Nghien CLPU thiFC nghiem tipang tac dong ILPC hoc cua ket cau tam tren nen phi tuyen chju tai trong dong dang song no
Interactive Experimental research of structural dynamics of the plate on nonlinear foundations under dynamic load wave explosion
Ngay nhan bai: 12/12/2015 Ngay siJa bai: 8/02/2016 Ngay cliap nhan dang: 16/03/2016
TOM TAT
Bki bao trinh b i y ccJ sd li thuyet vfe phflong phap phSn tii hflu han (PTHH), dp dung trong bai toan tinh k i t cau tam tiidng tac dong liic hoc v6i nen phi tuyfen, chiu tac dung cua tai trpng dong d^ng sdng no. Dong th6i, trinh bay md hinh thi nghi?m va kfet q u i thi nghifein n6 tai hien triicJng khu viJc huyfen Ba Vi, Ha Ngi (thang 11/2015). Tren cO sd chuong trinh HTSl da lap i3ng dung vao trong phan mem ANSYS, tinh toan trang thai dng suat, bien dang v i chuyfen vi cua ket cau tam va moi trilcfng nen trong mo hinh bai toan khong gian. Tien hanh so sanh d i n h gii kfet q u i giiia li thuyet v i thilc nghidm.
TH khoa: Tam, bien dang, nen phi tuye'n, song no.
ABSTRACT
This paper presents the theoretical basis of the finite element method (FEM), the application of structural plates calculate the dynamic interaction with non-linear foundation, strain to dynamic loads wave explosion. Also, presenting experimental models and experimental results at the scene blasting area in Ba Vi district, Hanoi (November 11/2015), On the basis of already set up programs HTSl application software into the ANSYS, stress state calculation, deformation and displacement of the structural plate and the foundation environment in the model space problem. Conducting comparative e'valuation of the results between theory and experiment.
Keywords: Plate, deformation, nonlinear foundation, wave explosion.
ThS Vu C6ng Hoang - Binh ehung Cdng binh PGS.TS Nguyen Ttftfng Lai - Hgc vien Ky thuat quan sU [email protected]
Vu Cong Hoang, Nguyen Tu'tfng Lai
1 . D a t vain d e
Cac nghien eflu II thuyet ve tam, mdi trudng nen da cd nhieu bdo cao khoa hoc cdng bd. Tuy nhien bdl toan tflOng tde ddng Iflc hoc giua ket cau t a m vk nin phi tuyen chju tdi trong sdng nd trong m d hinh bai toan khong gian t h i con rat han che, it dfldc cdng bd vd dac b i e t l d p h a n t h i n g h i e m v e v a n d e n a y .
Thfle t ^ eho thay, khi tinh toan tam tflOng tac vdi nen, hau het bd qua bien dang trUcft ngang trong t a m d o Iflc cat gdy ra (gid thiet cua Kirchhoff). Tuong tU, de d o n gian trong tinh toan, m d hlnh n^n dan hdi thfldng dfloc sfl dung rdng rdi [1][2], va bo qua dnh hUdng cfla bi^n miin khdo sat khi tdch ra khdi nen va viing mdi trudng con lai.
Coi khdi nen dfloc tdch ra dfl Idn de khdng cd sfl phdn xa cfla sdng lan truydn trong mdi trfldng. Vdi quan niem tinh todn tren t h i chua phdn dnh day dfl [S][7][8]. V) vdy, nghien eiSu ve van de tUOng tac ddng Iflc cfla k^t cau tam tren nen phi tuyen, chju tac dung eua tai trong ddng dang sdng nd do vu n6 gdy ra, trong bai todn khdng gian, cd y nghia thflc tien vd can thi^t ddi vdi edc cdng trinh quan sU. Do do, bai toan tUOTig tac ddng lUc hoc tam tren nen nhieu idp phi tuyen, m d td flng xfl cua mdi trfldng vdi ket cau, cd ke den anh hUdng cua dieu kien bien can dUoe di sau phdn tieh, nghien eflu trong li thuyet va dac biet la thflc nghiem.
