phdn tich on dinh ddn h l i t u y i n tinh va phi tuyen tmh va ddng ddng,
'ISLUIBSI
mmm
PHAN TiCH TAM CHIU UON CO SirdN TANG CtrdNG XIEN BANG LY THUYET BIEN DANG
TRUrOT BAC NHAT
NCS. ThS. LE TH! NHU" TRANG THS. PHAN HUY THgC KS. D d H O A N G T C I N G Trudng Dgi hpc Cdng nghg Giao thdng vgn tal
dao ddng t u y i n tinh vd phi t u y i n cua cdc k i t cau Idm bang vdt lldu FGM ed s u d n tang eudng lech tam nhu: t i m , panel try, vd thoai hai do cong vd vd tni trdn. Trong do s u dyng ly t h u y l t t i m vd eo d i l n va tfnh phi t u y i n hinh hgc cua von Karman Donnell de nhgn d u p c phuang trinh ca ban de khao sat ung xu tTnh va ddng eiia k i t e l u .
Khi be day ciia ket c l u tang len hogc k i t cau tare hudng dj hudng (vi dy n h u cd s u d n trye gfao, suon xidn), ly t h u y l t t i m c l d i l n cd the t r d nen khong t h y c s u phu h y p va e i n t h i l t phai xem xdt tdi cdc ly thuyet b i l n dgng truot. V i vdy, bdl bao ndy s d dung phuang phap t i l p can san d i u tdc dung sudn cai t i l n de t h u i n nhat k i t c l u v l mgt k i t c l u di hudng t u a n g d u a n g , qua dd ap dung ly t h u y l t bien dang t r u y t bgc nhat de xae djnh dang nghiem h i l n ciia do vdng Clia t i m .
2. PHU'aNG TR'INH C H O DAO
Xet tam ehu nhdt vdi c h i l u dai a, chieu rang b va c h i l u day h. T i m d u y c dgt trong he tog do D l Cac cd gde tpa dd d gdc cua tam, mat phdng xy tning vdl mat giij'a cua tam vd z Id tog dd c h i l u day tam ( - / i / 2 s z s / i / 2 ) .
Hinh 1. Md hinh tam cd sw&n xidn
So 9 nam 2017 1
KHOA HOC - CONG NGH£ I M I I I Li§n <ni bien dgng - ctiuySn vi tiieo ly tiiuy6t bien
dgng tRfat bac nii^t [8]:
fw_^,Vy,w^^ + v,^ + w^w^,0^ + w_^,^ + w j (2) trong do E\ va e° Id biln dang phdp vd / " Id biln dgng truot tgi mat trung binh eua tam vd -f^, -f^ la cac thanh phan bien dang truyt trong mat phang xz vd yz, ^ j , 0^ la gde xoay eua phap tuyin mat trung binh theo hai true x vd _y tuang ung.
Phuang trinh tuong thich biln dang:
gO +£0 _ / =0 (3) Ap dyng djnh ludt Hooke cho tam va sudn. Tich phdn bleu thuc ung sult-blln dgng va md men theo bl ddy tim, chleu cao sudn va ehuyin doi he trye tga dp dja phuang ciia sudn ve hg tpa dd toan eye Clia tim, ndi lye tim nhdn duoe:
^jy = "^eeY^, + ^66 (^x.> •*• ^y.x]' trong dd s^,s^ \i khoang cdch giua cde sudn tang 0 (, eudng theo hai phuong tuang dng. Hai gdc <p,,^n M = B-,e + B..e + D,,d) +D..<b , .> . , ^ . . . .- ^ .. ,.,. \ . •
y ^' "^ ^^ y ^^ '-' 22-ry.y' 1^ gQj, f^Q,p |jQ,| gyjo-n tang cudng xien theo hai Q =A w +A <f} , phuang so vdl try x..4,,y4j Id dl^n tfeh mat clt ngang
cua sudn va/,, I^, ^^,z.^ la md men quan tfnh vd dp '^y^•^\^x'^-^i^y"^^ix^x,^"^^ii't'y.y' Igch tdm eua sudn tang cudng tinh tdi mgt trung
A,, A^
S„
5,1
5 j ,
5„
^66
D,
i ) j
D^
D^
K
E, E.A, . ^ E,A, . ,
= -—^+ ^ ' - - ^ s i n ip + ^' ' ^ s i n y , , l - v s, s^
^ 1 ^,A, • 2 2 E , ^ . . 2 2
= -*— + —^•' ' " Sin (p,.cos(p,+ '^ -"^sin (p,.cos 2 ( 1 + v ) s^ ' Sj
E, E,A,z, , E,A,z, ,
= • T-{ ^' COS (p + '^ '^ ^ COS w l - v S| J j
£ , E .A ,z, , E ,A , z , ,
= — ^ - t - •i'Cos y . + I? I? ' COS y , . .E.V £ „ ^ , z , . , , E,A,z, . ,
= o„=—^+ ' ^' ' sm w,,cos m,+ ' ' ^' ' s m ni,,cos 1-V Jj ' Sj ^
£ , £ , - 4 , 2 , . . £ , . 4 , 2 , . ,
= — ^ + ' s m y , + '•' " ' s m ©,, l - v 5, Sj
= ^ — + s i n (p .cos ffl + " '^ ' s m OJ r o s 2 ( 1 + V) S| 5j
£ , £ , / , , EJ, ,
= ^ + ' ' c o s tp + '^ '•' COS tp,, 1 - V 5| J j
£ , v E,I, . , J £ , / , . , ,
= D -—^+ " s i n y .cos y +—•• " s m y .cos 1 - V J'j J j
£ , E,F . , E J , , ,
= — ^ + " ^' s m ffl + " - s m ffl, l - v Sj '^j
E E 1 EI
= , ^ .• + —''J.'' sin^(p,.cos^ffl. + " ' ' ' ^ s i n ' f f l , . c o s ^ i j 2 ( l + v ) Sj ' ' ^3 '
= 4 = K - r ^ .
