Bai Giang PP PTHH

Phng Php Phn T H Hn(PPPTHH)

Finite Element Method (FEM)

PhPhng Phng Php Php Phn Tn T HH H Hnn(PPPTHH)(PPPTHH)

Finite Element Method (FEM)Finite Element Method (FEM)

TrTrng ng i hi hc GTVTc GTVTBB mmn Sn Sc Bn Vc Bn Vt Lit Liuu

LLLLLLLLNGNGNGNGNGNGNGNG XuXuXuXuXuXuXuXunnnnnnnn BnhBnhBnhBnhBnhBnhBnhBnh

Cu trCu trc mc mn hn hcc

PhPhn 1. Bn 1. B trtr kin thkin thc v CHVRBDc v CHVRBDPhPhn 2. L thuyt PPPTHHn 2. L thuyt PPPTHHChChng 1. Vn ng 1. Vn chung chungChChng 2. Tnh hng 2. Tnh h thanhthanhChChng 3. Bng 3. Bi toi ton phn phng ng ChChng 4. Bng 4. Bi toi ton n i xi xng trcng trcChChng 5. Bng 5. Bi toi ton khn khng gian ng gian ChChng 6. Tm mng 6. Tm mng chu ung chu unnChChng 7. Vng 7. V mmngngChChng 8. Bng 8. Bi toi ton n ng lng lc hc hc vc v bbi toi ton n n n nhnh

PhPhn 3. Thn 3. Thc hc hnh tnh tonh tnh ton trn trn mn my tnhy tnhBBo co co vo v BBi ti tp lp ln (n (hhn nhn nhn: 15/09/2008n: 15/09/2008))nh ginh gi: B: Bo co co vo v BTL: 30%; thi: 70%BTL: 30%; thi: 70%

TTi lii liu tham khau tham kha

BBt but buc:c: PP PTHH, Nguyn XuPP PTHH, Nguyn Xun Ln Lu, NXB GTVT, 2007u, NXB GTVT, 2007Tham khaTham kha::

1. PP PTHH, H1. PP PTHH, H Anh Tun, TrAnh Tun, Trn Binh, NXB KHKT, 1978n Binh, NXB KHKT, 19782. PP PTHH, Chu Qu2. PP PTHH, Chu Quc Thc Thng, NXB KHKT, 1997ng, NXB KHKT, 19973. The Finite Element Method, Zienkiewicz O.C., Mc Graw 3. The Finite Element Method, Zienkiewicz O.C., Mc Graw --

Hill London 1977Hill London 19774. The Finite Element Method, Alan J. Davies, 4. The Finite Element Method, Alan J. Davies,

Clarendon Press 1980Clarendon Press 1980

Kin thKin thc bc b trtr

CC hhc vc vt rt rn bin dn bin dng:ng: SBVL, CHKC, LTSBVL, CHKC, LTH, LTDH, LTDo, CHMTLTo, CHMTLT

ToTon hn hc:c: PhPhng trinh vi phng trinh vi phn, n, o ho hm rim ring, tch phng, tch phn, n, tch phtch phn sn s, c, cc php tnh ma trc php tnh ma trn, gian, gia hh phphng trinh.ng trinh.

Tin hTin hc:c: MMt ngt ngn ng ln ng lp trinh (Visual C++, Visual Basic, Delphi,p trinh (Visual C++, Visual Basic, Delphi,Fortran, Math LAB, Math CAD) hoFortran, Math LAB, Math CAD) hoc tnh toc tnh ton trn trn Exceln Excel

BB trtr v Cv C hhc vc vt rt rn bin dn bin dngng

Vc tVc t ng sut:ng sut:

{ } { }Tzxyzxyzyx =

Vc tVc t bin dbin dng:ng:

{ } { }Tzxyzxyzyx =

Quan hQuan h bin dbin dng ng -- chuychuyn v:n v:

x

w

z

u;

z

w

z

v

y

w;

y

v

y

u

x

v;

x

u

zxz

yzy

xyx

+

=

=

+

=

=

+

=

=

=

w

v

u

x0

z

yz0

0xy

z00

0y

0

00x

zx

yz

xy

z

y

x

Hay { } [ ]{ }f=

(Ch(Chng 3 SBVL, Chng 3 SBVL, Chng 1+2 LTng 1+2 LTH)H)


Quan hQuan h ng sut ng sut -- bin dbin dng (ng (nh lunh lut Hooke):t Hooke):

( )[ ]

( )[ ]

( )[ ]( )

( )

( )zxzxzx

yzyzyz

xyxyxy

yxzz

xzyy

zyxx

E

12

G

1

E

12

G

1

E

12

G

1

E

1

E

1

E

1

+

==

+

==

+

==

+=

+=

+= { } [ ]{ }= C

[ ] ( )( )

( )

+

+

+

=

1200000

0120000

0012000

0001

0001

0001

E

1C

[C] - Ma trn cc h s n hi


Hay { } [ ]{ }= D

[ ]( )( )

( )

( )

( )

+=

2

2100000

02

210000

002

21000

0001

0001

0001

211

ED

[D] - Ma trn cc h s n hi


iu kiiu kin bin bin (n (KB)KB)

S

Sp

KB KB ng hng hc:c: trtrn Sn S c c u = v = w =0u = v = w =0

KB tKB tnh hnh hc:c: TrTrn Sn Sppc tac ta trtrng {p}ng {p}TrTrn Sn Stt -- SSp p khkhng c tang c ta trtrng hay ng hay {p} = {0}{p} = {0}