2. C Jc giS t h i e t t i n h t o a n va c d sd If t h u y e t
Khdo sdt tam be tdng day ddt tren nen (tuyen tinh, phi tuyen), chju tdi trong ddng sdng xung kich d o nd gay ra (Hinh 3). Can xde dinh dnh hfldng trang thdi flng suat bien dang eua ket eau tam va nen. Oe gidi bdl todn, thfla nhdn edc gid thiet sau:
-Vdt li&u cfla k^t cdu edng sfl dan hdi tuyen tinh;
- Ddi vdi tam, sfl dung gia thiet tinh t a m day cfla IVlindlin, vdi nen, sfl dung m d hinh nen Winkler vd nen phi tuyen dan d ^ ;
- He ket cau va moi trudng lam viee trong dieu kien bai todn khong gian; - Bi^n mien nghi&n cflu la bien khong phdn xa; Tai trgng tac dung iin be mat k^t cdu Id tdi trong song xung kich do nd trong khong khi gay ra;
- Trong qua trinh chju tdi, thoa man dieu kien lien tuc ve ehuyen vj tren be mat tiep xuc gifla ket cau vdi nen.
ifinh 1: Mo hinh ciia bai toan tam tren ren diiu tai trong song ni
3. H^ philcAig trinh PTHH t6ng quat phan ti'di dong lUC h M tam - nen 3.1. Cdc phuong trinh ee bdn cua tdm
Tfl gid thiet cua Mindiin ve tam, khi ke den anh hfldng ciia bien dang cSt, thi gde xoay 9 , , G,, dfldc bd sung m o t IflOng ifr,, ^, do Iflc cdt gay ra, khi bd qua bi^n dang mang, thi [9]:
trong d d : {e}^ Id bien dang trflot; { e ) , = { k . k^ k^ 6 , 0 ^ } ; k , = S e , / a x , k ^ = - a 9 . / a y , k^^=dQ^/dy-dQJdx Id vec t o dd cong;
ff, . e^ che gde xoay; [ s ] Id ma trdn ham dang; [ B ] - [[B,] [Bj] [B,] [ B J ] ;
(q)^ Id v ^ c t d chuyen vl nut phdn t f l ; { q } , = { w , 0 „ e^,...w^ 9,, 9,^) - Ndi Iflc ciia tam duoc xac dmh bdi:
K = [ D ] . R ' ^ ^ ! '
\P.\ [0] (2)
trong do: [ D J ; [ D J la ma tran dan hdi flng vdi bien dang udn va cat.
Trong (3) tdn tai bien dang udn vd bien dang c i t .
[DB,] = [DB,]^ + [DB,]^ (4) trong dd: [DB,]^ va [DBI]^ Id cdc ma trdn tinh m d men vd ma trdn
tinh Iflc c3t do chuyen vi nut I gdy ra.
- T h ^ nang toan phan eua phdn tCf tam chju udn bdi tdi trong ngang duoc bieu dien qua chuyen vl nut { q } ^ :
n.4(li:('iI=riDl[Bl<IAl{q).-fq}:j[NrpdA
^ I". ) K (5)
trong dd: [K]^ la ma tran dd cflng phan t f l , [ K ] ^ = J [B]^ [D]^ [ B ] d A ;
{P}^ I d v e c t o t d i p h a n t f l , {P}^= [ [ N f p d A
- Ma trdn do cflng [K]^ gdm hai thdnh phan lien quan den dp cflng udn vd do cflng trflot:
[ X ] , = J H ^ A = f J [k\ jJ| drds + j J [k]^ |J| drds (6)
Trfldng hgp tdi trong ngang phan bd deu {p=const):
{ P ) , = p | j [ N f | j | d r d s = p I I w , w , | j | [ N f (7)
3.2. Cdc phueng trinh cabin venen a. IWd hlnh nen cOa bai todn
M6 hinh vdt lieu n^n ddn deo dugc de suat bdi Mohr va Coulomb (1773), mat chay d^o dfldc dinh nghia bdi:
( c , - 0 3 ) = { i j , + o-j)sini))+2eeosi|> (8) trong dd e vh ^ lan Iflotld Ifle dinhdon viva gde masattrongciladat.
