Metal Foams: A Design Guide

134 Metal Foams: A Design Guide
results. For laterally loaded flat panel problems, non-dimensional coefficients
(designated Bi) relate the deflections to the applied loads. Details are given in
Section 6.3. The key results are repeated for convenience in Table 10.3. Their
use will be illustrated throughout the following derivations.
An analysis based on laterally loaded sandwich beams demonstrates the
procedure. The results are summarized in Figure 10.13, wherein the weight
is minimized subject to prescribed stiffness. The construction of this figure,
along with the indices, will be described below. The global weight minimum
has the core density c as one of the variables. This minimum is the lower
envelope of the minimum weight curves obtained at fixed c: three of which
are shown.
Weight index
Y = ψ 8B 1 /3α 2B 2
Y
0.2
1
0.8
0.6
0.4
ρ c /ρ s = 0.05
0 0.01
X
Minimum weight panels
0.1
Global minimum
Y = 3.19X 3/5
ρ c /ρ s = 0.59X 2/5
0.2
Global minimum
Constant ρc minima
0
0 0.02 0.04 0.06 0.08 0.1
0.05
0.1
Global
X = S B1 /3α2B2 /8)
Stiffness index
3/2
Figure 10.13 Minimum weight panels
0.2
F
b