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II.1.7.2 Out-of-plane shear thermo-elastic behavior

Starting with the out-of-plane shear constitutive equation (II.1.28) and of the expression defining the out-of-plane shear force vectors Qs lam one makes developments similar to those of section II.1.7.1 and defines the following quantities:

αsGhlam =-h2h2 g lam αs lam dz, = k=1N g lamk α s lamk z k - zk-1 . (II.1.66)

αsGh2 lam =-h2h2z g lam αs lam dz, = k=1N g lamk α s lamk zk2 - z k-12 2 . (II.1.67) They are used in the expression:
Qlam = Glam Γ lam -αsGhlam(T0 - Tref) -αsGh2 lamT,z. (II.1.68)

Correspondingly, one estimates the laminate out-of-plane shear CTE vectors:

α0s lam = Glam-1 αGh lam (II.1.69)
α1s lam = Glam-1 αGh2 lam (II.1.70)

These two expressions allow to write the expression of the inverse of (II.1.68):

Γ lam = Glam-1 Q lam + α0s lam(T0 - Tref) + α1s lamT,z.