St


CCch giach gia bbi toi ton CHVRBDn CHVRBD

GiaGia theo chuytheo chuyn v:n v: ChChn cn cc thc thnh phnh phn chuyn chuyn v ln v lm m nn

GiaGia theo theo ng sut:ng sut: ChChn cn cc thc thnh phnh phn n ng sut lng sut lm m n n

GiaGia hhn hn hp:p: ChChn mn mt st s ccc thc thnh phnh phn chuyn chuyn v vn v v mmt st sng sut lng sut lm m n n


CCch giach gia bbi toi ton CHVRBDn CHVRBD

Phng Php

PP Gia tch PP S

PP ngPP gn ng

(cc PP bin phn)Cc PP s gia

gn ng cc PTVFPP PTHH

M hinh chuyn v

M hinh ng sut

M hinh hn hp

PP Sai phn HH

PP Tch phn s

1. Trong nhm PP S1. Trong nhm PP S1. Trong nhm PP S1. Trong nhm PP S ccccn nhng PP nn nhng PP nn nhng PP nn nhng PP no na?o na?o na?o na?2. H2. H2. H2. Hy ny ny ny nu su su su s khkhkhkhc nhau chnh gia PP SFHH vc nhau chnh gia PP SFHH vc nhau chnh gia PP SFHH vc nhau chnh gia PP SFHH v PP PTHH?PP PTHH?PP PTHH?PP PTHH?

1. Trong nhm PP S1. Trong nhm PP S1. Trong nhm PP S1. Trong nhm PP S ccccn nhng PP nn nhng PP nn nhng PP nn nhng PP no na?o na?o na?o na?2. H2. H2. H2. Hy ny ny ny nu su su su s khkhkhkhc nhau chnh gia PP SFHH vc nhau chnh gia PP SFHH vc nhau chnh gia PP SFHH vc nhau chnh gia PP SFHH v PP PTHH?PP PTHH?PP PTHH?PP PTHH?

PhPhng Phng Php PTHHp PTHH

ChChng 1. Vn ng 1. Vn chung chungChChng 2. Tnh hng 2. Tnh h thanhthanhChChng 3. Bng 3. Bi toi ton phn phng ng ChChng 4. Bng 4. Bi toi ton n i xi xng trcng trcChChng 5. Bng 5. Bi toi ton khn khng gian ng gian ChChng 6. Tm mng 6. Tm mng chu ung chu unnChChng 7. Vng 7. V mmngngChChng 8. Bng 8. Bi toi ton n ng lng lc hc hc vc v bbi toi ton n n n nhnh

PhPhng Phng Php PTHHp PTHH

ChChng 1. Vn ng 1. Vn chung chung1.1 Kh1.1 Khi nii nim PP PTHHm PP PTHH1.2 H1.2 Hm chuym chuyn v. Hn v. Hm dm dngng1.3 Ph1.3 Phng trinh cng trinh c ban cban ca PP PTHHa PP PTHH1.4 Trinh t1.4 Trinh t tnh kt cu theo PP PTHHtnh kt cu theo PP PTHH

PP PTHH PP PTHH -- ChChng 1. Cng 1. Cc vn c vn chung chung1.1 Kh1.1 Khi nii nim PP PTHHm PP PTHH

Phng php phn t hu hn l phng php s gii cc bi ton c m t bi cc phng trnh vi phn ring phncng vi cc iu kin bin c th.

C s ca phng php ny l lm ri rc hacc min lin tc phc tp ca bi ton. Cc min lin tc c chia thnh nhiu min con (phn t). Cc min ny c lin kt vi nhau ti cc im nt. Trn min con ny, dng bin phntng ng vi bi ton c gii xp x da trn cc hm xp x trn tng phn t, tho mn iu kin trn bin cng vi s cn bng v lin tc gia cc phn t.

ng dng

Phng php Phn t hu hn thng c dng trong

cc bi ton C hc (c hc kt cu, c hc mi trng lin tc)

xc nh trng ng sut v bin dng ca vt th.

Lch s

PPPTHH c bt ngun t nhng yu cu gii cc bi ton

phc tp v l thuyt n hi, phn tch kt cu trong xy dng

v k thut hng khng. N c bt u pht trin bi

Alexander Hrennikoff (1941) v Richard Courant (1942).

S pht trin chnh thc ca PPPTHH c bt u vo na

sau nhng nm 1950 trong vic phn tch kt cu khung my bay

v cng trnh xy dng, v thu c nhiu kt qu Berkeley


Cc phn mm thng mi cho PPPTHH:

ABAQUS, ANSYS, LS-DYNA, Nastran, Marc,

COMSOL Multiphysics, SAP2000,

MIDAS, STAAP PRO, ETABS, PLAXIS ...

