Page 388 - Mechanics Analysis Composite Materials

Chapter 8. Optimal composite structures 313

(8.23)

where in accordance with Eqs. (4.72) and (5.28), (5.42)

and

In the general case, the panel can consist of layers made of different composite
materials. Using the optimality criterion developed in the previous section for the
fibrous structures we assume that the fibers in each layer are directed along the lines
of principal strains, or principal stresses because $2 = GI~$ for an orthotropic
layer and condition $3 = 0 is equivalent to condition = 0 (see section 2.4).

Using the third equation in Eqs. (4.69) we can write these conditions as
2(g. - E,) sin dicos di+ y.rI- cos 24; = 0 . (8.25)

This equation can be satisfied for all the layers if we take

&.v=&Y-&, y,,=0 . (8.26)

Then, Eqs. (8.23) yield

Nv = (BII+BI~)E, Nv= (&I +B22)~, Nry = (841 +B42)~