addition, from (2.209)
where
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
On solving (2.218) and (2.219) for the stresses, it follows that
where
It is noted that the in-plane stresses are only linear functions of x3. It then follows, on using (2.210), that all the equilibrium equations (2.120)–(2.122) are satisfied.
It now only remains to determine the value of the displacement component u3 describing the deflection of the beam. From (2.216) and (2.220)
