Metal Foams: A Design Guide

c/
Face
sheet
yielding
0.14
0.12
0.1
0.08
0.06
0.04
A
D
Maximum deflection
X
Optimum
Sandwich structures 131
ρc /ρs = 0.1
Π = 10−4 0.02
0
B
C
0 0.0005 0.001 0.0015 0.002 0.0025
log [(1/Π D )(c/ )]
1
a
Core yielding
Face yield
D
Core shear
δ − /
2
t /
Log (t/ )
3
Stiffness
b
C E
ρ c /ρ s
Figure 10.11 (a) A design map based on panel dimensions for Al alloy
sandwich panels at specified load index (5 D 10 4 ) and core density
( c/ s D 0.1), subject to an allowable displacement (υ/ℓ D 0.02). (b) A
schematic design map using modified coordinates suggested by
equation (10.7), showing trends with core properties and allowable stiffness.
Line (3) refers to core shear, line (1) to the stiffness constraint and line (2) to
face yielding
The example has been used to illustrate the process used to minimize the
weight subject to constraints on failure and deflection. In the present instance,
the process can be carried out analytically. Often, however, a straightforward
numerical approach is the simplest and most effective way to determine the
optimal design. The preceding example may be used to illustrate the numerical
methodology: