Nghien CLPU tifcyng tac dong ILFC hoc cua t i m day tren nen phi t u y l n chju tac dung cua tai trong dpng Research of Interactive Dynamic tiie Tliicl( Plate on Nonlinear Foundationsunder Dynamic Loads
Ngay nhan bai: 15/12/2014 Ngay sCra bai: 5/02/2015 Ngay chap nhan dang: 17/03/2015
Vu Cong Hoang, Nguyen Tu'tfng Lai
T O M
TAT:
Bai bao nghien cijfu tiiOng tac dong lUc iioc cua tam day co ke d i n anh hiidng cua bien dang mang tren nen phi tuyen b^ng phifdng phap phan tii hflu han (PTHH), mo hinh chuyen vi
vdi kieu phan tii chQ iih|t 04 nut, 12 chuyen vi niit co dieuki^n bien tt^ do theo chu vi. Bai toan dtldc dat va giai theo quan di^m tiiong tac dong life hgc. Thuat toan difdc xay ddng tren cd s6 cua li thuyet tinh toan tam day, phiiOng phap PTHH, duoc l|p theo ngon ngi3 Matlab ket hdp vcri phan mem Ansys.
Tii kh6a: Phiidng phap PTHH, tam day, bien dang, nen phi
tuyen,
ABSTRACT:
Articles interaction studies the dynamics of plate have to mention the influence of membrane deformation nonlinear platform by finite element method (FEM), the model displacement element with a rectangular pattern 04 nodes, 12 displacement boimdary nodes conditional freedom on the perimeter. The problem is set and the in view interactive dynamics. The algorithm is built on the basis of theoretical calculations thick plate, FEM method, have been prepared in accordance with Matlab language combined with ANSYS software.
Keywords: Finite element method (FEM), thick plate, deformation, nonlinear foundation.
ThS Vii Cong Ho4ng, PGS.TS Nguyen Ttfdng Lai Hpe vi?n Ky thuSt Quan sif
Email: vucQnghoang201I(ii'gmail.com
D i d o n g : 0966458558I . D a t v ^ n d e
Thyc te cho thay, ktii tinh toan t^m t u o n g xic vdi nin, hau het tid qua bien dang trUdt ngang t r o n g t a m cio liic cix gay ra (gl^ thiet cua Kirehhoff). Tuong tU, de d o n g i i n trong tinh toin, m d htnh nen 6hn h6i thudng duoc sis dung, Tuy nhiSn v6i quan niem tinh to5n tren thi chua p h i n inh d i y dCi tfnh chat va trang thai l i m viec cCia hi BSI to^n tUOng tac dflng iUc hoc t a m day tren nen phi tuyen can dUoc di sau phan tich v i nghien cCiU, dac biet trong c3c cong trinh quoc phong chju t i i trong dac bi^t,
2. Oat b i i t o i n va c i c gia t h i e t t i n h t o i n
Khao sat tam be t o n g day dat tren nen (tuyen t i n h , phi tuyen), chiu tai trong dflng dieu hoa va song xung kich d o no gay ra (Hlnh 1), C l n xic djnh i n h hu6ng cOa bien dang mang trong tam, trang thSi ilng suat, bien dang cua k^t cau t a m va nen. De g i i i bai toan, thifa nhan c i c g i i thiet sau:
- D O I vdl tam, sis dung g i i t h i e l t i n h t a m d i y cua Mindlin. Do do, xim chiu uon co xet den goc xoay, bien dang trUcrt
- Doi v6i n^n, sCf dung mo hinh nen Winkler va nen phi tuyen dan dio, bo qua khoi lUcJng cilia nen.
- Trong qua trinh chm t i i , thoci man dieu kien tien tuc v^ chuyen vi trgn b e m a t t i e p x u c g i u ' a k e t c a u vdl nen.
