Metal Foams: A Design Guide

c
t
p
p
Figure 10.9 Sandwich panel under uniform load
b
Sandwich structures 127
effect of different core densities. The objective is to choose the thickness of the
core, c, and the thickness of each of the two face sheets, t, so as to minimize
the weight of the plate. The width of the plate is assumed large compared
with ℓ and the design exercise focuses on a one dimensional, wide plate.
Deflection and failure constraints
The first step in the optimization process is identification of the constraints on
failure and deflection. For the sandwich plate under uniform transverse pressure,
face sheet yielding and wrinkling must be considered, as well as yielding
of the core (Figure 10.10). Deflection constraints must also be imposed to
ensure that deflections of an optimally designed panel do not exceed tolerable
limits. Normal crushing (indentation) of the core will not be at issue
because the loading pressure, p, will necessarily be small compared with the
compressive yield strength of the core material.
In the example considered, the face sheet material is the same as that of the
fully dense core material (i.e. s D f, s y D f y and Es D Ef). The relation
between the core modulus and density is taken to be
Ec/Es D ˛2⊲ c/ s⊳ 2
⊲10.22a⊳
where ˛2 is a quality factor, with ˛2 D 1 applying to a core material having
relatively inferior properties and ˛2 D 4 to a material with properties somewhat
higher than those currently available. The core is assumed to be isotropic with