Page 254 - Mechanics Analysis Composite Materials

Chapter 5. Mechanics of laminates 239

(5.41)

where I =0, 1, 2 and to = 0, tk = h (see Fig. 5.10). For thin layers, Eqs. (5.41) can
be reduced to the following form, which is more suitable for calculations:

k k

where hi = ti - ti-l is the thickness of the ith layer.
Thus, membrane, coupling, and bending stiffness coefficients of the laminate are
specified with Eqs. (5.28) and (5.42). Consider transverse shear stiffnesses which
have two diflerent forms determined by Eqs. (5.30) and (5.31). Because both
equations coincide for a homogeneous layer (see Section 5.2), we can expect that
the difference shows itself in laminates consisting of layers with different
transverse shear stiffnesses. The laminate for which this difference is the most
pronounced is a sandwich structure with metal facings (inner and outer layers)
and a foam core (middle layer) that has very low shear stiffness. For such
a sandwich, experimentally found transverse shear stiffness is S =389 kN/m
(Aleksandrov et al., 1960), while Eqs. (5.30) and (5.31) yield, respectively, S =
37200 kN/m and S = 383 kN/m. Thus, Eq. (5.31) provides much more accurate
result for sandwich structures. This conclusion is also valid for composite
laminates (Chen and Tsai, 1996).
A particular case, important for applications, is an orthotropic laminate for
which Eqs. (5.5) and (5.15) acquire the form:

(5.43)

where, membrane, coupling, and bending stiffnesses, B,,, C,,,,, and D,,,,, are
specified by Eqs. (5.28) and (5.42), while transverse shear stiffnesses are