Rasmus ÿstergaard forside 100%.indd - Solid Mechanics
Rasmus ÿstergaard forside 100%.indd - Solid Mechanics
Rasmus ÿstergaard forside 100%.indd - Solid Mechanics
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sij =<br />
⎡<br />
⎢<br />
⎣<br />
ν21 ν31 − − 0 0 0<br />
E22 E33<br />
1 ν32 − 0 0 0<br />
E22 E33<br />
ν23 1 − 0 0 0<br />
E22 E33<br />
1<br />
0 0 0 0 0<br />
G23<br />
1<br />
0 0 0 0 0 G31<br />
1<br />
0 0 0 0 0<br />
1<br />
E11<br />
− ν12<br />
E11<br />
− ν13<br />
E11<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
sij = 1<br />
E<br />
⎡<br />
⎢<br />
⎣<br />
σ12<br />
G12<br />
⎤<br />
⎥<br />
⎦<br />
1 −ν −ν 0 0 0<br />
−ν 1 −ν 0 0 0<br />
−ν −ν 1 0 0 0<br />
0 0 0 2(1+ν) 0 0<br />
0 0 0 0 2(1+ν) 0<br />
0 0 0 0 0 2(1+ν)<br />
σ22<br />
<br />
<br />
<br />
H22<br />
σ22 + iσ12 =<br />
H11<br />
1<br />
√ Kr<br />
2π iɛ−1/2 ,<br />
⎤<br />
⎥<br />
⎦<br />
<br />
<br />
<br />
<br />
ɛ β<br />
<br />
<br />
β = [(s′ 11s ′ 22) 1/2 + s ′ 12]#2 − [(s ′ 11s ′ 22) 1/2 + s ′ 12]#1<br />
√ ,<br />
H11H22<br />
<br />
#1 #2 #1 #2<br />
<br />
<br />
<br />
H11 = 2m<br />
H11 H22<br />
λ 1/4 (s ′ 11s′ 22 )1/2<br />
<br />
+ 2m<br />
#1<br />
λ 1/4 (s ′ 11s′ 22 )1/2<br />
<br />
<br />
#2<br />
<br />
m =<br />
H22 =<br />
(1+ρ)<br />
2 ,<br />
<br />
2m λ −1/4 (s ′ 11s′ 22 )1/2<br />
<br />
+ 2m<br />
#1<br />
λ −1/4 (s ′ 11s′ 22 )1/2<br />
<br />
,<br />
#2
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