Page 263 - Mechanics Analysis Composite Materials

248 Mechanics and analysis of composite materials

5.7. Antisymmetric laminates

In antisymmetric laminates, symmetrically located layers have mutually reversed
orientations. For example, while laminates [0"/90"/90"/0"] and [+#/ - 4/ - (p/ +4]
are symmetric, laminates [0"/90"/0"/90"] or [0"/0"/90"/90"] and [+4/-4/+4/-4]
are antisymmetric. In contrast to symmetric laminates which have maximum
bending and zero coupling stiffness coefficients, antisymmetric laminates demon-
strate pronounced coupling that can be important for some special applications
(e.g., robotic parts undergoing complicated deformation under simple loading, rotor
blades that twist under centrifugal forces, airplane wings twisting under bending,
etc.).
The simplest antisymmetric laminate is a cross-ply layer consisting of two plies
with angles 0" and 90", and the same thickness h/2 (see Fig. 5.13). Taking e = h/2
and using Eqs. (5.28) and (5.41) we arrive at the following stiffness coefficients
entering Eqs. (5.43):

h-
Bl1 = B22 = -(El +E*), BIZ = EIVIZh, 844 = GIZA,
2
h2 - -
CII = -c** = -(E* -El), c1* = 0, c44 = 0,
8

Comparing these results with Eqs. (5.45) and (5.46) corresponding to a quasi-
homogeneous cross-ply laminate we can see that the antisymmetric cross-ply
laminate has the same membrane and bending stiffnesses but nonzero coupling
coefficients CII and C22. This fact shows, in accordance with Eqs. (5.43), that
in-plane tension or compression of this laminate induces bending.
As another typical example of an antisymmetric laminate, consider an angle-ply
structure consisting of two plies with the same thickness h/2 and orientation angles
+4 and -4, respectively (see Fig. 5.14). The plies (or layers) are characterized with
the following stiffness coefficients:

Z

Y
Fig. 5.13. An antisymmetric cross-ply laminate.