Vdi bai toan dan deo ma trdn [ D ] dflgc thay bdng ma tran [ D 1 theo quan hpsd gia:
{do} = [D,„]{de} (9) TD l=rD 1 [De]{3r/aa}[aF/aa][Dj
L " J ^ 'J [SF/Sa][Dol{er/3cTl
trong do; { d o } Id v e c t o s d g i a ijfngsuat; [ D ^ ] Id ma trdn ddn deo;
r - Id ham the deo; [ D ^ ] = [ D ] - ma trdn lien he flng suSt - bi^n dang t u o n g flng vdi trang thdi dan hdi; F - ham tieu ehudn deo.
0 ^ tinh [ D ^ P ] can phdi b i i t tieu ehudn deo va ham t h ^ deo, Ti^u e h u i n deo M o h r - Coulomb dflpc v i l t :
F = V J ^ s i n [ 9 + | J - J | - c o s [ 9 + j J s i n i t i - ^ s i n i ) ) - c . c o s ( t i (ll)
trong a d : I,, J , , 4 - b d t b i l n t h i i nhat, thifc 2, t h i f 3 ; 9 -gde Lode.
b. Di^u k i f n bien cua mien nghien eflu
Bien cua mien nghien cflu t h f l d n g duoc chon d pham vi dil xa kel cdu, vdi bdi toan tTnh cd dang.
{ U } , = 0 (12) trong dd {U}|^ Id vec t o c h u y i n vi cfla cdc nut bien ngodi phin nin
khdo sdt.
Vdi bai toan dgng thi (12) khdng cdn phfl hop. Do dd, khi xet bi^n bien dang va khong phdn xa sdng tren chu vi mien nghien ciiu can bd sung cdc lien ket ddn hoi va lien ket nhdt (Hinh 2a)
(131 Hinh 3: Quy luat bien thien tai trong song xung kich
- Vdi sdng cdt lan truyen theo phfldng x:
T + k , w + e > = 0 Hay T - - k , w - c , w - Vdi sdng nen lan truyen theo phuong x:
o , + kpU^ + CpUp = 0 Hay a , = - k ^ u , - c^flp (14), Vdi: k , = G / l ; c , = p V , ; V , = 7 G 7 P ; k p = E / l ; c ^ ^ p V ^ ; \ = ^p-
Trong d d : G, E, p id mo d u n truot, dan hoi vd khoi Iflgng ri#ng cOa nln;l Id khodng each t f l ngudn song d^n bien gid d|nh; w , u. Id chuyin vj eua hat mdi trudng tai tiet dien theo phuong vudng gde vdi phflong truyen sdng vd theo phuong truyen sdng; w , u^ la thdnh phdn v$nt3c efla w , u , ; T , CT. la flng suat tiep, dng sudt phdp trin t i l t di§n tai bifin;,
i/,, Vp vdn tdc lan truyen song cdt vd sdng nen.
Cae dieu kien bien la cac Iflc phdn bd be mat, bieu diSn theo phflOng phdp PTHH cd dang:
J R j . l K , ] ( U J v a { R . } . [ C , ] { U ) (13 trong d d ' {R^^}, {R^} Id vec t o Iflc cdn ddn hdi va vie t d Iflc cin
sdng; [ K j , [ C J lama tran cdc h f s d d d c j J n g dan hdi vd ma trdn edc h^
sd cdn nhdt quy nut. Cac ma trdn ndy dflgc thiet ldp t f l edc ma tran
thdnh ph3n ([K J ^ , [C,]^.) cfla cac phdn t f l t i ^ p xflc (PTTX) vdi bi^n mien nghien cflu.
