Metal Foams: A Design Guide

Weight index, ψ
10 −1
10 −2
10 −3
ρ c /ρ s = 0.05
10 −6
0.1
0.2
Deflection
limited
10 −4
Load index, Π
0.3
Strength
limited
Sandwich structures 133
δ /L = 0.01
s y /E f = 0.007
10 −2
Figure 10.12 Weight index as a function of load index for optimally
designed Al alloy sandwich panels subject to an allowable displacement
(υ/ℓ D 0.01)
At a low load index, the core with the lowest relative density among the
four considered gives the lowest weight structure. At a higher load index,
a transition occurs wherein higher core densities produce the lowest weight.
Plots such as this can be used to guide the optimal choice of core density.
10.7 Stiffness-limited designs
Sandwich structures
Panels subjected to lateral loads are often stiffness-limited, as exemplified by
the panels in the previous section subject to lower load indices. The optimum
configuration lies away from the failure constraints and corresponds to a fixed
ratio of deflection to load, i.e. to a prescribed stiffness. Stiffness also affects
the natural vibration frequencies: high stiffness at low weight increases the
resonant frequencies. Minimum weight sandwich panels designed for specified
stiffness are investigated on their own merits in this section. The results can
be presented in a general form.
The concepts can be found in several literature sources (Allen, 1969; Gerard,
1956; Gibson and Ashby, 1997; Budiansky, 1999). The key results are reiterated
to establish the procedures, as well as to capture the most useful