Properties for Design of Composite Structures. Neil McCartney

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СКАЧАТЬ 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)

(2.221)

      where

(2.222)

      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)

(2.223)

      On using (2.215) and (2.222) it can be shown that

      СКАЧАТЬ