Stress Ratio Technique

The Stress Ratio technique takes a set of design variables, typically dimensions such as thicknesses, areas, or moments of inertia, and a corresponding set of constraints on allowable stresses, and modifies the design variables according to the relation:

Because the dimension $x$ can refer to any arbitrary dimension or property, the exponential factor $\mathrm{\beta }$ accounts for this. For example, if a frame structure were to be designed where the member cross-sections were assumed to be square with length $x$, the ideal value of $\mathrm{\beta }$ would be 0.5 for axial loads and 0.33 for flexural loads. In the Stress Ratio algorithm, all design variables use the same $\mathrm{\beta }$ with the understanding that the smaller the exponent, the more stable (and slower) the convergence.

The Stress Ratio technique assumes an inverse relationship between design variable and associated constraints and modifies the design variable based on the value of the critical associated constraint. Therefore, a naming convention is used to associate constraints and design variables. For example, constraints Stress1AtZone1, Stress2AtZone1, and Stress3AtZone1 are associated with design variable ThicknessAtZone1.