2
Design & Selection: Materials Indices
Material index
(
performance index
)
is a combination of materials
properties that characterizes the Performance of a material in a given
application.
Performance
of a structural element may be specified by the
functional
requirements, the geometry, and the material’s properties.
Performance
[ (Functional needs, F);
(Geometric, G);
(Material Property, M)
]
For
OPTIMUM design
,
we need to
MAXIMIZE
or
MINIMIZE
the
Performance.
MSE280
© 2007-2009 Moonsub Shim
Consider only the simplest cases where these factors form a
separable
equation
.
Performance = f
1
(F) f
2
(G)
f
3
(M)
From D. Johnson
Examples of Materials Indices
Function, Objective, and Constraint
Index
Tie,
minimum weight,
stiffness
E/
ρ
Beam, minimum weight,
stiffness
E
1/2
/
ρ
Beam, minimum weight,
strength
s
2/3
/
ρ
Beam, minimum cost,
stiffness
E
1/2
/C
m
ρ
Beam, minimum cost,
strength
s
2/3
/C
m
ρ
Column, minimum cost, buckling load
E
1/2
/C
m
ρ
C
m
=cost/mass
MSE280
© 2007-2009 Moonsub Shim
Spring, minimum weight for given energy storage
s
YS
2
/E
ρ
Thermal insulation, minimum cost, heat flux
1/(a C
m
ρ
)
Electromagnet, maximum field, temperature rise
k C
p
ρ
α
=thermal cond
κ
=elec. cond
Modified from D. Johnson
Why different dependences? – linear vs. square root etc.