Plotting a performance index on a chart

Performance indices can be plotted using either an index line, or by plotting a combined property on one axis (for example, E1/3/ρ).

There are two ways a performance index can be plotted on a chart:

As a combined property on one axis of a chart
Tip: To plot a specific performance index as a combined property on just one axis of a chart, click Advanced... in the chart stage window and type in the index equation. For example:

For a low mass, stiffness-limited, panel in bending (performance index = E1/3/ρ), type in: [Young's modulus]^(1/3)/[Density]

This technique is used by the Using Performance Indices, which enables you to quickly identify and plot performance indices, and removes the need to look up or derive performance indices.

Using an index line
To plot a performance index using an index line:
  1. Calculate the slope of the index line to plot by rearranging the performance index equation in terms of the performance index numerator:
    • Performance index: M = E1/3/ρ
    • E = ρ3 * M3
  2. As the software plots material properties on logarithmic scales, take the logarithm of each side:

    log(E) = 3log(ρ) + 3log(M)

    This is now in the form of an equation for a straight line (y=mx+c), where m is the gradient (or slope) and c is the y-intercept. This means you can draw an index line with slope 3 on a chart of Young's modulus vs. density, and all materials along this index line will have the same value (M) of the performance index (E1/3/ρ).

  3. Create a chart of the material attributes in the performance index, with the numerator on the y-axis, and the denominator on the x-axis. For the panel loaded in bending example (stiffness-limited and optimizing mass), plot Young’s modulus (E) on the y-axis and density (ρ) on the x-axis.
    Note: For more complicated performance indices, such as a stiffness-limited panel in bending and optimizing cost (M=E1/3/(Cm*ρ)), the x-axis would be plotted as a combined property. For example, Cm*ρ.
  4. Click Index line on the chart toolbar. Enter a slope value of 3, select Maximize the index, and click OK.
  5. Plot the index line by clicking a point on the chart for the line to pass through. Materials that maximize the index (those above the index line) will pass the selection stage.
  6. Optional: Reposition the line if necessary by dragging the line to pass or fail more materials.
  7. Optional: To find the optimal material (the one with the highest value of the performance index), rank the results by Stage 1: Index value (slope=3) in the Results pane.
    By default this list will be ordered from high to low.