3. H3. H3. H3. Hy cho bit tn v cc chc nng c bn cng nh u nhc im ca nhng phn mm thng mi ng dng PP PHH ????

3. H3. H3. H3. Hy cho bit tn v cc chc nng c bn cng nh u nhc im ca nhng phn mm thng mi ng dng PP PHH ????


MM hinh ri rhinh ri rc ha kt cuc ha kt cu


Chi tit kt cu M hinh phn t

MM hinh phhinh phn tn t


Chi tit kt cu M hinh phn t Chi tit kt cu M hinh phn t



Phn t c bit

Phn tc vt nt

Phn tv hn

Phn tban rang lc



Siu phn t



HHm xp xm xp x ((a tha thc xp xc xp x) (H) (Hm chuym chuyn v)n v)

PP PTHH PP PTHH -- ChChng 1. Cng 1. Cc vn c vn chung chung1.2 H1.2 Hm xp xm xp x. H. Hm dm dngng

KhKhi nii nimmHXXHXX ll hhm mm m ta gta gn n ng mng mt t i li lng nng no o c ca a

ccc c iim trong phm trong phn tn tThThng lng l ddng ng a tha thc c ----> > a tha thc xp xc xp xPhPhng phng php chuyp chuyn v (ly chuyn v (ly chuyn v ln v lm m n) n) ----> >

HHm chuym chuyn vn vDDng thng thcc

BBc, sc, s llng cng cc sc s hhng ph thung ph thuc vc vo o bbc tc t do cdo ca pha phn tn tiu kiiu kinn

HHi ti t

HHm xp xm xp x ((a tha thc xp xc xp x) (H) (Hm chuym chuyn v)n v)


CCc dc dng xp xng xp x

xa b

f

phn t

f(a)f(b)

fthcf(x) = 1111

2

)b(f)a(f1

+=

Xp xXp x hhng sng s

a b

f

x

phn t

f(a)f(b)

fthcf(x) = 1111+ + + + 2222x

Xp xXp x tuyn tnhtuyn tnh

a b

f

x

phn t

f(a)f(b)

fthcf(x) = 1111+ + + + 2222x+ 3333x2

Xp xXp x bbc haic hai

HHm dm dngng


y

z

x

i j

ui uju(x)

x

Vc tVc t chuychuyn v nn v nt vt v llc nc nt ct ca pha phn tn t

{ }

=

=

j

i

j

ie

u

u

u(x) = = = = 1111+ + + + 2222x

{ } [ ] [ ]{ }=

= Q

2x1f

1

Vc tVc t chuychuyn v cn v ca 1 a 1 iim trong phm trong phn tn t

{ } [ ]{ }=

=

= Ca1

01

u

u

2

1

j

ie

a

{ } [ ] { }e1C =

{ } [ ][ ] { } [ ]{ }ee1 NCQf ==

[N]-Ma trn hm dng

UiUj

{ }

=j

ie

U

UF

[ ] { } [ ] { } [ ] { } =eee S

T

V

T

V

Te dSqfdVpfdV

2

1U

Th nang toTh nang ton phn phn cn ca pha phn tn t

{ } [ ] [ ][ ]{ } { } [ ] { } { } [ ] { } =eee S

TeT

V

TeT

V

eTeTe dSqNdVpNdVBDB

2

1U

{ } [ ]{ } [ ][ ]{ }eBDD =={ } [ ]{ }eNf = { } [ ][ ]{ } [ ]{ }ee BN ==

PP PTHH PP PTHH -- ChChng 1. Cng 1. Cc vn c vn chung chung1.3 Ph1.3 Phng trinh cng trinh c banban

{ } [ ] [ ][ ] { } { } [ ] { } [ ] { }

+

=

eee S

T

V

TeTe

V

TeTe dSqNdVpNdVBDB

2

1U

{ } [ ]{ } { } { }eeTeeTe Pk2

1U =

[ ] [ ] [ ][ ]dVBDBkeV

T= Ma trMa trn n ccng phng phn tn t

{ } [ ] { } [ ] { } +=ee S

T

V

TedSqNdVpNP Vc tVc t tai phtai phn tn t

{ }[ ]{ } { } 0PkU ee

e

e ==

[ ]{ } { }ee Pk =


Ma trMa trn n ccng cng ca pha phn tn t


[ ]{ } { }ee Pk =[ ]k{ }eP Vc tVc t tai trtai trng cng ca pha phn tn t

{ } { }ee PF =

[ ]{ } { }PK =

PhPhng trinh cng trinh c ban cban ca pha phn tn t

PhPhng trinh cng trinh c ban cban ca kt cua kt cu

PP PTHH PP PTHH -- ChChng 1. Cng 1. Cc vn c vn chung chung1.4 Trinh t1.4 Trinh t tnh totnh ton kt cun kt cu

1. Ri r1. Ri rc ha kt cuc ha kt cu2. Ch2. Chn hn hm xp xm xp x3. Thit l3. Thit lp ma trp ma trn n ccng cng ca tng pha tng phn tn t4. Thit l4. Thit lp ma trp ma trn n ccng cng ca kt cua kt cu5. Th5. Thnh lnh lp hp h phphng trinh cng trinh c ban cho kt cuban cho kt cu6. X6. X l l iu kiiu kin bin binn----> giai h> giai h ptcbptcb7. Ho7. Hon thin thin bn bi toi tonn

PP PTHH PP PTHH -- ChChng 2. ng 2. Tnh hTnh h thanhthanh1.1 B1.1 Bi toi ton hn h thanhthanh

MMt st s mm hinh bhinh bi toi ton hn h thanhthanh

H dn phng Phn t dn phng

(chu ko nn)



Dn khng gian Phn t dn khng gian

Khung phng Phn t khung phng





Khung khng gian Phn t khung khng gian



Khung khng gian

Phn t khung khng gian



Cu treo dy vng Phn t dm, dy, khung phng


c c iim chung: m chung: y ly l bbi toi ton 1 chiu.n 1 chiu.