3. He p h u o n g t r i n h PTHH t o n g q u i t p M n t i c h d o n g iUc hoc t ^ m - nen
3 . 1 . Cic phiiorng t r i n h ca b i n cila t a m
lis g i i thi^t cua iVtindiin ve tam, khi ke den i n h hudng cua cic thanh phan bien dang c i t , t h i gdc xoay 6 ^ , By dUOc b o sung mflt lupng ^^, ^y d o luc c i t gay ra [4].
dw dw
(1) Nang iupng bien dang d i n hoi ciia t a m trong trUdng hop nay bao
•m bien dang uon va bien dang c i t :
U e = ^ H c T : r { e b } d V - . I j ( o , i T { e , i d V (2)
trong d d : { c T b } - { c i ^ Oy i ^ y j ; {ety] = {^x phan ling suat va bien dang uon cua tam;
l^xz V I
l^s) ^ l^xz Tyz j IS c i c thanh ph5n Ung suiit v i bien dang c3t,Khi ke den bien dang mang thi ma tran d o cUng cua phan tif tam se bSng tong ma Iran 66 cUng cua phan tiJ' m i n g ([k^y, L , ) v i
1061
phan t i l uon tam ( [ k ^ ] , ^ } . Ma tran do ciJng tai nut cila p h i n tiS [k, duac b i l u dien n h u sau [8]:
u-
[km]2x2 Kx:
[0]3X2 [ " b l B , '^([XTII)
Hk
ngllidt liliiBi
i^dui*'
injaiid
(II
' l i * *
trong do: [KJ] la ma t r i n d 6 cilng cua phan tCftam.
Khi b d qua bien dang mang, t h i thanh phSn vec t o cac d p cong va bi^n dang t r u o t dupc bi^u dien qua c i c t h i n h phan vec t o chuyen vi nOt phan t i l [11[4]:
trong do. ( E ) la bien dang trUot; ( e ) . ^ j k ^ ky K^y t^x 9 y | ; k x = 3 e y / 5 x , ky = - e e x / 9 y , K ) ( y = 5 9 y / 9 y - o e ^ / 5 x la vec t o d p cong; 0^ , Oy c i c gdc xoay d (1); [B] l i ma t r i n ham dang;
[B] = [ [ B i ] [ B 2 ] [ B 3 ] [ B 4 ] ] ; { q } ^ la v^c tO chuyen vi nut phan tCf;
{q}e = ( w i 6x1 6yl - W 4 6x4 6 y 4 ) - Nfll Iyc cua t ^ m duoc xac d m h bdi
Pul [0]
(5)
.[or i°cijii
trong dd, [ D y ] ; [ D ^ ] l i ma tran dan hoi ilng vdi bien dang uon va c k C h u y d ^ n C 4 ) t a c 6 :
H = S l D ] j B ] , { q } i = I [ D B , ] ( q } , (6) 1=1 i=l
Trong (6) t o n tai bien dang uon v i bien dang cat.
[DB|] = [DB|]^+[DB,]_. (7) trong dd [ D B J ] va [DB,] la cac ma t r i n tinh mfl men v i ma tran
tinh lUc cSt d o c h u y i n vi nOt i g i y ra, aN| ^N, ay dx dN| 3N|
dy dx
Wc'
0 0 0
ngang dUpc bieu d i l n qua chuyen vj nut )q) :
[A, I \ m
•jWlWeWe-Wla
trong d d ' [K] la ma t r i n d p cilng ph3n iCf,
We= j" [^l^[l^]t[^]'^'^= {'')e '^ "^"^^ '^' P*^^" ^^'
Ae
Ap
- Ma t r i n d o cUng [K] g o m hai thanh ph^n lien quan den dd cUng udn va dfl cilng trUcft
1 1 1 1 W e ^ I W e ^ A ^ J | [ k ] J j | d r d s + J J [ k ] ^ | J | d r d s (10)
Ae - 1 - 1 - 1 - 1 TrUdtig hop t i i trpng ngang phan bd deu (p=const):
1 1 n n
3.2. Cac p h i i o n g t r i n h cO b i n ve n e n
Thuc te dat nen khdng p h i i la mdi trUdng dan hoi tuyen tfnh, d o dd quan he Cfng suat bien dang khdng p h i i la hang so ma theo quan he phi tuyen.
