Metal Foams: A Design Guide

Sandwich structures 125
four sections deal with optimization, and with the comparison of optimized
sandwich structures with rib-stiffened structures. The benchmarks for comparison
are: (1) stringer or waffle-stiffened panels or shells and (2) honeycombcored
sandwich panels. Decades of development have allowed these to be optimized;
they present performance targets that are difficult to surpass. The benefits
of a cellular metal system derive from an acceptable structural performance
combined with lower costs or greater durability than competing concepts. As
an example, honeycomb-cored sandwich panels with polymer composite face
sheets are particularly weight efficient and cannot be surpassed by cellular
metal cores on a structural performance basis alone. But honeycomb-cored
panels have durability problems associated with water intrusion and delamination;
they are anisotropic; and they are relatively expensive, particularly
when the design calls for curved panels or shells.
In what follows, optimized sandwich construction is compared with conventional
construction to reveal where cellular metal sandwich might be more
weight-efficient. The results indicate that sandwich construction is most likely
to have performance benefits when the loads are relatively low, as they often
are. There are no benefits for designs based on limit loads wherein the system
compresses plastically, because the load-carrying contribution from the cellular
metal core is small. The role of the core is primarily to maintain the positioning
of the face sheets.
Structural indices
Weight-efficient designs of panels, shells and tubes subject to bending or
compression are determined by structural indices based on load, weight and
stiffness. Weight is minimized subject to allowable stresses, stiffnesses and
displacements, depending on the application. Expressions for the maximum
allowables are derived in terms of these structural indices involving the loads,
dimensions, elastic properties and core densities. The details depend on the
configuration, the loading and the potential failure modes. Non-dimensional
indices will be designated by 5 for the load and by for the weight. These
will be defined within the context of each design problem. Stiffness indices
are defined analogously, as will be illustrated for laterally loaded panels. The
notations used for material properties are summarized in Table 10.2. In all the
examples, Al alloys are chosen for which εf f
y y /Ef D 0.007.
Organization and rationale
Optimization procedures are difficult to express when performed in a general
manner with non-dimensional indices. Accordingly, both for clarity of presentation
and to facilitate comprehension, the remainder of this chapter is organized
in the following sequence: