Metal Foams: A Design Guide

Sandwich structures 137
The associated non-dimensional weight index defined in equation (10.11) is
Y D 2 p 3/2 1/2 ⊲3 2 ⊳
2⊲ c/ s⊳ ⊲10.36⊳
⊲1 2 ⊳
Curves of Y as a function of X are included in Figure 10.13 for three values
of the relative core density, c/ s. Each curve necessarily lies above the global
optimum, touching that curve only where its core density happens to coincide
with that of the globally optimized sandwich beam. Note, however, that the
minimum weight beams with fixed core density exhibit substantial stiffness
and weight ranges over which they are close to optimal. For example, the
beams with c/ s D 0.2 have weights which are only slightly above the global
minimum over the stiffness range, 0.02