Vdl viec sU dung mfl hinh vat lieu nen dan d^o dUpc de suat bdi Mohr v i Coulomb (1773), mat c h i y d^o dupc djnh nghia bdi [2][3]:
( a i - a 3 ) = { o i + a 3 ) s i n ( | ) + 2ccos(ti (12) trong dd c va ^ lan lucrt l i lUc dinh d o n vj va goc ma sat trong cua dat,
Oieu kien c i n b i n g gidi han Mohr - Coulomb:
oi-cT3.r + 2 c V n ^ ; m = tg2 4 5 ° ^ ! (13)
- Thi n i n g t o i n phan cua phSn t i l t i m chiu udn bdi t i i trong
Vdi bai toan dan deo thay ma tran [D] trong quan he i i n g suat b i 4 n d 3 n g { C T ) = [ D ] { E } b i n g ma trpn [ D e p ] theo quan he sd gia iing s u i t va sd gia bien dang:
ldo).[D,p](de) (14)
r „ 1 , „ , [DeKar/ito}[flF/8a][De][CepJ-lDel- [aF/a,][D,]{ar/a,) ' *'
trongdc) { d o } i i v e c t O s o g i a i l n g s u a t ; [ D e p ] l a m a t r a n d a n d i o ; I - l a h i m t h e d f o ; [ D e ] = [ D ] - ma t r i n lien he ilng suat - bien dang tuong ling vdi trang thai d i n h6i; F - ham ti&u c h u i n deo.
D ^ t i n h [ O e p l can p h i i bi^t tieu c h u i n deo va ham t h e deo. l i e u c h u i n deo Mohr - Coulomb duoc vi^t theo ham cua cac b i t bien Ung s u i t l l , J2 va e .
F = VJ2Sin[e + - ] - J — < : o s ( 9 + - ] s i n < t , - l l s i n 4 . - c . c o s < | i {16)
trong do: 1], J 2 , J3 - l » t trien t h U n h i t thiic 2, t h u 3 ; 6 -gcKLcxie.
Khi gcic ma sat trong ^-0 t h i tieu c h u i n deo Mohr - Coulomb trcj thanh tieu c h u i n deo Tresca.
™ H - W v a ( E } - ( U ) - . [ D ) = [ o ! i t H ] 3.3. PhifOng t r i n h can b ^ n g cua h e ket cau - nen Khi chiu tai trong dpng, chuyen vi, Ung s u i t va bien dpng trong hp ket cau t i m - n^n phu thupc vao thdi gian. Phuong trinh dpng iuc hoc ciia he CO dang [1]:
[ M ] { U ) + [ C ] { U ) + [K]{U) = {R) (17) trong dd- [ M ] , [ C ] , [K]: ma tran khoi lUOng, ma t r i n can, ma Iran do Cling cua he, { 0 } , { u } , { U } : v^c t p gia tdc, van tdc, chuyen vj nut cua he, {R} vec t o t i i trpng.
- Ma tran khdi iupng cda he: [ M ] = S [ M ] g = I J p[N J [N]^ d V ,
trong dd: [M] bao gdm [M].|. v i [ M i , l i ma t r i n khdi lUOng cua tam vacua nen; p m a t d d k h d i l u o n g ; [ N ] ma t r i n ham npi suy,
- M a t r a n c a n c u a h g : [ C ] = S [ C ] g = Z { ^ [ N J [ N ] g d V Ve
D 4 xay dung ma t r j n can nhot cua h^ cci xet din cac d i e trUng can khac nhau ciia cac viing, A.K.Chopra d ^ nghi dung cac he sd can Rayleigh khac nhau cho tiing vung xac ^ n h theo cac cflng thuc [1]:
[ C ] - Z a n [ M n ] + Pn[Kn] (18)
1n = (19)
t r o n g d d : T|n,an, Pn tUOng ling la t i s d can va cac hesd can Rayleigh ciia vung con t h u n trong h^; [ M n ] , [ K n ] la ma t r i n khdi iuong, ma tran dp cutig cua vung con t h i i n.
