Page 218 - Plastics Engineering

Mechanical Behaviour of Composites 20 1

Example 3.10 If a moment of My = 100 Nm/m is applied to the unidirec-
tional composite described in the previous Example, calculate the curvatures
which will occur. Determine also the stress and strain distributions in the global
(x-y) and local (1-2) directions.
Solution Using the D and d matrices from the previous Example, then for
the applied moment My = 100 N:

This enables the curvatures to be determined as
K~ = -3.87 m-', K~ = 12 m-', K~~ = 2.67 m-',
vYX = 0.328, vXY = 3.05

The bending strains in the global directions are given generally by
E = K.Z

Hence

f
(&y)max = f Ky (f) 0.012
=
(Yxy)max = f Kxy (f) = f 2.67 x

The stresses are then obtained from

so
a, = 0, ay = 150 MN/m2. tXy = 0

For the local directions, the strain and stress transformation matrices can
[ =To. [ "1
be used:

t12 TXY
so

cq = 26.8 MN/m2, a2 = 123.2 MN/m2, txv = 57.5 MN/m2