Page 256 - Mechanics Analysis Composite Materials
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Chapter 5. Mechanics of laminates 24 1
To calculate the actual stiffnesses of the laminate, we should put hi= 6, ti = is,
k = 2p, e = h/2, and h = 2p6 (see Fig. 5.10), where 6 is the thickness of a
unidirectional ply. Then, Eqs. (5.28) and (5.42) yield
where
(5.48)
63- p
2;;) = -El [12j2(1 + a)- 6j(3 + a)+ 7 + a],
3 ,j=l
63- *
@=gE1~[12j’(l+a)-6j(3cr+1)+7a+I],
j= I
where a = E2/E1.
Matching Eqs. (5.45), (5.46) and (5.47), (5.48) we can see that B,, =Bi,,, Le.,
membrane stiffnesses are the same for both models of the laminate. Coupling and
bending stiffnesses are also the same for mn = 12,44. There is no difference between
the models for a = 1 because the laminate reduces in this case to a homogeneous
layer.
Summing up the series in Eqs. (5.48) and using Eqs. (5.47) we arrive at
Taking into account that in accordance with Eqs. (5.46) and accepted notations
we can conclude that the only difference between the homogeneous and the
laminated models is associated with coupling coefficients CI~and C?? which are
