Properties for Design of Composite Structures. Neil McCartney

alt="sigma Subscript theta theta Superscript f Baseline equals sigma Subscript upper T Baseline minus phi period"/>(4.42)

      The substitution of (4.29)₃, (4.41) and (4.42) into (4.16) leads to

      (4.43)

      It is clear from (4.41) that σzzf is a constant, automatically satisfying (4.37)₂. The substitution of (4.31)₃, (4.39) and (4.40) into (4.16), applied to the matrix, leads to

(4.44)

      thus automatically satisfying (4.38)₂. The substitution of (4.29), (4.31), (4.39)–(4.44) into relation (4.14), applied to the fibre and matrix, leads to

(4.45)

(4.46)

      where kTf is the plane strain bulk modulus for the transverse isotropic fibre and kTm is the plane strain bulk modulus of the isotropic matrix, defined by (see (2.202))

(4.47)

      (4.48)

      It should be noted that

(4.49)

      where km is the bulk modulus of the matrix defined by (see (2.205))

      (4.50)

      It now only remains to determine the constant ϕ, which can be specified on applying the remaining condition (4.28)₅, because the conditions (4.28)₂, (4.28)₄ and (4.28)₆ are automatically satisfied by (4.25) and (4.33). It follows from (4.26), (4.27), (4.28)₅, (4.45) and (4.46) that

      (4.51)

      where

      (4.52)

      The displacement distribution is specified by (4.25)–( Скачать книгу