- Ma tran do cilng cua hi [ K ] : Bing tflng ma tr^n do ciing cua t i m va nen,
[K] = Z [ K ] ^ = Z ( [ K T ] , + [ K N ] e ) - 2 j [ B ] T [ D ] j B ] ^ d V ( 2 0 ) Ve
trong d d ma tran dp cilng cua tam dUpc tinh theo (3) v i (10); ma t r i n d d Cling cua nen dUpc tinh
[KNle-lMlHl^tdS
(21)trong dd k j l i dp cUng trong tCfng bUdc 6 c i c vung con n. vdi nen tuyen tinh k t = c o n s t , v d i nen phi tuyen k^ = P / t ^ / y f t ^
4 . ThA n g h i e m sd
4 . 1 . Bai t o a n 1 : Tam be tdng cd kich thUdc [2x3xO,5)m bien tU do theo chu vi d i t tren n i n cd Ep - 23809 k N / m ^ , V p - O . S ,
c = 8 . 8 k N / m ^ , ^ = 19,32°. V i t lieu tam co Ej = 2 . 6 5 e 7 k N / m ; v t = 0.2, Tam chiu t i i trong t i p trung dang di^u hda dat tai t i m , P(t) =2m(i)^esin(cot), m = 0 , 2 T , e = 0.1m, sd vdng quay 1850 vdng/phiit; thdi gian duy tri t i i t - 0.045 s, thdi gian khao sat t = 0,5s. Md hinh bai t o i n n h u Hinh 1.
Khdi nen duoc tach ra til b i n khflng gian mdi trudng, cd kich thudc cac chieu: rdng B= 4xa; d i i L= 4xb: chieu sau nen H= 7xa. B i i t o i n duac lap trinh tren Matlab ket hop vdi phan m e m ANSYS.
Hinh 1. MD hinh b^i todn tam tren nen
a. Trifcmg h o p 1 : Tam tr#n nen tuyen t i n h (TT) va phi tuyen (PT) khdng ke den bien dang cOa m i n g (KKBDM).
Gia tri Chuyen vi
tfng s u i t (kN/m') M o m e n MK(liNm) M o m e n MztkNm)
Niil
37 37 37 37
n
3 8 2 7
5498,92
122.15
112,49 TT (KKBDM)
3 8 0 7
4 9 1 0 7 1
113,02
103,19
%
052 1 0 6 9
7.47
826 PT 42.38
5481.52
116 J 107.72
(KlffiDM) 40.87 4878.08 10802 98.96
%
3.56 11.0 7.04 812 Bdng 2: G i i tn cUc dai cda chuyen vi, Ung suat tai c i c nilt khi KKBDM
M(
37 11 2 5
Chuyen viUV (mm) TT 38 07 37 68 3763 3799
PT 40.87 40.45 4038 4078
6,85
%
6.83 6.S3 6 85
tfng suat 5Y[kN/m2 JJ 4910,71 749,80 264,95 224.16
PT 437808 706,87 15972 183,43
0 66
%
5.72 3971 1817 B i n g 3 : Gia t n cUc dai c i l a m d m e n u o n t a i cac n u t khi KKBDM Nut
37 11 2 5
Mo men Mx (kN/m)
n
103.192 50,777 0.302 0 299
PT 98963 45,454 0.301 0.298
4.09
%
10.48 0.36 0.44
MD men Mz (kN/m TT 113 021 0452 0.453 76662
PT 108.016 0.45 0.451 71,39
4.43
%
0.38 036 6.87
4~! I
a l IJ
Hinh 2. Chuyen vi W ( t ) v J l i n g
1 .; ; 1—s:C'
!.|j ; ,. . ... ., „
\ llliill ' ' " ^ 1
suat o (
1 • i ) tai tarn tam KKBDM j 1 — TunBii*|
1 — m i w w i i
.i,,:::,-:_
; • • ;
wmmm^at
Hinh 3. Momen M x ( t ) , M 2 { t ) tai tam lam KKBDM
l O S j H W I K l K S i 6 . 2 0 1 5
Hinh 4 a) Kng suit trong nen phi tuyen Ki b) iJng suit trong nen tuyen tinh KKBDM
b. TrUcmg h o p 2: T a m t r e n n e n TT va PT k^ d e n b i e n d a n g m a n g (BDM)
B&ng 4 : Gia t n cUc dai cua c h u y e n v i , isng suat t a i c i c n u t k h i k e d ^ n B D M
Niit 37 11 2 5
Chuyen vi UV (mm
n
3827 378 37,75 38,17
PT 42.38 41.91 41.85 42.29
%
