Properties for Design of Composite Structures. Neil McCartney

alt="StartFraction partial-differential sigma 12 Over partial-differential x 1 EndFraction plus StartFraction partial-differential sigma 22 Over partial-differential x 2 EndFraction plus StartFraction partial-differential sigma 23 Over partial-differential x 3 EndFraction equals 0 comma"/>(2.121)

(2.122)

      where the stress tensor is symmetric such that

(2.123)

      When using cylindrical polar coordinates (r,θ,z) such that

      (2.124)

      the equilibrium equations (2.120)–(2.122) are written as

      (2.125)

(2.126)

      (2.127)

      where the stress tensor is symmetric such that

      (2.128)

      When using spherical polar coordinates (r,θ,ϕ) such that

      (2.129)

      the equilibrium equations (2.120)–(2.122) are written as

      (2.130)

      (2.131)

      (2.132)

      where the stress tensor is symmetric such that

      (2.133)

      2.13 Strain–Displacement Relations

      For the special case when the strain tensor εij is uniform, and on using (2.107), the displacement fields

      (2.134)

      and

(2.135)

      both lead to the same strain field given by

       Скачать книгу