Definitions

Function

This is simply a statement of the primary function of the design. A beam carries bending moments; a heat-exchanger tube transmits heat; a bus-bar transmits electric current.

Objective

This is the first and most important quantity that you wish to maximise or minimise. Commonly it is weight or cost; but it could be energy stored per unit volume (a spring, a flywheel); or energy dissapated in electrical heating (a bus-bar); or depth of dive (a submarine);—it depends on the application.

Constraint

They are design requirements which must be met and which therefore limit the optimisation process identified as the objective. Commonly these are: a required value for the stiffness; a required value for the safe load, moment, torque or pressure that can be supported; a limit on the operating temperature; or on resistance to sudden fracture.

It is essential to distinguish between OBJECTIVES and CONSTRAINTS—and that requires a little thought. For example: in the performance-limited design of a bicycle frame, minimising weight might be the OBJECTIVE, with stiffness, strength, toughness and cost as CONSTRAINTS ('as light as possible without costing more than £300'). But in a cost-limited design of a bicycle, minimising cost becomes the OBJECTIVE and weight becomes a CONSTRAINT ('as cheap as possible, without weighing more than 16kg).

Performance Index

1. Write down an equation for the OBJECTIVE. This is the 'objective function'.
2. Write down equations for the CONSTRAINTS. Eliminate the free variables in this objective function by using the CONSTRAINTS.
3. Read off the grouping of material properties which maximise the value of the objective. This is the PERFORMANCE INDEX.