PP PTHH PP PTHH -- ChChng 2. ng 2. Tnh hTnh h thanhthanh22.2 X.2 Xy dy dng ma trng ma trn n ccng phng phn tn t vv vc tvc t tai trtai trng phng phn tn t

1. Ph1. Phn tn t thanh chu ko nn dthanh chu ko nn dc trcc trc2. Ph2. Phn tn t gigin phn phngng3. Ph3. Phn tn t ddm chu um chu un phn phngng4. Ph4. Phn tn t thanh chu xothanh chu xon thun thun tn tyy5. Ph5. Phn tn t khung phkhung phngng6. Ph6. Phn tn t khung khkhung khng gianng gian7. Ph7. Phn tn t gigin khn khng gianng gian

PP PTHH PP PTHH -- ChChng 2. ng 2. Tnh hTnh h thanhthanh2.2 X2.2 Xy dy dng ma trng ma trn n ccng phng phn tn t vv vc tvc t tai trtai trng phng phn tn t

1. Ph1. Phn tn t thanh chu ko nn dthanh chu ko nn dc trcc trcy

z

x

i j

ui uju(x)

x


{ }

=

=

j

i

j

ie

u

u

u(x) = = = = 1111+ + + + 2222x

{ } [ ] [ ]{ }=

= Q

2x1f

1

Vc tVc t chuychuyn v cn v ca 1 a 1 iim trong phm trong phn tn t

{ } [ ]{ }=

=

= Ca1

01

u

u

2

1

j

ie

a

{ } [ ] { }e1C =

{ } [ ][ ] { } [ ]{ }ee1 NCQf ==

UiUj

{ }

=j

ie

U

UF

q(x)

[ ] [ ]x1Q =

{ } [ ]{ }=

=

= Ca1

01

u

u

2

1

j

ie

[ ]

=

a1

01C [ ]

=

a

1

a

101

C1 [ ] [ ][ ]

==

a

x

a

x1CQN

1

[ ] [ ] [ ][ ]=Ve

TdVBDBk


1. Ph1. Phn tn t thanh chu ko nn dthanh chu ko nn dc trcc trc

[ ] [ ][ ]

==

a

1

a

1NB

[ ] ED =

[ ] [ ] [ ][ ]

=

==

a

EA

a

EAa

EA

a

EA

Adxa

1

a

1E

a

1a

1

dVBDBka

0Ve

T

{ } [ ] { } [ ] { } +=Se

T

Ve

TedSqNdVpNP



{ } [ ] { }

==a

0

a

0

Tedx)x(q

a

xa

x1

dxqNP

Xc nh vc t tai trng phn t Di tai trng v nt

q0

q0

{ }

=

=

2

aq2

aq

dxq

a

xa

x1

P0

0a

00

e

a

q0a/2 q0a/2

q(x)

? ?

q

a

Tai trng phn b bc 1Tai trng phn b u

P

a

Lc tp trung



x { } [ ] { }

=

==P

a

x

Pa

x1

P

a

xa

x1

PNPTe

Pa

x1

P

a

x

T

a

EA T

{ } [ ] [ ]{ } { }

=

==

TEA

TEA

AdxTE

a

1a

1

dVDBPa

0Ve0

Te

Nhit thay i

EA T

Cch khc xc nh vc t tai trng phn t

(PP tnh theo SBVL)



q0

q0a/2 q0a/2

q0

a

q0a/2 q0a/2

a


2. Ph2. Phn tn t gigin phn phngngy

x

i j

vivj


{ }

=

j

j

i

i

e

v

u

v

u

a

Ui Uj { }

=

j

j

i

i

e

V

U

V

U

F

uiuj

Vi Vj

[ ]

=

0000

0a

EA0

a

EA0000

0a

EA0

a

EA

k

z


3. Ph3. Phn tn t ddm chu um chu un phn phngng

y

x

i j

vivj


{ }

=

zj

j

zi

i

e

v

v

a

{ }

=

zj

j

zi

i

e

M

V

M

V

F

[ ]

=

a

EJ4

a

EJ6

a

EJ2

a

EJ6a

EJ6

a

EJ12

a

EJ6

a

EJ12a

EJ2

a

EJ6

a

EJ4

a

EJ6a

EJ6

a

EJ12

a

EJ6

a

EJ12

k

z

2

zz

2

z

2

z

3

z

2

z

3

z

z

2

zz

2

z

2

z

3

z

2

z

3

z

zi zj

v(x) = = = = 1111+ + + + 2222x + 3333x2+ 4444x3

q(x)

HHm chuym chuyn vn v

Ma trMa trn n ccng phng phn tn tz



y

x

i j

vivj

a

zi zj

q(x) Vc tVc t tai trtai trng phng phn tn t

{ } [ ] { } [ ] { }

[ ]

=

+=

a

0

T

Se

T

Ve

Te

dx)x(qN

dSqNdVpNP

[ ]

