Page 396 - Mechanics Analysis Composite Materials

Chapter 8. Optimal composite structures 38 1

(8.45)

where

Now, assume that in accordance with results presented in the previous section the
optimal shell is reinforced along the lines of principal stresses, i.e., in such a way that
212 = 0. In accordance with the last equation of Eqs. (8.43), for such a shell yI2 = 0
and, as follows from Eqs. (8.44), E, = E/{ = EI = ~2.
Putting 212 = 0 in the last equation of Eqs. (8.45) we can conclude that for the
optimal shell

Nil- 1 --- (1 - n)cos2 4
-- (8.46)
N, n+(1-n)cos224 ’
where as earlier

(8.47)

Substituting N, and Np from Eqs. (8.40) into Eq. (8.46) we arrive at the following
equation for the meridian of the optimal shell:

(8.48)

The first two equations of Eqs. (8.45) yield the following expressions for stresses
acting in the tape of the optimal shell:

(8.49)

Taking into account that, in accordance with Eqs. (8.45)