Tutorial 3: Derivation of performance indices
1. Performance index for stiff and light flat panel
In this example we are free to alter beam thickness (t) to
attain desired stiffnessPanel thickness t is a free variable
a) By deriving an expression for the mass of the panel, justify
a performance index for specific stiffness of the panel, based on
free variable being panel thickness (t)b) Perform material
selection using performance index for calculated in a) for
maximising specific stiffness. Yield strength > 30MPa Fracture
toughness >5MPa.m0.5.Want to minimise cost
2. Performance index for strong and light flat panel
Figure A Panel in three point bending
The situation shown in the figure A shows a panel loaded in
three point bending; load F being in the middle of the loading span
(L). The width (w) of the panel is fixed, the thickness (t) is the
design free variable
a) Derive an expression for the mass of the panel that is
independent of the design free variable (thickness t). The derived
expression containing a material performance index for specific
strength. The loading is static and the panel must remain
completely elastic.
b) State the final material performance index in a form such
that it is to be maximised to allow ranking of candidate materials
for this
c) Table 1 shows properties for five candidate materials, for
each material calculate the material performance index for specific
strength and hence justify selection of the optimum material based
on highest value of the performance index (independent of material
cost constraints)
d) Modify the performance index to take into account material
cost (per Kg) and recalculate modified performance index for each
material so as to justify the most cost effective material for the
application Where M= bending momentI= second moment of area= stress
at distance y from panel neutral axis= density
Mg wrought(AZ31)Mg cast(AZ91)Al 7075 T6Ti-6Al-4VCFRP
(quasi-isotropic)
Yield strength(x 106 N.m-2)155145450900550
Density(Kg.m-3)17801800280044301575
Material cost (/Kg)2.252.221835
Table 1: Material properties of candidate materials
3. Material selection: Oars
Derive a material performance index to select materials for
light stiff oars.
Function: Light & stiff beam
Objective: Minimise mass, maximise stiffness
Constraintsa) Length (L) specifiedb) Bending stiffness (S)
specifiedc) Minimum Toughness specified d) Material cost, CM <
50/Kg
Circular cross- section: free variable: Radius (R)Assume loading
in bending, maximise specific stiffness
Given
Mass, m = A.L. = .R2. L.
Stiffness of C = Loading configuration constant = 24 for this
case E= Material elastic modulus, I = 2nd Moment of area
For solid cylinder, 2nd Moment of area
Using the performance index you have derived for a light stiff
oar along with the minimum toughness constraint to plot a selection
graph (use advanced function when plotting graph to plot relevant
functions on each axis.
Then assess the best four materials for price