+

+

+=

2

32

3

3

2

2

2

32

3

3

2

2

a

x

a

x

a

x2

a

x3

a

x

a

x2x

a

x2

a

x31N

z



y

x

i j

a

q Vc tVc t tai trtai trng phng phn tn t

i j

qa/2i

qa/2

qa2/12 qa2/12

{ }

=

12

qa

2

qa12

qa

2

qa

P

2

2

e

CCc trc trng hng hp khp khc xem bang 1.1 tr.28c xem bang 1.1 tr.28

z


4. Ph4. Phn tn t thanh chu xothanh chu xon thun thun tn tyy

y

x

i j


{ }

=

xj

xie

a

{ }

=xj

xie

M

MF

[ ]

=

a

GJ

a

GJa

GJ

a

GJ

kxx

xx

xixj

(x) = = = = 1111+ + + + 2222x


Ma trMa trn n ccng phng phn tn t

mx

Vc tVc t tai trtai trng phng phn tn t

{ } [ ]=a

0

Tedx)x(mNP

z


5. Ph5. Phn tn t khung phkhung phngng

y

x

i j

vivj

a

zi zjuiuj


{ }

=

zj

j

j

zi

i

i

e

v

u

v

u

{ }

=

zj

j

j

zi

i

i

e

M

V

U

M

V

U

F

z


6. Ph6. Phn tn t khung khkhung khng gianng giany

x

i j

vivj

a

zi zjuiujwi wj

xi xj

yi yj

y

x

i j

vivj

a

uiujwi wj

z

z

4. H4. H4. H4. Hy cho bit cc loi phn t thanh v ma trn cng phn t ca tng loi?4. H4. H4. H4. Hy cho bit cc loi phn t thanh v ma trn cng phn t ca tng loi?

Phn t khung khng gian

Phn t gin khng gian

SGK Tr. 31

y

z

x

PP PTHH PP PTHH -- ChChng 2. ng 2. Tnh hTnh h thanhthanh2.3 Bin 2.3 Bin i hi h trc ttrc ta a

HH tta a phphn tn t (h(h tta a a pha phng)ng)

y'

z'

x'

i j

x-trc thanh

y, z - l cc trc qun tnh chnh ca mt ct ngang thanh

chiu dng x, y, z - tam din thun

y

z

x

y

z x

y

zx

y

z

x HH tta a kt cu (hkt cu (h tta a ttng thng th))


Th d bin Th d bin i ti ta a cca pha phn tn t khung phkhung phngng

y

x

i

j

v i

v j

zi

zj

u i

u j

zy'

z'

x'

y x

i

v i u i

z

zi

v'i

u'i

zizi

iii

iii

'

cos'vsin'uv

sin'vcos'uu

=

+=

+=

{ }

=

=

zj

j

j

zi

i

i

zj

j

j

zi

i

i

e

'

'v

'u

'

'v

'u

100000

0cossin000

0sincos000

000100

0000cossin

0000sincos

v

u

v

u

{ } [ ]{ }ee 'T =

[T] - Ma trn bin i ta


Th d bin Th d bin i ti ta a cca pha phn tn t khung phkhung phngng

{ } [ ]{ }ee 'FTF ={ } [ ]{ }ee 'PTP =

[ ]{ } { }[ ][ ]{ } [ ]{ }[ ] [ ][ ]{ } [ ] [ ]{ }[ ]{ } { }ee

e1e1

ee

ee

'P''k

'PTT'TkT

'PT'Tk

Pk

=

=

=

=

[ ] [ ] [ ][ ]TkT'k 1=

[ ] [ ] [ ][ ]TkT'k T= - Ma trn cng ca phn t trong h ta kt cu


Bin Bin i ti ta a trong trtrong trng hng hp tp tng qung qutt

[ ]

[ ] [ ] [ ] [ ][ ] [ ] [ ] [ ][ ] [ ] [ ] [ ][ ] [ ] [ ] [ ]

=

000

000

000

000

T [ ]

=

'zz'zy'zx

'yz'yy'yx

'xz'xy'xx

Khung phng

( )'x,xcos'xx =

[ ]

=

100

0

0

'yy'yx

'xy'xx[ ] [ ] [ ][ ] [ ]

=

0

0T

Gin khng gian

[ ] [ ] [ ][ ] [ ]

=

0

0T [ ]

=

'zz'zy'zx

'yz'yy'yx

'xz'xy'xx

Gin phng[ ] [ ] [ ][ ] [ ]

=

0

0T [ ]

=

'yy'yx

'xy'xx

PP PTHH PP PTHH -- ChChng 2. ng 2. Tnh hTnh h thanhthanh2.4 X2.4 Xy dy dng ma trng ma trn n ccng tng tng thng th, vc t, vc t tai ttai tng thng th

PhPhng phng php ma trp ma trn n nh vnh v P

2a

12

31 2y

xy

x

y'

x'

u1 u2 u3

{ }

=2

11

u

u { }

=3

22

u

u

[ ]

=

122

121

112

1111

kk

kkk [ ]

=

222

221

212

2112

kk

kkk

{ }

=2

11

'u

'u' { }

=3

22

'u

'u'

[ ]

=

122

121

112

1111

'k'k

'k'k'k [ ]

=

222

221

212

2112

'k'k

'k'k'k

{ }

=

3

2

1

'u

'u

'u

{ }

=

010

001L

1

{ }

=

100

010L

2

{ } [ ] { }( )= ee L'

[ ] [ ] [ ] [ ]=

=en

1e

eeTe L'kLK { } [ ] [ ]

