Page 328 - Mechanics Analysis Composite Materials

Chapter 7. Environmental. special loading,and manufacturing <fleets 313

(7.27)

Total (elastic and temperature) generalized strains ET, yT and KT entering Eqs. (7.23)
and (7.24) can be expressed in terms of displacements and rotation angles of the
laminate element with the aid of Eqs. (5.3) and (5.14), i.e.

(7.28)

(7.29)

(7.30)

As follows from Eqs. (7.23), in the general case, uniform heating of laminates
induces in contrast to homogeneous materials, not only in-plane strains but also the
changes of laminate curvatures and twist. Indeed, assume that the laminate is free
from the edge and surface loads so that forces and moments in the left-hand sides of
Eqs. (7.23) are equal to zero. Because CTE of the layers, in the general case, are
different, thermal terms NT and MT in the right-hand sides of Eqs. (7.23) are not
zero even for the uniform temperature field, and these equations allow us to find
ET, yT and KT specifying the laminate in-plane and out-of-plane deformation.
Moreover, using the approach described in Section 5.10 we can conclude that
uniform heating of the laminate is accompanied, in the general case, by stresses
acting in the layers and between the layers.
As an example, consider the four-layered structure of the space telescope
described in Section 7.1.1.
First, we calculate the stiffness coefficients of the layers, Le.:
0 for the internal layer of aluminum foil:

0 for the inner skin:

0 for the lattice layer:

6
A\:' = 2E,.Lcos4 4,. = 14.4 GPa,
a,.
Sr
A$ = 2Er -sin4$r = 0.25 GPa,
a,.
6
A\:' = 2E,.Lsin' $cos' $ = I .91 GPa ,
ar