Crack Paths 2012

_

_

3 + v

_

H e rMer (l r ) : M r l

Q r l( l ) : Q r 2

Q r Z

Satisfying the boundary conditions (13) at the interface rIl one can obtain

equations for determination of the rest of unknownintegration constants:

_ l4 qh A l2—tAl2+K —K + q 1_5_5’ + B =0, _

l

2

l

2

) 8 E ;

NI1 (nil/,6 + 3M;1 (mp2 = 314,, (l)+ 0.4(q — p)h2G*;

(14)

N; (l) = 3/i(1-/i)M,,(i)/h

—0.1qhG*f/4,

__ M m _ _ _0.1qG*f

_ .

1

L ” .

where F, _ ZEh, (1 v)(1 [2)

8E” (1 v), G _4(I_V)[G, v(3+v)),

B(,5)=0l0(1—,5)[8—f1(fl)B2I321;

5’I85A’(1—fl)2h2/l2)=45(II1);

v" 2 1_ 3 E’ R2 I — ( )( 'BI)” ; Mr2(l)=q—(3+V)(l—(92);G I L ;

tI1+2A’(1—,B)2h2/l2; 21,

2 ( l — v — 2 v v ) G

16

R

2

f1(fl)=(1—fl)(5+2fl—fl2);

f=1—(1—2fl) (MO/10%)).

Solving the systems of equations (12) and (14) simultaneously, one can derive the

integration constant Al, the biggest deflection W1- (0) of the bottom part of the plate at

its center, and the moment M_l (l ) :

0R2

h2 _0,2(q—p)h2G*_0,lqh2G*f

2 1

2

A 1 — — m | : ( 3 + l / ) ( 1 + 6 ( g — 1 ) ) + 1 6 8 0 fl

5R2

3(1+v),BD 24(1+v),6’2D

9

w; (0) — qR4 5 1 %+[l -1jo4 - m -[202 1+l—"j+32ii[1+ 0%?M M+

_64D1+v 5

25(5+v)

3+v 5+vR2

l

)

+ q

h .f— q .1901);

(15)

0,292 q—p R2h2G* 0,1192 R2h2G*

3(1+v),BD

24(1+v),[)’ D 8E

l i l y - 1 ( 1 ) = , B 3 M , 2 ( I ) + ( ) , 4 I B 2 ( q _ p ) h 2 G * / 3 + 0 , l fl q h 2 f G * / l 2 =

3 2

I%(3+V)(1—92)+0,4,52(q—p)h2G*/3+0,1,Bqh2fG*/12~

Maximal stress o',‘1(0,i hO / 2) can be obtained from Eqs. (6), (13) as

_ M_ or](0,iho/2)Imi3+(g)i0,2G*p,

(16)

2,6h

2/3 h

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