9.69 9,82 98 9 72
tfnqsuatSV(kN/m2
n
549892 825.63 266 71 234.89
PT 5481.52 802,81 173,29 198 22
%
0-32 2-76 35 03 15 61 BInq 5: Gia tri cue dai cda m6 men uon tai cac nut khi Ve den BDM Nut
37 11 2 5
M6 men Mx (kN/m)
n
12215 066 066 81.15
PT 1162 0,65 0,65 74.82
%
4,88 0,60 0,62 7,80
Mo men Mz (kN/m)
n
112 49 52.84 0.44 0.44
PT 107 72 4661 0.43 0.43
%
424 1178 062 056
Hinli&.a) Ung suJt trong nen phi tuyen khi ke den BDM b) Ung sual trong nen tuyen tmh khi ke den BOM - G i i tri trong B i n g 1 cho thay: Anh hudng cua bien dang mang trong tam i i khong idn (TT la 0.52%, PT la 3.56%) doi vdi ciiuyen vi, NhUng v^ ndi lite t h i i n h hUdng d i n g ke Oieu nay duoc li g i i i la do
phan tU mang khdng chiu udn v i i n h hudng cua bien dang trupt d o iUccStgay ra.
- G i i tri t r o n g Bang 2 , 4 v i Hinh 2, 5 cho thay chuyen vi trong nen PT ldn hon TT trong c i hai truPng hpp ke den va KKBDM (6.85% va 9.69%). Dieu nay cho thay, khi ke den tinh d^o cCia vat lieu, moi trudng PT ( d i n deo) se ' m e m " hon, dan den ket cau chuyen vi \dn hon, d o n g thdi dao d o n g cua he tat nhanh hOn.
- Do t h i tren Hinh 2,3,5,6 v i g i i trj trong B i n g 2,3,4,5 nhan thay, npi iUc trong t i m va nen PT nho hOn trong nen TT trong c i hai trUdng hpp ke den v i KKBDM. Oieu nay cho thay, mdi trUdng PT (dan deo) cd t i n h "mem" do d o su h i p thu (ti^u hao) nang iupng cua t i i trpng dflng idn hon mfli trudng dan hdi TT, chu ki dao dflng cua he tSt nhanh hon, - Hinh 4 , 7 cho thay pham vi i n h hUdng (bien dang) cua nen PT Idn hon TT v i t h e o chieu sau (chieu cua lUc)
4.2. Bai toan 2: K h i o s i t h f chiu t i i trong no dudi dang xung.
p h i n b d deu tren m i t tam j^jj^AP^,^! n = 2 ;
APmax^SOOOkN/m"'; r = 0.145J, thdi gian khao sat t = 0 . 8 s , C i c tham sd hinh hpe gidng nhU b i i t o i n 1.
- K e t q u i tfnh toan
BAng 6; G i i t n cUc dai cila chuyen vi, U n g s u s i t t a i c i c m i l Nu
1 37 11 2 5
Chuyen VI UY (mm)
n
71,30 70,91 70,81 71,25
PT 90.41 89.99 89.89 90,36
%
21.14 21.2 21.23 21,15
|}ngsultSY(kN/m2)
n
12646 1071 79 50140 424.69
PT 125907 10321 284.54 344.23
%
0.44 3.7 43.25 18.95 B i n g 7; G i i tri cUc dai cua m d men uon tai cac n u t
Nut 37 11 2 5
Mo men Mx (kN/m) TT
9107 142 142 95-99
PT 74.08 142 142 7817
%
IS 66 0 0 18 56
Mo men Mz (kN/m)
n
63 64 81.55 095 094
PT 50.21 64.70 097 094
%
21.1 2066 2 07 0
p^r-^-
i 1 nUfin
i^B iv
• # - - • --— - - -
^ 1 1 ' ' • .; _.-^ .,-
^H.| ; j — T U B * *
ih7,Chuyen vi W ( t ) vaiJngsuat cT(t) taitamtam
Hinh 8. Mo men uon M ; , ( t ) , M 2 ( t ) taitamtam
- Chuyen vi dong cUc dai trong nen phi tuyen ldn hon nen tuyen tinh (21.14%) Tuy nhien k h i nang phuc hoi k^m hOn nen tuyen tinh, dieu nay t h e hien d i e tinh tre cua mfli trUdng " m e m " (dan d^o), Hinh
8,9.
