Page 218 - Mechanics Analysis Composite Materials
P. 218
Chapter 4. Mechanics of a composite layer 203
Using this expression and substituting E from Eq. (4.152) into Eq. (4.154) we
arrive at
(4.159)
where v = V.L!V.Gs-r*
Substitution of Eqs. (4.157) and (4.159) into the second equation of Eqs. (4.158)
provides the following governing equation of the problem under study:
d' u k'u=O , (4.160)
__
dy'
where
Using the symmetry conditions we can present the solution of Eq. (4.160) as
u = Csinhky .
Constant C should be found from the boundary conditions for free longitudinal
edges of the specimen (see Fig. 4.72) according to which zxv(y= fa/2) = 0.
Satisfying these conditions and using Eqs. (4.152), (4.153), (4.157), and (4.159) we
finally obtain:
(4.161)
