Properties for Design of Composite Structures. Neil McCartney

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Baseline equals StartFraction 1 minus nu Subscript t Baseline Over upper E Subscript upper T Baseline EndFraction left-parenthesis sigma Subscript r r Baseline plus sigma Subscript theta theta Baseline right-parenthesis minus StartFraction 2 nu Subscript upper A Baseline Over upper E Subscript upper A Baseline EndFraction sigma Subscript z z Baseline period"/>(4.101)

      On substituting for σzz using (4.100), it then follows that

(4.102)

      On subtracting (4.95) and (4.96),

(4.103)

      It follows from (4.94), on addition and subtraction, that

(4.104)

(4.105)

      Relations (4.102) and (4.104) then assert that

(4.106)

      Relations (4.103) and (4.105) assert that

(4.107)

      The addition and subtraction of (4.106) and (4.107) leads to the results

(4.108)

      (4.109)

      From (4.94) and (4.98), it follows that

(4.110)

      It is easily shown that the stress field given by relations (4.108)–(4.110) satisfies automatically the following equilibrium equations for any values of the parameters A, B, C and D (see (2.125)–(2.127))

      (4.111)

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