- Do thi Hinh 8 , 9 va g i i tri trong B i n g 6,7 cho thay ndi iUc cue dai
G.201561!in[K[|Oin|l
trong thdi gian chat t i l c6a nen tuyen t i n h Idn hcfli nen phi tuyen.
Oieu n i y phu hop vcri mdi t r u o n g cilng h o n thi ndi iUc Idn. Sau khi d d t i i , dao dpng ciia nen phi tuyen t i t nhanh hon. Oieu d o thay r i n g , mdi t r u d n g " m e m " co su hap t h u nang luong Idn hon.
4.3. Bai t o i i n 3: K h i o s i t anh hudng cila m d dun dan hdi E cila nen d^n chuyen vi va nfli luc cua h | , vdi E thay d6i nhU trong Bang 8.
Cic s6 lieu t u o n g tU nhU b i i t o i n 2.
B i n g 8 : M f l i t r U d n g c d E thay d o i toai mfli trUcmg
E(kN/m')
toai2 ioai 3 20000
Loai 4 22000
Loai 5 2400D - K e t q u i t i n h t o a n
B i n g 9: Gia tri cUc dai cua chuyen vi, ung suat tai t i m tam (nut
Loa
1 2 3 4 5
Chuyen vi UY (mm) TT 103.78 91,7214 83.6026 76.8986 70.7349
PT 11884 105 696 99.3743 94 6918 84 2418
%
12 67 13 22 15 87 18 79 16 03
Ungsua'tSY[kN/m2) TT 137024 134472 1306.83 1275.87 1256.99
PT 1341.07 1306.99 1291.67 1272-95 1231.02
%
2.13 2 81 116 023 2 07
Lo ai 1 2 3 4 5
B i i n g 1 0 : G i t n cue dai cua md men udn tai t i m ta Mo men Mx (kN/m)
n
89,5231 90,2125 91.3559 91.562 90,9805
PT 761019 74 3438 743757 742785 74162
%
14.99 17i9 ISiS 18.87 18,48
n ( 3 7 ) Mo men Mz (kN/m) TT 62,3315 618486 63.7069 63.9177 6 3 J 8 3 7
PT 51 5387 5 0 1 7 2 503JB1 50-2273 49-9301
%
1731 20,17 20.98 21.41 21,47
5. Ket l u a n
Bai bao da khao sat b i i toan he ket cau t a m - nen chju tai trong dieu hda, t i i trpng n o theo quan d i e m d d n g luc hoc trong bai toan . khflng gian, cd ke d e n vS KKBDM, cd m o d u n d i n hoi thay doL TU ket
q u i nhan th^y:
- A n h hudng cua bien dang m i n g trong tam day khi t i i t r o n g t i c d u n g v u d n g gdc v ^ mat tam i i khdng d i n g ke. Su chenh lech nay l i d o i n h h u d n g cOa bien dang t n / p t d o lUc c3t g i y ra.
- Chuyen vi v i bien dang t r o n g nen phi tuyen ldn hOn nen tuy^n t i n h . Bien dang (lun) cua n4n bao g o m b i ^ n dang d u (bien dang khdng c6 k h i nang phuc hoi] va b i ^ dang d i n hoi (bien dang cd k h i n i n g phuc hoi lai). Mdi trUdng cd tinh chat " m e m ' hon co chuyen djch idn hon.
