Creating trade-off curves
Plot performance indices on a chart and add a trade-off curve to identify optimal materials.
To create a trade-off curve:
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Identify the two conflicting objectives.
For the bicycle example above, the two objectives are to minimize mass and to minimize cost, with a stiffness-limited design.
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Calculate the two performance indices associated with these objectives.
- Either derive the indices from first principles, use the performance index finder, or consult a table of commonly-used indices.
- The bicycle frame is modeled as a stiffness-limited beam in bending,
with a free sectional area.
- The performance index to minimize for minimum cost: M1 = Cm ρ / E1/2.
- The performance index to minimize for minimum mass: M2 = ρ / E1/2.
- Cm = material cost per unit mass, ρ = density, E = Young’s modulus (N.B. Flexural modulus can be substituted by Young’s modulus for some materials, and they are assumed here to be the same).
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Create a chart with M1 on the x-axis and M2 on the
y-axis.
- Performance indices can be plotted on a chart axis by building an attribute expression. On the axis tab in the Chart Stage Settings dialog, click Advanced.
- Create an expression for the performance index from the list of attributes.

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Create a trade-off curve on the chart.
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Click
Curve on the chart stage
toolbar.
- Click the chart where you want the curve to start.
- Click other positions on the chart to create more points.
- To finish drawing the curve, press Enter, or double-click the final point.
-
Click
- Drag the curve to adjust the position of it if necessary.