==

en

1e

eTe 'PLP

{ }

=0

RP

1 { }

=P

0P

2

{ }

=0

R'P1 { }

=P

0'P2


PhPhng phng php ma trp ma trn n nh vnh v

[ ] [ ] [ ] [ ]

+== = 2

22221

212

211

122

121

112

111n

1e

eeTe

'k'k0

'k'k'k'k

0'k'k

L'kLKe

{ } [ ] [ ]

== =

P

0

R

'PLPen

1e

eTe


PhPhng phng php ma trp ma trn chn ch ss

[ ]

=

122

121

112

1111

'k'k

'k'k'k [ ]

=

222

221

212

2112

'k'k

'k'k'k

{ }

=

3

2

1

'u

'u

'u (1)

(2)

(3)

Ch s tng th{ }

=2

11

'u

'u' { }

=3

22

'u

'u'

(1)

(2)

(2)

(3)Ch s

cc b

(2)

(3)

(1)

(2)

(1) (2) (2) (3)

(3)

(2)

(1)

(3)(2)(1)

[K] =

k'111 k'12

1

k'211 k'22

1

k'112 k'12

2

k'212 k'22

2

{ }

=0

R'P1 { }

=P

0'P2(1)

(2)

(2)

(3)(3)

(2)

(1)

[P] =R

0

0

P


PhPhng phng php ma trp ma trn chn ch ss

PP PTHH PP PTHH -- ChChng 2. ng 2. Tnh hTnh h thanhthanh2.5 2.5 ThThnh lnh lp PTCB, xp PTCB, x l l iu kiiu kin bin bin, tnh chuyn, tnh chuyn v nn v ntt

KBBKBA

KABKAA

B

A

PB

PA

[ ]{ } { }PK =PhPhng trinh cng trinh c ban cban ca kt cua kt cu

[ ]{ } [ ]{ } { }ABABAAA PKK =+[ ]{ } [ ]{ } { }BBBBABA PKK =+

==

==>{==>{AA}}

==>{==>{PPBB}}

PP PTHH PP PTHH -- ChChng 2. ng 2. Tnh hTnh h thanhthanh2.6 2.6 HoHon thin thin bn bi toi tonn

XXc c nh vc tnh vc t chuychuyn v nn v nttVc tVc t llc nc nttVV bibiu u nni li lcc

TrTrng thng thi thi thc = Trc = Trng thng thi ci c nh + Trnh + Trng thng thi ti t dodo

PP PTHH PP PTHH -- ChChng 2. ng 2. Tnh hTnh h thanhthanh2.7 2.7 MMt st s trtrng hng hp cp cn chn ch

C chuyC chuyn v cn v cng bng bcc

1. Chuy1. Chuyn v nn v nt t b bng chnh chuyng chnh chuyn v cn v cng bng bcc2. Quy 2. Quy i chuyi chuyn v cn v cng bng bc thc thnh tai trnh tai trng nng ntt

1 1 22 3

y'

x'

1 2

1 2

Xem th d Tr. 60, 61Xem th d Tr. 60, 61


C gC gi i n hn hii

a/2

P

a/2 [ ]

+

=

a

EJ4

a

EJ6

a

EJ2

a

EJ6a

EJ6c

a

EJ12

a

EJ6

a

EJ12a

EJ2

a

EJ6

a

EJ4

a

EJ6a

EJ6

a

EJ12

a

EJ6

a

EJ12

k

z

2

zz

2

z

2

z

3

z

2

z

3

z

z

2

zz

2

z

2

z

3

z

2

z

3

z

c

1 2

1

Xem th d Tr. 62, 63Xem th d Tr. 62, 63


C gC gi xii xinn

[ ][ ]

[ ] [ ] [ ] [ ] [ ]

[ ]

11 12 1 1 1 1

21 22 2 2 2 2

1 2

1 2

.......... .......... ........... ..........

.......... .......... .......... ..........

m n

m n

T T T T

mm m mm mn

nn n nm nn

k k k k P

k k k k P

k k k k

k k k k

=

m

n

P

P

b)

y'

x'

y'

x'

y* x*

[ ]

=

cossin

sincos

Xem Tr. 66, 67Xem Tr. 66, 67

MM hinh nn Pasternakhinh nn Pasternak

PP PTHH PP PTHH -- ChChng 2. ng 2. Tnh hTnh h thanhthanh2.8 2.8 ddm trm trn nn n nn n hn hii

y

x

i j

vivj

a

zi zj

wj

xi xj

z

Nn Nn Nn

1

4 2 3

{ }

=

zj

xj

j

zi

xi

i

e

v

v

{ }

=

zj

xj

j

zi

xi

i

e

M

M

V

M

M

V

F

Xem Tr. 70, 71Xem Tr. 70, 71

PP PTHH PP PTHH -- ChChng 3. ng 3. BBi toi ton phn phngng3.1 Kh3.1 Khi nii nim bm bi toi ton phn phngng

z

h

x

y y

O

BBi toi ton n ng sut phng sut phngng

z

x

y

O

1

BBi toi ton bin dn bin dng phng phngng

Xem chXem chng bng bi toi ton phn phng ng ssch L thuyt ch L thuyt n hn hii

PP PTHH PP PTHH -- ChChng 3. ng 3. BBi toi ton phn phngng3.2 M3.2 M hinh ri rhinh ri rc ha kt cuc ha kt cu

