Page 389 - Mechanics Analysis Composite Materials

374 Mechanics and analysis of composite materials
These equations allow us to find strain, i.e.

(8.27)

and to write two relationships specifying the optimal structural parameters of the
laminate

Substitution of Bmnfrom Eqs. (8.24) results in the following explicit form of these
conditions:

(8.28)

To determine the stresses that act in the optimal laminate, we use Eqs. (4.69) and
(8.26) that specify the strains in the principal material coordinates of the layers
as = ~2 = E, yI2 = 0. Applying constitutive equations, Eqs. (4.56), substituting E
from Eq. (8.27) and writing the result in the explicit form with the aid of Eqs. (8.24)
we arrive at:

(8.29)

where

is the laminate stiffness coefficient.
If all the layers are made from one and the same material, Eqs. (8.28) and (8.29)
are simplified as