Page 390 - Mechanics Analysis Composite Materials

Chapter 8. Optimal composite structures 375

k

(8.30)

(8.31)

where

Laminates of uniform strength exist under the following restrictions:

For monotropic model of the unidirectional ply considered in the previous section,
n = 0, m = I, and Eqs. (8.30) reduce to Eqs. (8.9) and (8.10).
To determine the thickness of the optimal laminate, we should use Eqs. (8.31)
in conjunction with one of the strength criteria discussed in Chapter 6. For the
simplest case, using the maximum stress criterion in Eqs. (6.2), the thickness of
the laminate can be found from the following conditions CTI = or 02 = a,, so
that

(8.32)

Obviously, for the optimal structure, we would like to have hl = h2. However, this
can happen only if material characteristics meet the following condition:

(8.33)

The results of calculation for typical materials whose properties are listed in Tables
3.5 and 4.4 are presented in Table 8.2. As can be seen, Eq. (8.33) is approximately
valid for fabric composites whose stiffness and strength in the warp and fill
directions (see section 4.6) are controlled by the fibers of one and the same nature.
However for unidirectional polymeric and metal matrix composites, whose
longitudinal stiffness and strength are governed by the fibers and transverse
characteristics are determined by the matrix properties, a?/al << n. In accordance