Metal Foams: A Design Guide

130 Metal Foams: A Design Guide
Table 10.3 Coefficients for laterally loaded panels
Loading B1 B2 B3 B4
Cantilever End 3 1 1 1
Uniform 8 2 2 1
Both ends simply supported Central 48 4 4 2
Uniform 384/5 8 9 2
Both ends clamped Central 192 4 9 2
Uniform 384 8 12 2
The weight index is
D 2⊲t/ℓ⊳ C ⊲ c/ f⊳⊲c/ℓ⊳ ⊲10.27d⊳
Design diagrams
The remaining constraints on the design variables t and c, expressed
by equation (10.27), are plotted as three curves on a design diagram
(Figure 10.11(a)), using a particular case wherein the load index is 5 D 10 4
and the maximum allowable deflection is υ/ℓ D 0.02. The face sheets are
assumed to be aluminum and the foam core is also aluminum with c/ f D 0.1
and ˛2 D 1. Note that the face yielding constraint is independent of the
material, whereas that for core shear is independent of the face sheet thickness,
but is strongly affected by the core properties.
The relative core thickness cannot lie below the line for core yielding, nor
to the left of the curve for face sheet yielding, thereby excluding solutions
within the shaded areas of the figure. Similarly, because of the deflection
constraint, the solution cannot be to the left of the maximum deflection curve.
Consequently, the optimum resides somewhere along the solid curve ADC.
(Any combination of c/ℓ and t/ℓ lying to the right of these constraint curves
would have a larger weight than the combination with the same value of c/ℓ
lying on the closest constraint curve.) Note that, for this example, failure by
core yield does not limit the design because the other two are more stringent.
That is, the optimum design is limited either by face sheet yielding, above D,
or deflection constraint, below D. Evaluating along the two segments AD
and DC and then determining its minimum gives the optimum. It is found
to reside along DC at location X, where t/ℓ D 0.001 and c/ℓ D 0.032. The
corresponding weight minimum is obtained from equation (10.6d) as D
0.00638. That is, for load index 5 D 10 4 , the design is deflection limited.
This conclusion changes at larger 5, for reasons explained below.