a análise de placas laminadas compostas inteligentes

5.4 Relação constitutiva acoplada 74
também apresentado em Reddy (2004)
C11 = C11 cos 4 θ − 4C16 cos 3 θ sin θ + 2(C12 + 2C66) cos 2 θ sin 2 θ
− 4C26 cos θ sin 3 θ + C22 sin 4 θ
C12 = C12 cos 4 θ + 2(C16 − C26) cos 3 θ sin θ + (C11 + C22 − 4C66) cos 2 θ sin 2 θ
+ 2(C26 − C16) cos θ sin 3 θ + C12 sin 4 θ
C13 = C13 cos 2 θ − 2C36 cos θ sin θ + C23 sin 2 θ
C14 = C14 cos 3 θ + (C15 − 2C46) cos 2 θ sin θ + (C24 − 2C56) cos θ sin 2 θ + C25 sin 3 θ
C15 = C15 cos 3 θ − (C14 + 2C56) cos 2 θ sin θ + (C25 − 2C46) cos θ sin 2 θ − C24 sin 3 θ
C16 = C16 cos 4 θ + (C11 − C12 − 2C66) cos 3 θ sin θ + 3(C26 − C16) cos 2 θ sin 2 θ
+ (2C66 + C12 − C22) cos θ sin 3 θ − C26 sin 4 θ
C22 = C22 cos 4 θ + 4C26 cos 3 θ sin θ + 2(C12 + 2C66) cos 2 θ sin 2 θ
+ 4C16 cos θ sin 3 θ + C11 sin 4 θ
C23 = C23 cos 2 θ + 2C36 cos θ sin θ + C13 sin 2 θ
C24 = C24 cos 3 θ + (C25 + 2C46) cos 2 θ sin θ + (C14 + 2C56) cos θ sin 2 θ + C15 sin 3 θ
C25 = C25 cos 3 θ + (2C56 − C24) cos 2 θ sin θ + (C15 − 2C46) cos θ sin 2 θ − C14 sin 3 θ
C26 = C26 cos 4 θ + (C12 − C22 + 2C66) cos 3 θ sin θ + 3(C16 − C26) cos 2 θ sin 2 θ
C33 = C33
+ (C11 − C12 − 2C66) cos θ sin 3 θ − C16 sin 4 θ
C34 = C34 cos θ + C35 sin θ
C35 = C35 cos θ − C34 sin θ
C36 = (C13 − C23) cos θ sin θ + C36(cos 2 θ − sin 2 θ)
C44 = C44 cos 2 θ + C55 sin 2 θ + 2C45 cos θ sin θ
C45 = C45(cos 2 θ − sin 2 θ) + (C55 − C44) cos θ sin θ
C46 = C46 cos 3 θ + (C56 + C14 − C24) cos 2 θ sin θ
+ (C15 − C25 − C46) cos θ sin 2 θ − C56 sin 3 θ
C55 = C55 cos 2 θ + C44 sin 2 θ − 2C45 cos θ sin θ
C56 = C56 cos 3 θ + (C15 − C25 − C46) cos 2 θ sin θ
+ (C24 − C14 − C56) cos θ sin 2 θ + C46 sin 3 θ
C66 = 2(C16 − C26) cos 3 θ sin θ + (C11 + C22 − 2C12 − 2C66) cos 2 θ sin 2 θ
+ 2(C26 − C16) cos θ sin 3 θ + C66(cos 4 θ + sin 4 θ)
(5.67)