[ K . ] . . f h [ k ) [ N ] ; d s » i [ C , ] , . J h [ c ] [ N ] ; d s (,6) trong d d : [ k ] , [c] la he sfi dg ciJIng cua Iflc can dan hdi vd he so can
nhdt CLia Iflc cdn song tren m o t d o n vi dien tieh; fi - chieu day phan t f l ; ]N\ - ma trdn ham ngi suy.
Vdi bien t h i n g dflng: [ k j ^ r " ° l ; [ c ] - [ ' ^ ' ' ° 1
V 6 i b i e n n S m n g a n g : [ k ] = l > ^ J ' ^ ^ O 3.3. PhUOng trinh cdn bdng cua hi kit cSu - nen
Phflong trinh ddng Iflc hpc cua he cd dang [9]:
( M ] { U ) + [ C ] { U } + [ K ] { U } = {R) (,7) trong dd: [ M ] , [ C ] , [ K ] : ma tran khdi luong, ma tran edn, ma trdn
dfy cflng cfla hi. J u ) , { u J , {U} : vec t o gia tdc, van tde, chuyen vj nut cfla he, { R } vec t o tdi trgng.
- M a t r a n khdi Ifldng efla h | : [ „ ] = g [ ^ , ] ^ = f|p^;sj]^jN],dv;
t r o n g do: [IW]^ bao gdm [ M ] ^ va [M]^^ Id ma trdn khdi Iflgng cua tdm va cfla nen; p mat do khdi luong; [N] ma trdn ham nfli suy.
- Ma tran cdn cfla he: [C] = i;[C]^=ZJn[N]^[N]^dV
A.K.Chopra de nghl dung cac he sd can Rayleigh khae nhau cho tflng vung xac dinh theo cac cdng thflc:
(18) trong dd: nn' " n - Pn tflong flng la ti so can va cac hp so can Rayleigh ciia vung con t h f l n trong hp;
- Ma t r d n d d cfl'ng cfla he [ K ] : Bang t d n g ma t r a n dd c i i n g cua t d m va n e n .
(19)
[B,] Id ma trdn bao g o m cac ham ndi suy cfla phSn t f l . 'h, 0 O ]
[B,]= 0 h, 0 ; h , = - i ( l ± ^ , ) ( l ± n O 0 0 hJ
Ma trdn do cOng cOa PTTX trong he toa do cue bo:
"k^ 0 " '•
[K']-JJ[NrM[N]dxdy;[k]= 0 K,
trong d d [k] la ma trdn do cflng dan hdi theo p h u o n g t i e p tuyen vd phdp tuyen cfla phan tis. k „ , k j . Id d d cflng t i € p tuyen theo phflong X va y (vdt lidu dSng hfldng thi k „ =k,j,), k^^ do cflng phdp tuyen theo phflong z.
Quan he sd gia flng suSt vd sd gia b i l n dang trong PTTX dac nung bdi:
I
ACT 1 Ae, i Ae, 1A T „ i = [ k ] . A T ^ •; J A y „ U [ N ] { A U , , } (24) A T ^ J Ay^ l^^iyj
trong dd; { A U ^ } la v^c t o gia sd chuyen vi nflt efla PTTX trong hi tga do ehung,
4. T i l n hanh t h i nghidm tai hien trUdng 4.1. Md hinh thi nghiem kit cdu tdm trin nin
Tam be tdng edt thdp mac 350, kieh thfldc (axbxb) = (0,8x1,0x0,1 ] m . n h f l Hinh 4.
