Page 267 - Mechanics Analysis Composite Materials

252 Mechanics and analysis of composite materials

For practical analysis, this result is often used even if Poisson’s ratios of the layers
are different. In these cases it is approximately assumed that all the layers are
characterized with some average value of Poisson’s ratio, i.e.,

As another example, consider a sandwich structure described in Section 5.8. In the
general case, we again fail to find the desirable reference plane. However, if we
assume that the facings are made of one and the same material (only the thicknesses
are different), Eqs. (5.62) and (5.63) yield

h: +h3(h3 +2hl + 2h2)
e=
2(hi +h3)

Returning to the general case we should emphasize that the reference plane
providing Cm,= 0 for all mn does not exist in this case only if the laminate structure
is given. If the stacking sequence of the layers is not pre-assigned and there is a
sufficient number of layers, they can be arranged in such a way that C,, = 0.
Indeed, consider a laminate in Fig. 5.18 and assume that its structure is, in general,
not symmetric, Le., that 4 # zi and K # k. Using plane z = 0 as the reference plane
we can write the membrane-bending coupling coefficients as

Z

k

i’ i’
ktkssmmsu

Fig. 5.18. 1 ;ayer coordinates with respect to the reference plane.