Kt cu tKt cu tngng PhPhn tn t hinh hinh ch nhch nhtt

PP PTHH PP PTHH -- ChChng 3. ng 3. BBi toi ton phn phngng3.2 M3.2 M hinh ri rhinh ri rc ha kt cuc ha kt cu

Kt cu tKt cu tng chng chnn PhPhn tn t hinh hinh tam gitam gicc

PP PTHH PP PTHH -- ChChng 3. ng 3. BBi toi ton phn phngng3.3 Ma tr3.3 Ma trn n ccng phng phn tn t

PhPhn tn t hinh tam gihinh tam gicc

y

x

i

j

mvi

ui

um

vm

vj

uj

{ }

=

m

m

j

j

i

i

e

v

u

v

u

v

u

{ }

=

m

m

j

j

i

i

e

V

U

V

U

V

U

F

Xem Tr. 78Xem Tr. 78

PP PTHH PP PTHH -- ChChng 3. ng 3. BBi toi ton phn phngng3.3 Ma tr3.3 Ma trn n ccng phng phn tn t

PhPhn tn t hinh ch nhhinh ch nhtt

y

x

i j

m

vi

ui

um

vm

vj

uj{ }

=

p

p

m

m

j

j

i

i

e

v

u

v

u

v

u

v

u

p

up

vp

Xem Tr. 95Xem Tr. 95

PP PTHH PP PTHH -- ChChng 6. ng 6. Tm mTm mng chu ung chu unn6.1 Kh6.1 Khi nii nim kt cu tm mm kt cu tm mng chu ung chu unn

Tm chu uTm chu unn MM hinh phhinh phn tn t tm ch nhtm ch nhtt

PP PTHH PP PTHH -- ChChng 4. ng 4. Tm mTm mng chu ung chu unn6.2 Ma tr6.2 Ma trn n ccng phng phn tn t

PhPhn tn t tm ch nhtm ch nhtt

i

j

m

wi

wm

wj

wp

zy

xO

xi

yixj

yj

xm ymxp ypp

{ }

=

yp

xp

p

ym

xm

m

yj

xj

j

yi

xi

i

e

w

w

w

w

Ma trMa trn n ccng phng phn n tt (SGK Tr. 140)(SGK Tr. 140)

PP PTHH PP PTHH -- ChChng 5. ng 5. BBi toi ton khn khng gianng gian

MM hinh ri rhinh ri rc hac ha

Lp 1

Lp 2

Lp 3

Kt cu bn nhiu lp

S chia kt cu bn thnh cc PTHH khi lc din

y

z x Cc loi PTHH khi

Phn t t din Phn t ng din Phn t lc din

{ }

=

4

4

4

3

3

3

2

2

2

1

1

1

e

w

v

u

w

v

u

w

v

u

w

v

u


PhPhn tn t tt didin 4 n 4 iim nm ntty

zx

v1u1

w11

v2u2

w2

2

v3u3

w3

3v4

u4w4

4

zyxw

zyxv

zyxu

1211109

8765

4321

+++=

+++=

+++=


Ma trMa trn n ccng phng phn n tt (SGK Tr. 119)(SGK Tr. 119)

y

z x

v2

u2

w2 2

v3

u3

w3

3

v6

u6

w6 6

v1

u1

w1 1 v5

u5

w5 5

v8

u8

w8 8

v7

u7

w7

7 { }

=

8

8

8

7

7

7

6

6

6

5

5

5

4

4

4

3

3

3

2

2

2

1

1

1

e

w

v

u

w

v

u

w

v

u

w

v

u

w

v

u

w

v

u

w

v

u

w

v

u


PhPhn tn t lc dilc din 8 n 8 iim nm ntt

xyzzxyzxyzyxu 87654321 +++++++=

xyzzxyzxyzyxv 161514131211109 +++++++=


BBi toi ton n c giai c giai quyt bquyt bng phng phn tn tng tham sng tham s

xyzzxyzxyzyxw 2423222120191817 +++++++=


PhPhn tn t ng tham sng tham s

Phn t lc din trong h to tng th

y

z x

6

1

5

8

7 2

3 s

r

t

s

r

t

1

2 3 3

5

6 7

8

Phn t lc din trong h to a phng

(Ta t nhin)

(SGK Tr. 123(SGK Tr. 123--::--133)133)

[ ] [ ] [ ] [ ]=eV

Te dVBDBK

[ ] [ ] [ ] [ ] drdsdtJBDBK1

1

1

1

1

1

T

e

=

[ ] [ ] [ ] [ ] ( )( )kji t,s,r

2

1i

2

1j

T2

1kkjie JabsBDBWWWK

= = =

=

[ ] [ ] [ ][ ] ( )( ) [ ] [ ][ ] ( )( ) [ ] [ ][ ] ( )( )[ ] [ ][ ] ( )( ) [ ] [ ][ ] ( )( ) [ ] [ ][ ] ( )( )[ ] [ ][ ] ( )( ) [ ] [ ][ ] ( )( )

222221

212211122

121112111

t,s,r

T

t,s,r

T

t,s,r

T

t,s,r

T

t,s,r

T

t,s,r

T

t,s,r

T

t,s,r

T

e

JabsBDBJabsBDB

JabsBDBJabsBDBJabsBDB

JabsBDBJabsBDBJabsBDBK

++

++++

+++=


TTa a tt nhinhinn

i j

x P 0

l

x

1

l

xL1 =

l

xlL2

=

i(x1,y1) j(x2,y2)

k(x3,y3)