[ C ] . Z a . [ M . ] + | 3 . [ K j . , . . i ± f i ^
[K].i[K].-g([K,].+[K,].).iJ[B]:[D],[B].dV
trong do [K,-] ciia tam dflOc tinh theo (6); ma tfdn dp eflng cfla n l n dflgc tfnh:
[ K j ^ = ] [ N ] ^ [ N ] ^ k , d S (20) trong dd it, Id do cflng trong tflng bfldc d cac vflng eon n. vdi nen
tuyen t i n h k, = c o n s t , vdi nen phi tuyen k,=P|,,/y|,|
He ket cau t d m - nen Idm vi^c d d n g t h d i se xuat hien Iflc ma sat gifla tiai Idp vat lidu. Sfl d u n g m d hinh PTTX ba chi4u n h f l Hlnh 2b cho p h e p m d td sfl tdch t r f l o t gifla hai khfii tiep xuc vd t r f l o t gifla cac b l mdt v d i nhau [14],[15] e l ddm bdo sfl t f l o n g thich gifla hai be mdt t i l p xflc, cdc cap nflt d d i nhau gifla mdt t r e n va dfldi cfla phan t f l t u o n g flng Id 1 vd 5, 2 vd 6, 3 va 7, 4 va 8 cd cflng toa do, tfle Id phdn t f l c d d o ddy bdng k h d n g .
Quan he chuyen v i g i u ^ dinh vd ddy cfla phan t f l dflOc xdc dinh:
{ " i } 4 [ B , ] { q , } , . - [ B , ] { q , L _ ] = [N]{q} (21) t r o n g d o : [N] = [-B, - 8 , - B , - B , B, b, B, B.]
Hinh 4. Mat d t ngang va mo hinh tam thi nghiem
- Noi dung t h i nghiem: Do dp Ifle sdng nd, gia tde, b i l n dang do tde dung no trdn mat k i t cdu tam dat tU do tren dat nen gdy ra.
4.2. Thiit bi thi nghiim
• May do dong SCXI-1OOODC (Hinh 5a): La thiet bj do ddng da kenh bien dang hien dal do hang National Instrument cfla My ehe tao. Tdc do do lay mau cua may c d t h e dattdi333kS/s vdi mfle nhieu cflc thap. Tren may bo tri 4 khe cam d l cdu hanh edc loai eae do khdc nhau.
Hinh 5: May do fla kenh SKI-l OOODC va Sau do gia toe 353B33
• Cac loai dau do
-Oau do gia tdc 393C, 353B33 (Hlnh 5b) -Dau do ap Iflc ddt KDC-IMPA (Hlnh 6)
Hinh 6-{)au do ap lUc fla't KDC-IMPA
- Dau do dp Ifle khdng khi 113A31 (Hinh 7a)
I T ) ei«HiaiHit(af.iiBnmL)
B i S n cl?nB c u a t l ' m
^1 I L
k-a /
^ ' & i l Hmh 7-Dau do ap luc 113A31 va dau do bien dang- O a u d o bien d a n g : Loai PL-^0-11, c d d i e n t r d 1 2 0 a . (Hinh 7b)
HInhe Ddn dSu do hien dang va lay maud 4.3. Tiin hdnh tbi nghiem nd
- Thudc nd dung loai TNT bd trf theo tflng Iflgng nd cd trong IflOng lOOg, 200g, 400g d cac dg cao (H) khae nhau ( I m ; 1,2m, 1,5m), mdi Iflgng nd, mdi dd eao tien hdnh nd ba lan, mau dat dflgc lay dfldi day tdm (Hinh 8b) vd dflgc bdo qudn theo quy trinh mau thi nghiem.
- Oau do bien dang bd trf theo hai phuong nhfl Hinh 8a, ddu do gia tdc vd dp ifle ddt ddt d mat ddt dfldi tdm, ddu do dp lUc khdng khi ddt tren mat flat canh tam cdch tam tam 1,2m Hinh 9.
- T i l n hdnh gay nd va do tin hieu Hlnh 9, Hinh 10.
" 1 -
^ li^l, .. .
K »'^^k^ H
T h M s l a n [ s } Hinh 12: Bieu do bien dang t^i tam tam
Vdi cac sd lieu thf nghiem do dugc, dUa vdo thuc hi^n tinh toin bang chflong trinh HTSl, vS so sdnh g i f l ^ If t h u y l t vd thf nghiem.
