Читать книгу Properties for Design of Composite Structures - Neil McCartney - Страница 70

A solution is now sought of the following form

(4.72)

where A, α and β are constants to be determined. On differentiating the displacement field using the strain-displacement relations (2.139), it follows that

(4.73)

(4.74)

It follows directly from (4.14)–(4.17), (4.73) and (4.74) that

(4.75)

In addition, it follows from (4.17), (4.73) and (4.74) that

(4.76)

It is easily shown that the stress field automatically satisfies the equilibrium equations (4.20)–(4.22) for any values of the parameters A, α and β.

The following continuity conditions must be satisfied at the interface r = a between fibre and matrix

(4.77)

(4.78)

It then follows from (4.76) that

(4.79)

and from (4.72) that

(4.80)

The substitution of (4.80) into (4.79) then leads to

(4.81)