Page 214 - Plastics Engineering

Mechanical Behaviour of Composites 197

this simple single ply situation. However, its identity has been retained as it
has relevance in laminate analysis, to be studied later.
Returning to equation (3.28), the moments may be written as

h h

[MI = [Bl[~l+ PI[KI (3.30)

where [D] is the Bending Stiffness Matrix (= [Q]h3/12).
Equations (3.29) and (3.30) may be grouped into the following form
[:I
[E] = [: 4 (3.31)

and these are known as the Plate Constitutive Equations.
For this special case of a single ply, [B] = 0 and so the forces are related to
the strains by
[NI = [AI[&] (3.32)

(which is effectively [a] = [Q][E] as shown previously) or the strains are related
to the forces by
[E] = [a][N] where [a] = [A]-'

(which is effectively [E] = [S][a] as shown previously).
Also, for the single ply situation, the moments are related to the curvature
by
[MI = [DI[Kl (3.33)

or the curvature is related to the moments by

[K] = [d][M] where [d] = [D]-'
It should be noted that it is only possible to utilise [a] = [AI-' and [dl =
[DI-' for the special case where [B] = 0. In other cases, the terms in the [a]
and [d] matrices have to be determined from
[i :I=[, A B -' (3.34)

D]