P(x,y) A2

A3

A1

i(x1,y1,z1)

P(x,y,z)

j(x2,y2,z2)

k(x3,y3,z3)

m(x4,y4,z4)

A

AL 11 =

A

AL 22 =

A

AL 33 =

V

VL 11 = V

VL 22 =

V

VL 33 =

V

VL 44 =

(SGK Tr. 97)(SGK Tr. 97)

PP PTHH PP PTHH -- ChuyChuyn n : Ph: Phn tn t bbc caoc cao

1. Kh1. Khi nii nim phm phn tn t bbc caoc cao

2. ngh2. ngha ca ca pha phn tn t bbc caoc cao

3. C3. Cc dc dng phng phn tn t bbc caoc cao

HHm chuym chuyn v ln v l a tha thc bc bc nhtc nht----> ph> phn tn t tuyn tnhtuyn tnhHHm chuym chuyn v ln v l a tha thc bc bc 2 hoc 2 hoc cao hc cao hn n ----> ph> phn tn t bbc caoc caoMuMun hn hm chuym chuyn v ln v l a tha thc bc bc cao thi phai bc cao thi phai b sung ssung s nnt t ddc theo bic theo bin cn ca pha phn tn t

NNng cao ng cao chnh xchnh xc (phan c (phan nh tnh tt ht hn trn trng thng thi bin di bin dng ng ng sut cng sut ca pha phn tn t).).Giam bGiam bt st s llng phng phn tn t khi ri rkhi ri rc ha kt cu.c ha kt cu.Thch hThch hp vp vi tri trng hng hp tp tc c bin bin i ci ca tra trng chuyng chuyn v ln v llln.n.

(TLBS Tr. 27(TLBS Tr. 27--::--36, tr. 5336, tr. 53--::--64)64)

5. Trinh b5. Trinh b5. Trinh b5. Trinh by ty ty ty ta a a a tttt nhinhinhinhin trong phn trong phn trong phn trong phn tn tn tn t mmmmt chiu, 2 chiu vt chiu, 2 chiu vt chiu, 2 chiu vt chiu, 2 chiu v 3 chiu? 3 chiu? 3 chiu? 3 chiu? 5. Trinh b5. Trinh b5. Trinh b5. Trinh by ty ty ty ta a a a tttt nhinhinhinhin trong phn trong phn trong phn trong phn tn tn tn t mmmmt chiu, 2 chiu vt chiu, 2 chiu vt chiu, 2 chiu vt chiu, 2 chiu v 3 chiu? 3 chiu? 3 chiu? 3 chiu?

6. Trinh b6. Trinh b6. Trinh b6. Trinh by tch phy tch phy tch phy tch phn sn sn sn s? ? ? ? 6. Trinh b6. Trinh b6. Trinh b6. Trinh by tch phy tch phy tch phy tch phn sn sn sn s? ? ? ?

7. Trinh b7. Trinh b7. Trinh b7. Trinh by khy khy khy khi nii nii nii nim, cm, cm, cm, cch xch xch xch xc c c c nh ma trnh ma trnh ma trnh ma trn n n n ccccng, vc tng, vc tng, vc tng, vc t tai trtai trtai trtai trng ng ng ng trong phtrong phtrong phtrong phn tn tn tn t ng tham sng tham sng tham sng tham s cccca pha pha pha phn tn tn tn t lc dilc dilc dilc din 8 n 8 n 8 n 8 iiiim nm nm nm nt?t?t?t?7. Trinh b7. Trinh b7. Trinh b7. Trinh by khy khy khy khi nii nii nii nim, cm, cm, cm, cch xch xch xch xc c c c nh ma trnh ma trnh ma trnh ma trn n n n ccccng, vc tng, vc tng, vc tng, vc t tai trtai trtai trtai trng ng ng ng trong phtrong phtrong phtrong phn tn tn tn t ng tham sng tham sng tham sng tham s cccca pha pha pha phn tn tn tn t lc dilc dilc dilc din 8 n 8 n 8 n 8 iiiim nm nm nm nt?t?t?t?

9. Kh9. Kh9. Kh9. Khi nii nii nii nim, nghm, nghm, nghm, ngha va va va v ccccc loc loc loc loi phi phi phi phn tn tn tn t bbbbc cao?c cao?c cao?c cao?9. Kh9. Kh9. Kh9. Khi nii nii nii nim, nghm, nghm, nghm, ngha va va va v ccccc loc loc loc loi phi phi phi phn tn tn tn t bbbbc cao?c cao?c cao?c cao?

8. C8. C8. C8. Cc phc phc phc phng trinh cng trinh cng trinh cng trinh c bancbancbancbanca PP PTHH trong ba PP PTHH trong ba PP PTHH trong ba PP PTHH trong bi toi toi toi ton n n n ng?ng?ng?ng?8. C8. C8. C8. Cc phc phc phc phng trinh cng trinh cng trinh cng trinh c bancbancbancbanca PP PTHH trong ba PP PTHH trong ba PP PTHH trong ba PP PTHH trong bi toi toi toi ton n n n ng?ng?ng?ng?

Thank you very much for your kind attention !Thank you very much for your kind attention !

Documents

Bai Giang PP PTHH