Page 222 - Plastics Engineering

Mechanical Behaviour of Composites 205

As the strains are independent of 2 they can be taken outside the integral:

where, for example,

A11 = TalldZ = 2.
-h/2 0
[A] is the Extensional Stiffness Matrix although it should be noted that it also
contains shear terms.
Within a single ply, such as the fth, the e - terms are constant so,

In overall terms
P
[AI = CDhf (3.35)
f =I
Thus the stiffness matrix for a symmetric laminate may be obtained by
adding, in proportion to the ply thickness, the corresponding terms in the stiff-
ness matrix for each of the plies.
Having obtained all the terms for the extensional stiffness matrix [A], this
may then be inverted to give the compliance matrix [a].
[a] = [AI-'

The laminate properties may then be obtained as above from inspection of
the compliance matrix.
1 1 1
G=-
Ex = - E, = -
allh . a22h a66h
where h is the thickness of the laminate.
-a12 --a12
vx, = - Vyx = -
a11 a22