Page 227 - Plastics Engineering

210 Mechanical Behaviour of Composites

and once again using the expressions from the analysis of a single ply,

F hf
[MIL = J ([QI[&lZ + [al[Klz2)dz
f=1
hf-1

[MIL = [BI[EIL + [DI[K]L (3.39)
where [B] is as defined above and

lF
[Dl = 3 C[iZIf ch; - (3.40)
f=1
As earlier we may group equations (3.36) and (3.39) to give the Plate Consti-
[;I = [; :] [:I (3.41)
tutive Eauation as

This equation may be utilised to give elastic properties, strains, curvatures, etc.
It is much more general than the approach in the previous section and can
accommodate bending as well as plane stresses. Its use is illustrated in the
following Examples.
Example 3.12 For the laminate [0/352/ - 3521, determine the elastic
constants in the global directions using the Plate Constitutive Equation.
When stresses of a, = 10 MN/m2, u - -14 MN/m2 and txy = -5 MN/m2
y -.
are applied, calculate the stresses and strams in each ply in the local and global
directions. If a moment of M, = lo00 N m/m is added, determine the new
stresses, strains and curvatures in the laminate. The plies are each 1 mm thick.

El = 125 GN/m2, E2 = 7.8 GN/m2, G12 = 4.4 GN/m2, u12 = 0.34
Solution The locations of each ply are illustrated in Fig. 3.22.
Using the definitions given above, and the values for each ply, we may
determine the matrices A, B and D from

10
A= CiZf(hf -hf-l),
f=1