Metal Foams: A Design Guide

Table 5.1 Design requirements
Design analysis for material selection 57
Function Panel to support electronic
signal-generating equipment (thus carries
bending moments)
Objective Minimize weight
Constraints Must have length, ℓ, and width, b,
Must operate between 20°C and 120°C
Must be electrically insulating
Must be non-magnetic
Must not fail by plastic yielding
Free variable The thickness, t, of the panel
Table 5.2 Deriving material indices: the recipe (Ashby, 1999)
(a) Identify the aspect of performance, P (mass, cost, energy, etc.) to be
maximized or minimized, defining the objective (mass, in the example of
Table 5.1)
(b) Develop an equation for P (called the objective function)
(c) Identify the free variables in the objective function. These are the
variables not specified by the design requirement (the thickness, t, ofthe
panel in the example of Table 5.1)
(d) Identify the constraints. Identify those that are simple (independent of
the variables in the objective function) and those which are dependent
(they depend on the free variables in the objective function)
(e) Develop equations for the dependent constraints (no yield; no buckling,
etc.)
(f) Substitute for the free variables from the equations for the dependent
constraints into the objective function, eliminating the free variable(s)
(g) Group the variables into three groups: functional requirements, F,
geometry, G, and material properties, M, thus:
Performance P � f(F, G, M)
(h) Read off the material index, M, to be maximized or minimized
impact the objective since they influence weight. This constraint must be
coupled to the objective. To do this, we identify one or more material
indices appropriate to the function, objective and constraints. The material
index allows the optimization step of the selection. The method, in three
stages, is as follows: