Page 226 - Plastics Engineering
P. 226
Mechanical Behaviour of Composites 209
Analysis of Laminates
The general deformation analysis of a laminate is very similar to the general
deformation analysis for a single ply.
(i) Force Equilibrium: If there are F plies, then the force resultant, NL, for
the laminate is given by the sum of the forces for each ply.
F F hf
[NIL = CWIf = / [Olfdz
f =I f =1
hf-i
and using the definition for [a] from the analysis of a single ply,
F
[NIL. = E(@] . [&I [el . Z . [Kl)fdz
f =I
(3.36)
where
(3.37)
This is called the Extensional StifSness Matrix and the similarity with that
derived earlier for the single ply should be noted.
Also, the Coupling Matrix, [B] is given by
(3.38)
The Coupling Matrix will be zero for a symmetrical laminate.
(ii) Moment Equilibrium: As in the case of the forces, the moments may be
summed across F plies to give
F F hf
[MIL = C[MIf = / [UlfdZ
f =I f =I
hf-1
