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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σkl = ℜ[Kr iɛ ](2πr) −1/2 σ I kl (θ, ɛ)+ℑ[Kriɛ ](2πr) −1/2 σ II<br />
kl (θ, ɛ),<br />
i = √ −1 r <br />
k<br />
<br />
<br />
l<br />
iɛ <br />
r =cos(ɛln r)+i sin(ɛ ln r).ɛ<br />
<br />
<br />
ɛ = 1<br />
2π ln<br />
<br />
1 − β<br />
.<br />
1+β<br />
ℑ ℜ K<br />
<br />
σ I kl<br />
kl<br />
σ II<br />
K = K1 + iK2,<br />
<br />
<br />
<br />
<br />
θ,<br />
<br />
<br />
θ =0 θ =0 <br />
uj<br />
σ22 + iσ12 =(K1 + iK2)(2πr) −1/2 r iɛ .<br />
<br />
Δuj<br />
<br />
<br />
Δuj = uj(r, θ = π) − uj(r, θ = −π),<br />
<br />
j<br />
<br />
<br />
K <br />
<br />
Δu2 + iΔu1 =<br />
c1 + c2<br />
2 √ 2π(1 + 2iɛ)cosh(πɛ) Kriɛ+1/2 ,<br />
cm = κm +1<br />
,<br />
<br />
m =1 m =2<br />
iɛ <br />
<br />
r<br />
<br />
<br />
<br />
<br />
<br />
<br />
μm
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