How to use the Performance Index Finder

What is a performance index?

Performance indices are part of the materials selection methodology pioneered by Prof. Mike Ashby at the University of Cambridge. The indices are a method to rank and select materials in designs that require the optimization of two or more coupled properties.

A performance index is a ratio of material parameters to optimize in order to maximize the performance of a component, based on the specific function, limiting constraint, and objective of the design.

A performance index is defined by four design factors:

• The function is the basic geometry and load condition of the design (e.g. a panel loaded in bending).
• The limiting constraint is the main criterion to be met for the component to avoid failure (e.g. a stiffness-limited design, where a panel fails if it bends too far under an applied load).
• The objective is the main variable to optimize (e.g. minimize mass or cost).
• The free variable is the geometry parameter that is free to vary with material choice (e.g. the thickness of a panel).

Each combination of function, limiting constraint, objective, and free variable has a characteristic performance index. For example, a light (objective), stiff (limiting constraint), panel loaded in bending (function), with thickness as the free variable, has a performance index of E^1/3/ρ, where E=Young’s modulus (limiting constraint for stiffness) and ρ=density (objective for minimizing mass).

What is the Performance Index Finder?

The Performance Index Finder lets you find a performance index, based on specified design parameters, and to plot the index on a chart as a combined property. The parameters used in the performance index finder are related to the performance index you want to use:

• The function, which is the geometry of the component and how it is loaded.
• A fixed variable is one that has been constrained by the design.
• A free variable is a parameter whose value the designer is free to change.
• Constraints are the requirements that the design must meet. The limiting constraint represents the method by which the design is most likely to fail.
• The objective is the property to optimize the design for.

For designs that have multiple functions (e.g. loaded in both tension and bending), identify which function is the dominant loading geometry that the design is most likely to fail by, and use that loading geometry for the analysis.

How to use the Performance Index Finder

The performance index finder is only available for materials in MaterialUniverse. To create a chart using the performance index finder:

1. In the Selection Project window under Selection data, select a MaterialUniverse data template.
2. Under Selection Stages, click Chart/Index .
3. Select Performance Index Finder at the top of the axis tab.
4. Select a component from the Function and Loading list.
   • The performance index equation will be displayed along side the component notes, and whether the index should be Minimized or Maximized
5. Edit the other parameters of the component, if required. They will only be active if further settings are available
6. If applicable, select Cyclic loading.
   • Cyclic loading only applies to performance indices for strength limited designs, and should be selected when the component is subjected to a high level (10^7 cycles) of cyclic loading. When selected, the performance index uses the fatigue strength (at 10^7 cycles) in place of the yield strength. If cyclic loading is not selected, then the loading condition is taken as static. In cases where cyclic loading is always applicable, the setting will not be visible.
7. Set the axis settings, if required.

For effective material selection charts, there are three main types of charts that the performance index finder can be used to create:

1. A bar chart, to rank the materials based on the performance index value.
   
    
2. A trade-off curve, by plotting two different properties with the same limiting constraint. For example, plot mass per unit of stiffness vs. cost per unit of stiffness.
   
    
3. A coupling line chart, by plotting the same material property with two different constraints, and identify the method by which the materials are likely to fail first. For example, plot mass per unit of strength vs. mass per unit of stiffness.