Bang V Gia tncUc dai cua ling suat va bien dang khi sfl dung chuong trinh tinh HTSl
li^P^l
C a c I r i f g n g h g p t i n h t a ^ n vfri njtn tuydn Unh
Banq Vl
Tfl
. Gia tri CUC dai ciia mo men khi sildung chilong trinh ti'nh HTS
(kPa}
437,97
Cac truclnq h o p t i n h todn v6i nSn t u y f n t
Nin mpt ldp
(kNm
11,9 (kNm
9,7 Nen nhi^u ldp
{kNm 1 11,7
{kNm
)
9,6 Nen mat liip k^
d f n PTTX M l (kNm
12,2 CicVUdiKt h o p t i n h t o a n v 6 i n
M i (kNm
10.0 'l-S
NfnnhtfuMp kiaJnPTTX
(kNm Ml IkNm
11.7 1 9,6 n phi luyen 13.5 1 11,1 1 13,3 1 11,0 1 13,a 1 11,3 1 13J | l l j ) Bang 3 Sosarh ve gia tfi bien dang giOa thinghiem va li thuyet
Gia tn bien dang
nghiem (xlO-^)
1.97 (Kia
1,8
1,92
%
8,6 3
^4 (xlO^j
1,78
1,87
%
9,6
5,0 8
PTTX ( x l O ' l
3.4
3,5
,
43, 05 43, 71
Nin n h i l u
p r r e (xlO') 3,33
3,41
%
42, 23 Bang 4: So sanh ve qia t n flng suit qiila t h i nqhiem va
Gia t n ling sual
tir thf nghiem
IkPa)
522,05 li!lp (kPa)
381,35
392,57
*
26,9 5 24,8
Nen
(kPal
380,67
386,63 27.0
8 25,9
ithuyet
PTTX IkPa]
105Q.8
1081,62
,
50,3 2 51,7 3
N f n nhl£u ldp PTTX (kPa) l O W
1043,5
«
46, 64 49,
Hinh 10:flotinhi?utqil hien trucmg S.K€t qud t h f n g h i e m
Tdng sd ed 27 iin nd se cho 27 gid trj cho mdt tham sd do Gia trj dp Iflc sdng xung kich vd bien dang cua tam do nd gay do dflgc tfl thi nghiem sau khi da dfloc khflnhiem Hlnh 11, Hlnh 12. (gia tri dde trflng nhat)
Ap Ivc long n i n e kf<A Iren m t t rfm
Hlnh 11: Bieu do ap lUc song icung kich tren mat tim
T h M f h n l i l HI — T u y f n l i n h - ^ P h l t u y f o Hinh 13: Bieu do chuyen viva flngsuattaitamtam
6. K^t luan
- So sdnh sd lieu tinh todn dflgc lap trong Bdng 3 va Bdng 4, kit q\A trong cac bdng cho thay: khi khdng ke den PTTX {nin tuyen tfnh hay pW tuyen mot Idp hode nhieu Idp) cho gia tri gan dung vdi gid trj thi
Hlnh 14: Bieu do bien dang tai tam tam
nghiem (bi^n dang Id 2,54%, flng sudt la 27,08%). Khi ke d^n PTTX {mdt ldp hay nhieu Idp, tuyen tfnh hay phi tuyen) thi gid t n tinh todn If thuyet ldn hon thf nghiem (bi^n dang 43,71%, flng sudt 50,32%). Quy ludt ehuyen vl vd bien dang phfl hop vdi thflc te va trong cdc tdi lieu nghiem cfluvend[31[4][6].
- Mdi trfldng nin dat phi t u y ^ n md hlnh dan d4o, ddng vai t r d nhU ldp "ddm mim" lam gidm khd nang t u y l n sdng (dnh hfldng) tdi mdi trfldng xung quanh.
- Cdc sai sd g i u ^ li thuyet vd thf nghiem c6 the do dieu kien mdi trfldng (cac tham sd dnh hfldng) tdc ddng. Mfle do sai so ndy cd the chap nhan duge, t h u d n g thay trong cdc nghien eflu cfla cac tdc gia khdc v^ t h i nghi&m kit cau ddi vdi tdi trgng Id sdng nd.
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