----

, , , ,

. ,

2 , 3,

.

[1] 2[1] 2[1] 2[1] 2

2 )(,, xyyxyx = ,

.

(a)

0=+

+

X

yxyxx

0=+

+

Yyx

yxy (1.1)

(b) (- )

x

v

yu

yv

x

uxyyx

+

=

=

= (1.2)

(c) -

)(1 2 yxx

E

+

=

)(1 2 xyy

E

+

=

xyxyE

)1(2 += (1.3)

(d) ()

xxyx Tml =+

yyxy Tml =+ (1.4)

(e) ()

vvuu == (1.5)

2 , (1.4), (1.5) (1.1)-(1.3) ,

. ,

, .

.

0)()()( ******* =++++ dsvTuTdVvYuXdV S yxVV xyxyyyxx (1.6)

* . ,

, . ,

, .

[2] 2[2] 2[2] 2[2] 2

::::

, 1.1(b) ( )

, (1.6) .

V

e

, .

{ } { } { } { } { } { } =

S

T

V

T

V

T dSgfdVpfdVee

0*** (1.7)

, { }*f { }p { }g , , .

::::

1.2 () i, j, m , { }e ,

{ }f .

{ }( ) mmjjiiTe vuvuvu= (1.8)

{ } [ ]{ }ekk

kk

NvN

uN

v

uf =

=

=

3

1

3

1 (1.9)

kN , (Shape function) . ,

xy 1 , u

, .

yxu 321 ++= (1.10)

),(),,(),,( mmjjii yxyxyx mji uuu ,,

.

iii yxu 321 ++=

jjj yxu 321 ++=

mmm yxu 321 ++= (1.11)

321 ,, , (1.10) .

mmjjii uNuNuNu ++= (1.12)

++= 2/)( ycxbaN iiii

jmmji yxyxa =

mji yyb =

jmi xxc =

mm

jj

ii

yxyxyx

111

21

= (1.13)

i, j, m , .

Y v . ,

(1.10) .

---- ::::

(1.12) , (1.2) , .

.

{ } [ ]{ }exy

y

x

B

x

v

yu

yvx

u

=

+

=

= (1.14)

, [ ]B - , .

[ ]

=

mmjjii

mji

mji

bcbcbcccc

bbbB 000

000

21 (1.15)

[ ]B . , (2.11) ,

.

---- ::::

(1.3) .

{ } [ ]{ }

DE

xy

y

x

xy

y

x

=

=

=

2/)1(000101

1 2 (1.16)

::::

, (1.9), (1.13), (1.16) .

{ }( ) [ ] [ ][ ] { } { }( ) [ ] { } { }( ) [ ] { } =

S

TTe

V

TTee

V

TTe dSgNdVpNdVBDBee

0'*** (1.17)

,

[ ]TN ' . (1.17), { }e* , .

[ ] { } { } { } 0= egepee FFk (1.18)

, [ ]ek , { }epF { }egF , ,

dV tdxdt , .

[ ] [ ] [ ][ ] [ ] [ ][ ] == tBDBtdxdyBDBk TTe (1.19)

(1.20)

, ,

.

, (1.7) { } { }o + . { }o

.

{ } [ ]{ }oo D = (1.21)

, (1.17) .

{ } [ ] [ ]{ }tdxdyDBF oTeo = (1.22)

,

.

{ } [ ] { }tdxdypTF Nep

=

26

{ } [ ] { }dsgTF Neg

= '

24

:

, ,

.

[ ]{ } { }FK = (1.23)

, { } ,

{ } .

{ } [ ] { }FK 1= (1.24)

{ } , ,

. { } , (1.14) ,

(1.16) .

::::

(1.6) ,

.

,

, ,

,

.

.

{ } { } { } { } { } { } =V S

TT

V

Tp dSgfdVpfdV

21 (1.25)

{ } { }0=

p (1.26)

(1.26) (1.23) .

, ,

.