Page 320 - Mechanics Analysis Composite Materials
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Chapter 7. Eneirvnmental. special loading. and manufacturing effects 305
Fig. 7.2. Heat flows in coordinates x. 1’and XI. x?.
Changing variables xI, x’ for x, y with the aid of the following transformation
relationships:
x =XI cos 4 - x, sin 4, y = x, sin4 +x2 cos4
and substituting q1 and q2 into Eqs. (7.9) we arrive at
where
(7.10)
can be treated as the ply thermal conductivities in coordinates x, y. Because the
ply is anisotropic in these coordinates, the heat flow in the, e.g. x-direction induces
the temperature gradient not only in the x-direction, but in the y-direction as well.
Using Eq. (7.4) we can now determine the in-plane thermal conductivities of the
laminate as
where 1.,ti.are specified by Eqs. (7.10) in which 1.1.2 = and 4 = 4i. For &#J angle-
ply laminates which are orthotropic, = 0.
As an example, consider the composite body of a space telescope the section
of which is shown in Fig. 7.3. The cylinder having diameter D = 1 m and total
thickncss h = 13.52 mm consists of four layers, i.e.