- Ndi lUc trong tam v i nen phi tuyen n h d hcffi t r o n g nen tuy^n tinh, dieu d o cho thay nen phi tuyen (dan dio) cd t i n h " m e m " sU hSp t h u (tieu hao) nang lupng cua tai trpng dflng Idn hem so vdi nen tuy^n tinh (cutig hon) d o d d dao d d n g cila he t i t nhanh h o n .
- Khi d o cUng cua mfli trUdng tang dan deu, t h i chuyen vj cua he ket cau - nen g i i m dan, mUc d p giam cua nen tuyen t i n h cd tfnh chSt deu. M d men eua tam tren nen tuyen t i n h tang, nen phi tuyen t h i g i i m dan. Mile g i i m khong dang ke ti!r loai 2 den loai 5. Qng suat trong c i hai t r u d n g hap nen deu g i i m , nen tuyen tfnh cd tinh c h i t giam deu, nen phi tuyen mang t i n h cue tra.
- Khi tfnh toan, thiet ke e i c ket eau tam tren nen, c i n c i l ' v i o d i e tfnh cOa t i i trong, dac tinh cda m d hinh nin (dan hdi hay phi tuySn) d^
xem xet Ung xiS ciia he ket cau - nen de tU dd ed c i c d i n h gia va x i l if phii hpp vdr thuc te
T A I U | U THAM KHAO
|1] N g u y i n Thanh Binh (2012), Bai giang coo hoc Ly tliuyet vapfiimg phdp Unh liet can lam ¥0, Hoc n e n Ky thuat quan su
[2]. Nguyen Van Hoi (2002), Tfnh kS cSa tiOng tac vSnen dan ba, Tai lieu dOng d w hoc vien cao hoc thuoc cac diuyen nganh cong t i v i h , co hoc iing dung Hoc vien Ky thuat quan sU.
(3]. Nguyen Tifong Lai (2006), rinhkitca'u tumg tdc Main biin d,ang, Bai giang chuyen d l d i o s a u i l a i h . ( « .
j 4 ] . a i u Q u 5 c T h a n g ( 1 9 9 7 ) , / V i u ' i m 9 p h ( ^ p A a n r u ' / i u u A a / i , Nha x u i t b i n K h o a h o c v H y tiiuaL
[51. Anil K Chopra (1998), Dinamics of Stwctures - Theory ami Aplicotion to Eartbguake Engineering, Prentice - Hail Upper Saddle River, New Jersey
[ 6 ] . Klaus - Jurgen Bathe (1996), ?inite Element Procedure, Part One, Two Prentice - Hail IntemaQonal, Inc
[ 7 ] . Ph 0 , P.E John S.horvath iSI2m).Soil-StTaaurelnleraclion Researdi Pn^. BOSKSSI Concepts and Applications Overview, Manhattan College. School of Engineering. Center (a Geotechnology, Report No. C6T-2002-2, USA.
[8] Kaushalkumar Kansara (2004), Development of Membrane, Plate and Flat Shell Elements in Java, Thesis submitted to the Faoilty of the Virginia Polytechnic Institute & State University In partial iuKiilment of the requirements for the degree of M a s t n of sd«ice m Cml Engineering,
[ 9 ] . C S Knshnamoorthy (1995), Finite Element Analysis - Theory and F^ogramming, Tata McGraw-Hill Publishing Company Limits - New Delhi
ih 10. M o m e n uon M^{x), M ^ f t )
- Khi d o cUng cua mdi trUdng tang len, g i i t n chuyen vi cUc dai tai t i m t i m trong c i hai t r u d n g hop nen TT va PT giam dan, tuy nhien nen TT mUc dd g i i m tUdng ddi deu, con n^n PT giam khong deu va nhanh h o n (Hinh 10).
- Od thi Hinh 11 cho t h i y , m d men trong tam tren nen TT tang t u o n g ddi deu, cdn vdi n^n PT thi g i i m . MUc d d g i i m khdng d i n g ke (tir loai 2 -^ 5). tfng suat trong e i hai trudng hpp deu g i i m , vdi nen tuyen tinh mile d o giam t u o n g ddi deu, con nen phi tuyen t h i g i i m khdng deu Hinh 10.
110|B
