Properties for Design of Composite Structures. Neil McCartney

      where the strain parameters ε¯A, ε¯T, ε^A and ε^T, the through-thickness stress σt and the temperature difference ΔT are assumed for the moment to be known. From (2.143), (2.209) and (2.211), the in-plane strains and shear stress are given by

(2.212)

      The expression for ε22 in (2.209) is first solved for the stress component σ22 so that

      (2.213)

      It then follows from (2.209) that

      (2.214)

      where

(2.215)

      In addition, from (2.209)

(2.216)

      where

      (2.217)

      2.18.2 Stress and Displacement Fields

      The immediate objective is to determine the displacement component u₃ and corresponding stresses σ11, σ12 and σ12 in terms of the mechanical loading parameters ε¯A,ε^A,ε¯T,ε^T,σt and the temperature difference ΔT. From (2.209), (2.210) and (2.212), the in-plane stresses must satisfy the relations

(2.218)

(2.219)

      On solving (2.218) and (2.219) for the stresses, it follows that

(2.220)