Page 250 - Mechanics Analysis Composite Materials

Chapter 5. Mechanics qf laminates 235
For the admissible state we should apply

and use some admissible distribution for L-. The simplest approximation is
z,, = V;./hso that

-e
Substitution into condition (5.27) yields

Thus, Eq. (5.22) provides the lower bound for S55, and the actual stiffness satisfies
the following inequality:

So, constitutive equations for the generalized layer under study are specified with
Eqs. (5.5) and (5.15). Stiffness coefficients that are given by Eqs. (5.6)-(5.8), and
(5.17) or (5.19) can be written in a form more suitable for calculations. To do this,
introduce new coordinate t =z +e such that 0 d t d h (see Fig. 5.8). Transforming
the integrals to this new variable we get

(5.28)

where rnn = 1 1, 12, 22, 14, 24, 44 and

Fig. 5.8. Coordinates of an arbitrary point A.