Metal Foams: A Design Guide

140 Metal Foams: A Design Guide
where the web depth, ds, is defined in Figure 10.15, with E0 as Young’s
modulus for the material comprising the panel. At equal weights of the sandwich
and waffle panels, the web depth of the waffle is
ds
ℓ D
� �
72
125
�� ��
0 Ef 18˛2B2
f E0 B 2 �1/5 � �1/5 P/υ
1 bEf
⊲10.43⊳
Comparison with the result for c/ℓ in equation (10.31) for the globally
optimized sandwich panel at equivalent weights gives:
ds
c D
p �� 6
5
�� �
0 Ef
⊲10.44⊳
f
E0
This result is stiffness independent because the sandwich and waffle panels
have the identical functional dependence. Accordingly, a waffle panel made
from the same material as a sandwich panel ( f D 0, Ef D E0) has a slightly
smaller overall thickness at the same weight and stiffness. The choice between
sandwich and waffle panels, therefore, depends primarily on manufacturing
cost and durability.
10.8 Strength-limited designs
Cylindrical shells
Strength-limited sandwich structures can be weight competitive with stiffenerreinforced
designs (the lowest weight designs in current usage). Shells are
a more likely candidate for sandwich construction than axially compressed
panels or columns because both hoop and axial stresses are involved, enabling
the isotropy of sandwich panels to be exploited. There are two basic requirements
for sandwich shells: (1) sufficient core shear stiffness for adequate
buckling strength, (2) sufficiently large yield strength of the metal foam to
maintain the buckling resistance of the shell, particularly in the presence of
imperfections. Numerical methods are needed to determine minimum weights
of both sandwich and stringer-reinforced configurations. Some prototypical
results for a cylindrical shell under axial compression illustrate configurations
in which sandwich construction is preferred.
General considerations
The perfect cylindrical shell buckles axisymmetrically at a load per circumferential
length, N, given by (Tennyson and Chan, 1990)
N
EfR D
2tc
�
2 1 fR 2
� �
1 p ⊲10.45a⊳
2