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12(¯ω) = −σ2(¯ω) sin θ(¯ω) cos θ(¯ω)

Es(¯ω)t(¯ω)

l(¯ω)3

22(¯ω) =

σ2(¯ω) cos θ(¯ω) 2 cos2θ(¯ω)+8s(¯ω)

l(¯ω)3cos2α(¯ω)

sin3α(¯ω)+cos2β(¯ω)

sin3β(¯ω)+ 2 s(¯ω)

l(¯ω)2

(cot2α(¯ω) + cot2β(¯ω))!

Es(¯ω)t(¯ω)

l(¯ω)3h(¯ω)

l(¯ω)+ 2s(¯ω)

l(¯ω)+ 2 sin θ(¯ω)

γ12

γ12(¯ω) =

2τ(¯ω) cos θ(¯ω) 2s(¯ω)

l(¯ω)2

+ 4 s( ¯ω)

l(¯ω)31

sinα(¯ω)+1

sinβ( ¯ω)+h( ¯ω)

l(¯ω)3

+1

2h(¯ω)

l(¯ω)2!

Es(¯ω)t(¯ω)

l(¯ω)3h(¯ω)

l(¯ω)+ 2s(¯ω)

l(¯ω)+ 2 sin θ( ¯ω)

ZUij Z

E1Uij =σ1

11

E2Uij =σ2

22

ν12ij =−21

11

ν21ij =−12

22

G12ij =τ

γ12

m n

ith jth i j i = 1,2, ..., m

j= 1,2, ..., n

Zeq(¯ω)

E1ν12 E2

ν21 G12

E1eq(¯ω) = L(¯ω)

B(¯ω)

n

X

j=1

B(¯ω)j

m

P

i=1

2l(¯ω)3

ij (h(¯ω)ij +l(¯ω)ij sin θ(¯ω)ij ) sin2θ(¯ω)ij

Es(¯ω)ij t(¯ω)3

ij

E2eq( ¯ω) = B(¯ω)

L(¯ω)×

n

X

j=1

B(¯ω)j

m

P

i=1

Es(¯ω)ij t(¯ω)3

ij (h(¯ω)ij + 2s(¯ω)ij + 2l(¯ω)ij sin θ(¯ω)ij )

l(¯ω)3

ij cos2θ(¯ω)ij + 4s(¯ω)3

ij cos2α(¯ω)ij

sin3α(¯ω)ij

+cos2β(¯ω)ij

sin3β(¯ω)ij +s(¯ω)2

ij l(¯ω)ij (cot2α(¯ω)ij +cot2β(¯ω)ij )

−1

ν12eq(¯ω) = L(¯ω)

B(¯ω)

n

X

j=1

B(¯ω)j

m

P

i=1

(h(¯ω)ij + 2s(¯ω)ij + 2l(¯ω)ij sin θ(¯ω)ij ) sin θ(¯ω)ij

cos θ(¯ω)ij

ν21eq( ¯ω) = B(¯ω)

L(¯ω)×

n

X

j=1

B(¯ω)j

m

P

i=1

sin θ(¯ω)ij cos θ(¯ω)ij l(¯ω)3

ij (h(¯ω)ij + 2s(¯ω)ij + 2l(¯ω)ij sin θ(¯ω)ij )

l(¯ω)3

ij cos2θ(¯ω)ij + 4s(¯ω)3

ij cos2α(¯ω)ij

sin3α(¯ω)ij

+cos2β(¯ω)ij

sin3β(¯ω)ij +s(¯ω)2

ij l(¯ω)ij (cot2α(¯ω)ij +cot2β(¯ω)ij )

−1

G12eq(¯ω) = B(¯ω)

L(¯ω)×

n

X

j=1

B(¯ω)j

m

P

i=1

Es(¯ω)ij t(¯ω)3

ij (h(¯ω)ij + 2s(¯ω)ij + 2l(¯ω)ij sin θ(¯ω)ij )

2l(¯ω)ij s(¯ω)2

ij +h(¯ω)2

ij h(¯ω)ij +l(¯ω)ij

2+ 4s(¯ω)3

ij 1

sinα(¯ω)ij

+1

sinβ( ¯ω)ij

−1