Ciii tiet cac ii# s6 6u/q/c trinii bay cg tiie dirdi day:
binii cua tam. K = 5/6 la tie so di^u ciiinii trnpl [6].
H? ptiLFcng trinti can bang du'g'c viet nhif sau
e„+G„+?„-o
( £ , £ , £ ) - f I\,Z,Z')E dz Quan tie giOa bi^n dang v4 lyc doc du'gc suy ra tif -h/2 (4)
A, = i i =—'—+ '•^sm ffl,,cos g}^+ '•* s^sm yj.cos fflj,
'^^ '' '• rl-46ff,-i-2B-j'P„+<t>„) (6)
I S6 9 nam 2017 ©lSi®|}lJ©
aaaaa KHOA HOC-CONG NGHE
trong dd • / . , , \
Bnf^*[B,,*B^^-2B^)f^
^'AA2-4i42'4*1 - 4 2 / A . 4*2 = -42/A. +^2*,/,^ + A*i*,„ + (O21 +2^66)*w +(^2, *2Dl,),l,^^ + Dl^4,^^ + g„~0 (8) 4.-.4„/A, 4-4,/A, lB'-B'\f +B- f +D-A
K - [42^2, - 42AJ/A. S,*2 - [42^22 - ^B„]/A. +(A*2 + B ; ) * , ^ + ^ . " A . ^ " ^44«>,
4=[flu4,-s2,4,]A-4-h24,-s224,]A. (s'22-Bi,)f^+B;j^^*{D;,+D-^)<p^_^
,. „ , „ . „ I, +^;«»,^+aX„-45#,-45"'.,-o(io)
4 i 6 - V 4 6 > ^ 6 6 - ~ - ° 6 6 / 4 6 ' .. , / .. .. .. \ , . . .4 2 / « , + i 4 2 + 4 l + 4 6 ) / ^ + 4l/.KK».
Ttiay mol quan ti# gl&a bien dang va lyc doc vao +^2i**,x« + (A2 "^eel^i^tw"*"
gliJa mo men va iyc doc nhy sau: Dieu l<idn bi6n cCia t^m dygc viet cho tru'dyng hi^p tya don bon canh nhy sau
M =B'N +B'N +D'(II +D'(I) ,
' " ' " ' " " " " w . J V ^ = ^ ^ . M , - 0 , J V , - 0 tal;c = 0,a, w=N_^=<p^-M^-0, N^-Otaiy-Q,b. (12)
Bi^u i<ien bien (12) dyoc thoa man chinh x^c neu '^v = B,,f/,, + BM**,,^ + flss*,^, chon dang nghiem
w(jc,y) = i^sina;csin^y, 0^(j:,^] = 0,cosaxsmPy, A ' . - ' S H S . ^ V ; , * ^ , . A*2-B„fi; + «,2B2*2 + A2- ! > , ( x , r ) - 4 . , s i n a « o s ^ , , , a - W » ; / ! - W 6 ; ( " )
D* = B B' +B B* -i-D , *™"9 ^^ ^ '^ bien dg dp vdng, m vd « la nda budc . o n ' D D^ n sdng theo cdc phuang J:,^'tuang ungm, n = 1,3,5...;
•^22=^21^2+ -^22-^22+ ^22' $^,0^ Id blcn dp gdc xoay.
