Page 85 - Mechanics Analysis Composite Materials

70 Mechanics and analysis of composite materials

(3.26)

Compatibility equations follow from Eqs. (3.20) and (3.21), Le.,

1 1 - &-I) .
y, = -((E,
am
Using constitutive equations, Eqs. (3.19), we can write them in terms of stresses

Substituting stresses from Eqs. (3.25), (3.26) and introducing dimensionless
coordinate X =x/a (see Fig. 3.15) we finally arrive at the following set of governing
equations:

(3.27)

where in accordance with Eqs. (3.17)

(3.28)

With due regard to the second equation in Eqs. (3.25) we can take the general
solution of Eqs. (3.27) in the form

Fn(T)= Ane-j3 . (3.29)

Substitution into Eqs. (3.27) yields:

(3.30)

(3.31)

(3.32)