Page 227 - Mechanics Analysis Composite Materials

212 Mechanics and analysis of composite materials

(4.168)

Summing up the first two of these equations we get

Using the third equation we arrive at the remarkable result

(4.169)

similar to the corresponding formula for isotropic materials, Eq. (2.57). It should be
emphasized that Eq. (4.169) is valid for off-axis tension in the x-direction making
some special angle 4 with the principal material axis 1. This angle is given by
Eq. (4.79). Another form of this expression follows from the last equation of
Eqs. (4.168) and (4.169), i.e.,

(4.170)

For fabric composites whose stiffness in the warp and the fill directions is the same
(El =Ez), Eq. (4.170) yields 4 = 45".

4.7. Lattice layer

A layer with a relatively low density and high stiffness can be obtained with a
lattice structure which can be made by winding modified in such a way that the tapes
are laid onto preceding tapes and not beside them as in conventional filament
winding (see Fig. 4.86). Lattice layer can be the single layer of the structure as in
Fig. 4.87 or can be combined with a skin as in Fig. 4.88. As a rule, lattice structures
have the form of cylindrical or conical shells in which the lattice layer is formed
with two systems of ribs - a symmetric system of helical ribs and a system of
circumferential ribs (see Fig. 4.87 and 4.88). However, there exist lattice structures
with three systems of ribs as in Fig. 4.89.
In general, lattice layer can be assumed to consist of k symmetric systems of ribs
making angles 3$j (j= 1, 2, 3, ...,k) with the x-axis and having geometric