Properties for Design of Composite Structures. Neil McCartney

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СКАЧАТЬ Superscript m Baseline identical-to 0 comma"/>(4.27)

      where A_f, A_m and ϕ are constants to be determined.

      4.3.2 Solution for an Isolated Fibre Perfectly Bonded to the Matrix

      The boundary and interface conditions that must be satisfied are

(4.28)

      On differentiating the displacement field, it follows, on using (2.139) on setting uθ≡0, that.

(4.29)

(4.30)

(4.31)

(4.32)

      It follows directly from (4.17), (4.30) and (4.32) that for fibre and matrix

(4.33)

      On subtracting (4.14) and (4.15), it follows that for fibre and matrix

(4.34)

      (4.35)

      Relations (4.29) and (4.31) then assert that

(4.36)

      On substituting (4.33) and (4.34) into the equilibrium equations (4.20)–(4.22) it follows that

(4.37)

(4.38)

      On integrating (4.38)₁ subject to the condition (4.28)₁,

(4.39)

      and from (4.36) it follows that

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