Page 380 - Mechanics Analysis Composite Materials

Chapter 8

OPTIMAL COMPOSITE STRUCTURES

Advanced composite materials are characterized with high specific strength
and stiffness and, in combination with automatic manufacturing processes, make
it possible to fabricate composite structures with high level of weight and cost
efficiency. The substitution of metal alloys by composite materials, in general,
reduces the structure mass by 20-30%. However, in some special cases the number
of which progressively increases, the combination of material directional properties
with design conception utilizing these properties being supported by the possibilities
of modern composite technology gives a qualitative improvement of the structure
performance. Such efficiency is demonstrated by composite structures of uniform
strength in which the load is taken by uniformly stressed fibers.
To introduce composite structures of uniform strength, consider a laminated
panel shown in Fig. 8.1 and loaded by in-plane forces Ny,Nv, and Nxv uniformly
distributed along the panel edges. Let the laminate consist of k unidirectional
composite layers characterized with thicknesses hi and fiber orientation angles
#( (i = 1,2,3,. . .,k). For the plane stress state, the stacking sequence of the layers is
not important.

8.1. Optimal fibrous structures

To derive the optimality criterion specifying the best structure of the panel
in Fig. 8.1, we first use the simplest monotropic model of the unidirectional
composite (see Section 3.3) assuming that forces N,,N, and Nxy are taken by the
fibers only. For the problem of design, this is a reasonable model because
transverse and shear strength of a unidirectional composite ply (stresses 82 and 712)
are much lower than the ply strength in the longitudinal direction (stress 81).
~
Using Eqs. (4.68) in which we put 02 = 0 and t l = 0 we can write the following
equilibrium equations linking the acting forces with stresses a?)in the direction of
the fibers of the ith layer:

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