A ' 6 = 566-566 + ^ 6 6 '
Thl phuang trinh (13) vao phuang trinh tuang thfch Dua vdo ham ung suit fix,y) thda man dilu kign C'')' ^^ 9'^' Phuong trinh nhdn duye d l tim dgng
hdm ung suit, sau dd thl (13) vd bilu thuc tinh ham ung suit vdo phuong trinh (7 * 9), dp dyng phuang
^x '^ fyy'^y " fj^x'^xv = ~/>j (^) P^^P Galerkin nhgn dugc hg 3 phuang trinh sau
The phuong trinh (7) vao eua hg phuong trinh (5) li w 1 dy / * - 0 va phuang trinh tuang thich biln dgng nhgn dupc4 \h[^'^hi^x ^h^^i = ^ phuong trinh 4 I n f,<(> ,0 ,w cdc h g s l duyc trinh bay nhu dudi day:
^lyKSJnU© S6 9 nam 2017 I
KHOA HOC - CONG NGHE l l l l l
',2-[(A'2+2D;)a^^ + D-^;8']+
[B>' *(«,*, + B\^ -2B;,]a'fi' + Bl,fi']G,.
0.2
Io.l5
» 0.1
i
oos / -*-PliiwnE[71 / - ^ - B S b S o
lF4.006m;
(p600Pa.
Tu hai phuang trinh diu ciia (14) nit ra duyc mil quan he giiia ^j,^2 ^^^° '^'^^ ^^ ^^ ^°"9 ^' ^^^^
vdo phuang trinh (13) ta cd:
Hinh 2. So sinh kit qui do vong l&n nhit v&i kit qua cua Phwang [7]
D l ddnh gia higu qua ciia sudn tang cudng tdl dp vdng cua kit cau dudi tac dyng cua tal trpng phdn bo deu^Q, bai bao se tiln hanh khao sat tam cd sudn tang eudng trong cdc trudng hop khdng cd sudn tang eudng, sudn tang cudng dat Idch eae gdc khac nhau so vdi phuang x va anh hudng cCia cac thdng so hinh hpc khac tdl kit eau.
Bang 1. Do vong Ion nhat w^^Jmm) cua tim dwai tie dtjng cOa tdi trgng phan bi q^ theo kieh thw&c
tim, gdc xien cua sw&n
/.,+/,
I I - I I ^^I I - I I I
'22*33 '23*32 '22*33 '23*32/
Td phuong trinh (15) nhgn duyc bieu thuc tinh bidn dp dp vdng theo tai phan b l thay vdo (9) nhgn dupe
3. KtT QUA S6 VA T H A O LUAN
D l kiem tra tilp c^n cua bdi bdo, cdc kit qua s l dupe so sanh vdi kit qud ciia Phuong [7] khi su dyng lv- thuylt tam c l diln. Nhu quan sdt dupc trdn hinh 2, gia tri dO vdng Idn nhat cua tim cd sudn tang cudng trye giao (theo hai phuong x, y) trong tnj'dng hyp tam mdng thi kit qud tinh theo I;? thuyet CO diln va ly thuyet biln dang truyt bdc nhit cd sai s l rit nhd.
I So 9 nam 2017
Khdng sifCrn Su6n theo rngt phirang
Si/crn theo hai phirong (p, = 0°
ip,=JO"
ip, ^'^S"
iPi^(f.<p,^}5lf q>^^0°.q);^ISS°
<p, = <f.'Pi^^O°
iPj = }ff'.iPj=l35°
ip,^45'.ip2^135' q>,^3ff',<p,^90°
a = b = 2,0 m w(mm)
0.03 0.02Z1 0-0182 0-0173 0.0151 0 0144 0.0174 0.0127 0,0123 0 015
Hieu qua (%]
35 82 64.12 73 51 98 OB 10771 7197 135.10 14417 99-01
a = 20m,b = 40m w(mm)
0-0747 0.0379 0 0414 0 0468 00273 0.0295 0.0377 00315 0-0345 0O407
Hi^u qua {%)
97.15 80 55 5947 173.70 153,24 9825 137 33 116.63 83-44
Kfch thudc cua tam thep:
a = 2.0m,b = 4.0m,h = 0.0lm, Dgc trung vat lieu eua tam thep:
mmm
l l l l l KHOA HOC - CONG NGHE j
Bang 2. Bd vong lan nhat w^Jmm) cua tam dirai tac dt^ng ciia tai trong phan bS g^ theo kich thuvc vi I khoang each giira cac sir&n (q^-S.O kN/m', a = 2.0m,b.4.0m,h = 0.01m.^'^^i ' ^-2' ^ " " Q " " . 'i
v = 0.2, (p,-4S'.<p,-135'.b^i-b^,-0.005m.h^j-h^,-0.02m, s,-s^-0.2m) <
Khflng su^n Siiim 2 phirong Sai If ch (%)
^ , = * . 2 f > " ; 0.001 0.0025 1 0.005
h^, = h^, (m) 0.01 0.025 1 0.04
s, = s^ (m)
0.1 0.25 0.4
0.0747 0 0602
24.07 0.0468
59.47 0 0345 116.63
0.0589 24.90
0.0249 200.48
0.0098 662.03
0.023 224.54
0.0385 94.34
0.0468 59.47
E = E^^= £^2 = imGpa, V = 0.2,
Tai phan bo tren be mgt t i m : 9 ( , = 8 . 0 A : / v / m ^
Kfch t h u d c cua s u d n tang c u d n g thdp:
Z)^,=i'^2= 0.005m,
K\ = Kl = 0-02m,
J, = 5'2 = 0.2mCd the nhdn t h i y trong bdng 1, hieu qua gia eudng cua s u d n Id r i t Idn d l i v d i mdt l u y n g s u d n tang c u d n g nho. T n j d n g hpp kieh t h u d c cac cgnh bang nhau va gde dgt s u d n q), = 45°, g?^ = 135° higu qua tang cung k i t cau Id Idn n h i t khi dp vdng tang r i t mgnh, bien dg dp vdng giam tdi 144.17%. Trudng hyp higu qua nhd n h i t la trudng h y p s u d n dgt tnj'e giao song song vdi cae cgnh (trudng hop ban mat c l u toPC hudng).
T i l p tuc khao sat dp vdng ciia t i m theo kich t h u d e va khoang cdch giija cac s u d n trong bang 2. Thay d l i tung gia tn kich t h u d c s u d n trong khi cac gia tri khac giu nguydn. Cd t h l t h i y chieu cao s u d n dnh hudng Idn n h i t tdi hidu qua cua s u d n . Khi e h i l u eao s u d n la 4 cm thi higu qua ldn tdl 662.03%.
4. K £ T L U A N
Bai bdo da thiet ldp cac p h u o n g trinh c o s d theo ly t h u y l t b i l n dgng truot bdc nhat va d y a tren mOt phuang phap t h u i n n h i t hda k i t cau tam cd s u d n tang c u d n g xien. Giai he phuang trinh can b i n g vd tuang thich b i n g phuong phdp Galeri^in d l thu d u y c dang hien cua dO vdng theo tdi trgng. Cac k i t qua 50 da chl ra hieu qua tang c u d n g dgc biet cua gan xien gia c u d n g so v d i gan tnj-c giao •
^m
T A I L I E U THAM K H A O
[1] Dao Huy Bich, Dao Van Dung, Vu Hoai Nam. Nonlinear dynamical analysis of eccentrically stiffened functionally graded ^;,ii cylindrical panels. Composite Structures 94 (2012), 2 4 5 6 - 2 4 7 3 .
[2] Dao Huy Bich, Dao Van Dung, Vu Hoai Nam. Nonlinear dynamical analysis of eccentrically stiffened imperfect functionally^
graded doubly curved thin shallow shells.
Composite Structures 96 (2013), 384 - 395.
[3] Dao Huy Bich, Dao Van Dung, Vu Hoat Nam, Nguyen Thi Phuong. Nonlinear static , and dynamic budding analysis of imperfect eccentrically stiffened functionally gradedj*
circular cylindrical thin shells under amal ' compression. Intemational Joumal of Mechanical Sciences 74 (2013), 190 - 200.
[4] Dao Van Dung, Vu Hoai Nam. Nonlinear '•
dynamic analysis of eccenMcally stiffened | functionally graded circular cylindrical thin shells under external pressure and surrounded by an elastic medium. European Joumal of Mechanics A/Solids 46 (2014) 42 - 53.
[5] Vu Hoai Nam, Nguyen Thi Phuong, Dao Huy Bich. Dao Van Dung. Nonlinear static and dynamic buckling of eccentrically stiffened functionally graded cylindrical shells under axial compression surrounded by an elastic foundation. Vietnam Joumal of Mechanics 36(1) (2014), 2 7 - 4 7 .
[6] Brush D.O., Almroth, B.O., 1975. Buckling of bars, plates and shells. Mc Graw - Hill, Nevir Yoric | [7] N g u y l n Thj Phuong. Phan tfch tTnh t i m | phang vd panel tn^ composite co tinh b i l n Vn\^n m.
cd gdn gia owimg. Tgp chf Khoa hpc vd Ky thugt - Hgc vi^n Ky thugt quan s y 145 (2011).
S6 9n3m2017 I
